Analysis of Electrochemical Reactions

Department of Chemical Engineering University of San Carlos – Technological Center Nasipit, Talamban, Cebu City

ChE 412L Physical Chemistry Laboratory 2

Ion Mobility: Transference Number of Ions and Analysis of Electrochemical Reactions

Submitted by:

Duterte, Jan Rommel T.

An initial report submitted to Dr. Alchris W. Go Instructor, ChE412L

October 5, 2015

1.

INTRODUCTION An electrochemical cell consists of two electrodes in contact with an electrolyte; an

electrode and its electrolyte make up an electrode compartment. There are two types of electrochemical cell: galvanic, and electrolytic. Galvanic cells are electrochemical cells that produce electricity as a consequence of a spontaneous reaction occurring inside it, while electrolytic cells are electrochemical cells that require an external current source to drive a non-spontaneous reaction forward [Atkins and de Paula, 2014]. Electrochemical cells are most often used to decompose chemical compounds, in a process called electrolysis. Electrolysis involves forcing a current through a cell to produce a chemical change that is otherwise non-spontaneous. When an electric current is passed through the electrolyte solution, ions move towards the electrodes. Since these ions have different mobilities in an electric field, these ions contribute to charge transport. The transference (or transport) number, then, is the fraction of the total current carried by an ion [Wilson et. al., 1968]. At

+/−¿

infinite dilution, the transference number is related to the current ( I ¿

) and charge (

+/−¿ +/−¿ +/−¿ transport, ion mobility ( u ¿ ) and ionic conductivity ( Λ ¿ ): q¿ t +/- =

t +/I q u Λ = +/- = +/- = +/- = +/t + + t - I + + I - q+ + q - u+ + u- Λ+ + Λ -

The sum of the cation and anion transference numbers is 1. Transference numbers in the experiment were determined using the Hittorf method. This method is based on the principle that the concentration changes occur around the electrodes due to the migration of ions from one electrode compartment to another. These concentration changes are related to the charge transported by the anions by Faraday’s constant:

−¿ =

F ( ∆ n A−∆ n C ) 2

q¿

2

−¿ q = q+ +q ¿ . Using the mass changes

The total amount of charge used is

of the copper electrodes in the coulometer,

z R F(∆ m C −∆ m A ) q1 = 2M q = It .

The total amount of charge can also be given by The anion transference number is then

q−¿ M(∆ n A−∆ n C ) = q zR ( ∆ m C−∆ m A ) −¿= ¿ t¿

and t+ = 1 –

−¿ t¿ .

In the experiment, two reactions are occurring: in the transference vessel and in the coulometer. The reactions in the transference vessel are:

+

-

Cathode

2 H(aq ) +2 e → H2 ( g)

Anode

2 H2 O→ O2 (g) +4 H+(aq) +4 e-

In the coulometer,

Cathode

Cu 2+ ( aq) +2 e → Cu ( s )

Anode

Cu (s ) → Cu (aq ) +2e

2+

-

3

The spontaneity of an electrochemical reaction can be determined from the sign of its cell potential because the sign of the cell potential determines the sign of the change in the Gibbs free energy of the reaction, ΔG, as shown below.

ΔG =−qε where

ε = ε°−

RT lnQ nF

The equation states that the cell potential is directly related to the change in free energy between the reactants and products in the cell [Zumdahl and Zumdahl, 2012]. This relationship is important because it provides an experimental means to obtain ΔG for a reaction. It also confirms that a cell will spontaneously run in the direction that gives a positive value for ε cell; a positive cell potential corresponds to a negative ΔG, which is the condition for spontaneity. 2.

OBJECTIVES 2.1 ION  

To determine the transference numbers of nitrate and hydronium ions To discuss the effect of mass on the transference number of an ion



To describe the reactions that occur in the cathode and anode regions of



the transference vessel and copper coulometer To analyze the thermodynamic properties and material balance of the

2.2 ECR

electrochemical reactions 3.

