Nernst Equation (Electrochemistry) Formula & Examples

Nernst Equation

The Nernst equation is used in electrochemistry to calculate an electrode potential (or cell potential) under non-standard conditions. It links electrical potential to temperature, the number of electrons transferred, and the reaction quotient Q.

📌 Nernst Equation (General Form)

E = E° − (RT / nF) ln(Q)

E = electrode/cell potential under the given conditions (V)
E° = standard potential (V) (standard conditions)
R = gas constant (8.314 J·mol⁻¹·K⁻¹)
T = temperature (K)
n = number of electrons transferred in the balanced redox reaction
F = Faraday constant (96485 C·mol⁻¹)
Q = reaction quotient (uses activities; often approximated with concentrations/partial pressures)

25°C shortcut (log base 10)

At 25°C (298 K), the Nernst equation is commonly written using log base 10:

E = E° − (0.05916 / n) log₁₀(Q)

(0.05916 V is an approximation from 2.303RT/F at 298 K.)

What is Q (reaction quotient)?

For a general reaction:

aA + bB ⇌ cC + dD

The reaction quotient is:

Q = ( [C]^c · [D]^d ) / ( [A]^a · [B]^b )

Pure solids and pure liquids are usually omitted from Q (activity ≈ 1).
Gases typically use partial pressures (or activities) rather than concentration.

Using the Nernst equation for cell potential

For a full galvanic cell, you can use:

E°cell = E°cathode − E°anode
Then apply the Nernst equation to get Ecell under non-standard conditions.

🧮 Worked Example 1 (at 25°C)

For the overall reaction:

Zn(s) + Cu²⁺(aq) ⇌ Zn²⁺(aq) + Cu(s)

Assume E°cell = 1.10 V, n = 2, and concentrations:

[Zn²⁺] = 0.10 M
[Cu²⁺] = 1.0 × 10⁻³ M

Step 1: Write Q (omit solids Zn and Cu):

Q = [Zn²⁺] / [Cu²⁺] = 0.10 / (1.0×10⁻³) = 100

Step 2: Use the 25°C form:

E = 1.10 − (0.05916 / 2) log₁₀(100)

Since log₁₀(100) = 2:

E = 1.10 − (0.02958)(2) = 1.10 − 0.05916 = 1.0408 V (≈ 1.04 V)

🧮 Worked Example 2 (concentration cell idea)

A concentration cell uses the same half-reaction on both sides but different ion concentrations. A common takeaway:

If concentrations are equal, E = 0.
The larger the concentration difference, the larger E.

For a simple concentration scenario at 25°C with n = 2:

E = (0.05916 / n) log₁₀( [higher] / [lower] )

(Exact form depends on how Q is defined for the chosen half-reaction/cell reaction.)

Common mistakes to avoid

Wrong n: n must match electrons in the balanced overall redox equation.
Wrong Q: include only species that appear in the balanced reaction (and omit pure solids/liquids).
Temperature units: use Kelvin in the RT/nF form.
Log type: ln (natural log) vs log₁₀ (base 10) — don’t mix them.
Sign issues: check you’re using E°cell and Q for the same overall reaction direction.

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