Nernst Equation

Standard cell potentials (E°) assume everything is at 1 M concentration, 1 atm pressure, and 25°C. Real cells almost never operate under those conditions. The Nernst equation tells you the actual cell voltage when concentrations deviate from standard.

The Nernst Equation

What the Equation Tells You

The Nernst equation is a GPS for electrochemistry. E° tells you where you would be under standard conditions. The correction term -(RT/nF)lnQ adjusts for where you actually are.

Key Predictions from the Nernst Equation

The critical insight: As Q increases (products build up), the cell voltage decreases. This makes intuitive sense - as the reaction approaches equilibrium, there is less driving force to push electrons.

What Happens at Equilibrium

At equilibrium, $Q = K$ and $E = 0$:

$0 = E° - \dfrac{RT}{nF}\ln K$

Rearranging:

$\displaystyle E° = \dfrac{RT}{nF}\ln K$

This is the equation from the previous section that connects E° and K. The Nernst equation at equilibrium derives it naturally.

Worked Example

For the Daniell cell under non-standard conditions:

Zn(s) + Cu2+(aq) -> Zn2+(aq) + Cu(s)

Given: E° = +1.10 V, n = 2, [Zn2+] = 2.0 M, [Cu2+] = 0.010 M, T = 25°C.

Q = [Zn2+]/[Cu2+] = $\frac{2.0}{0.010}$ = 200

Using the simplified Nernst equation:

E = 1.10 - ($\frac{0.0592}{2}$)log(200)

E = 1.10 - (0.0296)(2.30)

E = 1.10 - 0.068 = +1.03 V

The cell voltage is lower than E° because products (Zn2+) are concentrated and reactants (Cu2+) are dilute. The reaction quotient is large (Q > 1), reducing the driving force.

How Concentration Changes Affect E

Understanding how concentration changes affect cell potential connects directly to Le Chatelier’s principle:

• Increasing reactant concentration (e.g., more Cu2+) decreases Q, which makes the correction term less negative, increasing E
• Increasing product concentration (e.g., more Zn2+) increases Q, making the correction term more negative, decreasing E
• Diluting products decreases Q and increases E