METHODOLOGY 3.1 Materials The materials used in the experiment were aqueous HNO 3 (69 w/w%, ρ = 1.42 g/mL), solid NaOH (97 w/w%), aqueous H 2SO4 (96.5 w/w%, ρ = 1.84 g/mL), solid crystals of CuSO4⦁5H2O (99.5 w/w%) dried potassium hydrogen phthalate (C 8H5KO4 or KHP), methyl red and phenolphthalein indicator and distilled water (H 2O). 4

3.2 Equipment and Apparatus 50 mL Erlenmeyer flask

iron clamp

250 mL beaker

iron stand

5 mL pipette

copper electrodes

pipettors

carbon electrodes

250 mL volumetric flask

3000 mL beaker

base buret

thermometer

digital stopwatch

transference vessel

connecting cords

power supply

multimeter

analytical balance

3.3 Procedure The glassware to be used were first washed and dried thoroughly. Two different solutions were to be prepared: 250 mL of 0.1 M HNO 3 and 0.5 M CuSO4/H2SO4 solution. The nitric acid solution was prepared by measuring out 1.61 mL of stock HNO3 using a 10 mL graduated cylinder, pouring the measured quantity into a 250 mL volumetric flask that was half-filled with distilled water, and then filling the volumetric flask with distilled water up to the 250 mL mark; the flask was then shaken by inverting the flask and shaking the bulb while keeping the neck steady. The acidified copper sulfate solution was prepared by measuring out 6.90 mL of stock H2SO4 using a 10 mL graduated cylinder and pouring the measured quantity into a 250 mL volumetric flask that was half-filled with distilled water; to this, an aqueous solution containing 31.3675 g CuSO 4·5H2O was added and the resulting solution diluted with distilled water to the 250 mL mark. The 0.1 M NaOH solution that was on hand was standardized against approximately 0.5 g potassium hydrogen phthalate (KHP) using phenolphthalein as an indicator and two trials were performed; similarly, two 5.00 mL aliquots of the prepared HNO3 solution were titrated against the standardized NaOH solution using methyl red as an indicator to determine its initial concentration. The transference apparatus was then set up. First, the three arms of the double Utube were filled with equal volumes (with the electrodes in place) of the prepared nitric acid; the level was marked on the glass using a permanent marker. The electrodes were then removed and the liquid level also marked on the glass. The Utube’s central arm was then clamped onto the iron support rod and the double U-tube submerged into the large water-filled beaker, ensuring that the marked level was 5

submerged in the water bath. The positive jack of the power supply was then connected to the electrode terminal at the U-tube’s left arm (transference anode). At the same time, the copper coulometer was assembled. The copper sheets were labeled according to which electrode they were to become, weighed dry, then fixed onto the electrode holder. The electrodes were then submerged in a beaker containing the acidified copper sulfate solution. A wire was connected between the electrode terminal at the U-tube’s right arm (transference cathode) to the slot at the electrode holder for the left electrode (coulometer anode). A wire was connected between the slot at the electrode holder for the right electrode (coulometer cathode) to the multimeter ammeter jack, and another wire between the multimeter ground to the power supply ground thus completing the circuit. The power supply was then turned on and the electrolysis left to proceed for 90 minutes. Current readings from the multimeter and the water bath temperature were taken every ten minutes. At the end of the electrolysis, a 5 mL electrolyte aliquot was taken from each transference vessel electrode compartment and titrated against the standardized NaOH to determine its concentration. The power was then turned off and the set up dismantled. The double U-tube was then washed and the marked volume of the anodic and cathodic regions determined by filling them with water up to the mark, then pouring the water into a graduated cylinder for measurement. The copper sheets were washed and dried thoroughly before weighing them again. 4.

