Electrochemistry :  Nernst Equation and Faraday's Law

Let's review what occurs in a galvanic cell:

• The zinc electrode is losing mass as Zn metal is oxidized to Zn2+ ions which go into solution.
• The concentration of the Zn2+ solution is increasing.
• Anions, negative ions (e.g. Cl-), are flowing from the salt bridge toward the anode to balance the positive charge of the Zn2+ ions produced.
• The copper electrode is gaining mass as Cu2+ ions in the solution are reduced to Cu metal.
• The concentration of the Cu2+ solution is decreasing.
• Cations, positive ions (e.g. K+), are flowing from the salt bridge toward the cathode to replace the positive charge of the Cu2+ ions that consumed.
A reaction may start at standard-state conditions, but as the reaction proceeds, the concentrations of the solutions change, the driving force behind the reaction becomes weaker, and the cell potential eventually reaches zero.

**When the cell potential equals zero, the reaction is at equilibrium.

Nernst Equation - Can be used to find the cell potential at any moment in during a reaction or at conditions other than standard-state.

E = cell potential (V) under specific conditions

E= cell potential at standard-state conditions

R = ideal gas constant = 8.314 J/mol-K

T = temperature (kelvin), which is generally 25C (298 K)

n = number of moles of electrons transferred in the balanced equation

F = Faraday's constant, the charge on a mole of electrons = 95,484.56 C/mol

lnQc = the natural log of the reaction quotient at the moment in time

• Reaction quotient (Qc) - The mathematical product of the concentrations of the products of the reaction divided by the mathematical product of the concentrations of the reactants.
• Since the temperature is generally 25C (298 K), three of the terms in the above Nernst equation can be considered constants: R, T, and F.  Substituting the values of these constants, results in the following equation:

For the reaction:

There is a transfer of 2 electrons, so n = 2.

At equilibrium E = 0 and Qc = Kc:

The Nernst equation can be rearranged as follows:

This equation can be used to calculate the equilibrium constant for any oxidation-reduction reaction from its standard-state cell potential.

Sample Calculation

Calculate the cell potential for the following system:

Write the half-reactions with the half-cell potentials:

Multiply the reactions to get the lowest common multiple of electrons:

 Faraday's Law - The amount of substance consumed or produced at one of the electrodes in an electrolytic cell is directly proportional to the amount of electricity that passes through the cell.  By definition, one coulomb (C) of charge is transferred when a one-ampere (amp) current flows for one second (s):  Faraday's Constant - The charge on a mole of electrons:  F = 96,454.56 C Michael Faraday