Chemistry 460 Problems: SET 1, Statistics and Experimental Design

Chemistry 460 Problems SET 1, Statistics and Experimental Design 1. In a certain copper analysis, results are consistently low by 0.5 mg. a. What is the relative % error if the total copper in the sample is 25 mg? 200 mg? b. If an ore sample with 4.8% Cu were to be analyzed by this method, what size sample should be taken to keep the determinate error below 0.1% ? 1.2% ? 2. A gravimetric method for Se involves a consistent loss of 1.8 mg of the Se due to precipitate solubility. Find the % error due this determinate error in a determination which uses a 0.45 g sample of around 1.8% Se. 3. A bronze sample weighing around 4 g is to be analyzed spectrophotometrically for Mn. If the absorbance can be read to the nearest 0.003 unit and an absorbance in the vicinity of 0.250 is expected, how large a sample should be weighed out on an analytical balance that has a mass uncertainty of 0.5 mg so that the weighing uncertainty is less than 10% of the spectrophotometric uncertainty ? 4. The following data represent a clinical analysis for plasma calcium concentrations for a number of individuals. Find s for the determinations for each individual set and then determine a pooled s for the method. Units for the analysis are mg%. #1 3.02, 3.07, 3.10, 3.16, 3.27 #2 3.96, 4.01, 4.09, 4.20 #3 3.62, 3.70, 3.82, 3.83, 3.89 #4 3.36, 3.56, 3.62 #5 3.21, 3.22, 3.25, 3.35, 3.37, 3.46 5. A method for the analysis of particulate lead in air gives the analytical results listed below (units are ug Pb/m3). Find a pooled s for the method. Sample #1 1.5, 1.2, 1.3 Sample #2 2.0, 2.3, 2.3, 2.2 Sample #3 1.8, 1.7, 1.4, 1.6 Sample #4 1.6, 1.3, 1.2, 1.5, 1.6 6. A method for the analysis of Au in sea water has consistently had a standard deviation of 0.025 ppb. Calculate the 99% confidence interval based on this method for 2, 3, and 5 measurements. 7. The determination of chromium in an ore sample gave the following results: 28.53, 28.47, 28.39, 28.72, 28.64 . Find the mean, standard deviation, and the 95% confidence interval. 8. A standard method for total chlorinated hydrocarbons has a standard deviation of 0.030 ppm. Find the 95% confidence interval for the mean of four replicate measurements by this method. How many measurements must be made if the 95% confidence interval is to be reduced to below 0.017 ? 9. The standard deviation for a CO analysis in exhaust gases has been found to be 0.80 ppm based on a large amount of past experience. Find the 90% confidence interval for triplicate measurements and estimate the number of measurements needed to reduce the 90% confidence interval to below 0.50 ppm . 10. A method for serum potassium gave the following results (mg%) : 15.4, 15.6, 15.3, 16.4 Find the 90% confidence limits for the method. 11. A manufacturer of light bulbs claims that they will last an average of 1200 hours with a standard deviation of 100 hours. a. How many bulbs in a lot of 400 would be expected to burn for more than 1400 hours ? b. If 30 of the bulbs burn out in less than 1000 hours, does this invalidate the claim ? 12. Rocks gathered from the moon had national interest and many analytical groups cooperated in gathering data on them. The results in the table below show the results for some of the minor elements on a single basalt rock. They show remarkable agreement for an interlaboratory study. Concentrations are listed in µg/g. Group P S K Cr Mn_ 1 440 1620 407 2820 2020 1

2 – – 340 2680 1940 3 300 – 660 2800 2090 4 430 1700 415 2670 2250 5 390 1800 330 2870 2170 6 500 1880 340 2950 2050 a. Check each elemental analysis for outliers at the 90% confidence level. b. Report the mean and resd(%) of each elemental analysis with the correct number of significant digits. c. Which element has the largest uncertainty? Is this the one with the largest relative range ? 13. The NBS prepared a stainless steel for distribution as a standard. Two different samples of the alloy gave the following results for % Cr. #1 57.76 57.81 57.59 57.73 57.67 57.79 57.67 57.79 57.88 58.07 57.64 #2 57.67 57.40 57.55 57.77 57.88 58.00 57.61 57.80 57.56 57.61 57.51 a. Find the mean, standard deviation, and resd for each sample. b. What is the highest confidence level at which these samples are the same? This could be taken as a measure of the sample homogeneity. c. With this data, how many determinations were needed to obtain a confidence level range of 0.5% ? d. How should samples of this alloy be labeled when sent to analytical laboratories as a standard ? 14. An electrochemical method for % ethanol in naturally fermented beverages is to be validated by comparing its results with those of the more traditional and tedious distillation followed by volume and density measurement method. Results are shown in the table below for the same samples. Sample Beer#1 Beer#2 Beer#3 Wine#1 Wine#2 Wine#3 Electrochem 3.48 4.32 3.80 5.90 10.60 8.49 Dist./V,D 3.47 4.35 3.82 5.83 10.72 8.58 a. What is the highest confidence level at which the two methods yield the same result? b. Which of the two methods is more desirable? Explain. 15. An instrumental determination involves injection of the sample and a decision is to be made whether to buy an automatic injector or to use a small syringe manually. One factor to consider is whether there is a significant difference in precision in the two methods. Manually, a series of twelve injections of the same sample gives instrument readings of: 96, 100, 98.5, 100, 98.5, 100, 101.5, 100.5, 101, 97.5, 101.5, 101 . The manufacturer of the auto injector quotes similar data for a series of ten injections as: 1677, 1673, 1663, 1672, 1678, 1658, 1648, 1665, 1685, 1696. a. Calculate the resd for both methods. b. Which method seems more precise? Is this difference significant at the 95% confidence level? c. Assume there is a resd of 11.% in the final result independent of injection method, due to the combined best injection and sampling method errors. What is the best way to improve the determination. d. Will the $1200 auto-injector worth the investment? Why?

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16. The sulfate in ground water is commonly determined by measuring the turbidity that appears on the addition of excess BaCl2. A turbidimeter is calibrated with the series of standards listed below as well as the result from an unknown. Sample (mg/L) 0.00 5.00 10.00 15.0 20.0 Unknown Reading 0.06 1.48 2.28 3.98 4.61 3.67 a. Plot the data and the least-squares line; report the best line equation. b. Report the fit of the points to the line, sr. c. Find the unknown concentration and resd, assuming that the result shown is from one, and then from the average of 6 replicate readings. d. If 20 blank determinations yielded an average of 0.12 with an s of 0.27, find the detection limit. 17. The following data were obtained in a calibration for an ion-selective calcium electrode. pCa 1.00 2.00 3.00 4.00 5.00 Unknown mV 65.1 31.9 2.7 –27.7 –53.8 +20.3 a. Determine the equation of the least squares best line; plot the points and the best line. b. Determine the quality of the line fit, sr. c. Calculate the unknown pCa and its resd assuming 1, 2, and 8 replicates are used for the detn. d. Find the molar concentration of Ca2+, s, and resd for each of the situations described in part c. 18. The following diffusion currents are observed in the polarography of solutions of methyl vinyl ketone. Concentrations are in mM and currents in µA. [MVK] (mM) 0.500 1.50 2.50 3.50 4.50 5.50 A B Current (µA) 3.76 9.16 15.03 20.42 25.33 31.97 6.3 27.5 a. Determine the equation of the best straight line; plot the points and the best fit line. b. Determine sr and the resd of the points from the line. c. Determine the concentrations of unknowns A and B; assuming one determination and then four replicate determinations; find the resd for each. d. 19 blank determinations gave a mean current of 0.99 µA with s = 0.036 µA. Find the detection limit for the method. e. 16 standard solutions containing 1.50 mM analyte yielded a mean current of 9.35 µA with s = 0.22 µA. Similarly, the standard at 5.50 mM gave a mean current of 32.16 µA with an s = 0.47 µA. Find the calibration and analytical sensitivities at each concentration. 19. An assay for nitrate reductase, which catalyzes the reduction of nitrate to nitrite, is done by mixing portions of the enzyme and then it is stopped after 10.00 min by bubbling oxygen into the solution to deactivate the enzyme. Then two reagents are added which produce are diazotized by any nitrite ion present to form a purple dye which absorbs at 540 nm. The blank contains all reagents but nitrate ion. The final solution volume is 2500 µL. Calibration standards were produced by adding variable amounts of nitrite ion to an aliquot of the blank and diluting to 2500 µL. Solution (µM) Blank +20 +40 +60 +80 +100 Unknown Absorbance 0.004 0.273 0.548 0.805 1.090 1.358 0.664 o The activity is defined as: 1 unit reduces 1 µmol of nitrate/min to nitrite at 30 C, at pH 7. a. Determine the sensitivity in Absorbance/unit. b. The unknown contained 23.8 mg of dry enzyme. What is its specific activity ?

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20. Estimate the result, s and the resd (%) from the calculations listed below. The numbers in parentheses after the number are the standard deviations in the last place of the preceeding number. Pay attention to the correct number of significant digits in the result. a. 16.9286(1) + 16.8797(1) = b. 16.9286(1) − 16.8797(1) = c. [.0354(3) + 7.147(2)-2.8610(3)]1/5 = d. [3.69(2)x10−3 + 7.87(8)x10−4]2 = e. 64.4(2) * .381(7) = f. [18.18(3) * 4.764(9)]1/2 = g. 26.94(8) / .0496(4) = h. [.9194(8) / 46.18(3)]4 = i. [29.67(2)−8.51(1)] / [6.36(2) + 4.85(2)] = j. [7.614(8)−6.923(5)] / [14.2468(2)−13.6719(1)] = k. {3.44(1)x10−5 / [.100(4) + .250(1)]}1/3 = l. [44.41(2) − 3.12(1)] * .2048(6) /[12.6349(1) − 12.2775(1)] = m. [765(1) * 3.564(4)/192.5(2)]5 = n. log[878(4)] = o. log[.04957(4)] = p. 10^[3.64(1)] = q. 10^[−7.191(2)] = 21. A 55 gal drum of chemical wastes contains about 1.45 gal of lumps of metallic solid at the bottom, a layer of water insoluble liquid, and an aqueous layer filling the drum to the top. The water layer made up 56% of the total liquid volumn, and a 5.21 mL portion of the solid had a dry weight of 11.224 g. A 10 mL aliquot of the aqueous layer was dried at 110oC, and weighed 201.4 mg. A similar evaporation of 100 mL of the non-aqueous layer yielded 643 mg of dry solid. The solids isolated were dissolved in acid and assayed for As. The solid from the bottom contained 23.7 ppm As, the solid from the aqueous layer contained 312 ppm As and the solid from the other layer contained 31.6 ppm As. a. What is the total mass of non-volatile solid in the barrel? b. What is the mass of As in the barrel? c. An alternate method of direct As assay of the aqueous layer yielded a value of 7.5 µg As/mL. Does this suggest the presence of volatile As compounds? If so, what % of the total As do they contain? 22. The EPA tested a method for PAH (polynuclear aromatic hydrocarbons) that consisted of adding the specified amounts of the listed hydrocarbons to waste water that contained no detectible amounts of these compounds. Samples were distributed to sixteen different environmental laboratories. The method consisted of extraction of the water samples using methylene chloride, evaporating the solutions to a small specified volume, and the running a capillary GLC determination on a chromatograph with FID. The highest and lowest estimates were omitted in the following listing as likely to be outliers. Compound Conc. ng/L Reported Values Chrysene 1.0 0.64, 0.70, 0.92, 0.80, 0.45, 0.59, 0.72, 0.63, 0.84, 0.75, 0.61, 0.86, 0.58, 0.77 Benzofluoranthenes 1.0 0.48, 0.96, 0.85, 0.90, 0.60, 0.69, 0.69, 0.88, 0.08, 0.76, 0.20, 0.33, 0.30, 0.39 Benzo(a)pyrene 10 6.9, 5.0, 5.7, 7.8, 5.2, 4.0, 7.3, 8.0, 7.6, 5.2, 5.4, 8.5, 4.7, 6.5 Dibenz(a,h)anthracene 50 32, 22, 37, 39, 44, 22, 24, 27, 34, 40, 30, 37, 17.8, 46 a. Calculate a mean % recovery and resd for each compound. b. If a method must have a minimum error of 50% to be useful, which compounds can be determined by this method ? Would you have doubts about these methods? These are typical results so you can understand some of the doubts about any trace analysis results. 23. A determination of NO in exhaust gases is done by bubbling the gas through a bubbler containing Co(DMG)2 in o-dichlorobenzene, and measuring the increase in absorbance of the solution in the bubbler. The focus of this question is the recovery of NO in this method. The initial complex will be abbreviated as CoL2. 1

Main reaction:

K = 5.4 x 107

CoL2 + NO → CoL2(NO)

Note that this equilibrium constant requires concentrations to be used as M and gas pressures as atm. The equilibrium constant expression can be arranged, realizing that [CoL2] is equal to [CoL2]initial − [CoL2(NO)], to yield: PNO =

It's easy to show that : Cout and Cin

CoL2( NO ) ∗1 / K CoL2

initial

− CoL 2( NO )

% collection efficiency = 100 * {1 - (Cout/Cin)} are the ppm (mole or volume fraction x 106) NO in the gas at the outlet and inlet of the bubbler.

Assume the bubbler contains 25 mL of 1.0 x 10-3 M CoL2, the gas averages 10 ppm NO and has a total pressure of 1.00 atm, and that the flow rate through the bubbler is 75 mL/min. a. What is the efficiency of NO collection initially ? b. How many moles of NO can be collected before the pressure drops to 98%? c. What volume of sample can be passed through the bubbler before collection efficiency drops to 98%, and how long will the contents of the bubbler last? 24. Suppose an instrument response, A, is proportional to concentration, C. Then, Asample = S * Csample S is the instrument sensitivity, the conversion factor between instrument response and concentration. Similarly, for a spike that does not effect the sample volume significantly, Aspiked sample = S * (Csample + Cspike) Derive an expression for Csample in terms of the variables above, but not including S 25. A copper analysis is run by Atomic Absorption. Three 5 mL aliquots are used for a standard addition technique, with 0, 5 µL, and 10 µL spikes of 100 ppm Cu standard solution added. Normally, the calculation of the spike concentration is done assuming no volume change occurs. a. Calculate the true concentration of the spike assuming volume additivity, and assuming perfect accuracy in all other volume measurements. b. Find the % error (with sign) made with the usual assumption for both spiked solutions. c. If the random error associated with the AA spectrophotometer is 0.5% and the random error in aspirating the sample into the spectrophotometer is 1.8%, find the random relative error for the method and compare its size to the determinate error found in part b. 26. A chromium in water analysis is done using an computer controlled sampler in a continuous flow spectrophotometric system. In the system, the appropriate reagents are pumped into mixing tees along with the sample, the mixture is passed through a delay loop and finally through a section of transparent tubing in a spectrophotometer where the absorbance of the solution is read. The sequence is to run a blank, sample, and sample with two successive different spikes. Completely independent triplicate measurements are made on each solution whose absorbance is measured. The results below were obtained. Calculate the concentration of Cr in each sample, estimate the error in each, and comment on the necessity for the added complexity of the method of standard additions.

1

Solution Blank Sample 1 Sample 1 + Spike 1 Sample 1 + Spike 2

ng Cr/mL 0.000 ? ? +2.000 ? +4.000

Absorbance 0.001, 0.000, 0.003 0.078, 0.083, 0.086 0.213, 0.214, 0.212 0.337, 0.350, 0.341

Blank Sample 2 Sample 2 + Spike 1 Sample 2 + Spike 2

0.000 ? ? +2.000 ? +4.000

0.009, 0.005, 0.005 0.058, 0.054, 0.058 0.191, 0.188, 0.199 0.310, 0.318, 0.305

Blank Sample 3 Sample 3 + Spike 1 Sample 3 + Spike 2

0.000 ? ? +2.000 ? +4.000

0.002, 0.000, 0.003 0.537, 0.548, 0.531 0.667, 0.659, 0.666 0.805, 0.784, 0.790

27. An electrochemical method for dissolved oxygen promised to save a great deal of labor and tedious wet chemistry. The following data was obtained for ions that seemed to be likely interferants. Each was run in triplicate on samples known to contain 3.50 mg/L O2, and the reported values are the means of all trials. Added ion @ 0.1 ppm @ 1.0 ppm @ 10 ppm @ 100 ppm 2– 3.4 – 3.5 3.4 S2O3 3.4 3.9 – 6.4 CrO423.5 – 4.9 7.8 OClFind a best value for a correction factor, F, that fits the data to the equation: [O2] = [O2]instrument + F * [interfering ion] Comment on this method of allowing for instrumental problems and its likelihood of success for routine analyses. 28. The method of standard additions may be used in exponential relationships as well as linear relations, though the arithmetic of calculations is a little different. Suppose the instrument response follows the dependence: R = S * Cm where R is the instrument response (reading), S is the instrument sensitivity, C is the concentration of analyte in the sample, and m is a constant. This can be converted to a linear relation by taking the log of both sides of the equation. Assume that a sample is spiked with concentrations d1 and d2, so that the instrument response R1, and R2 are observed. If A is defined as: A = log(R2/R)/log(R1/R) a. Derive the equation A = log(1 + d2/C)/log(1 + d1/C). How can it be used to find C from measured values of R, R1, and R2 without determining S and m? b. Using the ISE data below and the method developed in a., find the Ca2+ concentration. c. Assume a linear relation and calculate the Ca2+ from the data below. Repeat assuming an exponential relation as in the initial equation. Compare the results and comment. Sample 22.5 mV

Sample + 20 ppm Ca2+ 44.0 mV

Sample + 40 ppm Ca2+ 107.0 mV

29. RNA polymerase II(B) has an activity defined as: 1 unit catalyzes the addition of 10 pmole of UTP (uridine5'-phosphate) into DNA in 15 min under specified pH,T, and ionic strength. The assay is done by using labeled (3H) UTP, precipitating the modified DNA that contains UTP only, and counting the radioactivity of the 1

precipitate. In this series of assays, the purification of an RNA polymerase is followed by this method using a preparation of 3H UTP that yields 4.1 x 104 nuclear decay events/s (dps) in a 100 pmol sample. Finish the table below. Purification Step Result 1 2 3 4 Total Protein Isolated (mg) 164,000 6830 1310 86 22 Sample Used (µg) 20,000 200 100 50 10 Precipitate Activity (dps) 4860 12100 2420 17200 8900 Total Enzyme Activity (units) 9720 ? ? ? ? % Original Activity retained 100 104 ? ? ? 30. The differential pulse polarogram below shows the blank line below and the sample trace above. The dashed line is the peak base line drawn by the computer according to its instructions. Extrapolate the blank line and the sample line to the left until they merge. a. Calculate the % error in the peak height caused by the computer instructions. b. Calculate the % error in the peak area caused by the computer instructions. c. Imagine a set of computer instructions that will calculate the correct baseline, and write an outline of these instructions.

Current

.5

.6 Voltage (vs. SCE)

.7

.8

31. The recorder output below comes from the spectrophotometric detector in a continuous flow analyzer that is used for nitrite detection. Each sample is injected into the system, and successive samples are separated by air bubbles to prevent contamination. The sample is mixed with reagents that form a color with nitrite ion, and some delay is provided before the slug of treated sample reaches the detector. Of course, you can see where each sample stops by the sudden drop in absorbance when the air bubble flows through the detector. The sequence of samples in this test run (which is just a sequence of standards to test the system) is: 2, 6, 10, 14, 18 µM NO2 standards, followed by the same sequence in reversed order. Then the 2, 18, 2 µM samples are run in sequence to check for cross contamination, followed by 5 successive injections of the 6 µM sample. Assume injections are of 100 µL samples. a. What is the sensitivity of the system in As/µg NaNO2 ? b. Make precision checks (resd) on the first series of runs. Can you note a bias from cross-contamination between the increasing concentration and the decreasing series? Also note any differences in the shape of the As plots for the ascending vs descending series. c. The 2, 18, 2 series of injections allows you to make a numerical estimate of cross-contamination. Assuming the increase in As of the second 2 µM injection is due to carry-over from the previous 18 µM injection, approximately how much sample (%) is carried over to the next sample. d. Keeping the previous parts in mind and assuming the readout is exactly on the scale shown, what are the limits of detection (µg) for NaNO2 ?

