Crystal Violet (2)

A KINETIC STUDY: REACTION OF CRYSTAL VIOLET WITH NaOH

OBJECTIVES The objectives of this experiment are: •

To study the reaction rate of crystal violet with NaOH using USB650 Red Tide Spectrophotometer. •

To determine the reaction order with respect to each of the reactants.

BACKGROUND Reaction Chemistry Chemical kinetics is the study of reaction rates. In this experiment, the kinetics of the reaction between crystal violet and NaOH will be studied. A USB650 Red Tide Spectrophotometer will be used to monitor the crystal violet concentration as a function of time. The reactant and product structures and the reaction stoichiometry are shown in Figure 1. All of the reactants and products shown in Figure 1 are colorless except for crystal violet which has an intense violet color. Thus, during the course of the reaction, the reaction mixture color becomes less and less intense, ultimately becoming colorless when all of the crystal violet has been consumed. The following is the balanced molecular equation:

Here, "R" is used to represent crystal violet “C25H30N3Cl”.

Given below is the Stoichiometry of the Reaction between Crystal Violet and NaOH (Net Ionic species)

The crystal violet color is due to the extensive system of alternating single and double bonds which extends over all three benzene rings and the central carbon atom. This alternation of double and single bonding is termed conjugation, and molecules which have extensive conjugation are usually highly colored. Trace the conjugation in the crystal violet structure and note that in the reaction product, the three rings are no longer in conjugation with one another, and hence, the material is colorless. Kinetic Rate Laws The rate of the crystal violet/NaOH reaction is given by the following generalized rate law: (1)

Rate = k [OH-] x [CV] y

Where, k is the rate constant for the reaction, CV is an abbreviation for crystal violet (CV is an aqueous chloride solution), C25H30N3+, x is the reaction order with respect to OH-, and y is the reaction order with respect to CV. The values of x and y will be determined experimentally. Possible x values are 1 or 2 (first order or second order). Possible y values are also 1 or 2. In this experiment, the initial [OH-] is made much greater than the initial [CV]. Thus, the [OH-] change, during the time that the CV is consumed, is negligible. For this reason, [OH-] x can be treated as a constant and Equation (1) can be written as follows,

(2)

Rate = k′ [CV] y

Rate = k [OH- ]x [CV] y and if [OH ]o >> [CV ]o , then, Rate = k' [CV]y Where: k′

= k [OH-] x ( k′ is termed a pseudo rate constant.)

The integrated form of the pseudo rate law (2) depends on the reaction order with respect to CV. The integrated rate laws for y = 1 and 2 are given in Equations (3) and (4). Compare each with the general form of a linear equation, y = mx + b, in which y is identified as ln [CV] t in Equation (3) and as 1/ [CV] t in Equation (4): (3)

ln [CV]t = - k′ t + ln [CV]o

(4) 1 [CV] t

=

k′ t

+

1 [ CV]o

In Equations (3) and (4), • [CV]o is the concentration of crystal violet in the reaction mixture at time zero, before any reaction has occurred; • [CV]t is the concentration at any time t during the course of the reaction.

Calculus derivation of equation (5)-

Calculus Derivation of Equation (4) for y = 2 d[CV] = k ' [CV ]2 dt [CV] t t d [CV ] Now, ∫ − = k ' ∫0 dt [CV] o [CV ]2

Define : Rate = -

[ CV ]t

1  1 1 ⇒ = ( k ' ) ⋅ t ⇒ = k ' ⋅ t + [CV ]  [CV ]t [CV] [ CV ]o where, slope = m = k' Plot of graph between 1/ [CV] and time in min-

o

1/ [CV]=o k’ 0 T Slope

Note: ✔ If a plot of ln [CV]t versus time is linear, then y = 1 and the reaction is first order in CV. ✔ If 1/ [CV] t versus time is linear, then y = 2 and the reaction is a second order reaction in CV. Only one of these plots will be linear. For the one that is linear, the resulting straight line slope (its absolute value) equals the pseudo rate constant (k′ ).

Crystal violet solutions obey Beer’s law. Thus, the relationship between percent transmittance and the CV concentration is given by: (5)  %T  At =− log =ε bc  100 

In Equation (5), • At is the reaction solution absorbance at any time t; • ε is the CV molar absorptivity, • b is the cell path length (1.00 cm); and • c is the CV molar concentration at time t, [CV]t. Thus, Beer’s law can be used to calculate [CV] t from each photocell percent transmittance reading during the kinetic run.

EXPERIMENTAL PROCEDURE Measurements 1. Use a 10 mL graduated cylinder to obtain 10.0 mL of 0.10 M NaOH solution. 2. Use another 10 mL graduated cylinder to obtain 10.0 mL of 2.5 × 10–5 M crystal violet solution. 3. Prepare a blank by filling a cuvette 3/4 full with distilled water. 4. Use a USB cable to connect the Spectrometer to your computer. Choose New from the File menu. 5. To calibrate the Spectrometer, place the blank cuvette into the cuvette slot of the Spectrometer, choose Calibrate ►Spectrometer from the Experiment menu. The calibration dialog box will display the message: “Waiting 90 seconds for lamp to warm up.” After 90 seconds, the message will change to “Warmup complete.” Click “OK”.