RESULTS AND DISCUSSION 4.1

Ion mobility Four pieces of information are needed to determine the transference numbers of the

−¿

+

¿ nitrate ( N O 3 ) and hydronium ( H 3 O

) ions: the change of concentration of the nitric

acid solution in the cathodic and anodic compartments of the transference vessel and the change in the masses of the electrodes in the copper coulometer. Table 1 below shows the change of concentration of the HNO3 in the cathodic and anodic compartments of the transference vessel. Table 1. Concentration changes in the transference vessel compartments

Compartment (V = 22.8 mL) Cathode Anode

Molarity (M) Before electrolysis After electrolysis 0.0601 0.0811 0.0981

Change in the amount (Δn, mol) -4.8x10-4 3.9x10-4

6

The concentration determined here is the concentration of the hydronium ion in the compartment; more H+ is present in the anode because it is the site where H + is produced and since the hydronium ions move from the cathode to the anode, and less H + is present in the cathode since H+ is reduced there to hydrogen gas. In the coulometer, the copper electrodes change their masses during the electrolysis. Table 2 below shows these changes. Table 2. Mass changes of the copper coulometer electrodes

Mass (g) Before electrolysis After electrolysis 4.0406 4.0999 6.8404 6.7589

Electrode Cathode Anode

Change in the mass (Δm, mol) 0.0593 -0.0815

The reactions will be discussed further in the succeeding section. For this part’s purposes, the required information is now complete and the transference numbers are calculated. Two methods of calculating the transference numbers will be compared: that when the value for q is obtained using the mass changes of the copper electrodes, and that when the value for q is given by q = It. For the second method the current values are plotted against time and fitted to a curve, so that the total charge is actually given by 5400

q 2 = ∫ I dt = 0

5400

∫ ( −3.209x 10−10 t 2 +9.895x 10−7 t+0.0346 ) dt=170.0019 C 0

Table 3 shows the values of the transference values using both calculation methods; literature values taken from the PHYWE discussion on the transference number apparatus. Table 3. Transference numbers of the ions using two different calculation methods

Values using q1 Literature values at 25°C

Values using q2

experimental at 27°C

Percent error (%)

experimental at 27°C

Percent error (%)

t+

0.8300

0.8037

3.17

0.7531

9.27

−¿ t¿

0.1700

0.1963

15.47

0.2469

45.24

The transference numbers can be interpreted in terms of the mobilities of the ions involved. Ion mobility is directly proportional to the speed at which the ion moves through the medium, and this in turn is inversely proportional to the radius of the ion. Thus, an ion with a small radius (such as the H+ ion) moves quickly through the solution, has a high mobility, and 7

carries more of the total charge; conversely, an ion with a large radius (such as the

−¿ ¿ N O3 )

moves slower through the solution, has lower mobility, and carries less of the total charge. Additionally, a lighter ion can move faster than a heavier ion. The small difference between the experimental and literature values (for the first method) is due to the different temperatures at which the experiments were conducted. The second method gives values that are farther away from the literature values, and this is because of the way that the total charge is calculated; the first method uses the change of the masses of the copper coulometer electrodes (which takes into account all of the fluctuations of the power supply) while the second method depends on the current readings at each ten-minute interval (which does not take into account any fluctuations within the intervals). 4.2

Analysis of electrochemical reactions Two electrochemical reactions are being studied in the experiment: the reaction at the

transference vessel and the reaction at the coulometer. It is to be noted that in an electrolytic cell, the anode and cathode is still the site of oxidation and reduction, respectively, but the anode carries the positive charge and the cathode the negative charge. The reactions in the transference vessel are as follows: Cathode

4 H+(aq ) +4 e- → 2H 2 (g )

ε° = 0

Anode

2 H2 O→ O2 (g) +4 H+(aq) +4 e-

ε° = -1.23 V

The reactions explain why bubbles of gas were observed at both compartments: hydrogen ions were being reduced to hydrogen gas at the cathode and water was being split into oxygen gas and hydrogen ions at the anode. The stoichiometry of the reactions also explains why more bubbles were observed at the cathode than at the anode: for every mole of oxygen gas, two moles of hydrogen gas were produced. The cell potential is then

ε = ε° = ε °C + ε°A = -1.23 V and the change in the Gibbs free energy is given by

ΔG =−qε where q has already been calculated previously. The table below shows the values for the change in free energy using the two values of the total charge calculated previously. 8

ΔG

Table 4. Change in free energy for the electrolysis of nitric acid For q1 = 213.804 C For q2 = 170.002 C 262.98 J 209.10 J

A difference of is observed between the values for ΔG using different values of the total charge. The positive value confirms that the reaction is indeed non-spontaneous. At the coulometer, the reactions are:

5.