1

.6 .5 .4

.3 Absorbance .2

.1 0 0

100

200

300

400

500

600

time (s)

SET 2, Basic Spectophotometry 1. Convert the following absorbances to percent transmittance. (a) 0.526 0.102

(c) 1.191

(d) 3.35

(b)

(e) 0.006

2. Convert the following percents transmittance to absorbance. (a) 0.05% 2.3%

(c) 37.2%

(b)

(d) 99.8% (f) 0.17%

3. Calculate the following values. Assume that the index of refraction is 1.000. wavelength (in µm) of radiation with frequency of 8.58 x 1013sec−1 wavelength (in cm) of radiation with photon energy of 7.95 x 10−13 erg. frequency, in wave numbers of radiation with wavelength of 6.00 µm.

(a) The (b) The (c) The (d) The energy

per photon (ergs) of radiation of wavelength 380 nm. (e) The frequency (Hz) of radiation of wavelength 700 nm. frequency (cm−1) of radiation with energy of 4.41 x 10−13erg.

(f) The

4. A meter has been defined as 1,650,763.73 wavelengths in vacuum for a specific electronic transition for 86Kr. Calculate the following values for this radiation in vacuum to as much accuracy as possible. (a) frequency (in cm −1) (b) wavelength (nm) (c) frequency 1

(Hz) 5. An X−ray has a wavelength of 1.68 Angstrom, and some visible light has a wavelength of 550 nm. Calculate: (a) the energy (J) of each (b) which has longer wavelength and which has higher energy. 6. Calculate the wavelength of electromagnetic radiation which has a frequency of 100 Hz. 7. A 12 dynode photomultiplier is found to deliver an average anode current of 0.92 mA over a period of 4.2 ns, as a pulse resulting from a single ejected photoelectron. Calculate the multiplication factor per dynode. 8. Complete the following table: Solution

A

T

%T

a

0.682

?

?

b

?

?

21.7

c

?

0.572

?

9. Assuming all three of the following solutions contain the same chemical species and all values were obtained at the same wavelength, complete the following table. Solution A a (L / g • cm) b (cm) c (g/L) a 0.602 125 2.00 ? b 0.498 1.00 ? c ? 5.00 1.52 x 10−4 10. Prove that A = 2 − log(%T)

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11. The meter on a Spectronic 20 has a 127 mm long scale and can be read to the nearest 0.5 mm, an accuracy of about 0.5% T. This is a limitation on the precision of reading. Considering this one factor, what is the expected relative precision in concentration at the following As readings: a) 0.0025 b) 0.040 c) 0.200 d) 0.400 e) 0.800 f) 2.000 12. On the Cary 15 recording spectrophotometer, over the range of absorbances below, the error in absorbance is around 0.010, pretty much independent of the absorbance reading. This arises from a number of factors including recorder dead band, pen tip thickness, paper shrinkage, and cell placement. Calculate the relative error (%) caused by these problems at the values below. a) As=0.771 b) T = 43.2% c) As = 1.912 d) T = 3.51% e) T = 99.12% d) As = 0.0026 13. Why is the opening of slits to obtain more power at the detector not a suitable alternative to the proper installation and alignment of the source lamp? 14. Mesityl oxide exists in two isomeric forms : CH3C(CH3)=CHCOCH3 and CH2=C(CH3)CH2COCH3. One exhibits an absorption maximum at 235 nm with a molar absorbtivity of 12,000; the other isomer shows no high intensity absorption beyond 220 nm. Identify the isomers. 15. Assign the structures shown to the respective isomer on the basis of this information: the α−isomer shows a peak at 228 nm (ε = 14,000) while the β−isomer has a band at 296 nm (ε = 11,000).

O

O

Structure 2

Structure 1

16. Vitamin D (calciferol), measured at a wavelength of 264 nm, its maximum in alcohol, follows Beer's Law over a wide range, with a molar absorptivity, ε = 18,200 . (a) If the formula weight is 397, what is the value of "a" (units = g/L)? (b) What range of concentration, expressed in percent, can be used for analysis if it is desirable to keep the absorbance between the limits of 0.4 to 0.9 ? Assume b = 1 cm . 17. For each of the following situations, predict whether Beer's Law would show an apparent negative deviation, a positive deviation, or practically no deviation at all. (a) The absorbing substance is the undissociated form of a weak acid. (b) A metal is being determined by means of a color-forming reagent. (c) In the same system as (b), an insufficient amount of reagent is added to react completely with the three most concentrated standards of the ten examined. (d) There is a large amount of stray light in this spectrophotometer. (e) The bandwidth of the spectrophotometer is quite large. (f) The signal to noise ratio of the spectrophotometer is quite small. 18. A method has been reported for the spectrophotometric determination of the chlorate impurity in the ammonium perchlorate used in rocketry. This is based on the reduction of chlorate to free chlorine: ClO3− + 5 Cl− → 3 Cl2 + 3 H2O The chlorine then reacts with benzidine (1) to give the colored product (2) with a maximum absorption at 438 nm.

1

(1) NH

NH

2 + Cl 2

2+

+ 2 Cl 2 NH

NH

2

2

(2)

Experiments with standard potassium chlorate solutions showed the following straight line relation to hold under prescribed experimental conditions (in 10.0 mm cuvets): As = (1.17x103)C − 0.186, where C is the molar concentration of potassium chlorate. (a) Explain why (2) gives a colored solution while (1) does not. (b) What color is the solution of (2) ? (c) Does this system follow Beer's Law ? (d) The term "−0.186" was ascribed to a reducing impurity in the reagents. Explain why this would be expected to give a subtractive term. (e) A sample of 6.000 g of commercial ammonium perchlorate was suitably treated with reagent and diluted to 100.0 mL. A portion of this showed an absorbance of 0.450 in a 10.0 mm cuvet at 438 nm. Calculate the concentration of ammonium chlorate in the ammonium perchlorate in terms of mole percent. 19. The iron in an unknown is determined as the 1,10−phenanthroline complex. The dissolved sample was placed in a 100 mL volumetric flask, approximately 50 mL of water was added and the pH was adjusted to 3.5 . 4 mL of hydroquinone and 4 mL of 1,10−phenanthroline solutions were added, the solutions diluted to volume, mixed and an absorbance of 0.906 obtained. Since this high reading might give a high relative error, a 50 mL aliquot of the colored solution was transferred to another 100 mL volumetric flask, the pH again adjusted to 3.5, and more hydroquinone and 1,10−phenanthroline solutions were added. This was diluted to the mark and mixed. The absorbance was 0.450 . How should the blank have been prepared? 20. A silicate rock is to be analyzed for its Cr content. A sample is ground to a fine powder, and 0.5000 g portion is weighed out for analysis. By suitable treatment the material is decomposed, the chromium being converted to sodium chromate. The filtered solution is made up to 50. mL with 0.1 M sulfuric acid, following the addition of 2 mL of 0.2% diphenylcarbazide, which gives a red-violet color with Cr(VI), A standard solution is available containing 15.00 mg of pure K2Cr2O7 per liter. A 5.00 mL aliquot of the standard is treated with 2 mL of the diphenylcarbazide solution and diluted to 50. mL with 0.1 M sulfuric acid. The absorbances of the final solutions at 537 nm are found to be: standard, As = 0.354 ; unknown, Ax = 0.272 . What is the amount of chromium in the rock expressed as % Cr2O3 ? 21. Caffeine, C8H10O2N4 . H2O (formula weight = 212.1), has been shown to have an average absorbance of 0.510 for a concentration of 1.000 mg/100 mL at 272 nm. A sample of 2.500 g of a particular soluble coffee product was mixed with water to a volume of 500 mL and a 25 mL aliquot was transferred to a flask containing 25 mL of 0.1 M sulfuric acid. This was subjected to the prescribed clarification treatment and made up to 500 mL. A portion of this treated solution showed an absorbance of 0.415 at 272 nm. (a) Calculate the molar absorptivity of caffeine. (b) Calculate the number of grams of caffeine per pound of the soluble coffee product. Assume b = 1 cm throughout. 22. The molar absorptivity of the nitrite ion is 23.3 at 355 nm, and the ratio of the absorptivity at 355 to that at 302 nm is 2.50. The molar absorptivity for the nitrate ion is negligible at 355 nm and 7.24 at 302 nm. A particular mixture of nitrite and nitrate salts gave A302 = 1.010 and A355 = 0.730 . Calculate the molarities of both ions in the mixture. Assume b = 1 cm. 23. The solubility of BaCrO4 is to be determined at 30oC through the color produced by diphenylcarbazide in a saturated solution. An excess of the solid BaCrO4 is shaken with water in a constant temperature bath for a long enough period to assure equilibrium. A 10 mL aliquot of the supernatant liquid is transferred to a 25 mL 1

volumetric flask and treated with 1 mL of 3 M sulfuric acid and 1 mL of 0.3% diphenylcarbazide and diluted to the mark. The absorbance is then determined at 540 nm. A standard solution containing 0.800 ppm of Cr(VI) is also measured. The results are: Astd = 0.440 and Ax = 0.200. Assuming Beer's Law to hold, calculate the solubility of barium chromate in g/100 g of water. Also calculate Ksp for BaCrO4. 24. The Co(II) chelate of 1−hydroxyanthroquinone has a molar absorptivity of 6080 at 410 nm and 3190 at 480 nm. What must the molar concentration of a solution of the chelate be in order to yield an absorbance of 0.432 when used with a 1 cm cell and read at 410 nm ? Which wavelength is more sensitive, and by how much (%) ? 25. The absorptivity of a compound (M.W. = 223) at 760 nm was 750 L/g−cm. Calculate its molar absorptivity at that wavelength. 26. A plot of absorbance against concentration was shown to be linear in a determination of boron in soils. The slope of the line was 0.200 absorbance units for every 2.00 ppm of boron. The intercept of the absorbance axis was 0.040. Quadruplicate determinations of one soil sample gave values of As as 0.344, 0.336, 0.340, and 0.340. Report the mean, absolute range and absolute standard deviation in terms of ppm B . 27. The dissociation of the complex between thorium and quercetin can be expressed as: ThQ2 ⇐⇒Th + 2 Q (omitting charges). A solution was made 2.30 x 10−5 M in thorium and contained enough excess of quercetin to insure that all of the thorium was present as the complex. The absorbance of the solution was 0.780. When the same amount of thorium is mixed with a stoichiometric amount of quercetin, the absorbance was 0.520. Find the value of the formation constant for the complex. 28. One of the most sensitive spectrophotometric methods for a metal is the formation of the 4,4'−bis(dimethylamino)thiobenzophenone of Pd, which has a molar absorptivity of 2.12 x 105. Assuming normal spectrophotometric errors require an As of 0.003 to be noted as a signal above background noise, a. What is the lowest M of Pd2+ that can be detected ?(assume a maximum practical optical pathlength). b. What is the minimum weight of Pd that is detectible, assuming an appropriate cell volume to go with the pathlength above ? 29. A 0.425 g cast iron sample is dissolved and oxidized by sodium periodate in the acidic solution. This solution is diluted to 250 mL in a volumetric flask and the resulting solution has an absorbance of 0.393 at 545 nm. Past student results have yielded an average molar absorptivity for permanganate ion of 2085. What is the % Mn in the cast iron sample? 30. The purity of nucleotides can only be determined by using their molar absorptivities since since they crystallize with variable numbers of waters of hydration. ε for 5'−CMP is 1.30 x 104 at 280 nm. An 81.4 mg sample of the sodium salt of 5'−CMP was dissolved in 25 mL of water. A 100 µL aliquot of this solution is diluted to 10 mL and its absorbance is found to be 0.826 in a 9.85 mm cell. a. Calculate the M assuming 100% purity. b. Calculate the M based on the UV absorption by the sample. c. Estimate the average number of water molecules per 5'−CMP in this solid. 31. A student prep of a mixture of o− and p−nitroaniline is done by taking 10.2 g of aniline, acetylating it with acetic anhydride, nitrating the resulting acetanilide, and then hydrolyzing the resulting nitroacetanilides using hot NaOH. After recrystallization from aqueous ethanol, a yield of 11.4 g of product is obtained. The characteristics of the products is done by measuring the absorbance of a solution containing 1.80 mg in 100 mL of ethanol in a 1 cm cell at 287 and 347 nm. These As values are 0.323 and 0.870 respectively. From the tabulated data for molar absorptivities, find the % yield of each nitroaniline and the % purity of the product as nitroanilines. Molar Absorptivity at: 285 nm 347 nm o−nitroaniline 5260 1260 p−nitroaniline 1420 9230 32. In the preparation of a calibration curve for an analysis with an old spectrophotometer, the following values 1

were obtained, with concentrations measured in mg/L . mg/L 0.00 1.00 2.00 3.00 4.00 6.00 7.00 8.00 9.00 10.00 Io 98.0 97.0 100.0 99.5 100.0 100.0 99.0 98.2 100.0 100.0 I 98.0 77.2 63.5 50.0 41.3 27.9 23.4 20.3 18.1 16.4 Calculate the absorbances and plot against concentration. Do these data indicate a negative, positive, or no deviation from Beer's Law ? 33. In the determination of acetone in biological fluids, the following calibration curve and unknown data were obtained. Concentrations are in mg% . Solution Absorbance Reagent Blank 0.053 2.0 mg% 0.097 4.0 0.143 6.0 0.190 8.0 0.221 10.0 0.238 Normal blood 0.119 Ketotic blood 0.222 Normal urine 0.150 Ketotic urine (dil) 0.230 All absorbance measurements were against a water blank. Determine the ketone concentrations in each of the four unknowns and assuming a 1:25 dilution was used, calculate the ketone concentration in the undiluted urine. 34. A 1.256 g sample of ore was dissolved, the chromium(VI) was reduced to chromium(III) and the solution was diluted to 100 mL. A primary standard chromium(III) solution was obtained by reducing 10.00 mL of 0.5000 M K2Cr2O7 and diluting this to 100 mL. Working standards were prepared by transferring 2, 4, 6, and 8 mL aliquots of the primary standard to four 100 mL volumetric flasks and diluting. A reagent blank was used. The following absorbances were obtained at 440 nm. Sample (mL) 0 2.00 4.00 6.00 8.00 Diluted ore Absorbance 0.000 0.104 0.213 0.316 0.425 0.322 Calculate the concentrations of Cr(III) (mg/L) in the primary standard solution and each of the working standards and use these to calculate the % Cr in the ore. 35. The coenzyme NADH is a reducing agent that is used or can be used in many biological reactions. It absorbs strongly in the ultraviolet with a maximum absorbance at 340 nm. This a convenient region for enzyme assays because enzymes, being largely protein, have a low absorbance in this region. When a large amount of nonabsorbing substrate and NADH are present in a reaction mixture containing a small amount of enzyme, then when NADH is oxidized to the non-absorbing NAD+, the reaction is zero order in NADH so that the rate of absorbance loss is constant. The activity of the enzyme can then be expressed as the µmole NADH lost per second. Suppose the following calibration data was obtained for NADH: mmole NADH/L 0.100 0.200 0.500 0.800 Absorbance 0.112 0.226 0.547 0.895 In a mixture containing 0.500 mmole of NADH, 200 µL of an enzyme preparation and 0.1 mole of substrate per liter, the following data were obtained. Time (min) 1 2 4 6 8 10 Absorbance 0.511 0.499 0.477 0.451 0.420 0.394 a. Draw a least squares calibration line, with an estimate for the line fit error (sr) . b. Draw a plot of As as a function of time with a least squares line and find its line fit error (sr). c. Report the activity of the enzyme as umole NADH consumed/L . s . Also include a relative error estimate as the square root of the sum of the squares of the line fit errors. 36. To each of a series of buffered solutions below was added the same amount of bromcresol purple indicator solution. Absorbances were measured at the wavelength maximum of 585 nm. Plot the resulting data and 1

determine pKa and Ka for the indicator. pH Abs.

5.0 0.151

5.3 0.204

5.6 0.320

6.0 0.652

6.1 0.795

6.4 1.10

6.8 1.55

7.0 1.76

7.2 1.89

7.6 2.0

37. Graph the data and determine the Ka of the following compounds. p−Nitrophenol Papaverine (cation form) 3 ε × 10 ε × 104 pH 317 nm 407 nm pH 239 nm 252 nm 3.0 9.72 0.33 2.0 3.36 5.90 4.0 9.72 0.33 3.0 3.36 5.90 5.0 9.72 0.50 4.0 3.39 5.83 6.0 9.03 1.66 5.0 3.48 5.63 6.2 8.61 2.28 5.6 3.86 5.19 6.4 8.19 3.99 5.8 3.93 4.91 6.6 7.36 5.14 6.0 4.30 4.61 6.8 6.39 7.22 6.2 4.61 4.15 7.0 5.55 9.16 6.4 4.86 3.71 7.2 4.45 11.65 6.6 5.22 3.30 7.4 3.61 13.40 6.8 5.46 2.77 7.6 2.92 15.00 7.0 5.66 2.51 7.8 2.08 16.90 7.4 6.03 2.00 8.0 1.81 17.50 8.0 6.27 1.63 9.0 1.39 18.33 11.0 6.43 1.56 10.0 1.39 18.33 12.0 6.44 1.56 38. Determine the acidity constant for each indicator from the absorbance data as a function of pH. These data were measured at an ionic strength of 0.05 M. Bromphenol Blue Methyl Red Bromcresol Purple λmax = 592 nm λmax = 530 nm λmax = 591 nm pH Absorbance pH Absorbance pH Absorbance 2.00 0.00 3.20 2.00 4.00 0.00 3.00 0.18 4.00 1.78 5.40 0.24 3.60 0.58 4.60 1.40 6.00 0.66 4.00 0.98 5.00 0.92 6.20 0.87 4.40 1.43 5.40 0.48 6.40 1.13 5.00 1.75 6.00 0.16 6.60 1.37 7.00 2.10 7.00 0.00 7.00 1.72 8.00 2.00

1

−

39. A series of solutions is prepared in which the amount of iron(II) is held constant at 2.00 mL of 7.12 x 10 4 − M, while the volume of 7.12 x 10 4 M 1,10−phenanthroline is varied. After the dilution to 25 mL, absorbance for these solutions in 1.00 cm cuvets at 510 nm are as follows: 1,10−phenanthroline, mL 2.00 3.00 4.00 5.00 Absorbance 0.240 0.360 0.480 0.593 (a) What is the composition of the complex? (b) What is the formation constant for the complex?

