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What is the Nernst Equation and Cell Potential?

Q: What is the Nernst equation formula?

E_cell = E° − (RT/nF) ln Q, or at 25°C: E_cell = E° − (0.0592/n) log₁₀ Q.

Q: What is cell potential?

Cell potential (E_cell) is the voltage a galvanic cell produces under given conditions; it depends on E° and Q via the Nernst equation.

Q: How does temperature affect the Nernst equation?

Higher T increases the coefficient (RT/nF), so E_cell changes more dramatically with Q.

Q: Relate the Nernst equation to ΔG.

ΔG = −nFE_cell, and at equilibrium ΔG = −RT ln K, giving ln K = nFE°/RT.

Cell potential (E_cell) is the voltage produced by an electrochemical cell, determined by the standard cell potential E° and the Nernst equation. The Nernst equation accounts for non-standard conditions like concentration and temperature.

Short answer

The Nernst equation is E_cell = E° − (RT/nF) ln Q, which predicts the cell voltage under any conditions. At equilibrium (Q = K), E_cell = 0.

Cell potential vs. log Q at 25 °C (n=2, E°=1.0V)

x: log Q · y: E_cell (V)

Try it: interactive calculator

Cell potential E_cell

—V

= 1.5 - (0.0592/2)*log10(1)

Standard cell potential E°1.5 VElectrons transferred n2 molReaction quotient Q1

Step-by-step worked examples

A galvanic cell has E° = 0.76 V and at 25°C with n = 2, Q = 0.1. Find E_cell.

E_cell = E° − (0.0592/n) log Q
E_cell = 0.76 − (0.0592/2) log(0.1)
E_cell = 0.76 − (0.0296)(−1)
E_cell = 0.76 + 0.0296 = 0.790 V

At what value of Q does E_cell = 0 for E° = 1.0 V and n = 2?

E_cell = 0 = E° − (0.0592/n) log Q
(0.0592/2) log Q = 1.0
0.0296 log Q = 1.0
log Q = 33.78
Q = K_eq ≈ 6×10³³

If E° = 0.34 V, n = 1, and Q = 10, find E_cell at 25°C.

E_cell = 0.34 − (0.0592/1) log(10)
E_cell = 0.34 − 0.0592(1)
E_cell = 0.34 − 0.0592
E_cell = 0.281 V

Flashcards

Quick quiz

Q1.The Nernst constant 0.0592 V applies at…

Correct answer: B. 0.0592 is derived from (2.303RT/F) at 25°C (298 K).

Q2.If E_cell > 0, the reaction is…

Correct answer: C. Positive E_cell means ΔG < 0, so the reaction is spontaneous.

Q3.As Q increases toward K, E_cell…

Correct answer: C. Higher Q in the Nernst equation means −ln Q is less negative, so E_cell decreases.

Q4.At equilibrium, what is the relationship between K and E°?

Correct answer: B. At equilibrium E_cell = 0, so 0 = E° − (RT/nF) ln K, thus ln K = nFE°/RT.

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Common mistakes

✗

The Nernst equation ignores temperature effects. — Correct: Temperature T is a key variable in the Nernst equation.

✗

Higher Q always means higher E_cell. — Correct: Higher Q means lower E_cell (ln Q increases, −ln Q decreases).

✗

E° only depends on concentrations. — Correct: E° is a constant for a given redox couple; it's independent of concentrations.

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E_cell = 0 means the reaction is impossible. — Correct: E_cell = 0 at equilibrium; the reaction is reversible and stopped.

FAQ

What is the Nernst equation formula?

E_cell = E° − (RT/nF) ln Q, or at 25°C: E_cell = E° − (0.0592/n) log₁₀ Q.

What is cell potential?

Cell potential (E_cell) is the voltage a galvanic cell produces under given conditions; it depends on E° and Q via the Nernst equation.

How does temperature affect the Nernst equation?

Higher T increases the coefficient (RT/nF), so E_cell changes more dramatically with Q.

Relate the Nernst equation to ΔG.

ΔG = −nFE_cell, and at equilibrium ΔG = −RT ln K, giving ln K = nFE°/RT.