Determining the Standard Reduction Potentials of Different Electrochemical Half-Cells

ABSTRACT The experiment deals with determining the standard reduction potentials of different electrochemical half-cells through pairing it with Cu2+(0.1 M)|Cu half-cell and then comparing it with the theoretical value. Galvanic or voltaic cells contain the anodic and cathodic cell reactions, and in order to get the value of Ecell, we add both half-reactions. The more positive the Ecell,the more negative ΔG would be, thus, giving us a spontaneous reaction. After comparing the cell potentials, formation constant of [Cu(NH3)4]2+ and the Ksp of Cu(OH)2, we’ve seen that their deviation where great, since for Ksp, the value does not only depend on the concentrations of the reactants but also with their respective ionic strengths. There are many different factors affecting the value of the cell potential and the emf reading, namely: concentration, temperature and reaction quotient. Other than human error, these factors affect the calculated values for Ecell.

INTRODUCTION Electrochemistry is the branch of chemistry that deals with the relationship of electricity and chemical reactions. Batteries, control of corrosion, metallurgy and electrolysis are some of the many applications of electrochemistry in everyday life. Electrochemistry always involves an oxidation-reduction process, wherein electrons are transferred from one substance to the other. This reaction is thermodynamically spontaneous and thus releases energy in the form of heat into their surroundings, and when in a controlled system, it produces electricity. Devices which carry out this process are called electrochemical cells.

There are two types of electrochemical cells: electrolytic and voltaic cells. Electrolytic cells are those in which nonspontaneous chemical reactions are supplied with an electrical charge to drive the process to spontaneity. On the other hand, voltaic or galvanic cells are those in which spontaneous reactions occur to produce electrical energy. Electrochemical cells have two conductive electrodes, the anode (oxidation) and the cathode (reduction). For a voltaic cell, the positively charged electrode is the cathode and the negative one is the anode (see Figure I). As seen in Figure II, while for an electrolytic cell, the cathode is negatively charged electrode, making the anode the positive one. These electrodes are immersed in an electrolyte solution. A salt bridge (for a voltaic cell) is used to maintain electrical neutrality by putting in ions in solution.

Figure I. Voltaic or Galvanic cell.

Figure II. Electrolytic cell.

The potential differences between electrodes, Ecell, also called cell voltage or electromotive force (emf), is the measure of the amount of energy per unit charge. The charge accounted is caused by the oxidation-reduction reaction where the electrons move from one electrode to another, specifically from anode to cathode, through an external circuit. It signifies the spontaneity of a reaction - a positive Ecell accounts to a spontaneous reaction. A standard electrode potential, Eºcell, is a measure of the tendency for a reduction process to occur at an electrode. These reduction potential values are based from the Standard Hydrogen Electrode or SHE which is given a reduction potential value of 0. We can relate the standard and nonstandard value of the electrode potential using the Nernst Equation:

Ecell = E˚cell –

where R is the gas constant given at 8.314 J/mol K, T is the absolute temperature at 298 K, n is the number of moles of electrons transferred, and F is the Faraday’s constant (96485 C/s). With this equation, we can also relate Ecell with pH, equilibrium constant and concentration of the involved species.

Another important relationship of cell potential is with Gibb’s free energy, ΔGº given in the equation

ΔGº= -nFEºcell

RESULTS AND DISCUSSION Half-cell standard reduction potentials were determined in the first part of the experiment by pairing the different half cells with Cu2+(0.1M)|Cu half-cell which has a given standard reduction potential of 0.34 V. Some of the half-cells underwent electrolysis first with the use of graphite electrodes and an electric current generated from a dry cell connected in series.

Table I. Determination of Cell Potential
Half-cell
(written as reduction half-cell) Voltmeter Reading (V)
Zn2+|Zn 1.004
Fe2+,Fe3+|C -0.188
Cl-, Cl2|C -0.520
Br-, Br2|C -0.479
I-, I2|C -0.261

The setups are mainly galvanic cells and the cell potentials were measured using a voltmeter. For Table I, our reference electrode is Cu2+|Cu, which is always on the positive terminal, undergoes reduction (reduction takes place in the cathodic half-cell).

Table II. Determination of Standard Reduction Potentials
Half-cell Standard Reduction Potential
(experimental),
V Standard Reduction Potential (book value), V Percent Error
Zn2+|Zn -0.664 -0.763 12.98%
Fe3+|Fe2+ 0.528 0.771 31.52%
Cl2|Cl- 0.8496 1.359 37.48%
Br2|Br- 0.3822 1.065 64.41%
I2|I- 0.8665 0.536 61.67%

The calculated standard reduction potential of each half-cell are shown in Table II. Comparing it with the theoretical values, deviations were observed. Discrepancies were probably caused by defective experiment set-up. For the electrolysis part, we can say that errors were caused by delay in the measurement of emf reading because we should’ve read it immediately after electrolysis so that X-, X2|C would not be disturbed.