6.00 0.700

8.00 0.720

10.00 0.720

12.00 0.720

40. The Method of Continuous Variation (Job's Method) was used to investigate the species responsible for the − absorption at 510 nm when the indicated volumes of 6.72 x 10 4 M iron(II) solution were mixed with sufficient −

6.72 x 10 4 M 1,10−phenanthroline to equal a total volume of 10.00 mL, after which the entire system was diluted to 25 mL. 1.00 cm cuvets were used. Fe(II) ,mL 0.00 1.00 1.50 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Abs. 0.000 0.340 0.510 0.680 0.794 0.680 0.565 0.450 0.355 0.223 0.108 0.000 (a) What is the composition of the complex? (b) What is the molar absorptivity of the complex? 41. Find the composition of the iron(II)−1,10−phenanthroline complex from the following data based on the 510 nm absorbance peak. The data were obtained by mixing the amounts of material stated and diluting to 25 mL. You should also find the molar absorptivity and the complex ion formation constant. Iron(II) Held Constant at Ligand Held Constant at − 4 5.00 mL of 7.00 x 10 M 10.00 mL of 2.10 x 10−3 M M Ligand As M Iron(II) As 1.00 0.177 0.50 0.177 2.00 0.235 1.00 0.352 3.00 0.352 1.50 0.530 4.00 0.470 2.00 0.706 5.00 0.585 2.50 0.883 42. The following data were obtained for the complex of Xylenol Orange and Bi3+. Use this data to find the composition of the complex, and its formation constant. These reactions are run in 0.1 M H2SO4. In the table, T stands for the total of the Bi3+ + Xylenol orange concentrations added. Absorbances are measured at 548 nm. 0.051 0.097 0.148 0.184 0.206 0.195 0.165 0.104 0.056 T = 2.4 x 10−5, As : Bi3+/T : T = 3.2 x 10−5, As :

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

0.073

0.149

0.213

0.269

0.285

0.277

0.220

.155

0.071

43. The following data is for the equilibrium between reduced and oxidized forms of cytochrome−C. The spectra are measured in a quartz cell with semi−transparent electrodes at different applied potentials vs SCE after the system has come to equilibrium. Find: a. The fraction in the reduced form at each intermediate potential, assuming that at the two extreme potential only oxidized or reduced form is present. b. From the equilibrium quotients, [Red]/[Ox], find n in the Nernst equation, since a plot of E vs log Q should have a slope of 59/n . c. Find Eo' from the point where Q=1.

1

.40 [Red] -250 mv

As

.30 -10.0 mv

+10.0 mv .20 +30.0 mv

+50.0 mv .10 [ox] +250 mv

0

450

500

550

600

λ (nm)

SET 3, Other Spectroscopies 1. The absorbance at 440 nm and 545 nm may be used for the simultaneous determination of the Cr2O72− and MnO4− ions in 1 M sulfuric acid. All measurements were in a 1 cm cuvet. The following data were obtained from standards and an unknown solution. Solution Absorbance at 440 nm 550 nm − − 0.334 0.060 4 2 9.02x10 M Cr2O7 0.068 0.931 3.96x10−4 M MnO4− Unknown Mixture 0.210 0.529 (a) Calculate the molar absorptivities for both ions at 440 and 550 nm. (b) Calculate the molar concentration of both ions in the unknown. 2. The simultaneous determination of titanium and vanadium in steel can be done for each as there hydrogen peroxide complexes. When 1.000 g samples of steel were dissolved, colors developed, and diluted to 50 mL in a volumetric flasks, the presence of 1.00 mg Ti gave an absorbance of 0.269 at 400 nm and 0.134 at 460 nm. Under similar conditions, 1.00 mg of vanadium gave an absorbance of 0.057 at 400 nm and .091 at 460 nm. For each of the following samples, 1.000 g in size, and ultimately diluted to 50 mL, calculate the % Ti and % V from the absorbance readings. Sample # 1 2 3 4 5 6 7 8 9 As400

0.172

0.366

0.370

0.640

0.902

0.600

0.393

0.206

0.323

As460

0.116

0.430

0.298

0.436

0.570

0.660

0.215

0.130

0.177

1

3. Ferrocyanide and ferricyanide can be determined simultaneously in the IR in aqueous solution using IRTRAN (MgF2) cells. In a photographic bleach solution, the following data were obtained: Base line flat at 0.043 As. At 2040 cm−1, As = 0.258; at 2115 cm−1, As = 0.515 . Using the facts below, find the molarities of the two solutions as measured in the 50 µm cell. Ferrocyanide ion has absorption max at 2040 cm−1 with ε = 4.23 x 103, and a linear range from 3.1x10−4 to 0.04 M. Ferricyanide ion has an absorption maximum at 2115 cm−1 with ε = 1.18 x 103 and a linear range from around 0.001 to 0.1 M. 4. The Raman spectrum of carbon tetrachloride is obtained with a helium−neon laser at 632.8 nm. Stokes lines are observed at 641.6, 645.6, and 651.7 nm. (a) Calculate the position of the Raman lines in cm−1 (b) At what frequencies (cm−1) and wavelengths will the anti-Stokes lines appear? 5. The fundamental absorption frequency for the ketone group in MIBK occurs at 1728 cm−1. Calculate the absolute wavelength of the Raman line generated using an argon ion laser working at 514.5 nm or at 488.0 nm.

1

6. The absorption spectra for tyrosine and tryptophan in 1 M NaOH are shown in the illustration below. Select appropriate wavelengths for the simultaneous determination of each component in mixtures and explain your reasoning. 5 Tryptophan

4 ε

3 4 (/10 ) 2

Tyrosine

1 0 240

260

280

300

320

λ(nm) 7. The following facts are abstracted from an old paper. (a) Both As and Sb can be oxidized from the +3 to +5 oxidation state by Br2. Arsenic is more readily oxidized than antimony. (b) Sb(III) forms a complex with chloride ion (in 6 M HCl) which absorbs in the ultraviolet at 326 nm whereas Sb(V), As(III) and As(V) do not. (c) KBrO3 and KBr dissolved together in water form a stable solution that will liberate bromine quantitatively upon being added to an acid solution according to the equation: BrO3− + 5 Br− + 6 H+ → 3 Br2 + 3 H2O (d) Free Br2, in the presence of excess bromide ion, absorbs strongly in the ultraviolet, including the vicinity of 326 nm, though its maximum is at a shorter wavelength. Bromide ion alone shows no such absorption. On the basis of the above facts, show how As(III) and Sb(III) can be determined simultaneously by a spectrophotometric titration at 326 nm and sketch the expected titration curve. 8. (a) Why are 1 cm cells seldom used in liquid studies in the IR region? (b) Why are mirrors used instead of lenses in IR spectrophotometers? 9. What is the absorbance of an 11.8 mg/L solution of methylene chloride at its IR frequency of maximum absorbance if a = 1325, b = 0.05 cm ? 10. Benzene has a mass absorptivity of 4950 at 1350 cm−1. Calculate the liquid concentration in mg/ml necessary to yield an absorbance of 0.010 in a 0.05 mm cell at this frequency. 11. The apparent mass absorptivities are given for various infrared absorbers. Calculate the minimum concentrations (mg/ml) determinable in 0.025 mm cells, using 0.005 absorbance units as the minimum detectable signal. (a) a = 900 for CHCl3 at 1216 cm−1 (b) a = 1320 for CH2Cl2 at 1259 cm−1 (c) a = 2900 for C6H6 at 1348 cm−1 (d) a = 6080 for COCl2 at 1810 cm−1 (e) a = 4400 for ClCH2COCl at 1821 cm−1 (f) a = 1010 for water at 1640 cm−1 1

1

12. Estimate the minimum concentration detectable in 0.05 mm cells for each of the following compounds. Assume an absorbance of 0.01 is adequate for detection. Compound Phenol Aniline Acrylonitrile Acetone Isocyanate momomer (in polyurethane foam) 3600 3480 2250 1720 2100 Frequency(cm−1) ε (L/mole-cm) 5000 2000 590 8100 17,000 13. The sulfur content of organic sulfonates and sulfonamides can be determined turbidimetrically using barium sulfate precipitation after preliminary digestion to destroy organic material. A 25.0 mg sample of a sample containing p-toluenesulfonic acid monohydrate was digested and then a 1/10 exact aliquot was transferred to a 10 mL volumetric flask. The appropriate reagents to stabilize a preciptate were added and the solution diluted to volume. Then 5.00 mL of 1.34 M barium chloride solution was added with controlled shaking. After a 25 minute shaking period, the apparent absorbance (turbidance) was found to be 0.295. A standard ammonium sulfate solution containing 200 µg of sulfur, treated in the same way gave a turbidance reading of 0.322 Assuming a linear relation between amount of sulfur and turbidance in this range, find the % purity of the p-toluenesulfonic acid monohydrate sample. 14. A 1.00 g sample of a cereal was extracted with acid and treated to isolate the riboflavin plus a small amount of extraneous material. The riboflavin was oxidized by the addition of potassium permanganate, the excess of which was removed by hydrogen peroxide. The solution was transferred to a 50 mL volumetric flask and diluted to the mark. The fluorometer was adjusted to read 100 scale divisions with a stock solution of quinine sulfate. 25 mL of the prepared solution was transferred to the sample cell and read 6.0 scale divisions. A small amount of sodium dithionite was added to convert the oxidized riboflavin back to riboflavin, and the solution then read 55 scale divisions. The sample was replaced, in the same sample holder by 24 mL of the original oxidized sample plus 1 mL of a standard 0.500 µg/mL riboflavin solution. Addition of a small amount of sodium dithionite to this solution yields a reading of 92 scale divisions. Calculate the µg of riboflavin/g cereal. 15. A 2.00 g sample of pork is to be analyzed for its vitamin B1 content by the thiochrome method. It is extracted with HCl, treated with phosphatase, and diluted to 100 mL. An aliquot of 15 mL is purified by adsorption and elution, during which process it is diluted to 25 mL. Of this material, two 5 mL portions are taken; one of them is treated with Fe(CN)63− and then both are made up to 10 mL for fluorometric examination. A standard solution of thiamine containing 0.2 µg/mL is subjected to similar treatment, except that the portion introduced into the adsorption column is made up to its original volume after elution, that is, it is not diluted. Two 5 mL aliquots were taken, one oxidized, and both are made up to a final volume of 10 mL for measurement of fluorescence. The following measurements are made: Solution Std., oxidized Std., reduced Sample, oxidized Sample, blank Rel. Fluorescence 62.4 7.0 52.0 8.0 Find the vitamin B1 content of the pork in µg/g.

1

16. It has been shown that the Hantzsch reaction can be used in a very sensitive analysis for either aldehydes or primary amines (including ammonia). In the presence of 2,4−pentandione (acetylacetone), a cyclic compound is formed at pH 6 that is strongly fluorescent. The reaction is: O MeC

Me

R1 CH

O

O

CMe

CH 2

CH

C

C

O

O

O

1

O

MeC

CMe + 3 H2 O

+ Me

Me

NH 2 R

R

R

2

Me

N 2

(a) If ammonia is in excess, the fluorescent power, after subtraction of a blank value is nearly linear with concentration of formaldehyde from 0.005 to 1 µg/mL. What will the approximate linear range be for the determination of traces of aniline with excess formaldehyde present? (b) The absorption maximum of the fluorescent compound shows a fairly intense maximum at 410 nm (ε = 8000), too great to be accounted for by two isolated β-unsaturated ketone groups. Can you offer a good explanation? 17. In the determination of the fluorimetric determination of 7H−benz(de)anthracene−7−one (BO) as an air pollutant, considerable interference is encountered from fluorescent polynuclear hydrocarbons. The latter fluorescence is more readily quenched by m−dinitrobenzene (DNB), a fact that makes the analysis possible. Addition of 15% DNB to the solution reduces the fluorescent power of 5 x 10-6 M BO from 0.7 to 0.4 (relative units). If this amount of DNB reduces the interfering materials' fluorescence to 0.005 of its original value, how great an improvement in "sensitivity" would result from the use of the quenching reagent? 18. The absorption spectrum of a fluorescent substance determined with a conventional spectrophotometer is likely to be in error because of fluorescence. Suppose a compound has an absorption maximum (hence an excitation maximum at 290 nm and a fluorescence emission maximum at 350 nm. (a) At what wavelength would you expect the greatest error in the absorption spectrum? (b) Would the observed absorbance be too large or small at this wavelength? (c) Would your answers be different for a spectrophotometer in which radiation from the lamp passes through the cuvet before dispersion in the monochromator? Explain. 19. 80

60 %T 40

20

0 1100

1000 cm

900 -1

800

From the partial Infrared spectra shown above, calculate the ratio of the concentrations of the absorbing 1

compound in the two samples, assuming the absorption is due to the same species. 20. The following data were obtained in the spectrophotometric titration of 1.00 mL of Cu(II) with a chelating agent. The concentration of the chelating agent was 1.68x10−3 M. A 2:1 (chelate:copper) compound with a molecular weight of 396 is formed. The titration is monitored in a 1 cm cuvet. Titrant,mL Absorbance

0.100 0.260

0.200 0.380

0.300 0.500

0.400 0.620

0.500 0.740

0.600 0.747

0.700 0.754

0.800 0.766

0.900 0.768

1.000 0.770

Ignoring dilution corrections, plot the data and determine the original Cu2+ concentration. 21. A mixture of sodium acetate and o−chloroaniline solutions, 10 mL each, was titrated in glacial acetic acid at 312 nm with a 0.1010 M HClO4 solution. Sodium acetate does not absorb in the ultraviolet, but it is a stronger base than o−chloroaniline. The titration results below (corrected for dilution) were obtained. Plot the results and find the concentration of sodium acetate and o−chloroaniline in the original solutions. mL titrant 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Absorbance 0.68 0.68 0.68 0.68 0.67 0.66 0.63 0.56 0.42 mL titrant Absorbance

8.25 0.37

8.50 0.32

8.75 0.26

9.00 0.20

9.25 0.14

9.50 0.09

10.50 0.02

11.00 0.02

11.50 0.02

22. In a photometric titration of magnesium with 0.00130 M EDTA followed at 222 nm in a 1 cm cuvet, the following procedure was used. All reagents except the solution containing magnesium were placed in the titration cell and the instrument adjusted to give a 100% T reading (0 Abs). The following readings were observed after additions of the standard EDTA: mL EDTA added 0.00 0.14 0.40 0.60 0.80 1.00 Absorbance 0.000 0.014 0.200 0.429 0.657 0.906 At this point, the unknown magnesium solution was added and the absorbance fell to 0. The titration was continued as below. mL EDTA added 1.00 1.50 2.00 2.50 2.80 3.00 3.20 3.40 3.60 3.80 Absorbance 0.00 0.020 0.065 0.160 0.240 0.360 0.580 0.803 1.000 1.220 Plot the results, explain the curves obtained, and calculate the µg of Mg in the sample. 23. Sketch the photometric titration curve of phosphoric acid with sodium hydroxide, using methyl orange as indicator and monitoring the red color at 522 nm. On the same graph, plot the photometric titration curve for the titration of the same solutions, but using phenolphthalein as indicator and following the absorbance at 553 nm, to follow the red color associated with the phenolphthalein endpoint. 24. The dl-alanine IR spectrum has an absorbance maximum at 850 cm−1. A series of standard solutions and an unknown were prepared. The same cell and spectrophotometer were always used. The following data were obtained using the baseline method. In this method, the baseline is drawn and a %To is estimated on the baseline at frequency of the peak maximum. Sample (mg ala/mL) 1.25 2.50 3.75 Unknown %To 60.1 58.7 60.6 59.7 %T 77.7 37.6 30.2 33 What is the alanine concentration in the unknown?

1

25. The presence of ethylene in samples of ethane is determined by using the absorption band of ethylene at 2080 cm−1. A series of standards gave the following data: % Ethylene 0.50 1.00 2.00 3.00 Absorbance 0.120 0.240 0.480 0.719 Calculate the percentage of ethylene in unknown sample that had an absorbance of 0.412 when using the same cell and procedure. 26. The following data are for the apparent absorbance of cyclohexanone in cyclohexane solution at 1715 cm−1 in a 0.10 mm cell. Conc.(g/L) 5 10 15 20 25 30 35 40 45 50 Absorbance 0.190 0.244 0.293 0.345 0.390 0.444 0.487 0.532 0.562 0.585 (a) Plot these data and find the range over which Beer's Law is followed after the necessary background correction is made. (b) Calculate the value of the molar absorptivity. 27. The element beryllium was determined in an ore sample by fusion with sodium carbonate of a 750 mg sample. The carbonate mass was dissolved in HCl and diluted to 250 mL. A 10.0 mL aliquot was transferred to a 25 mL volumetric flask, the appropriate reagents to complex beryllium and fluoresce were added and the solution diluted to volume. This sample and a series of standards were read using 366 nm excitation and reading emission at 570 nm. Calculate the % of beryllium in the ore. Standard concentrations are in µg/mL concentration units. Sample Blank Unknown 2.0 5.6 7.8 12.0 Intensity 0.0 87 16.7 46.7 65.0 100 28. A 5.00 g sample of cereal was analyzed for thiamine (Vitamin B1). The entire sample was extracted with HCl, purified by ion exchange, eluted with an acidic KCl solution and oxidized with a basic ferricyanide solution to the yellow fluorescent pigment, thiochrome. This was followed by an extraction into 20.0 mL of i-butyl alcohol. A series of standards of standards and a blank were also prepared. Calculate the µg of thiamine in 1 g of cereal from the data obtained below. Standard concentrations are in µg thiamine/mL in i-butyl alcohol. Sample 0.00 0.05 0.12 0.24 cereal extract Intensity 0.0 20.8 50.0 100.0 42.0 29. Nitrates may be determined by their quenching of the fluorescence of the dye fluorescein. Working standards were prepared by diluting 0, 0.05, 0.10, 0.30, and 0.40 mL of a 1 x 10−4 M nitrate solution to volume with concentrated sulfuric acid in a 50 mL volumetric flask after adding 5 mL of 10−7 M fluorescein. A 0.5 mL sample of creek water was treated the same way. Find the nitrate concentration (µg/mL) in the creek water from the fluorescence data below. Sample(mL added): 0.00 0.05 0.10 0.30 0.40 Creek water Intensity: 100 92 86 55 40 73

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30. In the determination of total sulfur in soil, a 0.448 g sample of the soil is dried, ground, and fused with a mixture of sodium and potassium nitrates. The product was dissolved in HCl and boiled to remove carbonates. A nitric acid solution, slightly contaminated with sulfate, was added to improve the detection limit. The solution was boiled again, 5 mL of a dilute barium chloride solution added, and then it was diluted to volume in a 50.0 mL volumetric flask. The sulfur in the original soil is then present as suspended barium sulfate and was determined turbidimetrically at 490 nm. Standard solutions containing sulfate were prepared using the same solutions. Using the data below: (a) Determine the sulfur concentration in the diluted unknown. (b) Assuming the nitric acid reagent contributed 1.1 mg/L sulfur to the diluted unknown, calculate the amount of sulfur in the soil extract from the soil sample itself. (c) Find the sulfur concentration (mg/g) in the original soil. Sample (mg S/L) 2.0 4.0 6.0 8.0 10.0 12.0 Unknown Absorbance 0.32 0.59 0.84 1.08 1.28 1.40 0.65 31. Solutions of varying amounts of aluminum were prepared, 8−hydroxyquinoline was added and the complex was extracted with chloroform. The chloroform extracts were all diluted to 50 mL and compared in a fluorometer. The readings below were obtained. Al (µg/50 mL) 2 4 6 8 10 12 14 16 18 Fluorometer Reading 10 19 28 37 45 53 60 66 71 After plotting the data, state over what concentration range the fluorescence is linear in concentration. 32. The common coenzyme NADH is very fluorescent in its reduced state with an absorption maximum at 340 nm and an emission maximum at 465 nm. The following emission intensities were found from standard solutions. µmole NADH/L 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 Intensity 4.50 9.06 13.28 18.05 21.99 27.45 31.00 35.86 a. Plot the points on an accurate graph and draw the least squares line. b. If an unknown yields an average intensity of 25.27 as the result of 3 readings, what is the concentration of NADH in the unknown and the relative estimated error ? c. Is there any of the downward curvature associated with fluorescence assays visible ? SET 4, Atomic Spectroscopy 1. Calculate the iron content in a diethyldithiocarbamate extract using the following data from an atomic absorption spectrophotometer. µg Fe added to Absorbances 200 mL samples Blank Sample 0.020 0.090 0.00 0.214 0.284 2.00 0.414 0.484 4.00 0.607 0.677 6.00 2. The following data have been obtained for nickel by atomic absorption. Plot a calibration line and find the concentration of nickel in the unknown. Sample 2 ppm 4 6 8 10 Unknown %T 62.4 39.8 26.0 17.6 12.3 20.4 3. A 1.013 g sample of a copper-beryllium alloy is dissolved in 5 mL of dilute nitric acid, and the solution is diluted to 1 liter with distilled water. The atomic absorption working curve is non-linear but the sample is known to contain around 2% beryllium. Standards have therefore been prepared containing 20 and 25 µg/mL of beryllium and each standard also contains 1000 µg Cu/mL. (a) Why include this amount of copper in the standards? (b) If the percent transmittance readings for the standards are 44.7 and 38.0 respectively, and for the 1

unknown is 40.9, what is the concentration of beryllium in the sample? 4. Duplicate 0.5 g samples are digested in 5 mL of HCl, and evaporated to dryness after the addition of 3 mL of nitric acid. Then 15 mL HCl and 40 mL of hot water are added and the solutions cooled. To one sample, 1 mL of a 5.0 µg/mL gold standard is added. Each sample is then treated with 5 mL of hydrochloric acid and the resulting chloroauric acid is extracted into 5 mL of methyl isobutyl ketone. If the atomic absorption calibration line is straight, what is the gold concentration in the ore (µg/g) if the two absorbance readings are 0.22 and 0.37 for the two samples? 5. Various aliquots of a 0.100 µg Ca/mL stock solution were diluted to the mark with deionized water in 50 mL volumetrics as was a 5.00 mL ground water sample. From the AA readings below, find the ppm CaCO3 in the ground water sample. Sample (mL stock) 1.00 2.00 3.00 4.00 5.00 Ground Water Absorbance 0.150 0.270 0.436 0.552 0.661 0.336 6. A waste water sample was assayed using AAS with the method of standard additions. 25 mL aliquots of the sample was placed in a 50 mL volumetric flask and then the stated mL of a 10 µg Cu/mL stock solution were added and the mixture diluted to the mark with deionized water. Find the Cu concentration (µg/mL) in the stock solution. If you can, take careful account of the non-linearity in the plotted data. mL 10 ppm Cu Stock 0.00 2.00 4.00 6.00 8.00 Absorbance 0.231 0.323 0.407 0.469 0.517