Cathode

Cu 2+ ( aq) +2 e → Cu ( s )

Anode

Cu (s ) → Cu 2+ ( aq ) +2e

CONCLUSION The transference number is a quantity that can be used to determine other important

quantities, such as the charge transport and ion mobility. Hittorf’s method is one way of determining the transference numbers, and it involves using the concentration changes in the anode and cathode because of the movement of ions. The calculated value of the hydronium ion transference number is t+ = 0.8037 and the nitrate transference number is t_ = 0.1963. There are many factors that affect the transference number, mass being one of them; a lighter ion can move faster than a heavier ion through the medium, will transport more of the total charge, and thus will have a greater transference number. Oxidation-reduction reactions that occur in electrolytic cells are non-spontaneous and need an external current source in order to be driven forward. In the transference vessel, water is split into hydrogen and oxygen gas at the cathode and anode, respectively; in the coulometer, copper metal is dissolved as copper (II) ions and redeposited as metal at the anode and cathode, respectively. Because the reactions are non-spontaneous, a positive change in free energy is observed. 6.

ANSWERS TO POST-LAB QUESTIONS

6.1

Determination of transference numbers of ions a) Carefully observe the cathode and anode regions during electrolysis. What gas is produced in the cathode/anode areas during the electrolysis of nitric acid?

9



During the electrolysis of nitric acid, oxygen gas is produced at the anode and hydrogen gas is produced at the cathode.

b) Write down the species involved in the electrolysis of nitric acid by determining the reactions that occur in the cathode and anode regions of the U-tube. +

-

Cathode

4 H(aq ) +4 e → 2H 2 (g )

Anode

2 H2 O→ O2 (g) +4 H+(aq) +4 e-

Overall reaction

2 H2 O→ O2 (g) + 2H 2 (g )

c) Determine the transference numbers of the hydronium and nitrate ions.

Values using q1 Literature values at 25°C tH

+

N O−¿ 3 t¿

Values using q2

experimental at 27°C

Percent error (%)

experimental at 27°C

Percent error (%)

0.8300

0.8037

3.17

0.7531

9.27

0.1700

0.1963

15.47

0.2469

45.24

d) Discuss the relationship between transport number and mass of ions. 

Heavier ions move slower than lighter ions through the medium and so transport less of the total charge. Transport number is then inversely proportional to the mass of the ion.

6.2

Analysis of electrochemical reactions a) Describe what the reactions in the transference vessel and coulometer are and which ones occur at the cathode or anode. Furthermore, describe the stoichiometry of these reactions. 

In the transference vessel, the reactions are as follows.

Cathode

4 H+(aq ) +4 e- → 2H 2 (g )

10

+

-

Anode

2 H2 O→ O2 (g) +4 H(aq) +4 e

Overall reaction

2 H2 O→ O2 (g) + 2H 2 (g )

The reaction stoichiometry shows that for every mole of oxygen gas, two moles of hydrogen gas are produced at the electrodes. In the coulometer, the reactions are as follows.

Cathode

Cu 2+ ( aq) +2 e → Cu ( s )

Anode

Cu (s ) → Cu (aq ) +2e

2+

-

No overall reaction occurs at the coulometer, since the copper (II) ions produced at the anode are then reduced to copper metal at the cathode. b) What is the importance of the transference vessel and the coulometer in the electrolytic determination of transference numbers? 

The transference vessel is where we can measure the concentrations of the electrolyte in each compartment both before and after electrolysis, and so allows us to calculate the transference numbers. The coulometer provides an experimental means to determine the total amount of charge used by measuring the change in mass of the copper electrodes before and after the electrolysis.

c) Predict the mass changes in the copper electrodes if the nitric acid concentration in the transference vessel is greater than 0.1 molar. Explain your answer. 

The mass changes will be larger. Increasing the nitric acid concentration increases the number of charge carriers available; with more charge carriers, more charge can flow through the apparatus in the same span of time. The increased charge will manifest itself as a greater mass change of the copper electrodes.

d) Compare the calculated value of the total charge quantity from equation 6 with the value obtained from q = It and discuss your answer. 