6. Determine the optimum wavelength for examining the crystal violet solution and set up the mode of data collection. • Empty the blank cuvette and rinse it twice with small amounts of 2.5 × 10–5 M crystal violet solution. Fill the cuvette about 3/4 full with the crystal violet solution and place it in the spectrometer. • Click . A full spectrum graph of the solution will be displayed. Note that one area of the graph contains a peak absorbance. Click to complete the analysis. • To save your graph of absorbance vs. wavelength, select Store Latest Run from the Experiment menu. • To set up the data collection mode and select a wavelength for analysis, click on the Configure Spectrometer Data Collection icon, , on the toolbar. • Click Abs vs. Time (under the Set Collection Mode). The wavelength of maximum absorbance (λ max) will be selected. Click . Remove the cuvette from the spectrophotometer and dispose of the crystal violet solution as directed. 1. To initiate the reaction, simultaneously pour the 10 mL portions of crystal violet and sodium hydroxide solutions into a 250 mL beaker and stir the reaction mixture with a stirring rod. Empty the water from the cuvette. Rinse the cuvette twice with ~1 mL amounts of the reaction mixture, fill it 3/4 full, and place it in the Spectrophotometer and close the lid on the Colorimeter and click collect button on the computer screen. 2. Absorbance data will be collected for three minutes. Discard the beaker and cuvette contents. 3. Analyze the data graphically. Data Analysis 1

Plot 1/[CV]t (y-axis) versus time in minutes (x-axis). If the reaction between crystal violet and NaOH is second order in crystal violet, this plot will be linear. If it is not second order, this plot will be curved. Test for linearity with a first order (or linear regression) curve fit. Look at the actual data points. If they clearly follow a curved departure from the regression line it should be concluded that the reaction is not second order in crystal violet.

2

Prepare and print a carefully labeled graph for the plot which exhibited the best linear relationship. Include the first order (or linear regression) curve fit line. With this plot you have identified y, the reaction order with respect to [CV]. Record the value of y on the report sheet. The absolute value of the slope for the straight line (shown in the regression equation at the top) is the best value of k′ . Record this value with proper units and to the correct number of significant figures.

Graph-

CALCULATIONS We see that the graph between crystal violet and NaOH is linear. Thus, the reaction is second order in crystal violet. Also, we see that the k′ we obtain is a pseudo rate constant, whose value depends upon the OH- concentration, i.e. k′ = k [OH-] x Also, that the maximum absorbance wavelength is 576.0 nm.

CV Reaction Order (y) Key equation: Rate = k′ [CV] y where, y = 2 ○ y=2 ○ k′ = 0.02 min -1 (from graph)

Rate Constant (k) Key equation:

k′ = k [OH-] x

For determination of “x” ⇒ 0.02 min −1 = [5 ×10−3 ]x = (0.005)x ⇒ ln(.02) = xln(0.005) ⇒ x = 1.97 ≈ 2

Now, determination of “k” Where, x = 1.97~ 2 (approx)

1 • [OH− ] = 0.05M ×   = 5.0 ⋅10−3 M  10  • k ′= k[OH − ] x ⇒ 0.02 = k(0.005)2 0.02 ⇒k= ⇒ 8 × 105 × 10−5 ⇒ 8 Lmol−1 min−1 −5 2.5 × 10

RESULT Theoretical Final rate law:

Rate = k [CV] 2 [OH-] 2

{via plot of 1/ [CV] vs. time}

Order of Reaction:

Second Order

Theoretical Rate Constant (k)

k = 8.0 L mol-1 min-1

PRECAUTIONS AND SOURCES OF ERRORS •

Sodium hydroxide solution is caustic. Avoid spilling it on your skin or clothing.

•

Crystal violet is a biological stain. Avoid spilling it on your skin or clothing.

•

To correctly use cuvettes, remember: • Wipe the outside of each cuvette with a lint-free tissue. • Handle cuvettes only by the top edge of the ribbed sides • Dislodge any bubbles by gently tapping the cuvette on a hard surface. • Always position the cuvette so the light passes through the clear sides.

•

When you are finished DO NOT FORGET to remove the sample cuvette from the spectrophotometer!

•

Clean all pipettes that were used to transfer crystal violet solutions with a small portion of 6 M HCl located in the hood. Place the waste in your waste beaker. Pour all remaining solutions into your waste beaker. Dispose of them in the appropriate waste bottle. Absorbance Spectrum

The extent to which a sample absorbs light depends strongly upon the wavelength of light. For this reason, spectrophotometry is performed using monochromatic light. Monochromatic light is light in which all photons have the same wavelength. In analyzing a new sample, a chemist first determines the sample's absorbance spectrum. The absorbance spectrum shows how the absorbance of light depends upon the wavelength of the light. The spectrum itself is a plot of absorbance vs wavelength and is characterized by the wavelength (λmax) at which the absorbance is the greatest. The value of λmax is important for several reasons. This wavelength is characteristic of each compound and provides information on the electronic structure of the analyte. In order to obtain the highest sensitivity and to minimize deviations from Beer's Law (see subsequent pages on this topic), analytical measurements are made using light with a wavelength of λmax.