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7. An organic compound, believed to be dibasic and have empirical formula C9H16N4O7 was rapidly precipitated from aqueous solution using Ba(ClO4)2 solution. 21.0 mg of the dried precipitate was dissolved in 6 M HCl and diluted to 100 mL in a volumetric flask. 5 readings were taken on all the solutions listed below, with uncertainties in the last digit(s) indicated using the usual conventions. ppm Ba Blank 1.00 4.00 10.00 14.0 20.0 30.0 Sample As 0.000(7) 0.044(3) 0.178(4) 0.483(12) 0.684(21) 0.993(36) 1.512(88) 0.762(18) a. Find the % Ba in the original precipitate, and the uncertainty in the value. b. Estimate the purity of the compound isolated. c. Estimate the limit of detection for barium in this method. 8. An ICP determination of Mn was made on a blood sample. The traces below show the emission signal as a function of time when a 25 µL sample was injected into the aspirated blank solution. Then, samples of blood were spiked with variable amounts of Mn from a standard, and diluted 1:10 with dil. HCl. The second set of emission signals below were obtained. a. Find the concentration of Mn in the sample. b. Estimate the standard deviation of the method. c. Estimate the certainty of the Mn determination, and comment on the apparent limits of detection and interferences.

Mn signals from 25 µL undiluted blood

diluted original

+0.005 ppm Mn

+0.01 ppm Mn

+0.02 ppm Mn

9. A calibration curve was obtained for use in the determination of iron in plant tissue using plasma emission. All samples and standards were treated the same way. The following data were obtained. Numbers are ppm iron in the standards. Sample 0.0 ppm 2.3 6.5 10.0 12.3 A B C Intensity 19 34 58 73 77 75 30 50 Plot the intensity against concentration, determine the concentration of Fe in A, B, and C, and estimate the accuracies of each determination. 10. In the arc emission determination of lead in an alloy, using a fixed amount of magnesium as an internal standard, the results below were obtained. Calculate the concentrations of the unknowns. Concentrations of standards are stated in mg/mL. Sample: 0.151 0.201 0.301 0.402 0.502 A B C Reading (Pb): 7.3 8.7 7.3 10.3 11.6 8.8 9.2 10.7 Reading (Mg): 17.5 18.5 11.0 12.0 10.4 15.5 12.5 12.2 11. In a determination of cadmium using tin as an external standard in an emission spectrograph, the following data were obtained. Use an intensity ratio calibration line to determine the cadmium concentrations in the unknowns. Cadmium standard concentrations are in ppm (µg Cd/ml). 1

Sample: Reading (Cd): Reading (Sn):

2.0 8.0 16.0

4.0 8.9 7.3

6.0 9.7 4.6

8.0 11.9 3.9

10.0 16.4 4.0

A 13.0 4.8

B 7.0 12.0

12. A 2.00 µg Cd2+/mL concentration was used as in internal standard in a simultaneous ICP-AES determination of Cu2+. 10 mL of the stock Cd2+ solution and 10 mL of the copper solution to be determined were diluted to a final volume of 25 mL. The emission line of Cu was measured at 324.75 nm and that of Cd at 326.11 nm. Determine the Cu concentration in the unknown. Cu concentrations in the known solution are the concentration in the 10 mL aliquot before final dilution. Intensities are relative to an iron internal standard. 12.0 24.0 36.0 48.0 60.0 unknown [Cu2+] , ng/mL 324.75 nm, Intensity 17.8 38.0 53.4 71.1 93.0 61.1 326.11 nm, Intensity 30.6 32.0 29.4 29.9 30.9 30.1 13. A magnesium analysis was run on a brine using DCP-AES and a 25 ng/mL Mo internal standard. The Mg line at 285.213 nm and the Mo line at 281.615 nm were monitored sequentially. The standard solutions were made by taking 1 mL of a 2.5 µg/mL Mo stock solution, variable amounts of magnesium stock solutions and diluting to the mark in 100 mL volumetric flasks to achieve the final Mg concentrations listed. The brine solution was prepared in a parallel fashion, using 100 µL of a 1:1000 dilution of the original brine. Find the Mg concentration in the original brine. 1.5 15 150 1500 15000 Diluted Brine Mg2+ conc. (ng/mL) Intensity at 285.213 0.83 4.2 22 144 924 327 Intensity at 281.615 1.8 1.5 1.6 1.7 1.8 1.9 14. A milk sample was to be assayed for Sr by ICP-AES, using Vanadium as an internal standard. A strontium stock solution was prepared by dissolving 211.5 mg Sr(NO3)2 in 1 L and then diluting 1 mL of this solution to 1 L to make the final stock solution. Similarly, 101.0 mg of vanadium metal sponge was dissolved in 10 mL conc. HCl, diluted to 1 L and the 1 mL of this solution was diluted to 1 L to make the vanadium stock solution. The milk was prepared by evaporating 50.0 mL to dryness, dry ashing the residue, dissolving the residue in 5 mL conc. HCl and diluting the solution to 10 mL in a volumetric flask. Final solutions were prepared by adding 1 mL of the V stock, a variable amount of the Sr stock solution or 1 mL of the milk preparation and diluting to the mark in 25 mL volumetric flasks. The emission lines of Sr at 460.73 nm and V at 437.92 were monitored simultaneously giving the results below. Find the ppb Sr in the milk. mL Sr stock 1.00 2.00 3.00 4.00 5.00 Milk Prep. 470.73 nm emission 33.7 60.0 109.1 149.8 163.1 75.9 437.92 nm emission 17.8 16.5 19.3 19.6 17.0 18.3 15. Predict the change in sensitivity of a Ca determination when changing from an nitrous oxide / acetylene flame(2600 K) to an Ar plasma torch (6000 K), assuming ionization is the only change occurring, and that the ionization energy is as in the handbook. a. Conclude whether ionization would have an appreciable effect on the sensitivity to absorption. b. What is the increase in fraction of excited atoms if the lowest available energy excited level for Ca atoms is 2.93 ev above the ground state ? Do not ignore the fraction of atoms calculated as ionized in part a.

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16. Al is to be determined in whole blood by ICP. Blood levels of Na, K, Ca, and Mg are normally observed to be 140 mM, 6.5 mM, 3.4 mM, and 1.6 mM respectively, with a normal variation of 2.5%. All these metals effect the emission of Al at 396.15 nm as shown by the experimental table below. This table shows the emission reading for a 1.0 ppm Al sample with added concentrations of metal ion (ug/mL) as shown, after using the standard 1.0 mg Al/L standard with no added metal to adjust the reading to 100. µg cation/mL Ca K Mg Na 3000 – – – 195 1000 – 192 – 188 − − 750 186 182 500 181 178 152 174 250 172 166 146 159 100 159 149 133 142 50 148 139 127 134 10 126 118 116 116 a. At normal levels, which ion will produce the largest variation in Al readings by expected 2.5% variation, and how much is this effect? What the maximum variation that could be produced at these levels by the combined effects of all the ions (assuming the emission enhancements are independent)? b. If a ten-fold dilution of the samples were made before running, which cation would be most troublesome, and what variation in Al reading could it produce over its normal range of variation ? c. Suggest a method of minimizing the errors caused by the normal variations of these ions in blood samples. 17. For the analysis of cement samples, a series of standards were prepared and the emission intensities for sodium and potassium were measured at 590 nm and 768 nm respectively. Each standard solution contained 6500 µg Ca/mL to compensate for the effect of the bulk calcium upon the readings. The results are given below. Numbers are µg metal/mL. Sample 0.0 10 25 50 75 100 Cements: A B C + 3 22 46 69 87 100 28 58 42 Na emission 0 15 33 58 80 100 69 51 63 K+ emission For each sample, 1.00 g was dissolved in acid and diluted to 100 mL. Calculate the % Na2O and K2O in each cement. 18. Boron gives a series of bands due to the radical BO2 that lie in the green portion of the spectrum. Although the overlapping band systems present a problem in the measurement of the flame background, the minimum between adjacent band heads can be used for this background correction. The following data were obtained for standards (µg B/mL) and unknowns at a 518 nm peak and a 505 nm minimum. Find the concentrations of boron in the samples. Sample 0 50 100 150 200 A B C 518 nm emission 36 44 52 60.5 68.5 45 85 66 505 nm emission 33 36 39 42.5 45.5 36.5 65 50 19. A calibration curve for the flame emission determination of strontium at 460.7 nm was obtained in the presence of 100 µg/mL calcium and in the absence of added calcium. The results are listed below: 0.0 0.25 0.5 1.0 2.5 5.0 7.5 10.0 Sr2+(µg/mL) Emission (No Ca) 0 2 6 16 44 94 150 200 Emission (Ca added) 13 18.5 24 36 70 125 181 238 (a) Plot a calibration line, and also make a log-log plot. (b) What is the most likely cause of the upward curvature in the region of low concentrations when calcium is absent? (c) Why does the addition of calcium straighten the calibration line and increase the net emission reading for strontium?

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20. A propane/air flame for the emission analysis of Na and K in serum samples, with 500 ppm added Li as internal standard and ionization suppressor. The serum samples were prepared by diluting 10 Samples(µg Mg/mL) :L of serum to 10.00 mL using 500 ppm Li stock solution. The 1.00 ppm Na standard was used to set the emission meter reading at 1.00. From the data below, report the mg% Na and K in the two serum samples. The lines used are: 589 nm for Na, 671 nm for Li, and 766 nm for K. Sample (ppm) Readings @ Na K Li 589 nm 671 nm 766 nm 0.5 0.5 500 0.43 0.57 31.2 1.0 1.0 500 1.00 1.26 36.5 5.0 5.0 500 4.9 6.5 36.3 10.0 10.0 500 8.8 11.9 31.8 Sample #1 2.9 10 s) rather than using a well defined plug. (b) Using too low a temperature at the injector so that the sample does not vaporize quickly. (c) Increasing the temperature of the column. (d) Increasing the flow rate. (e) Doubling the length of the column. (f) Doubling the recorder chart speed. 4. What is H for a 2 m column if a peak with a retention time of 10.0 min has a width of 30 s? 5. The adjusted retention distance for a lipid sample on a gas chromatograph with a 1.5 m column was 59.6 cm. The recorder chart speed was 3.61 cm/sec, the width of the peak at the base was 12.0 cm. Calculate the number of theoretical plates and the HETP. 6. Calculate the Rf value of a pesticide separated by thin layer chromatography in which the sample spot moves 6.8 cm as the solvent moves 21.3 cm . How far would the sample spot move if the solvent had only moved 15.0 cm ? 7. A gas chromatographic peak had a retention time of 65 seconds. The base width, obtained from intersection of the base line with the extrapolated sides of the peak, was 5.5 s. If the column was 6 feet long, what was the HETP (cm/plate) ? 8. It is desired to just resolve two GLC peaks with retention times of 85 and 100 s using a column that has a HETP of 1.5 cm/plate under the operating conditions to be used. What length column is required, assuming both peaks have the same base width ? 9. The chromatogram below is for fatty acids in chloroform. The 3 mm x 1 m column is filled with 25% 1

petroleum based grease (Apiezon L) on 80-100 mesh Chromosorb W. The detector is a TCD detector and it is assumed to be of equal sensitivity to all the compounds on a molar basis. The first peak is for solvent and the others, sequentially, are the C12, C14, C16, and C18 acids. Assuming that there is 62 mg of the C18 acid in the sample, find the weights of the other acids in the mixture. CCl 4 1.5

C

12 C 14

1.0

C 16

millivolts

C18

.5

0

start

10

20

30

40

50

time (/min )

b. Calculate asymmetry factors for each complete peak and comment on the reason the rather poor peak shape is expected. How is the problem normally avoided ? c. Using the first and last complete peaks, calculate the number of theoretical plates, and suggest a reason for the disparity. 10. For the chromatogram whose peaks are listed below below: a. What is the expected retention time for pentane? b. Within the instrument sensitivity, is there any ethane in the sample? Compd: Air ? ? ? Propane ? n-butane ? tr (s): 12 61 94 129 162 206 250 298

? 331

11. Compound Y is eluted in 15.0 min, Z in 25.0 min. A non-retarded substance, X, requires 2.0 min. (a) What are the capacity factors for Y and Z on this column? (b) What is the selectivity for Y over Z ? (c) What fraction of the actual elution time does Y spend in the mobile phase? (d) Of the 25 minutes required to elute Z, how much time does the average Z molecule spend in the stationary phase? 12. The width of a certain peak is 50 sec and its retention time is 50 min. How many theoretical plates does the column contain under these conditions? 13. Isooctane and octane give retention times of 800 and 815 sec on a column known to have 8100 theoretical plates. (a) What resolution will be obtained if a sample containing both compounds is run on this column? (b) Assuming the retention times to be unchanged, how many plates would be required to achieve a resolution of 1.00 ? (c) Assuming the retention times to be unchanged, how many plates would be required to achieve baseline resoluton ( R ≥ 1.5 ) ? 14. The constants in the Van Deemter equation for a particular column at 150o were found to be: A = 0.08 cm, B = 0.15 cm2/sec, and C = 0.03 sec. What is the optimum mobile phase velocity for this column? (See #15) What is the corresponding minimum HETP ? 15. Obtain an expression for Hmin and uopt in terms of A, B, and C by differentiating the Van Deemter equation and setting dH/du = 0. 16. The following data are obtained in a chromatographic analysis: tm = 1.0 min, tr = 5.0 min for the compound, Vstat = 2.0 mL, Flow rate = 50 mL/min find k', Vm, K, and Vr for the compound. 1

17. Van Deemter constants are given for two columns of equal length: A (cm) C (sec) B (cm2/sec) Column #1 0.18 0.40 0.24 Column #2 0.05 0.50 0.10 (a) Which of these two columns gives the larger number of theoretical plates if the carrier gas velocity is .50 cm/sec ? (b) What is the optimum velocity for column #1 ? (See #15) 18. The following data were obtained for an pesticide, 2,4-D, on a gas chromatograph at 90o C: flow rate 160 mL/min; chart speed 3.20 cm/min; retention time for sample 44.0 cm; retention time of air 4.1 cm. Calculate the retention volume and the capacity factor for 2,4-D.

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19. The adjusted retention volumes (Vr−Vm) of a homologous series of saturated hydrocarbons separated by GLC are given below: Hydrocarbon Propane Butane Pentane Hexane Heptane V'r (mL) 47.5 90.0 175 348 685 The gas flow rate was 70 mL/min. From the appropriate log plot, estimate the adjusted retention volume and the adjusted retention time for octane. 20. For a gas chromatographic system, the following van Deemter coefficients are found: A = 0.001 cm, B = 5 cm2/sec, and C = 0.0005 sec. Find the optimum flow velocity and the corresponding HETP. (Use the result from #15) 21. Some optimization procedures in HPLC originate from the idea of generating the maximum number of plates within the shortest possible time, that is, minimizing tr/N . Under what conditions can this be achieved? Because of equipment limitations, what does this approach lead to in terms of tr and the pressure drop across the column? 22. For compounds M and N, distribution studies between water and hexane, respective partition coefficients between water and hexane have been found to be 5.81 and 6.22. (K = Cwater/Chex) The two materials are to be separated on a silica gel column containing adsorbed water using hexane as an eluent. The ratio of stationary phase volume to mobile phase volume is 0.422. Calculate the capacity factor for each material and the selectivity factor. (a) How many plates are needed to provide R = 1.5 ? (b) How long a column is needed to produce a HETP of .0022 cm? (c) If the flow rate is 7.10 cm/min, what are the tr values for the two molecules? 23. Using a 1.0 m column packed with Carbowax 20M on a GLC equipped with a TCD detector, the following data were obtained: Compound air hexane hexene benzene tr (min) 1.9 9.9 10.7 13.7 W½ (min) 0.76 0.82 1.08 (a) Find the average number of plates a average plate height for the column. (b) Find the resolution between adjacent compounds. (c) If a resolution of 1.5 was to be achieved for hexane and hexene, find the number of plates required, the length of column needed, and the tr for hexene on the resultant column. (d) If the stationary and mobile phase volumns were 39.8 and 134.2 mL respectively, find the partition coefficient for each of the three compounds, their capacity factors and the selectivities for each pair. 24. A 4 m column containing 15% DEGS as the stationary support with a TCD yields the following retention times. Plot the logs of adjusted retention times vs carbon number and draw whatever useful conclusions you can from the plot. How well do the alkanes fit the criterion as a homologous series? Compound: CH4+air ethane propane propene i-butane butane i-butylene tr (min): 1.8 2.4 3.6 4.3 5.5 7.5 8.6 Compound: tr (min):

trans-2-butene 10.6

cis-2-butene 12.3

1

i-pentane 13.6

pentane 18.2

25. The following data were obtained on a 3mm x 3 m 15% methyl silicone oil on Chromosorb W column. The flow rate measured by a soap film flow meter at the outlet is 25.5 mL/min. Room temperature is 22oC and the column temperature is 112oC. Atmospheric pressure is 745 Torr and the inlet pressure is 4.18 atm. The tabulated widths are in units of min at half-height. Compound diethyl ether hexane ethylbenzene tr' (min) 1.78 6.82 19.02 1/2 Width (min) 0.15 0.45 1.64 a. Find the adjusted and net retention volumes for each compound. b. Find the Resolution between adjacent peaks, and H based on each peak. 26. What N value is required to achieve a resolution of 1.5 (cross-contamination < 1% ) for two compounds whose selectivity ratio is 1.10 if: a. the capacity factors are ~ 50 on a packed column. b. k' values are 5. c. the capacities are 0.5 on a capillary column. d. For each case above, find the minimum length column columns needed, assuming H = 0.2 mm for packed columns and 5 mm for capillary columns. 27. From a graph of the following data, estimate the optimum carrier gas velocity and the HETP at this velocity. HETP (cm) 0.622 0.275 0.325 0.450 0.581 0.732 0.865 Flow rate (mL/min) 5.0 10.0 15.0 20.0 25.0 30.0 35.0 28. The following GLC data were found for individual 2 µL injections of hexane in a gas chromatograph with a 3 m column. Calculate the number of theoretical and HETP at each flow rate, and make a plot to determine the optimum flow rate. Use tr', the relative retention time as a plotting parameter. Flow rate(mL/min) 26.4 31.7 39.9 50.2 62.7 71.8 90.3 120.2 tm(min) 3.54 3.10 2.58 2.24 1.89 1.74 1.49 1.18 tr(min) 12.69 11.31 9.83 8.62 7.62 7.17 6.37 5.49 Peak width(min) 0.95 0.81 0.68 0.54 0.47 0.43 0.39 0.35 29. The following data was obtained under the same conditions as the problem above, using 2 µL heptane samples. to is the retention time for air, and the peak height is measured in chart paper units with 100.0 being the full calibrated width of the paper. Fo is the flow rate (mL/min) at the soap film flowmeter. Fo to tr Height 1/2 Width 122. 92 73. 64. 51. 41. 33. 27. 18.