Table III. Determination of E˚cell
Cell Notation (Galvanic) Ecell (V) E˚cell (V)
Cu|Cu2+(0.01M)||Cu2+(0.1M)|Cu 0.229 0.200
Zn|Zn2+(0.1M)||[Cu(NH3)4]2+(0.033M), NH3(0.53M)|Cu 0.838 1.180
Zn|Zn2+(0.1M)||OH-(0.10M), Cu(OH)2|Cu 0.788 1.271 For the second part of the experiment, only cell potentials were determined but this time, conditions were made complicated. In this part of the experiment, we have measured the cell potentials of the following: the concentration cell, redox reaction cell involving complexes and the electrochemical cell with partially soluble solid. Using the Nernst equation, we calculated for the standard reduction potentials of each half-cell. Deviation were quite large, probably due to human error. The summary of calculated values are seen in Table IV.

Table III. Calculated Values of ΔG, Ksp and Kf
Cell Notation (Galvanic) ΔG, J Ksp Kf
Cu|Cu2+(0.01M)||Cu2+(0.1M)|Cu -4.419 × 104 - -
Zn|Zn2+||[Cu(NH3)4]2+, NH3|Cu 1.62 × 105 - 1.639 × 107
Zn|Zn2+||OH-, Cu(OH)2|Cu 5.04 × 10-12 -

Using the obtained equation which relates Gibb’s free energy and the standard reduction potential, ΔGº= -nFEºcell, we obtained the values which has deviation (see Calculations) slightly greater than usual. For the Ksp and Kf values, we got percent error with values like 99.999% and >>>10,000% which is very much unacceptable.

CONCLUSIONS AND RECOMMENDATION(S) Percentage errors in the values obtained may have come from the delay in time the solutions’ emfs were measured. Also, factors like concentrations and temperatures must have affected the reactions. A defective galvanic cell or a faulty experimental set-up obviously accounts to a large percent deviation. Almost all of the reactions are spontaneous except for those which have a negative value of Ecell, and a positive value for ΔG. We can also conclude that reduction occurs at the cathode, the positive electrode, whereas for the negative electrode, oxidation takes place. Spontaneous reactions accounts to all positive cell potentials. We also learned that the concentration of a solution affects the cell potential of a reaction cell, as seen in the Nernst equation.

APPLICATION(S) Experimental evidences performed by Mr. Robert Dickerson and John Lenoir of University of Southern California suggest that electrochemical phenomena play an important role in the mechanism of tooth enamel deterioration. After performing experiments including the set-up of a Galvanic cell having a tooth enamel as the liquid junction, conclusions are made, namely:
 electric potentials, which result from the ionic membrane characteristics of enamel, provide an electric driving force for possible degradation of enamel by electric means and subsequent caries formation;
 there is a possible short circuiting by regions of low pH in a tooth enamel that causes its deterioration.

The effect of fluoride could help eliminate these short circuits of the oral electric potentials. These experiments could give way to new knowledge in dental chemistry.

REFERENCES [1] Brown, T.L., LeMay, E., Bursten, B.E. Chemistry: The Central Science, Tenth Edition. Pearson Education, Inc. New Jersey. 2006.
[2] Chang, R. Chemistry 7th Edition. McGraw-Hill. New York. 2002.
[3] Masterton, W. L., Hurley, C. N. Chemistry Principles and Reactions. Thomson Learning Asia, Singapore. 2005.
[4] Delahay, P. New instrumental methods in electrochemistry: theory, instrumentation and applications to analytical and physical chemistry. Interscience Publishers, New York. 1993.
[5] Peksok, R.L., Shields, L.D., Cairns, T., McWilliam, I.G. Modern Methods of Chemical Analysis 2nd Edition. Johnwiley and Sons, New York. 1968.
[6] Skoog, D.A., West, D.M., Hoiler, F.J., Crouch, S.R. Fundamentals of Analytical Chemistry. Brooks/Cole. 2004.
[7] Dickerson, R.A., Lenoir, J.M. Dental Enamel Electrochemistry. J Dent Res Vol. 52 No. 2. March-April 1973.

