The Nernst Equation

E = Eº - (0.0591 / n ) x log (Q)

The Nernst equation shows how the cell potential depends on the concentration, or molarity, of what the components are in the cells.

In this problem, Q is equal to the product of the concentration of products divided by the product of the concentration of the reactants. In other words,

Q = ([products][products]…) / ([reactants][reactants]...)

Also, n stands for the moles of electrons; Eº is the standard cell potential; E is the cell potential. At equilibrium, E = 0 and Q = K.

Here is an example to find cell potentials under a certain condition:

Suppose you have a zinc electrode submerged in a  0.80M Zn2+ solution connected to a 1.30M Ag+ solution containing a silver electrode, through a salt bridge. At 25°C, determine the cell potential.

First, write out the half reactions and look up their cell potentials.
Zn2+ + 2 e− → Zn(s)(−0.76V)

Ag+ + e− --> Ag(s)(+0.80V)

Then write the balance equation and find E°.

Zn(s)→ Zn2+ + 2 e− (s)(+0.76V)

2Ag+ + 2e− → 2Ag(s)(+0.80V)

Zn(s)+ 2Ag+→ 2Ag(s) + Zn2+ E°=1.56V

Now it’s time to use the Nernst Equation!

Knowing Zn2+is 0.80M and Ag+ is 1.30M, you can use these numbers to find Q:

And when balancing the equation you can find n from the number of moles of electrons which is 2.

Finally, plug in your results in to the Nernst equation.

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