1.40 1.70 1.95 2.10 2.45 2.80 3.30 3.75 5.05

4.45 5.35 6.15 6.65 7.65 8.85 10.35 11.70 15.84

50.0 61.0 65.4 68.3 69.5 79.9 78.5 76.7 72.5

0.15 0.34 0.38 0.41 0.49 0.64 0.76 0.90 1.48

a. Find the corrected flow rate, tr', and Vr' for each flow rate. b. Find N and H for each flow rate, and plot H vs the corrected flow rate. c. Plot both peak height and area on the same graph vs flow rate, and comment on the significance for ease of quantitation.

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30. Hydrochlorothiazide, an anti-hypertensive agent, may be quantitatively separated by HPLC and monitored at 271 nm. The following data were obtained on six identical aliquots of the same urine. Graph the data and determine the µg/mL of analyte in the urine sample. Added analyte (µg/mL) 20 40 60 80 100 120 Absorbance at peak 0.224 0.258 0.291 0.325 0.359 0.392 31. Carbon tetrachloride is toxic enough that it is banned for use as a cleaning fluid. In the quantitative determination of the carbon tetrachloride in an accepted cleaning fluid, the following data were obtained by spiking 10 mL samples with portions of carbon tetrachloride. From the data, find the concentration (µL/mL) of carbon tetrachloride in the original sample. CCl4 added (µL): 0.0 1.0 2.0 3.0 67 87 110 130 Peak area (mm2): 32. In this GLC detection method, the sample is effluent from the sample is completely oxidized, the water produced removed by a trap and the carbon dioxide produced is allowed to flow through a TCD detector. In a certain experiment, seven components gave peaks with integrated areas as follows: pentane hexane 3-methylhexane heptane 2,2,4-trimethylpentane toluene octane Area: 2.00 5.72 2.21 8.15 1.92 3.16 5.05 (a) Find the mole % and weight % of each hydrocarbon. (b) Point out some advantages and disadvantages of this oxidation procedure. 33. A mixture of organics was made up as in the table below. When 0.25 µL of this mixture was injected into a gas chromatograph with a phenylmethyl silicone column and a TCD detector, the areas in the table (cm2) were obtained. a. Calculate the detector's weight response for each compound compared to benzene. b. Within what % is the expected equal response/mole compound observed ? Compound: n-hexane cyclohexane benzene toluene Wt(mg): 161 189 232 167 Area: 16.71 18.15 21.35 15.32

1

34. The chromatogram shown below is for a gaseous (low boiling liquid) fuel mixture. The chromatogram is being run for an accurate estimate of the heat content in kJ/m3 of the gas. The table below lists the components in their chromatographic order, the relative response per unit volume of the gas, the attenuation factor used in recording the chromatogram, and the heat of combustion of the compound in MJ/m3 a. Which component is present in the largest amount, and what is its volume fraction? b. What component contributes the largest amount to the heating value? c. What is the heat of combustion of the mixture in MJ/m3 ? Compound

methane

ethane

propane

methylpropane

butane

Response Factor ∆Hcomb

3.00 16 37.6

2.53 128 65.8

1.94 1 93.7

1.86 32 121.1

1.79 1 122.0

methylbutan e 1.79 8 148.9

pentane 1.73 1 149.2

mv

Inject

0

2

4 6 time ( /min)

8

10

12

14

16

18

SET 6, Liquid Chromatography 1. What types of compound may be better separated by HPLC than GLC ? 2. In what order would the following compounds bve eluted from an alumina column using hexane as the eluting solvent ? CH3CH2OH, CH3CHO, CH3CO2H ? 3. What solvent should you use to separate a series of hydrocarbons CH3(CH2)xCH3 on an alumina column? 4. A particular normal phase separation specifies the mobile phase be 10% methylene chloride in hexane. Unfortunately, the laboratory supply of methylene chloride has been used up. What mobile phase might be substituted that has approximately the same strength ? 5. A particular compound is eluted from a silica gel column too rapidly when dioxane is used as the mobile phase. Will methyl isobutyl ketone make the compound move faster or slower? 6. On a C18 bonded phase, a particular compound moves too slowly in a 50% methanol in acetonitrile solvent. What adjustment should be made in the ratio of solvents ? 7. During the separation of carbohydrates using a bonded aminoalkyl functional group, an increase in the water 1

concentration of the acetonitrile/water mobile phase decreases retention. Is the bonded phase acting in the "normal" or the "reverse" mode ? 8. Some headache preparations contain aspirin and phenylpropanolamine. Suggest an HPLC method for the separation employing ion suppression plus ion pair reverse phase chromatography. 9. Linear alkyl benzene sulfonates are the major surfactants in household detergents. Therefore, the detection of such materials and their separation based upon the alkyl chain length in environmental samples is desirable. Reverse phase techniques using a methanol/water solvent resulted in only two major peaks and no peaks for individual alkyl members. Success is achieved if the ion pairing technique is used. Predict the effect of counterion size on retention considering ammonium, tetramethylammonium and tetrabutylammonium chlorides as ion pairing reagents. 10. Amphiprotic compounds, such as the monofunctional amino acids, are difficult to chromatograph. (a) What two different approaches could be used if ion exchange is selected ? (b) Suggest two different approaches if reverse phase ion pair chromatography were to be selected. 11. The separation of adenosine mono-, di-, and tri-phosphate (AMP, ADP, and ATP) was done in a little over 3 min using 0.4 M KH2PO4 with 3% methanol using a 15 cm x 2 mm column packed with 10 µ particles with a 3aminopropyl siloxane bonded phase. The mobile phase viscosity was 1.4 cP, the flow rate 1.66 mL/min at a pressure of 2900 psi. Suggest improvements with reasons in the operating procedure. 12. In a normal phase HPLC separation, a solute had a retention time of 29.1 min while the sample loop yielded a peak at 1.05 min. The mobile phase was a 1:1 mixture of chloroform and hexane. Find the k' for the solute and suggest a mobile phase composition to bring the k' to a value of 10. If the original composition (1:1) had not successfully separated two solutes, in what direction should the mobile phase be changed? 13. For each of the following samples, develop a scheme for ion chromatography by suggesting column, eluent, detector, and suppressor device including the chemical stripping action as appropriate. (a) Analysis of fruit juices for Na+, K+, and NH4+ . (b) Separation of tetraethylammonium and tetrabutylammonium ions. (c) Determination of Cl−, SO42−, and PO43− ions in water supplies and sources. 14. In a separation of nucleosides on an HPLC column with a UV detector, peaks appeared that were identified as follows: Sample loop - 1.0 min, uridine - 7.5 min, inosine - 10.0 min, guanosine - 14.3 min, adenosine - 17.8 min, cytidine - 24.0 min. On another column of different dimensions, but packed with the same stationary phase, the sample loop peak arrived at 1.2 min and uridine at 13.3 min. Another component was eluted at 25.0 min. What was it? 15. The following data were found from an HPLC experiment, on a column 25.2 cm long at a flow rate of 0.323 mL/min with Vs = 0.166 mL and Vm = 1.39 mL. For compounds #1, 2, 3, and 4, a chromatogram gives: Compound: Sample loop #1 #2 #3 #4 tr: 3.1 min 5.4 13.3 14.1 21.6 Width: 0.27 min 0.41 1.07 1.16 1.72 (a) Find N for each peak, the average N, and the standard deviation. (b) Find k' and the partition coefficient for each compound. (c) For the last two peaks find the resolution, selectivity factor, the length of column needed to give resolution 1.5 and the time required for this resolution. 16. In an HPLC study, a stationary phase was prepared by derivatizing the surface of a proprietary silica gel, Corasil II, with a silane derivative. In a study of column efficiency, the following data were obtained for benzene in a mobile hexane phase. HETP (mm) 0.75 0.81 0.94 0.103 0.118 0.132 0.146 Flow rate (cm/sec) 0.10 0.20 0.40 0.50 1.20 1.50 1.80 Plot the HETP vs velocity and compare the result with a similar plot for GLC. 1

17. Just as in the derivation of the equations used for deriving the k', Rf can be for a solute can be expressed in terms of the mole fraction of the solute in the mobile phase and related to k'. a. Derive a simple equation showing the relation of Rf and k' for a solute. b. Find the k' for estradiol, whose Rf value is 0.32 on a standard silica TLC plate. c. The selectivity factor for estriol relative to estradiol on this same type of silica gel as a column is 1.25. If a difference of 0.02 in Rf is required for spots to be visibly resolved, can the two steroids be separated on a TLC plate ? 18. The changes in k' for tyrosine on a reversed phase column with pH are shown below. The solvent is 95% 0.02 M phosphate buffer with 5% ethanol. pKa values for tyrosine are 2.20, 9.11, and 10.07. pH 2.3 4.8 6.5 8.9 11.4 k' 3.33 1.75 1.56 1.94 7.28 a. Determine what the ionic charge of tyrosine is at each of the pH values given. b. If the mechanism of retention is strictly reversed-phase, which form should have the highest k' ? c. With these results, infer which kinds of interaction are occurring on this column 19. The chromatogram below arises from chromatographing the nitroanilines on 10 µ alumina in normal phase chromatography, using a mobile phase of mixed dichloromethane and hexane at a flow rate of 1.6 mL/min and a 254 nm UV detector. The peaks represent 1 µg each of injected compound. The center of the strange backward N figure on the base line may be taken as the point when the solvent from the sample loop reaches the detector; each horizontal scale division is 20 s. The order of elution of the isomers is: ortho, meta, para where para is last. a. Find k' for each of the isomers. b. Find the selectivity factor for each isomer relative to o−nitroaniline. c. Explain the small size of the para−nitroaniline peak in this mixture containing equal weights of the isomers. mo-

0.06 As

p0

36

18

54 ( /s )

20. The following graph shows how the tr varies for amino acids on a specific column varies with the total concentration of acetate buffer at a pH of 5.20. The effect is considered to be largely an ionic strength effect. a. State which of the compounds has a large charge and its sign at this pH. b. Use the result of part a to decide on the main mechanisms operative in the separation and to infer the nature of the column.

1

pH=5.15

35 30

Trp

25

Pro

Retention time ( /min) 20

Ala

15

Arg Glu His Asn

10

Asp

5 0 0

80 60 40 20 Acetate concentration ( /mM)

100

21. The chromatograms below are for 4.6 mm x 250 mm analytical columns using 50% methanol : 50% water as the mobile phase at 1.0 mL/min with 254 nm UV detection. In sequence, the bands in each chromatogram are: 1 = uracil, 2= phenol, 3. = acetophenone, 4 = nitrobenzene, 5 = methyl benzoate, 6 = toluene. The difference is the column packing which is a reversed phase material of different carbon chain length. a. Find the partition constant, Ks, for toluene on each column, assuming Vs is constant. b. A simple picture of the stationary phase is that the carbon chains project straight out from the surface, so that the volume of the stationary phase, Vs, should be proportional to the carbon chain length. Verify the usefulness of this picture by finding the ratio of the K values for the columns, assuming Vs varies as the carbon chain length of the stationary phase and comment on your results. 1

2 3

C 18 4 5 6

0

2

4

6

8

10

12

time ( /min)

1

14

16

18

20

22

24

6

1

0

2

2

4

C8 3

4

C 1 5

1

2 3 4 5

6

6 8 10 12 14 16 time ( /min)

0

2 4 6 time ( /min)

8

22. Assume that two different columns are available for separating a pair of enantiomers. One of these yields 20k theoretical plates, a selectivity factor of 1.25 and a k' value of 3.0 for the later eluting enantiomer. The second column yielded half-widths of around 1.5 min after a retention time of 2 hr (to = 3.0 min), but a selectivity factor of only 1.05. a. Which column gives the best resolution ? b. Keeping everything else constant, would doubling the number of theoretical plates for the first column or doubling the selectivity of the second column change the choice of column ? 23. Suggest a type of liquid chromatography (including column type, detector, and mobile phase components suitable for the separation of: (a) Ethanol and propanol (b) Barium and strontium ions (c) Phenanthrene and anthracene (d) Butanoic and pentanoic acids (e) High molecular weigh glucosides (f) Polyethylenes (g) A mixture of water-soluble dyes (h) A barbiturate mixture (i) The amino acid hydrolyzate from a protein (j) The nucleosides from a nucleic acid digestion (k) Enantiomers of 2-butanol (l) Components of a cold remedy (m) Tartaric acid isomers (n) Common anions found in well water (o) Cations found in plasma (p) Components of a soft drink (q) Vitamins in a nutritional supplement (r) Aromatics in a gasoline 24. A gel electrophoresis experiment is run on a mixture of cytochrome C and its oligomers. The resulting gel is scanned with a densitometer, resulting in the chromatogram shown below. In essence, this is a plot of absorbance at 400 nm as a function of distance traveled. Since oligomerization of the protein has little effect on the absorbance of the chromophore, the amount of absorbance is proportional to the mass of compound present for any n−mer. Assuming the original mixture had a mass of 16.8 µg of protein, find the mass and % of each component in the mixture. The peaks in sequence represent the hexa−, tetra−, tri−, di−, and monomer from left to right, i.e., the monomer travels furthest.

1

Dimer Hexamer

Monomer

Trimer Tetramer

As

0

2

4 6 8 Distance from Origin ( /cm)

12

10

14

25. The following data was obtained on a polystyrene gel column using dimethyl formamide as eluent. The standard compounds are Carbowaxes, i.e. polyethylene glycols. What is the M.W. of a Carbowax with a Vr = 14.6 mL on this column ? Molecular Weight : 1.1 k 5.5 k 22 k 84 k 770 k Vr (mL) : 17.2 16.3 15.0 13.9 12.5 26. On a certain Sephadex column with an exclusion limit of 80 k, a protein with M.W. = 150,000 has Vr = 8.0 mL. 2-Naphthol had a Vr of 70.0 mL. What is the molecular weight of an enzyme with a Vr of 45.3 mL ? 27. Find the M.W. of a digestive enzyme from the size exclusion chromatography data below. Compound(M.W.) :

Tr (min) :

Urease(483k)

22.3

Ovalbumin(46.0k)

52.4

Myoglobin(16.9k)

65.8

Cytochrome C(13.0 k)

69.6

Unk.

61.4

28. On a size exclusion column, retention volumes for the individual peaks with their molecular weights are given below. The base line width of the last peak is 0.47 mL. What is the effective operational operating range in molecular weight units, Vm, Vs, and the partition coefficients for the first four peaks. Indicate on your volume axis where K=0 and K=1. Vr (mL): 3.55 4.45 5.05 5.81 5.93 Molecular weight: 8.1 M 1.8 M 500 k 25.1 k 76

1

29. The chromatogram shown below is for a set of narrow molecular distribution polyethylene samples on a polystyrene gel size exclusion column. A RI detector is used to monitor the mobile phase, which is THF flowing at 1.7 mL/min. The standards are eluted in order of decreasing molecular weight as 500k, 110k, 37k, 10.0k, and 2.10k. These are followed by a negative peak at the right end from the sample loop. The time scale is 2 min/div. Assume the highest molecular weight standard is entirely excluded. a. Calculate the molecular weight of a polypropylene that has a retention volume of 12.0 mL. b. Estimate the high and low limits for molecular weights for compounds that can be separated using this column.

Detector Response

0

2

4 time ( /min)

6

8

10

30. A size exclusion chromatogram is shown below, between 8 and 18 min of the run. The peaks on either side of the main peak are due to molecular weight standards of 278k, 171k, 53k, and 31k. The huge peak at the right is the original solvent used for the polymeric mixture. What is the molecular weight of the material in the center peak ?

?

Response 171k

278k

0

8

10 12 time ( /min)

53k 31k

14

16

18

SET 7, Ion Selective Electrodes 1. An ion selective sulfate electrode was used with an SCE to obtain the following data: [SO42−] (M) 0.10 0.030 0.0004 0.00025 6x10−5 mv +225 +183 +108 +5 −50 Plot potential vs log of the sulfate concentration, and determine the slope of the line (is it Nernstian?) and the 1

concentrations of unknowns giving potential readings of +142 mv, and +50 mv. 2. A calcium ion selective electrode was used to determine the Ca2+ in a well water sample. The following calibration data were obtained 0.08 0.009 0.003 0.001 Unknown [Ca2+] M: 4x10−5 2x10−5 mv: 125 +90 +70 +53 −3 −15 +100 a. Plot the calibration line and determine the unknown concentration. b. Decide what extra standard would be needed to improve the calibration line. c. Would using a pH of 13 cause high, low or the same results? What would be the effect of a high phosphate concentration be on the accuracy of a calcium determination? d. What is the expected potential if 20 mL of the 2 x 10−5 M standard is mixed with 30 mL of the 4 x 10−5 M standard? 3. A Pb2+ ion selective was used to determine the lead concentration in a water sample using a Pb ISE and an SCE. The following data are to be used to determine: a. The lead ion concentration in the water sample (ppm). b. The uncertainty in this estimate. c. The limit of detection for Pb2+. Unk. [Pb2+] (M) : 1.0E−1 1.0E−2 1.0E−3 2.5E−5 2.5E−6 1.0E−6 2.5E−7 1.0E−7 1.0E−8 mv : −108 −80 −54 16 44 57 62 65 66 47 4. On a single graph, plot the electrode potential vs log C of the ionic species for the following: a. Ag|Ag+ b. Cu|Cu2+ c. Pt,H2|H+ d. Al|Al3+ e. Fe|Fe2+ f. Ag|AgCl,Cl g. Zn|Zn2+ h. Pt|Q,H2Q,H+ 5. The cell below gives a potential of −500 mv. What is the pH of the unknown solution? AgAgCl,Cl−(1.00 M) H+(unknown M) H2(0.50 atm), Pt 6. What is the pH of a solution at 25o C if a potential of 703 mv is observed between a hydrogen electrode and an NCE in the solution ? 7. a. The cell below was used for the determination of pCrO4. Calculate the pCrO4 from the observed cell potential of 413 mv. Ag Ag2CrO4(satd.),CrO42−(x M) SCE b. Calculate the pSO4 of the unknown solution in the cell below from the observed potential of 576 mv. Hg Hg2SO4(satd), SO42−(x M) SCE 8. A membrane type ISE for Cu was found to have a potential of 124 mv vs SCE when in contact with 3.35 x 10−3 M Cu2+. When an unknown Cu2+ solution was used, the potential was 305 mv. Find the unknown [Cu2+] ignoring changes in junction potential and assuming Nernstian response.