APPENDIX A. WORKING EQUATIONS (1) ; where [X2] = concentration of halogen gas I = average current t = time in seconds F = Faraday’s constant = 96485 C/mol e- VX- = volume of halide ion

(2) Ecell = Ecathode - Eanode
(3) Ecell = E˚cell – Ecell = E˚cell – E˚cell= Ecell +
(4) Ecathode = E˚cathode – Ecathode = E˚cathode –
(5) Eanode = E˚anode – Eanode = E˚anode –
(6)
Ecell= E˚Cu2+|Cu - E˚Zn2+|Zn - Consider the rxn: Cu2+ + 4NH3 → [Cu(NH3)4]2+ Kf = [Cu2+] = Ecell = E˚Cu2+|Cu - E˚Zn2+|Zn - (7) log Kf =(Ecell(expt) - E˚Cu2+|Cu + E˚Zn2+|Zn +
(8) ΔGº= -nFEºcell

where: Ecell = cell potential E˚cell = standard cell potential Ecathode = cathodic cell potential E˚cathode= standard cathodic cell potential Eanode = anodic cell potential E˚anode = standard anodic cell potential R = gas constant = 8.3145 J/mol K T = absolute temperature = 298.15 K Q = concentration quotient of the Reaction n = number of moles of electrons transferred Kf = formation constant ΔGº = change in free energy

B. SAMPLE CALCULATIONS A. Determination of Half-cell Standard Reduction Potentials, E˚red

(1) For Zn|Zn2+(0.1M)||Cu2+(0.1M)|Cu anode: Zn → Zn2+ + 2e- cathode: Cu2+ + 2e- → Cu Zn + Cu2+ → Zn2+ + Cu E˚cell= 1.004 + = 1.004 + 0.0296 E˚cell= 1.0336 V

E˚anode = E˚cathode - E˚cell E˚Zn|Zn2+= 0.34 – 1.0336 E˚Zn|Zn2+= -0.6936 V

% error = (2) For Cl-(0.1M), Cl2

anode: 2Cl- → Cl2 + 2e- cathode: Cu2+ + 2e- → Cu 2Cl- + Cu2+ → Cl2 + Cu E˚cell= Ecell + = -0.520 + E˚cell= -0.5096 V

E˚anode = E˚cathode - E˚cell E˚Cl2|Cl- = E˚Cu2+|Cu - E˚cell = 0.34 – (-0.5096) E˚Cl2|Cl- = 0.8496 V

% error =

B. Applications of Electrochemical cells

(1) Cu|Cu2+(0.01M)||Cu2+(0.1M)|Cu anode: Cu → Cu2+ + 2e- cathode: Cu2+ + 2e- → Cu Cu + Cu2+(0.1M) → Cu2+(0.01M) + Cu

E˚cell = Ecell + = 0.229 + E˚cell = 0.20 V

ΔG = -nFEcell =
ΔG = -4.419 × 104 J

Ecathode = E˚Cu2+|Cu – = 0.34 – 0.0296 Ecathode(theo) = 0.3104 V

Eanode = E˚Cu|Cu2+ – = -0.34 – 0.0296(-2) Eanode(theo) = -0.2808 V

Ecell= 0.3104 – (-0.2808) Ecell(theo)= 0.5912 V

% error =

(2) Zn|Zn2+(0.1M)||[Cu(NH3)4]2+(0.033M), NH3(0.53M)|Cu anode: Zn → Zn2+ + 2e- cathode: Cu2+ + 2e- → Cu Zn + Cu2+ → Zn2+ + Cu

Ecell = E˚Cu2+|Cu - E˚Zn2+|Zn – Ecell(theo)= 0.9856 V

ΔG = -nFEcell =
ΔG = 1.62× 105 J

% error =

log Kf =(Ecell(expt) - E˚Cu2+|Cu + E˚Zn2+|Zn + = 0.838 – 0.34 – 0.6936 + Kf = 1.639 x 107

% error in Kf = 99.999%

References: [1] Brown, T.L., LeMay, E., Bursten, B.E. Chemistry: The Central Science, Tenth Edition. Pearson Education, Inc. New Jersey. 2006. [2] Chang, R. Chemistry 7th Edition. McGraw-Hill. New York. 2002. [3] Masterton, W. L., Hurley, C. N. Chemistry Principles and Reactions. Thomson Learning Asia, Singapore. 2005. [4] Delahay, P. New instrumental methods in electrochemistry: theory, instrumentation and applications to analytical and physical chemistry. Interscience Publishers, New York. 1993. [5] Peksok, R.L., Shields, L.D., Cairns, T., McWilliam, I.G. Modern Methods of Chemical Analysis 2nd Edition. Johnwiley and Sons, New York. 1968. [6] Skoog, D.A., West, D.M., Hoiler, F.J., Crouch, S.R. Fundamentals of Analytical Chemistry. Brooks/Cole. 2004. = 0.34 – (-0.5096) E˚Cl2|Cl- = 0.8496 V