20.6 – 20.7 Student Notes

IV. Equilibrium Constants from emfs

A. Background info

1. ΔG – free energy – thermodynamic quantity defined by the equation G = H – TS – is a reaction spontaneous

2. ΔG = w_max

3. ΔG = - n F E°_cell

B. Calculating the Free-Energy Change from Electrode Potentials

Using standard electrode potentials, calculate the standard free-energy change at 25° C for the reaction

Zn (s) + 2 Ag⁺ (aq) à Zn²⁺ (aq) + 2 Ag (s)

C. Calculating the Cell emf from Free-Energy Change

Suppose the reaction of zinc metal and chlorine gas is utilized in a voltaic cell in which zinc ions and chloride ions are formed in aqueous solution.

Zn (s) + Cl₂ (g) à Zn²⁺ (aq) + 2 Cl^- (aq)

Calculate the standard emf for this cell at 25° C from standard free energies of formation (see Appendix C).

D. Equilibrium constants

E°_cell = (0.0592/n) log K (values in volts at 25° C)

a. Relationship of equilibrium constants

b. Calculating the Equilibrium Constant from Cell emf

The standard emf for the following voltaic cell is 1.10 V:

Zn (s) / Zn²⁺ (aq) ║ Cu²⁺ (aq) / Cu (s)

Calculate the equilibrium constant K_c for the reaction

Zn (s) + Cu²⁺ (aq) ¯ Zn²⁺ (aq) + Cu (s)

V. Dependence of emf on Concentration

A. Nernst Equation

1. Def – an equation relating the cell emf to its standard emf and the reaction quotient

2. Equation

c. Calculating the Cell emf for Nonstandard Conditions

What is the emf of the following voltaic cell at 25° C?

Zn (s) / Zn²⁺ (1.00 x 10^-5 M) ║ Cu²⁺ (0.100 M) / Cu (s)

The standard emf of this cell is 1.10 V.

B. Determination of pH

What is the nickel (II)-ion concentration in the voltaic cell

Zn (s) / Zn²⁺ (1.00 M) ║ Ni²⁺ (aq) / Ni (s)

if the emf is 0.34 V at 25° C?