1

9. A glass/SCE combination electrode was found to develop a potential of −41.2 mv in a pH 6.86 buffer, and −200.4 mv with an unknown solution. Find the pH and [H+] of the unknown. If a change in junction potential of 1.0 mv occurs between the standard and reference solution, what range of [H+] is possible, and to what % error does this correspond? 10. Using a liquid membrane ISE for magnesium ion and an SCE reference, the potential of −271.4 mv was found using a 2.56 x 10−3 M Mg2+ solution. An unknown gave a potential of −190.1 mv. What is the pMg of the unknown ? Assuming an uncertainty in the measurement of 2 mv in the measurement, what range of Mg2+ is possible, and what is the corresponding % accuracy? 11. A fluoride solid state electrode has a selectivity coefficient of 0.10 relative to hydroxide ion. At 0.01 M fluoride concentration, what hydroxide ion concentration can be tolerated? What is the lower pH limit when using the fluoride electrode if a 1% error is tolerable and samples and standards are not adjusted to the same pH value ? 12. If calcium ion activity is to be measured with a liquid membrane electrode in samples containing up to 0.7 M sodium ion, estimate the minimum level of calcium which can be measured under these conditions. Assume a maximum level of 5% interference is tolerable. The selectivity coefficient for sodium is 0.0001 . 13. What is the maximum concentration of interfering anions that can be tolerated for a 1 % interference level when measuring 10−5 M BF4− with a fluoroborate liquid ion exchange membrane electrode ? The interfering anions and their selectivity coefficients are: OH− = 0.001; I− = 20; NO3− = 0.1; HCO3− = 0.004; SO42− = 0.001 . 14. With a glass sodium ion selective electrode, a potential of −127 mv was observed for 1.0 x 10−4 M NaNO3. When this solution was adjusted to pH 4 using HNO3, the observed potential changed to +11 mv. Find the selectivity coefficient for H+ . 15. A series of solutions containing Cd2+ at 1.00 x 10−2 M and various Cu2+ concentrations was prepared. Find the selectivity of this Cu selective electrode toward Cd2+. 3E−3 1E−3 3E−4 1E−4 3E−5 1E−5 [Cu2+] (M) mv 209.2 193.5 178.2 166.6 166.2 165.9 16. A nitrate ISE gave a potential of −22.4 mv when in 1.0 x 10−3 M NaNO3 and a potential of −24.8 mv in a solution that was 1.0 x 10−3 M in both NaNO3 and NaCl. What is the ISE selectivity toward Cl− ? 17. Calculate the relative error in a Ca2+ determination in sea water using a Ca ion selective electrode. Typically, sea water contains 400 ppm Ca2+ and 1400 ppm Mg2+. The selectivity coefficient of this Ca ISE for Mg2+ is 0.015. 18. What are the maximum levels of each of the following ions that may be present in a determination of 1 x 10− 4 M Ca2+ using a calcium liquid membrane ISE if the error is to be less than 10%? Ca ISE selectivity coefficients are listed below each ion. Zn2+ Fe2+ Pb2+ Mg2+ Na+ 3.5 0.75 0.60 0.015 0.003

1

19. A fairly rapid method for measuring selectivity coefficients is to equilibrate the electrode in a solution of the ion for which the electrode is selective. Then aliquots of the interfering ion are added and the potential is measured after each aliquot. The equations describing the potentials for a cation ISE are as below if the interfering and the electrode ion are of the same charge: E1 = C + {RT/nF}ln ai E2 = C + {RT/nF}ln (ai + kijaj) Combine the two equations and take antilogs in such a way that they yield a linear function that yields kij directly from the graph of the function. 20. Use the equation derived above to determine selectivity coefficient of a iodide ISE for bromide ion from the data below, where the initial solution is 50 mL of 1.0 x 10−4 M KI. Reading (mv) −130.2 −131.5 −133.9 −137.5 −140.8 added mL 1.0 M KBr 0 0.50 1.00 2.00 2.00 21. If no nitrite selective electrode is available, suggest an indirect way to measure nitrite ion activity using a different ion selective electrode. 22. Using a solid state sulfide ISE, what is the total sulfide concentration in a 100 mL sample that gives a potential reading of −845 mv before the addition of 1 mL of 0.1 M AgNO3 and a reading of −839 mv after the addition ? 23. Derive an equation for the potential of a CO2 electrode as a function of the partial pressure of CO2 in a sample. 24. The fluoride electrode can be used to measure lanthanum ions, La3+ . Derive the relation between the potential of the electrode and the activity of La3+ . 25. Exactly 25 mL of 0.1000 M silver nitrate was pipetted into each of two beakers. Silver electrodes were placed in each and they were joined by a KNO3 salt bridge. This gave a potential of 0 mv. A 10.00 mL aliquot of lead nitrate was added to one beaker and 10 mL of water to the other which gave a potential of 0.070 mv between the electrodes. If the lead nitrate was prepared by dissolving a 10.00 g sample of lead in nitric acid and diluting to 100 mL, calculate the % silver in the lead. Estimate the accuracy of the analysis if the potentiometer has a maximum uncertainty of 1 µv. 26. A cell is assembled with two platinum wires as electrodes dipping into separate beakers which are connected by a salt bridge, each beaker containing 25.00 mL of a mixture of Fe2+ and Fe3+ ions with each ion at 1 M . Now 1.00 mL of a solution of a reducing agent is added to one side, and the potential difference changes from 0.0 mv to 26.0 mv. Find the normality of the solution of reducing agent. 27. An aqueous solution (pH = 5.0) is to be examined for its free fluoride ion concentration. A 100 mL portion of the solution, measured with a fluoride electrode, is found to give a reading of 120 mv against a suitable reference electrode. Exactly 1.00 mL of a 0.100 M solution of KF is added to the test solution, giving a new potential reading of 132 mv. Calculate the fluoride ion concentration in the solution. 28. A 372.1 mg sample of a toothpaste is boiled with 50 mL of a citrate buffer to extract the sodium fluoride, cooled and diluted to 100.0 mL. The potential of a fluoride ISE/SCE electrode system dipping in a 25 mL aliquot of the solution was −182.3 mv . Addition of 5.0 mL of a solution containing 1.10 µg F−/mL raised the potential to −144.6 mv. Find the % F- in the toothpaste. 29. A 25.0 mL portion of an diluted milk sample had a potential of 147.0 mv when measured using a Ca ISE/SCE system. Addition of a 5.00 mL aliquot of 2.02 x 10−3 M CaCl2 gave a potential of 161.4 mv. Addition of a second 5.00 mL aliquot yielded a reading of 171.5 mv. What is the [Ca2+] in the sample ? 1

30. 1 mL of 6 M NaNO3 is added to 50 mL of milk on a magnetic stirrer and then an iodide ion selective electrode and a double junction reference electrode with NaNO3 in the outer compartment are inserted. The potential is read and then four successive aliquots of 0.002 M KI are added, the potential being read after each addition. The results are listed in the table below. Calculate the µg I− / mL in the original milk. Aliquot added (µL) 0 100 100 200 200 Potential (mv) −50.3 −64.9 −74.1 −86.0 −94.2

SET 8, Coulometry 1. A constant current of 1.500 A is passed through a number of electrolytic cells connected in series for 1 hour to the nearest second. The cells contain an excess of the electrolytes listed. For each, tell what substance is deposited at the cathode, and calculate the quantities in g or mL (STP) for gases. a. Cu(NO3)2 b. NaOH c. K4[Fe(CN)6] d. HgI2 e. Pb(NO3)2 f. [Ag(NH3)2]Cl 2. In coulometric titrations, how many µg of each of the following corresponds to 1 mA−s ? a. OH− b. Sb(III) to Sb(V) c. Cl− d. Cu(II) to Cu e. As2O3 to H3AsO4 f. Cr2O72– to Cr3+ 3. How many mg of each would be deposited by 3.378 C ? a. Cu from Cu2+ b. PbO2 from Pb2+ c. Sn from SnCl62−

d. Cl− as AgCl at an Ag anode

4. A solution is 0.2 M in Ag+ and 10−4 M in Cu2+. Assuming the potentials below predict which metal will plate first and at what potential. Then find the potential at which the second metal will begin to deposit. What potential is required to low the silver ion to 10−6 M ? What will the concentration of the first element be when the second begins to deposit? Ag+/Ag 0.799 V : Cu2+/Cu 0.337 V 5. In the coulometric titration of 8-hydroxyquinoline, bromine is generated at the anode and hydrogen is generated at the cathode. 2 Br− → Br2 + 2 e− 2 H+ + 2 e− → H2 The bromination reaction is: C9H7OH + 2 Br2 →C9H5ONBr2 + 2 HBr (a) How many moles of electrons are required per mole of 8-hydroxyquinoline? (b) How many g of hydrogen are liberated at the cathode per mole of 8-hydroxyquinoline? (c) How many s are required to titrate 2.13 mg of 8-hydroxyquinoline at a current of 9.22 mA ? 6. A protein sample is analyzed by a Kjeldahl procedure by digesting with sulfuric acid to convert protein nitrogen to ammonium sulfate. The ammonia produced is determined by adjusting the pH to 8.6 and titrating coulometrically with electrogenerated hypobromite ion: Br− + 2 OH− → OBr− + H2O + 2 e− 2 NH3 + 3 OBr− → N2 + 3 Br− + 3 H2O a. If the titration is performed using 18.56 mA and the endpoint occurs at 127.3 s, how many mg of protein are present in the sample assuming that 6.25 mg of protein are present per mg of protein nitrogen ? b. If a constant current source is to be constructed to read directly in µg of protein titrated, what current must be supplied so that the time in seconds is equal to the µg of protein? 7. For a solution that is initially 0.01 M in silver and 0.5 M in copper(II) ions: a. What cathode potential is needed for the complete deposition of silver b. What cathode potential is needed for 99.9% completion of silver plating? 1

SHE?

c. How much silver remains in the solution when the cathode potential has been brought to −0.45 V vs

8. During the deposition of copper from a chloride medium in the presence of hydrazine hydrochloride, the following current/time readings were found. Current(A): 3.00 3.00 2.85 2.70 2.2 1.8 1.2 0.8 0.50 0.30 Time(min): 1.00 2.00 3.00 4.00 5.0 6.0 7.0 8.0 9.0 10.0 Current(A): 0.18 0.12 0.075 0.052 0.036 0.027 0.020 0.016 0.016 Time(min): 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 20.0 Graph log I vs t, and determine the constant k from the linear portion of the line. Estimate the time required for the copper to be reduced to 0.1% after the initial current required to reduce Cu(II) to CuCl2− . 9. In a constant potential coulometric titration of UO22+ to U(IV), an initial current of 90.0 mA is observed that decreases exponentially with a k = 0.0058 s−1. If the titration time was 7.36 s, how many µg of U(VI) are titrated ? How much time is needed for a 99% complete titration ? 10. Sketch the expected current-potential curves for each of the following coulometric systems: a. The titration of an acid with electrogenerated OH− in a KBr solution using an Ag anode. b. The generation of excess bromine in a KBr solution followed by the generation of Cu(I) to react with unused bromine. c. The titration of Zn2+ with electrogenerated ferrocyanide ion. 11. The diagram shows coulometric titration behavior for reduction of three ions in 1 M phosphate solutions at a pH of 2. 100

MnO4– /

80

Mn2+ Fe3+ / Fe 2+

60

%

Red ucti 40 on

VO2+ / VO2+

20

0 1.1

.9

.7

.5

.3

.1

-.1

-.3

-.5

Electrode Potential vs SCE

a. Outline a procedure for determining each element in a mixture of the others by controlling the cathode potential. b. Assuming the vanadium and iron reactions are reversible, outline a constant current procedure for the determination of iron(II) in the presence of V(IV). c. Outline a procedure for determining the amounts of V(V) and V(IV) in a mixture containing both oxidation states. 12. Anthranilic acid (o-aminobenzoic acid) can be brominated by electrolytically generated bromine at pH 4 to produce tribromoaniline. Small amounts of copper can be determined by precipitating Cu(II) anthranilate, Cu(C6H4NH2CO2)2, dissolving the precipitate and coulometrically titrating the liberated anthranilic acid. The copper in a 1.00 g sample of a tissue sample is wet digested with a mixture of nitric and sulfuric acids, and the resulting filtered solution neutralized and treated with excess anthranilic acid. The precipitate is filtered, washed, 1

and redissolved; the resultant solution with excess KBr added is then coulometrically titrated at a current of 6.43 ma, requiring 22.40 min to reach the endpoint. Write equations for the main titration reaction and calculate the ppm Cu in the sample. 13. Copper in a brass tack was determined by a coulometric titration with a constant current of 20.0 mA. Making the bad assumption of 100% current efficiency and a single cathode reaction, what is the % Cu in the tack if a 10.00 mg sample requires 400 s ? Why are the assumptions so bad ?

1

14. Copper in an alloy (≈ 75% Cu\10% Sn\15% Pb) is to be determined by electrodeposition from a 0.5 M HCl solution. Ignoring chlorocomplexes, what fraction of the Cu can be deposited before either of the other metals begins to deposit ? 15. Silver is to be deposited from a 0.0100 M AgNO3 solution containing 2.0 M HNO3. The electrolysis cell consists of two smooth platinum electrodes and has a resistance of 0.25 ohm with these solutions. What voltage must be applied to obtain an initial current of 750 mA? 16. At a potential of −1.0 V vs SCE, CCl4 in methanol is reduced to chloroform at a mercury electrode. At −1.8 V, chloroform is reduced to give methane under the same conditions. An 823 mg sample containing chloroform, carbon tetrachloride, and electrolytically inert organics is dissolved in methanol and electrolyzed at −1.0 V until the current drops to almost zero requiring 9.17 C according to a coulometer in series with the cell. The reduction is then continued at −1.8 V which requires an additional 61.22 C. a. Write half-reactions for the two electrode reactions, assuming calomel, Hg2Cl2 is the chloride containing product formed. b. Find the % carbon tetrachloride and chloroform in the mixture. 17. The Karl Fisher method for determination of water is a very important method in industry This is done in an anhydrous mixture of iodine, sulfur dioxide, pyridine, and methanol. The reagent, containing iodine, is used as titrant until a biamperometric endpoint is reached when excess iodine is present in the mixture. The conventional method of writing this reaction is: H2O + C5H5N.I2 + C5H5N.SO2 + C5H5N + CH3OH → 2 C5H5N.HI + C5H5NH+[SO4CH3-] This reaction is simply the oxidation of SO2 by I2, though complicated by the solvent. The important point is that the redox reaction cannot occur if H2O is not present to supply an O atom to the S containing product. a. Write the aqueous analog of this reaction. b. Draw the Lewis structures of each of the products. c. This reaction is most commonly done coulometrically with automated endpoint. If a 1.000 mL sample requires 212 s at a current of 100.0 mA, what is the water concentration in the sample in µg/mL ? 18.a. How many mg of silver would be obtained on a silver coulometer when a current of 8 mA is passed for 30 min? b. How many mL of hydrogen at STP would be obtained from a water coulometer with this same charge ? Which coulometer would be preferred for this small charge ? 19. How many seconds are required to generate enough OH− at 7.2 µA to react with 10 µL of 0.001 M HCl, assuming the generating reaction is: 2 H2O + 2 e− →H2 + 2 OH− 20. An alloy is analyzed for its copper content by constant potential coulometry. A 0.500 g sample is dissolved and electrolyzed at a mercury pool electrode at −0.3 V vs SCE. A titration coulometer is placed in series with the electrolysis circuit. At the end of the electrolysis, a total of 40.0 mL of 0.0510 M HCl is required to bring the pH in the coulometer back to its initial pH. What is the % Cu in the alloy? List the advantages and disadvantages of this coulometric titration compared to the corresponding volumetric titration. 21. Under a given set of electrolysis conditions, 500 µg of silver was deposited at the cathode and oxygen liberated simultaneously at the anode. Find the number of µmole of hydrogen ion added to the solution, and the change of pH assuming an initial 200 µL of unbuffered solution initially at pH 7. 22. In an electrolytic determination of bromide in 100 mL of solution, a silver anode was found to have gained 873.5 mg after electrolysis was complete. Calculate the initial [Br−]. Find the potential of the silver electrode at the beginning of the electrolysis, assuming the solubility product for AgBr is 4 x 10−13.

1

23. The calibration factor for a digital integrator is 0.00267 µequiv/count. Find the normality of an acid solution which produced 40.72 counts during a titration of 10 mL of unknown. 24. A 0.5 M potassium solution in a gas coulometer yielded 22.33 mL total of hydrogen and oxygen at 24.0o C and 740 Torr. Allowing for the vapor pressure of the solution (22.3 Torr), how many coulombs were used ? 25. Calculate the concentration of acid in a 10.0 mL aliquot that required a titration time of 165 s for a phenolphthalein endpoint at a cathode. The voltage drop across a 100 ohm series resistor was 0.849 V. 26. In an electrolytic determination of Br− in 100.0 mL of solution, the amount of charge was determined as 105.20 C. What is the weight of Br− in the original solution ? What potential should be used at a silver electrode in this analysis assuming a Ksp of 4 x 10−13 for AgBr? 27. How long should a constant current of 100.0 mA be passed through a solution to prepare 100 mL of a 0.0100 M Ni2+ using an anode of pure nickel? 28. The copper from a 0.400 g sample of a brass was deposited electrolytically at a controlled cathode potential. The cell was placed in series with a recording ammeter. Determine the number of coulombs used by determining the area under the curve and use this to calculate the % copper in the alloy. State why this curve does not follow the simple exponential law. 1.25 1.00 A .75 .50 .25 0 0

5

10

15

20

25

time ( /min)

29. What current in mA is required for constant current coulometry so that a timer reading in seconds would read directly in microequivalents of electrode reaction ? 30. A factory effluent water is to be analyzed for Cu, Pb, and Cd by anodic stripping after deposition on a mercury thin film electrode at −1.0 V for 90 min using a 200 mL sample. This completely deposits the metals present as shown by a drop in plating current to a negligible value. Scanning the solution anodically yields three peaks corresponding to the oxidation of the three metals. Integration of the peaks yields areas corresponding to 12.5 µC at the Cd potential, 41.0 µC for Pb, and 38.2 µC for Cu. Find the concentration of each metal in ppb (ng/mL). 31. A solution that is 1 x 10−5 M in Cu2+ is to be analyzed by anodic stripping from a hanging mercury drop. If the volume of the drop is 0.001 cm3 and the electrolysis current is 0.500 µA, how long must the plating process be continued to give a 10−3 M amalgam ?

