Conc

CHM 1046
General Chemistry II
Dr. Michael Blaber

Electrochemistry

Effect of Concentration on Cell EMF

The EMF of a redox reaction in a voltaic cell is determined not only by the type of redox reaction, but also the concentrations of the reactants and products (i.e. the reducing agent and oxidizing agent)

The EMF of the cell will fall as the reactants are used up and products increase in concentration
At equilibrium concentrations of reactants and products, the EMF = 0. Electrons flow spontaneously in a redox reaction because the system is attempting to achieve equilibrium. When equilibrium is achieved, net electron flow is zero.

Hint: Next time you find a dead battery, don't say "hey, this battery is dead". Instead, say "hey, the redox reaction in this voltaic cell has attained equilibrium, and now the electromotive force is zero". Do this when you visit your folks at home (don't do this in the dorm).
The Nernst Equation

Walther Hermann Nernst (1864 - 1941) was a German chemist who came up with an equation that related the EMF of a redox reaction on the concentration of reactants and products

Free energy and the equilibrium constant (this is from the section on thermodynamics)

DG = DG⁰ + RT lnQ
where Q is the reaction quotient

Relationship between DG and the electromotive force (from that genius Faraday)

DG = -nFE
where n = moles of electrons transferred, F = 96,500 J/V mole e^-, E = EMF in volts

Substituting into the free energy equation:

-nFE = -nFE⁰ + RT lnQ

solving for E yields:

A common form of the equation does away with the natural log and puts the equation in the form of log₁₀:

Yet another simplification occurs if the temperature of the reaction is known. For example, 298K is a common reference temperature for redox reactions (this is room temperature). At 298K the value of 2.303*RT/F = 0.0592 V mole:

This is the Nernst Equation. It allows us to do the following for redox reactions:

If we know the value of E⁰ and we measure the EMF of the cell (under non-standard conditions) we can determine the value of Q (and therefore the concentrations of reactants and products)
If we know the value of E⁰ and the concentrations of reactants and products, then we can determine the resulting EMF of the cell

A redox reaction for the oxidation of zinc by copper ion is set up with an initial concentration of 5.0M copper ion and 0.050M zinc ion. What is the cell EMF at 298K?

Zn(s) + Cu²⁺(aq) ® Zn²⁺(aq) + Cu(s)

In this case the value of n (the number of electrons transferred from Zn to Cu²⁺ in the redox reaction) is 2. The Standard EMF, E⁰, is 1.10 volt. Therefore, at 298K the Nernst equation gives:

Note: remember to ignore the "concentration" of solids in the equilibrium expression

E = 1.10 - 0.0296*log(0.05/5)

E = 1.10 + 0.0592 = 1.16V

This would seem to follow Le Chatelier's principle; we have loaded up the reaction with a high relative concentration of reactant (Cu²⁺) and the EMF is higher than the EMF under standard conditions (i.e. 1M or 1atm concentration for all reactants and products)

Equilibrium Constants for Redox Reactions

What happens when the redox reaction achieves equilibrium concentrations of reactants and products?

From thermodynamics, DG = 0
If DG = 0, then from Faraday's analysis of the EMF, E = 0 (because DG = -nFE, and n and F are positive and non-zero, so E must be zero)
In other words, if the redox reaction is at equilibrium, there is no longer any net reduction or oxidation reaction that drives an electromotive force (the cell is "dead")

or, rearranging to solve for K:

What does this equation tell us?

This says that the equilibrium constant is directly related to the standard EMF for the redox reaction (conversely, the standard EMF for the reaction is directly related to the value of the equilibrium constant)

A redox reaction where the equilibrium lies far to the right, will have a large value for K, and a large value for the standard EMF

If we can calculate the standard EMF for a reaction (by comparing the relative difference between the two half-reactions) we can derive the equilibrium constant for the reaction

2000 Dr. Michael Blaber