The calculated value of the total charge using the copper electrode mass changes is 213.80 C, while that of

q =∫ I dt is 170 C. The observed difference can be 11

attributed to the fluctuating current supply. The first method, involving the mass changes of the copper electrodes, is much more accurate since the electrode mass changes are proportional to the applied current; thus, the mass changes are representative of the actual amount of current that has been used. The second method, on the other hand, does not take into account the fluctuations in the power supply as well as the first method does because the interval between each current reading was 10 minutes and the current fluctuated significantly within each interval. e) Determine the change in the Gibbs free energy of the electrolysis of nitric acid. 

The value for q from the first method will be used.

ε = ε° = ε °C + ε°A = -1.23 V

(

ΔG =−qε = − (213.80 C ) −1.23 7.

J =262.98 J C

)

REFERENCES

_____ Operating Manual. PHYWE Transference Number Apparatus. Laboratory Experiments in Chemistry. Gottingen: PHYWE Systeme GmbH & Co. KG. Atkins, P. and de Paula, J. (2014). Atkins’ Physical Chemistry. 10th edition. Oxford: Oxford University Press. Wilson, J. M., et.al. (1968). Experiments in Physical Chemistry. 2nd edition. New York: Pergamon Press. Zumdahl, S. S. and Zumdahl, S. A. (2012). Chemistry: An Atoms First Approach. International edition. United States of America: Brooks/ Cole Cengage Learning.

8.

APPENDIX 8.1 Variation of current with time

12

0.04

f(x) = 0 ln(x) + 0.05 R² = 0.47 f(x) = - 0x^2 + 0x + 0.03

0.04 0.03 0.03 0.03

Current (A)

0.03 0.03 0.03 0.03 0.03

0

600

1200

1800

2400

3000

3600

4200

4800

5400

Time (s)

8.2 Standardization of sodium hydroxide (NaOH) TRIAL 1 0.5118 45.20 20.20 25.00 0.1002

Mass KHP, g Final buret reading, mL Initial buret reading, mL Volume NaOH dispensed, mL NaOH concentration, M Average NaOH concentration

TRIAL 2 0.5124 47.30 22.20 25.10 0.1000 0.1001 M

8.3 Determination of HNO3 concentration INITIAL Trial 1 Trial 2 5.0 5.0 15.7 19.7 11.6 15.7 4.1 4.0 0.0821 0.0801 0.0811 M

Volume HNO3, mL Final buret reading, mL Initial buret reading, mL Volume NaOH dispensed, mL HNO3 concentration, M Average HNO3 concentration

FINAL Cathode Anode 5.0 5.0 41.7 38.7 38.7 33.8 3.0 4.9 0.0601 0.0981

8.4 Solving transference numbers

V CHN O = VAHN O =22.8 mL 3

3

n Ci = n Ai = VHN O M HN O = 3

3

mol L )(0.0811 =1.85× 10 (22.8 1000 L )

-3

mol

13

n Cf = VCHN O M CHN O =

mol L 0.0601 =1.37×10 (22.8 1000 )( L )

A n Af = V AHN O MHN O =

mol L)(0.0981 =2.24×10 (22.8 1000 L )

3

3

3

3

−3

−3

mol

mol

∆ nC =−4.8× 10-4 mol, ∆ n A =3.9×10 -4 mol m Ci =4.0406 g, m iA =6.8404 g, m Cf =4.0999 g, m fA =6.7589 g C

A

∆ m = 0.0593 g, ∆ m = −0.0815 g For the first method,

−¿ q¿ ¿ ¿ −¿ = 0.8037 q−¿ = 0.1963, t + =1−t ¿ q −¿ = ¿ t¿ For the second method,

−¿ q¿ ¿ ¿ 5400

5400

q 2 = ∫ I dt = 0

∫ ( −3.209x 10−10 t 2 +9.895x 10−7 t+0.0346 ) dt=170.0019 C 0

−¿ = 0.7531 q−¿ = 0.2469, t + =1−t ¿ q −¿ = ¿ t¿ 8.5 Initial report attached.

14

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