1

32. Coulometric titration of phenol with bromine to yield tribromophenol is carried out for 321.2 s at a generating current of 12.36 mA. How many mg of phenol were present in the sample ? 33. The thickness of silver plating is measured by masking a plated object except for a 1.00 cm circle. The object is placed in electrolyte with the exposed circle completely immersed and the silver plating is anodically stripped at a current of 98.5 mA. The plating just disappears at 23.8 s. What is the average thickness of the plating? 34. A common clinical analysis is the coulometric titration of chloride in serum. The results are expressed in meq/L. If a 100 µL sample is titrated, what current should be used so that seconds of titration time equals meq/L of chloride ion in the serum ? 35. The results below were obtained during the titration of three 1.00 mL aliquots of an As(III) solution with electrogenerated iodine at pH 8 using amperometric indication of the endpoint. Graph the results and determine the molarity of arsenic(III) in the solution. The timer is calibrated in µmole of iodine, and is not reset between readings. The current for the detection system has units of µA. Pretitration Aliquot 1 Aliquot 2 Aliquot 3 µmole µA µmole µA µmole µA µmole µA 0.00 0.4 15.0 0.4 164.9 0.4 286.1 0.4 5.10 0.7 50.0 0.4 200.0 0.4 350.0 0.4 9.90 1.3 100.0 0.4 250 0.4 400.0 0.4 15.0 1.7 149.5 1.3 273.8 1.0 402.0 0.8 154.5 2.0 277.4 2.2 406.3 1.6 160.0 2.6 280.8 2.7 411.0 2.1 164.9 3.0 286.1 3.2 416.1 2.8 36. In the coulometric determination of permanganate ion by generation of Fe(II) from Fe(III), the permanganate was completely reduced to Mn(II) by a constant current of 2.50 mA after 10.37 min. Find the permanganate concentration in the initial 25.00 mL of solution. 37. In the coulometric titration of H3AsO3 with electrogenerated I2 , a time of 132.6 s was required using a constant current yielding a 620 mv drop across a 100.3 ohm resistor. Find the amount of As2O3 present. 38. Using currents of 1−10 ma and titration times of 100−300 s, what range of amounts of mercaptans may be present in 50 mL of solution ? Assume a reaction of : Ag + RSH → AgSR + H+ + e− 39. Determine the equivalent weight of an organic acid if 0.0400 g in an alcohol-water mixture required a constant current of 50 mA for 500 s to generate sufficient hydroxide ion to reach a phenolphthalein endpoint ? 40. Ceric ion is to be determined by coulometric titration using electrogenerated ferrous ion, with potentiometric endpoint detection using a Pt/SCE combination. The theoretical endpoint is at 800 mv. An acidified solution contained around 0.005 mole of ferric ion in 250 mL. A pre-titration was run using around 0.2 µmole of Ce(IV). Then a 1.00 mL aliquot of the unknown Ce(IV) solution was added and the titration run. Coulometer readings are in arbitrary time units, but empirical calibration at the experimental current shows one unit is 4.79 x 10-4 µF. Find the µg Ce(IV)/mL in the unknown. Pre-titration Titration Potential(mv):830801790893861820814810803794Coulometer:20120170170470720750770790810

1

41. Traces of aniline can be determined by reaction with excess bromine to generate tribromoaniline. Reversing the polarity of the working electrode, the excess bromide can be determined by a coulometric titration with Cu+. Br2 + 2 Cu+ → 2 Br− + 2 Cu2+ When a large excess of KBr and CuSO4 is added to a 25.00 mL sample containing aniline, the aniline is titrated using the working electrode as an anode at a current of 1.002 mA for 3.46 min. The electrode polarity is then reversed and the same current used for cathodic generation. 0.48 min are required to reach the endpoint. Find the ppb (ng/mL) aniline in the original sample. 42. A 7.336 g sample of an arsenical fungicide was digested using mixture of sulfuric and nitric acids, and the resultant solution treated with excess hydrazine to reduce the arsenic to H3AsO3. After the excess hydrazine was removed, the solution was buffered to pH 8 and coulometrically titrated using an excess of KI to electrogenerate I2 at a current of 110.2 mA. The required time to reach a starch-iodine endpoint was 11 min and 14 sec. What is the % As in the sample ? 43. 50.0 mL of a 0.3 M Ce3+ solution is used with a Pt anode to titrate iron(II) using a biamperometric endpoint. A constant 100.0 mA source is used for 135 s to titrate a 10.00 µL sample of an Fe2+ solution. What is the concentration of the sample in g/L? 44. A 1.371 g vegetable oil sample is made up to 100 mL in chloroform and saturated with CuBr2. The solution is oxidized anodically for 300.0 s at a current of 75.0 mA. After a brief rest, the excess Br2 is titrated coulometrically by reversing the cell leads and passing a current of 75 mA through the solution for 43.0 s. This cathodic reaction generates Cu(I). What is the iodine number of the oil ? 45. A coulometry cell with Pt cathode and an isolated anode contains 0.1 M KBr whose pH is found to be 6.31. 2.00 mL of a strong acid solution is added to the cathode section and a potential applied so that a current of 31.2 mA flows. The pH is monitored with a pH meter and the potential was removed after 226.5 s when the pH had just reached 6.31 again. What is the normality of the acid? 46. A process stream contains strong base. It is to be monitored by diverting a small amount through a tiny bypass tube to which electrogenerated acid is added just before the stream reaches a pH electrode. A computercontrolled electronic loop regulates the current so the pH electrode is always maintained at pH 6.86. If the flow rate of the by-pass tube is called V and represents 1.02% of the process stream, write an expression for the [OH−] of the stream in terms of the current, I. 48. Continuous monitoring of an effluent stack gas is done by bubbling a sample of the gas through a coulometric cell containing acidic KI with a slight excess of I2. The amount of I2 is kept constant using computer control to maintain a constant current at biamperometric electrodes by regulating the current flow into the coulometric cell. Any SO2 in the stack gas sample is oxidized by the iodine to sulfate ion. When the sampled gas has a flow rate of 1.227 L/min, the average current used was 1.132 mA over a ten minute period. What is the concentration of SO2 (µg/m3) in the stack gas? 49. The iron in a 23.65 mg sample was completely oxidized to Fe3+ using hydrogen peroxide and the excess peroxide was boiled away. Coulometric titration with Ti3+ required 111.6 s at a current of 1.870 mA to reach the potentiometric endpoint. What is the % Fe in the sample?

1

50. A Kjeldahl digestion of a protein is done in sulfuric that converts the protein nitrogen to ammonium ion. The digested material is diluted to 100 mL in a volumetric flask and a 1 mL aliquot is removed and the pH adjusted to 9.0. The aliquot is titrated coulometrically with electrogenerated hypobromite ion, requiring 138.3 s at a current of 9.855 mA. how many mg of N are present in the original sample? Br− + 2 OH− → BrO− + H2O + 2 e− 2 NH3 + 3 BrO− → N2 + 3 H2O + 3 Br−

SET 9, Voltammetry 1. The polarographic diffusion current of a 0.003 M NiCl2 solution is 15 µA. If the solution volume is 15 mL, how long will it take to reduce 1% of the Ni2+ in the cell? 2. The polarogram of a sample solution is shown. Before the solution was made up to volume in 0.1 M KCl, enough Cd2+ was added to bring [Cd2+] up to 0.03 mM. Identify and estimate the concentrations of the other two metals present in the non-ferrous alloy sample. 18

Current ( µ A)

12

6

0 0

-.2

-.4 -.6 -.8 -1.0 Applied Voltage vs SCE ( /Volts)

-1.2

-1.4

3. On the conventional DC polarogram shown below, identify the five different metals present in the 0.1 M KCl solution.

Current (µA)

0 0

-.2

-.4 -.6 -.8 -1.0 Applied Voltage vs SCE ( /Volts)

1

-1.2

-1.4

4. Identify the six metals present in the derivative polarogram shown below which was obtained in 0.1 M HCl. 1.0

Current ( µ A) 0.5

0 0

-400

-800

-1200

Applied Potential vs SCE ( /mv)

5. The polarogram of a sample containing sufficient Cd2+ to bring its concentration to 2 × 10−4 M was added before dilution to volume with 0.1 M HCl. Identify and find the concentration of the other two metals present.

1.5

Current 1.0 ( µ Α)

0.5

0 -200

-600

-1000

Applied Potential vs SCE (mv)

6. Compare polarographic determinations with amperometric titrations with respect to (a) relative accuracy (b) permissible range of applied potentials and (c) applicability of each method with regard to types of ions and ranges of concentration. 7. Suggest an explanation for the differences observed below for the reduction of Cu(II) in various media. Medium id/(Cm2/3t1/6) 0.1 M HNO3 1.0 M HCl 0.5 M sodium tartrate 1 M NH4Cl/1 M NH3

3.24 3.39 2.24 3.75

8. The polarogram for 20.0 mL of a solution that was 0.00365 M in Cd2+ gave a wave with id = 31.1 µA. Calculate the % change in concentration if the current in the limiting region were allowed to continue for 5, 10, and 30 min.

1

9. It is normally assumed in a polarogram that no depletion of analyte occurs during the experiment. Check this by calculating the fraction of Cd2+ consumed over a 30 min period in 15 mL of 0.500 mM CdSO4 if the average current observed is 5 µA. 10. A solution of 0.002 M CdCl2 in 0.1 M KNO3 gives a diffusion current of 25.0 ma; the drop time of the capillary is 15 drops/min and the weight of 25 drops is 130 mg. What is the diffusion coefficient of Cd2+ in this solution? 11. An organic substance is reduced polarographically. At a concentration of 0.00020 M, it yields a wave with a diffusion current of 20.4 µA when a capillary with a flow rate of 3.4 mg/s and a drop time of 2.7 s is used. If the diffusion coefficient of the compound in the supporting electrolyte has been determined to be 9.0 × 10-6 cm2/s, what is the n value for the polarographic reduction of the compound ? 12. A 0.005 M CdCl2 solution in 0.1 M KCl shows a diffusion current of 50.0 µA at −0.8 V vs. SCE . The mercury is dropping at a rate of 18.0 drops/min, and 10 drops were found to have a mass of 0.0382 g. Calculate the diffusion coefficient, D. If the capillary were replaced by another for which the drop time is 3.0 s and 10 drops weigh 0.0425 g, what will be the new diffusion current value ? 13. Calculate applied potential values at the DME corresponding to currents of 1,2,3 µA, etc. up to 9 µA for three hypothetical reductions in each of which E½ = −1.000V vs. SCE and id = 10 , but for which n = 1, 2, and 3 respectively (at 25o C). Plot these data on a single graph so that the three curves intersect at the half wave point. For the same data, plot on another sheet the quantity log[i/(i-id)] vertically vs. EDME as the horizontal axis. 14. A DME at flow rate of 6.96 mg/s an drop time of 1.37 s was used for the reduction of an organic compound with diffusion constant of 6.2 × 10-6cm2/s . A 4.00 × 10-4 M solution of the compound yielded a diffusion current of 9.10 µA. Find n for the reaction. 15. An organic compound underwent a 2 electron reduction at a DME. The diffusion current of 10.1 µA was produced by a 9.6 × 10−4 M solution. if the electrode flow rate was 0.988 mg/s and the drop time 6.53 s, find the diffusion coefficient for the compound. 16. A zinc solution of unknown concentration gives a polarographic diffusion current of 5.00 µA. A 5.00 mL portion of 0.0010 M Zn2+ is added to 10.00 mL of the unknown solution yielding a new polarographic current of 12.24 mA. What is the concentration of Zn2+ in the unknown? 17. The diffusion current of lead in an unknown solution is 5.60 µA. One mL of a 0.00100 M lead(II) solution is added to 10.0 mL of the unknown and the diffusion current due to Pb2+ is increased to 12.2 µA. What is the lead concentration in the unknown? 18. The following 3 solutions were prepared for a standard addition determination of Cd2+ with polarographic currents as shown. What is the concentration of Cd2+ in the unknown? Each solution contains 50 mL of supporting electrolyte in addition to the materials listed. a. 50 mL H2O → 7.5 µA b. 25 mL H2O + 25 mL sample → 51.6 µA c. 15 mL H2O + 25 mL sample + 10 mL 0.0004 M Cd2+ → 75.8 µA 19. An unknown containing Cu2+ produces a diffusion current of 12.3 µA on a polarogram. By adding 100 µl of 0.00100 M Cu2+ to the original 5 mL of solution, the new current is found to be 28.2 µA. What is the concentration of Cu2+ in the original unknown ? 20. A 1.000 g sample of zinc metal is dissolved in 50 mL of 6 M HCl, diluted to the mark in a 250 mL 1

volumetric flask. A 25.00 mL aliquot is transferred to the polarographic cell and deaerated with nitrogen. A polarogram in the range of 0 to −1 V vs. the mercury pool electrode shows a wave at −0.65 V with a diffusion current of 32.0 scale divisions. A 5.00 mL portion of 0.0005 M Cd2+ is added directly to the cell, deaeration carried out and a second wave is observed at the same potential, but with a diffusion current of 77.5 units. Calculate the % Cd impurity in the zinc metal. Note that the supporting electrolyte is ZnCl2/HCl. 21. Small concentrations of nitrate ion can be determined in 0.1 M ZrOCl2 supporting electrolyte by the difference in diffusion current before and after the reduction of nitrate by ferrous ammonium sulfate with an applied potential of −1.2 V vs SCE at the DME. The following data were recorded for two standards and an unknown: Solution id before reduction id after reduction 10.0 ppm 87.0 µA 22.0 µA 5.0 ppm 48.5 µA 15.2 µA Unknown 59.0 µA 17.0 µA Find the concentration of nitrate ion in the unknown. 22. Find the mg of Cd/mL of sample from the following standard additions data which are corrected for residual current. ID # Sample(mL) mL 0.400 M KCl mL 0.00200 M Cd2+ mL H2O id (µA) a. 15.0 20.0 0.00 15.0 79.7 " 15.0 20.0 5.00 10.0 95.9 b. 10.0 20.0 0.00 20.0 49.9 " 10.0 20.0 10.0 10.0 82.3 c. 20.0 20.0 0.00 10.0 41.4 " 20.0 20.0 5.00 5.00 57.6 d. 15.0 20.0 0.00 15.0 67.9 " 15.0 20.0 10.0 5.00 100.3

1

23. The figure below shows the differential pulse stripping voltammogram for the determination of copper, lead, and cadmium in a fish sample. A 100 g sample was wet ashed with a mixture of perchloric and sulfuric acid, and diluted to 100 mL. A 10 mL aliquot was diluted to 25 mL and deposition carried on for 90 s at a hanging mercury drop electrode at −0.9 V vs SCE. The unlabeled scan was the sample. The labeled scans are spiked 10 mL aliquots spiked to produce the spike concentrations as listed below when diluted to the final 25 mL volume. All the anodic scans start at the same current and voltage, but the lettered scans are displaced for better visibility. Determine the ng of each metal present/g fish(ppb). Spike Concentrations (ng/mL) Sample Cd2+ Cu2+ Pb2+ A 0.05 0.5 0.5 B 0.10 1.0 1.0 C 0.20 1.5 1.5 20 na

C B A

I

Sample (unspiked)

-0.9

-0.7

-0.5

-0.3

-0.1

0.1

V vs SCE

24. Iron(III) is reduced to iron(II) at potentials below +0.4 V vs SCE and is further reduced to iron metal at −1.5 V vs SCE. A DME polarogram is run on a solution containing Fe3+ and/or Fe2+. The cell current is 12.5 µA at 0 V and 30 µA at −1.5 V. Which iron species are in solution and what are their relative concentrations ? 25. The cell below, with internal resistance of 7.82 ohm, is to be used to supply a current of 75.0 mA. Calculate the initial expected potential. Pt  VO2+(1.0 × 10−5 M), VO2+(0.165 M), H+(0.10 M) Br−(0.150 M), AgBr(satd)  Ag 26. The resistance of the cell below is 4.61 ohm. What will the initial potential be when a current of 10.6 ma is drawn from the cell ? Pt  Fe(CN)64−(0.036 M), Fe(CN)63−(0.0027 M) Ag+(0.017 M)  Ag

1

27. An amperometric titration of B2+ with A3+ is to be run. The equation is: A3+ + B2+ → B3+ + A2+ The relevant polarograms for A and B are shown below.

+I 0

a

b

c

E

-I A2+

3+ B 2+ B

3+ A

Sketch the shape of the amperometric titration curves for applied potentials of a, b, c. Be sure to indicate whether the current measured is cathodic(+) or anodic(−) Mark where the equivalence point occurs with an "X". Neglect volume changes and assume all species have the same diffusion coefficients. Explain the shapes of the curves. 28. Tin(IV) in acidic pyrogallol solution gives a two plateau polarogram with each step of equal height at −0.20 and −0.40 V vs SCE. Note the standard cell potentials for reduction of Sn4+ and Sn2+. a. Explain why two equal steps are observed. b. Which form of tin, Sn(IV) or Sn(II), is more strongly complexed by pyrogallol; how do you know, and why? 29. The following reaction is reversible and has a half-wave potential of −349 mV vs SCE at a DME in pH 2.5 buffer. Predict the half wave potential at pH = 1.0, 3.5, and 7.0. Assume the half reaction below. Ox + 4 H+ + 4 e− → R 30. Cu2+ forms a precipitate with benzoin oxime in an ammoniacal solution. The Cu(NH3)42+ present in a supporting electrolyte, consisting of 0.5 M ammonia with 0.1 M ammonium chloride, is reduced stepwise giving polarographic waves at −0.2 and −0.5 V vs SCE. Benzoin oxime gives a polarographic wave at −1.6 V vs SCE, Sketch the shape of the expected amperometric titration curve at −0.8 V vs SCE. Also sketch the curve expected at −1.7 V vs SCE. If Ni(II) and Zn(II) were to be present in the solution being titrated, which potential would be preferred ?

1

31. Benzoin oxime (Cupron) is a precipitating agent for Cu2+. In a medium consisting of 0.1 M NH4Cl and 0.05 M NH3 (pH=9.3), cupron is reduced at the DME giving a wave at −1.63 vs SCE. In the same medium, copper gives a double wave as shown by curve b. Sketch the titration curves expected in the amperometric titration of copper by cupron at applied potentials of both −1.0 and −1.8 vs SCE. a. Which potential would be preferred for the titration of copper in the absence of interfering substances? b. Which would be more liable to interference by reducible impurities?

µA

a

b

0

-.5

-1.0

-1.5

-2.0

V vs SCE

32. Ag+ ion in an NaClO4 solution as supporting electrolyte, is reducible at the DME at the potential of the SCE. Cl− ion, in the same medium gives an anodic wave at +0.25 V vs SCE. It is possible to determine whether the complex AgCl2− is reducible under these conditions by titrating Ag+ with Cl− amperometrically, using the DME. Sketch and explain the titration curves which might result. 33. The polarogram below is observed at a silver electrode vs SCE for: a. silver ion solution b. chloride ion solution. A titration of 10 mL of 1.0 mM silver nitrate with 1.0 mM sodium chloride is to be done biamperometrically using two silver wire electrodes. Assume a negligible amount of Ag+ or Cl− can come from AgCl

1.2

a. b. c. d.

b

a

Current

0.8

0.4

0.0

Volts

Sketch the expected titration curve with a 100 mv potential applied to the electrodes. Sketch the titration curve when a 600 mv potential is applied to the electrodes. State the anodic and cathodic reactions occurring in each section of each curve. How does method b. differ from a normal amperometric titration?

1

34. The graph below shows a continuous graph of an amperometric titration of cyclamate ion in 1 M H+ with the working electrode at +1.1 vs SCE. The peaks show when an 250 µL aliquot of 1.00 M NaNO2 has been added, and the decrease of current shows the consumption of titrant according to the stoichiometry below. NHSO 3-

N2

HNO 2

SO 42-

H

H2O

other products

a. Plot the steady current vs. mL titrant added b. What is the weight of calcium cyclamate in the original sample? c. What reaction is the source of the steady current in each region of the titration? 100 80

I

60

anodic (µA) 40 20 0

0

2 4 time ( /min)

6

8

10

35. Sketch the expected biamperometric titration curve for the titration of 25 mL of 0.05 M K4Fe(CN)6 with 0.05 M Ce(SO4)2. Continue 5 mL past the equivalence point, and assume a maximum current of 75 µA at the applied potential of 50 mv applied to the twin Pt electrodes. a. Write the chemical equation for the titration. b. Write the chemical equations occurring at both the positive and negative electrode that carries the current. c. What metal species are present at the endpoint when no current is flowing? 36. The data below were obtained at 25o C with Cd2+ in a supporting electrolyte composed of 0.1 M KCl with 0.005% gelatin at an applied potential of −1.0 V vs SCE. The recorder sensitivity is 0.25 µA/mm with a drop time of 2.47 s and a flow rate of 3.30 mg/s. The data below were obtained. Current(mm): 4.5 [Cd2+] (mM): 0.0

11.0 0.20

21.0 0.50

37.5 1.00

54.0 1.50

70.5 2.00

86.5 2.50

29.5 Unknown

a. Find the cadmium concentration of the unknown. b. A 25.0 mL aliquot of the unknown above is transferred to the cell. To this solution is added exactly 5.0 mL of 0.0120 M Cd2+. The diffusion current is now 92.6 mm. Find the unknown concentration again and compare with the result above. c. At the same time the solution above was prepared, a second solution was also prepared, identical except that it contained Zn2+, 10.0 mL of 0.0100 M Zn2+ in a total volume of 100 mL. The corrected diffusion current was 32 mm for the zinc wave. Calculate the concentration of the unknown cadmium ion by the internal standard method and compare to the other two results.

