Electrochemical Cells - 1st Year

Basic topics

(i) The relation between the e.m.f. of a cell and the free energy change of the cell reaction. The Nernst equation.

(ii) The measurement of the e.m.f. of a cell. Tests for reversibility. Standard electrodes and their characteristics.

(iii) The conventions relating to electrochemical cells. Standard half cells. Standard electrode potentials. The determination of standard electrode potentials by both direct and indirect means, e.g. Cu/Cu2+ , Na/Na+.

Bibliography

Good books to read, if you can get hold of them, are C.W.Davies, Electrochemistry, and the appropriate chapter of D.H.Everett, Introduction to Thermodynamics, if you can find them. Otherwise, use Atkins and, if you need to look up something particular use the old S.Glasstone, Textbook of Electrochemistry, but beware of the different sign convention. More recent books are Electrode Potentials Compton & Sanders, OUP Chemistry Primer Series. Also Physical Chemistry, Atkins.

Problems

General procedure for doing electrochemical problems

(i) Write down the cell reaction remembering the convention that the reaction is such that Reduction occurs at the Right hand electrode.

(ii) Write down the free energy change for the reaction you have written using

μi = μi O + RTlnai

and

ΔG = Gright − G left

where left and right refer to the reaction, not the cell. Then use

ΔG = − nFE

to obtain an expression for the emf of the cell. n is the number of electrons involved in the reaction that you have written.

(iii) Finally, remember that the e.m.f. of the cell is the potential of the right hand electrode relative to the left hand one (cell as written).

Where the question number is enclosed in a button, e.g. , you can obtain help or comments about the question by clicking it.

The emf of the cell Ag|AgCl(s)|HCl(aq.)|Hg2Cl2(s)|Hg is 45.5 mV at 298 K and dE/dT is 0.338 mV K-1. Find ΔGO , ΔHO and ΔSO for the cell reaction.

The following standard entropies at 298 K have been determined from heat capacity measurements: SAg = 42.8, S AgCl = 96.6, SHg =77.7, S Hg2Cl2 = 197.4 J K−1 mol−1 .

Use these values together with your cell value to determine the entropy change associated with the cell reaction at 0 K. Comment on your results.

The hypothetical cell M|H2|NiSO 4, NH3 (aq.)|Ni has a standard emf of -0.75 V at 298 K, the cell reaction being

1/2H2 + 1/2Ni2+ = 1/2Ni + H+

The ammonia effectively stabilizes the Ni2+ by the formation of Ni(NH3)2+ . In the extraction of Ni by the Sherritt-Gordon process, a mixture of hydrogen, ammonia and nickel sulphate solution is heated in an autoclave. Assuming that apart from hydrogen and its ion everything is in its standard state, what is (a) the emf of the above cell at pH 9, 1 atm pressure of H 2, and 298 K, (b) the minimum temperature at which hydrogen will reduce nickel ions to nickel at pH 9, p H2 = 1 atm., and (c) the minimum pressure of H2 required to do the same thing at pH 9 and 298 K?

The following emf measurements were obtained at 298 K:

Pt|H2(1 atm.)|HCl(0.1 M) in H 2O|AgCl(s)|Ag E = 0.3532 V

Pt|D2(1 atm.)|DCl(0.1 M) in D 2O|AgCl(s)|Ag E = 0.3498 V

Neglecting any isotope effects on the activity coefficients, calculate the standard electrode potential of the deuterium electrode.

Solid Ag Cl conducts electricity sufficiently that the cell

Ag|AgCl(s)|Cl2|Ag

is reversible with the AgCl either solid or liquid. The emf of the cell as a function of temperature is given below:

T/K 573 623 673 723 773 823 873
E/V 1.000 0.975 0.949 0.924 0.904 0.887 0.871

Calculate the enthalpy and entropy of fusion and the melting point of AgCl, justifying any equations or assumptions that you use.

The standard potential of the Cl−(aq.)|AgCl(s)|Ag(s) electrode in the vicinity of T = 298 K has been found to fit the expression

EO/V = -0.00558 + 2.6967x10 -3(T/K) - 8.2299x10-6(T/K) 2 + 5.869x10-9(T/K) 3

Find the standard Gibbs free energy, the standard enthalpy, and the standard entropy of the silver|silver chloride half cell reaction at 298 K.

The standard emf of the cell H2(g)|HCl(aq.)|Cl 2(g) is 1.3583 V at 298 K. Find the standard Gibbs free energy of formation of AgCl(s).

The cell

Pt|H2(10atm.)|KOH(1M)|O 2(5 atm.)|Pt

has an e.m.f. of 1.69 V at 300 K where the vapour pressure of water is 0.03 atm. The cell reaction is

H2(g) + 1/2 O2(g) → H2O(l)

Calculate ΔGO for the reaction

Derive the Nernst equation relating the EMF of an electrochemical cell to the activities of its constituents.

At 298 K, the cell

Pt,H2(1atm) HCl(aq.) AgCl,Ag

has an EMF of 0.3409 V when the activities of the H+ and Cl− ions are 0.1 mol dm−3. Determine the standard electrode potential of the Cl−|AgCl,Ag electrode.

Given that the standard electrode potential of Ag+|Ag is 0.7991 V, determine the solubility product of AgCl.

The equilibrium constant for the disproportionation reaction

2Cu+(aq.) → Cu(s) + Cu2+(aq.)

is 1.2 x 10+6 at 298 K and the standard potential of the couple

Cu2+(aq.) + 2e → Cu(s)

is +0.34 V, also at 298 K. Determine the standard potential of the couple Cu+(aq.) + e → Cu(s) at 298 K.