1

37. The following data were obtained for a series of Pb2+ solutions. 0.00 0.51 1.02 2.04 3.06 4.08 5.10 [Pb2+] (mM): id (µA): 1.32 5.65 10.70 19.08 27.91 36.08 45.82 a. Plot a calibration line, and determine the best straight line by least squares, recording the fit of the points to the line. b. Calculate the concentration of lead and the resd for each of the following results. The number in parentheses is the number of replicate determinations. i. 2.76 µA(2) ii. 7.75 µA(1) iii. 7.75 µA(3) iv. 26.32 µA(3) v. 40.01 µA(1) c. Find the theoretical value for id/[Pb2+] assuming D for Pb2+ is 9.8x10-6 cm2/s; the reaction product is Pb(Hg), the drop time is 2.88 s, and the flow rate is 2.63 mg/s . Calculate the % error from the observed value. 38. The following polarographic data were obtained for the reduction of Pb2+ to its amalgam from solutions that were 0.00200 M in Pb2+, 0.100 M in KCl, and contained variable concentrations of the anion A−. From the halfwave potentials, derive the formula of the complex and its formation constant. 0.0000 0.0200 0.0600 0.1007 0.301 0.502 [A−] (M) E vs SCE (mV) −405 −473 −507 −516 −547 −558

SET 10 High Energy Spectroscopies 1. The mass absorption coefficient for Ni, measured with the Cu Kα line is 49.2 cm2/g. Calculate the thickness of a nickel foil that was found to transmit 36.1% of the incident power of an incident beam of radiation. 2. For Mo Kα radiation (71.1 pm), the mass absorption coefficients for K, I, H, and O are 16.7, 39.2, 0.0, and 1.50 cm2/g respectively. a. Calculate the mass absorption coefficient for a solution containing 8.00 g of KI in 92.0 g of water. b. The density of the solution above is 1.05 g/cm3. What fraction of the radiation from a Mo Kα source will be transmitted by a 0.50 cm layer of the solution? 3. A solution of iodine in ethanol had a density of 0.794 g/cm3. A 1.50 cm layer was found to transmit 27.3% of the radiation from a Mo Kα source. Use the data of Problem 2 above to: a. Calculate the % I2 present, neglecting absorption by the alcohol. b. Assuming the mass absorption coefficient for C is 0.70 cm2/g, correct the result above for the absorption due to alcohol. 4. An ESCA electron was found to have a kinetic energy of 1073.5 ev when a Mg Kα source was used ( λ = 989.00 pm). The electron spectrometer had a work function of 14.7 ev. a. Calculate the binding energy of the emitted electron. b. If the signal was from a S(2s) electron, was the sample S2–, S0, SO32–or SO42–? c. What would the kinetic energy have been if an Al Kα source had been used ( λ = 833.93 pm)? d. If the ejected electron from the original source had been an Auger electron, what would its kinetic energy have been with the Al Kα source ? 5. An ESCA electron was found to have a kinetic energy of 1052.6 ev when ejected with an Al Kα source ( λ = 833.93 pm) and measured in a spectrometer with a work function of 27.8 ev. The electron is believed to be a N(1s) electron from NaNO3. a. What is the binding energy for the electron ? 1

b. What would the kinetic energy of the electron if Mg Kα ( λ = 989.0 pm) source were used ? c. How could one be sure that peak was an ESCA and not an Auger electron peak? d. At what binding and kinetic energies would a peak for NaNO2 be expected when the Al Kαsource was used with the same spectrometer? 6. A sample of 35S contains 10 mCi activity. After 174 days how many disintegrations per minute occur in the sample ? 7. What % of the original activity of 32P, 131I, and 198Au remains after 14, 30 and after 60 days ?

1

8. What fraction of the following isotopes remain after 24 hours ? a. 59Fe b. 45Ti c. 47Ca d. 33P 9. A PbSO4 sample contains 1 µCi of 200Pb. What storage period is needed to assure that its activity is less than 0.01 µCi ? 10. Estimate the standard deviation and the relative standard deviation associated with counts of : a. 100.0 b. 750 c. 7.00 × 103 d. 2.00 × 104 . 11. Estimate the relative standard deviation associated with a counting rate of 200 cpm that is observed for 40 s, 80 s, 4.0 min, and 12.0 min. 12. Estimate the absolute and relative uncertainty associated with a measurement of 800 counts at the 50%, 90%, and 99% confidence levels. 13. The decay of a particular halogen, subjected to several hours of irradiation, provided the following data: Time(min) 10 18 24 32 36 40 50 60 80 120 180 240 cpm 1800 1400 1215 970 880 800 650 550 430 330 270 230 Plot the decay curve using the log of the activity vertically, and analyze it into its component parts, finding the initial activities and half-lives. Identify the specific halogen. 14. To a crude mixture of organic compounds containing some benzoic acid and benzoates is added 40.0 mg of benzoic acid-7-14C (activity = 2000 cpm). After equilibration, the mixture was acidified and extracted with an immiscible solvent. The extracted solid, following removal of solvent, was purified by recrystallization of the benzoic acid to a constant melting point. The purified material weighed 60.0 mg and had an activity of 500 cpm. What was the weight of benzoic acid in the crude mixture ? 15. Estimate the relative uncertainty at the 90% confidence level associated with the corrected counting rate obtained from a total counting rate of 300 cpm for 14 min and a background count of: a. 9 cpm for 2 min b. 9 cpm for 10 min c. 18 cpm for 2 min d. 40 cpm for 2 min 16. The background activity of a laboratory, measured for 3 min, was found to be around 9 cpm. What total count should be taken in order to keep the relative uncertainty less than 5.0 % at the 90% confidence level with a total counting rate of : a. 90 cpm b. 300 cpm c. 600 cpm 17. A fermentation broth was known to contain some Aureomycin. To a 1.000 kg portion of the broth, 1.00 mg of Aureomycin containing 12C (specific activity = 153 cpm/mg). 0.20 mg of crystalline Aureomycin was isolated from the mixture with a net activity of 412 counts in 100 min. Calculate the weight of Aureomycin/kg broth. 18. A 2.00 mL portion of a solution containing 0.120 µCi / mL from tritium was injected into the bloodstream of a dog. After allowing time for mixing, a 1.00 mL blood sample was found to have an activity of 15.8 cps . What is the blood volume of the dog? 19. An organic compound is being analyzed for N by isotope dilution. A measured amount of the compound containing 15N instead of 14N is added. After conversion of all the nitrogen to N2, a mass spectrometer shows the following peak heights. Calculate the % of nitrogen which is 15N . m/e 28 29 30 Height 978.5 360.6 52.5 20. A mixture is to be analyzed for penicillin by isotopic dilution. A 10.0 mg portion of pure, radioactive penicillin with an activity of 4500 cpm/mg is added to the sample. From the mixture, just 0.35 mg of pure penicillin is isolated and, on the same apparatus, its activity is found to be 390 cpm (background corrected). 1

What was the penicillin content of the original sample ? 21. A mercury assay on an animal tissue sample is to be done by neutron activation. A 652 mg sample and a standard solution containing 213 ng of Hg as HgCl2 were irradiated for 3 days in a thermal neutron flux of 1012 neutron/cm2 s . After irradiation was done, 25.0 mg of Hg as Hg2Cl2 was added to each, both digested in a nitric acid/sulfuric acid mixture to oxidize organic material with precautions to prevent losses due to evaporation. HCl was added and the resultant HgCl2 was distilled from the reaction mixtures. The mercury in each of the distillates was deposited electrolytically on gold foil electrodes resulting in an increase in weight of 13.5 mg for the sample and 14.6 mg for the standard. The gamma activity was found to be 860 cpm for the sample and 1112 cpm for the standard for a 10 minute counting time. Find the ppm Hg in the tissue, and calculate the 95% confidence interval for the result, assuming the major source of uncertainty is the decay process. 22. A method for the simultaneous determination of U and Th in minerals requires the measurement of the combined U+Th by radioactivity, and the determination of the Th/U ratio by X-ray emission spectroscopy. The combined radioactivity is expressed as % equivalent uranium, i.e., that amount of uranium in pitchblende necessary to give an equal activity. The Th/U ratio is taken as the ratio of peak heights for the Lo lines of Th and U. The U and Th contents are given by the relation: x + 0.2 x * y = % equivalent U where x is the % of uranium and y is the Th/U weight ratio. For a particular counting apparatus, 1% equivalent U corresponds to 2100 cpm above background. A 1.00 g sample of a monazite sand, when prepared and counted according to the standard procedure, gave 2780 cpm (background corrected). X-ray examination gave peaks of 72.3 scale divisions for Th Lo and 1.58 divisions for U Lo, Calculate the % U and Th in the sample. 23. The streptomycin in 500 g of a synthetic mixture was determined by the addition of 1.34 mg of pure antibiotic containing 14C which had a specific activity of 223 cpm/mg using a 30 min count. From the mixture, 112 ng of purified streotomycin was isolated with a count of 654 counts in 60.0 min. Find the ppm streptomycin in the mixture and calculate the 90% confidence limits for this result.

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24. The beta radiation from a sample is to be measured with a maximum permissible uncertainty of 1%. The cumulative data below is recorded. Elapsed time (min) 0 5 10 15 20 25 30 Background (cpm) 0 127 249 377 502 672 793 Sample (cpm) 0 2155 4297 6451 8602 10749 12907 What minimum time is required to give the required precision, how long would the background have to be counted, and what is the actual corrected cpm with its resd ? 25. A "reverse dilution" method is described below for the determination of the oxidation products of propane. The sample to be oxidized is propane-2-14C. Among the products is found a considerable quantity of 2propanol-14C. To a mixture of products was added a measured amount of inactive 2-propanol and a portion isolated by conventional fractionation. The following data were obtained. Find the % of propane converted to 2propanol. Amount of propane-2–14C = 10 mmole; Specific activity of inital propane = 72.8 µCi/mmole; Inactive 2-propanol added = 16 mmole; Specific activity of isolated propanol = 5.8 µCi/mmole. 26. The penicillin in a mixture was determined by adding 0.981 mg of the pure compound having a specific activity of 5420 cpm/mg. After equilibration, 0.406 mg of pure material was isolated with a net activity of 343 cpm. Calculate the amount of penicillin in the sample. 27. In studying the solubility of slightly soluble salts it was necessary to determine the concentration of oxalate solutions in the ppm range. This analysis is to be carried out by precipitaion of 45CaC2O4. Calculate the oxalate concentration (ppm) in a sample from the following data. A standard solution is prepared which is 0.680 M in CaCl2 and has an activity of 2.00 × 104 cpm/mL (background corrected). To a 100.0 mL sample of trace oxalate solution is added 5.00 mL of the standard solution. No precipitate is visible beyond a slight turbidity. A few drops of FeCl3 is added and the solution made basic with ammonia to precipitate Fe(OH)3. The precipitate is collected on a small filter paper using suction, washed once, dried, and coiunted. The counting apparatus is known by prior experiment to have a 30.5% efficiency for 45Ca β emission. The time required for a preset count of 6000 is 18.60 min. The background is 150 counts in 5 min. (The efficiency correction need not be applied to the standard solution) 28. Identical electrolytic cells fitted with silver anodes and platinum cathodes are arranged in series. Exactly 1.00 mL of a solution containing 41.2 ng of KI labeled with 131I and 5.00 mL of an acetic acid/acetate buffer were placed in one cell. A 5.00 mL aliquot of an iodide containing sample was added to the acetate buffer contained in the second cell. After passing a substoichiometric quantity of electricity through the cells, the anodes were removed and counted for β activity. Calculate the weight of I-/mL if the activity determined by a 4.00 min count for the electrode from the cell containing the standard was 4130 cpm and that from the cell containing the unknown was 3550 cpm. Also find the 95% confidence limits for the result assuming the major source of uncertainty is the decay process.

1

29. An isotope dilution method for the determination of C using a 13C tracer is done by mixing the sample with some succinic acid containing around 30 atom % 13C. The mixture is oxidized to CO2 and H2O, and the resulting CO2 is examined in a mass spectrometer. The ratio of mass 45 to 44 (corrected for the natural isotopic composition of O) is taken as the 13C/12C ratio, designated "r". In natural carbon, the abundance of 13C is 1.11% and 12C is 98.9%, which must be taken into account. The relevant equations are as below: 13C = W (4/119.3)(r /r +1) + W (X /12.01)(0.0111) s T T T s C 12C = W (4/119.3)(1 /r +1) + W (X /12.01)(0.989) s T T s C 12C and 13C are the numbers of mmoles of the respective isotopes present in the in the mixed sample, s s rs is the observed ratio, rs = 13Cs/12Cs WT and WT are the weights in mg of tracer and sample, rT is the ratio for pure tracer compound oxidized in the same manner, and XC is the quantity sought, the weight fraction C in the unknown. a. Explain the above equations and derive an expression for XC from them in terms of Ws, WT and rs. b. In a particular anaysis, 156 ng of sample and 181 ng of tracer were taken. The ratio rs was found to be 0.206. The tracer contained 31.41% of its carbon as 13C. Calculate the % C in the sample. 30. The following data is a portion of a gamma ray spectrum. Channel # 21 22 23 24 25 Counts 331 324 322 326 398

26 507

27 895

28 941

Channel # 30 31 32 33 34 35 36 37 Counts 935 892 496 396 302 254 232 237 a. Plot the data. Indicate the baseline for the peak. b. Estimate the average background for the peak. c. Calculate the total number of counts under the peak and the standard deviation.

29 962 38 235

31. A 25.00 mL aliquot of a chloride solution was treated with 10.00 mL of 0.0110 M AgNO3. Then the excess Ag+ was back titrated 6.46 x 10-4 M KCl solution containing a small fraction of 36Cl-. The supernatant liquid was sampled using a pumping system after each aliquot of the labeled KCl titrant was added yielding the results below. What is the chloride concentration of the original solution ? Titrant mL 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 cpm 106 117 125 139 146 154 178 243 353 482 630 795 32. A silver solder was weighed, dissolved in nitric acid, and diluted to the mark in a 100 mL volumetric flask. A 100 µL aliquot of a silver nitrate solution containing some 110AgNO3 with a background corrected activity of 25,500 cpm/mL was added a 10 mL aliquot of the sample. Then a few drops of 0.1 M HCl was added and the AgCl formed was collected on a sintered glass disc and found to have a background corrected activity of 1136 cpm. The weight of the precipitate was found as 21.3 mg after drying. What is the weight of Ag in the original solder sample ?

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33. An isotopic dilution was done on a 0.367 g rock sample by digesting it and adding a 30.00 µg spike of rubidium enriched with 87Rb. The mass spectrum of the rsulting solution showed an 87Rb peak 1.12 times the 85Rb peak. The isotopic composition of the spike is 95.4% 87Rb, the remainder being 85Rb. Calculate the µg/g Rb in the sample. Do not forget to consider the natural abundance of isotopes in Rb which is also a mixture of 85Rb and 87Rb. 34. The decay of 87Rb to 87Sr by β decay has a half life of 4.8 x 1010 year. A rock was dated by looking for Strontium-87. The ratio of 87Sr/86Sr was 2.25 by mass spectrometry. Assume the 87Sr/86Sr ratio was 0.700 when the igneous rock cooled at its formation (This is the natural isotopic abundance). Other isotopic ratios found by mass spectrometry are 86Sr/88Sr = 0.119 and 84Sr/88Sr = 0.007 . Chemical analysis yielded values of 15.5 ppm Sr and 265.4 ppm Rb. a. Using this data and the Handbook, calculate the average atomic mass of Sr in the rock. b. What was the original concentration of Rb in the rock in ppm? c. What % of the original 87Rb in the rock has decayed? d. What is the age of the rock since it was cooled ? 35. Suppose you are to determine small amounts of Ta and Nb in an ore which contains at 25 times as much Nb as Ta. How can you achieve as large an X-ray fluorescence signal from Ta with minimum Nb interference? 36. 1.00 L of a water sample is treated with excess ammonium sulfide to precipitate metal ions, Ni2+, Mn2+, and Zn2+, and the sample is collected on a small circle of filter paper. The X-ray fluorescent intensities, are 4.8 cps for Ni, 3.6 cps for Mn, and 6.5 cps for Zn after background correction. Standard samples of these metals after the same treatment and background yield calibration values of 58 cps / µg Ni, 22 cps / µg Mn, and 15.3 cps / µg Zn. Find the µg / L of each metal in the water sample. 37. An ESCA investigation of silver deposition on a silicon surface (semiconductor contacts) is characterized by using Mg Ko radiation. The beam diameter is 1 mm and has an analysis depth of 2 nm. The instrument is sensitive to about 0.001 of a monolayer of Ag. a. What is the limit of detection in terms of Ag atoms? b. What is the limit of detection in g Ag? c. What are the limits of detection in g/ cm3 and µg /g ? Assume homogeneous mixture. 38. It is difficult to quantitate the relative amounts MoO3 and MoO2 in mixtures, as with many mixed oxidation state transition metal oxides. For this case, however, it is found that 3d electrons are sensitive enough to environment so that at ESCA resolution, it is possible to distinguish the oxidation states with reasonable resolution. The two peaks to be used are at 230.9 ev for Mo(IV) and at 235.6 ev for Mo(VI). The calibration data below is for % MoO3 and the ratio of electrons scattered with energy 235.6 ev to those with energy 230.9 ev. Uncertainties in the ratio are generally around 0.1 to 0.2. %MoO3 Ratio of Ee

0.0 1.30

5.0 1.41

10.0 1.71

20.0 2.09

25.0 2.30

40.0 2.94

%MoO3 55.0 60.0 75.0 80.0 90.0 95.0 Ratio of Ee 3.45 3.60 4.17 4.53 5.02 5.05 Unknowns gave the following results (duplicates) for the electron energy ratio: a. 2.65(15) b. 1.75(15) c. 4.23(10) Calculate the %MoO3 in each and estimate the uncertainty of the determination.

45.0 3.00

50.0 3.32

100.0 5.07

39. The iodide in a brine is to be determined. Two identical cells are set up with silver anodes. Each cell contains 10 mL of an equimolar 0.1 M acetate/acetic acid buffer, and 1 mL of solution containing 1.0 µg of K129I with activity 3.10 × 105 cpm. A 5 mL portion is added to the first cell and a 5 mL portion of distilled water is aded to the second. The cells are placed in series to insure equal currents flow in each and the anodes are 1

held at –0.1 V vs SCE. The electrolysis is stopped after 15 min and the anodes are counted, yielding 2.08 × 104 cpm and 1.08 × 105 cpm respectively. a. Write the expected anode reaction. b. Find the ppm iodide in the brine. 40. The ratio of Mn to Fe in an alloy is to be found by neutron activation. The steel is placed in a reactor for 50 hours, and then the activity of 56Mn/59Fe was found to be 1. × 105 using a gamma ray spectrometer. The following data are to be used to calculate the result without further experimental calibration. Neutron Capture Nuclide Natural Abundance Cross Section Half-Life 55Mn 100% 13.3 Barns 56Mn = 2.57 hr 0.33% 1.2 Barns 58Fe 59Fe = 45 day What is the Mn/Fe weight ratio? 41. Co analyses in steel are commonly done by isotopic dilution. A 1.103 g sample of a steel is dissolved in a perchloric/sulfuric acid mixture and diluted to 100 mL. A 2 mL of a spike solution are pipetted into the solution, and two electrodes are placed in the solution and a current is applied so that some Co2O3 plates out at the anode. The anode weight has increased by 14.88 mg and it has an activity of 2.6 × 103 dpm. The spike solution contained cobalt at a concentration of 3.0 g/L and had a specific activity due to 60Co of 1.60 × 107 dpm/g Co. What is the %Co in the steel ?

1