🎓 Prepared by students from Boğaziçi University

What is the Nernst Equation?

The Nernst equation calculates a cell's actual potential when concentrations differ from standard conditions. It shows how ions, reactants and products shift the voltage, predicting a cell's real-world output.

Short answer

E = E° − (RT/nF)ln(Q), where E is actual potential, E° is standard potential, R is gas constant, T is temperature (K), n is electrons transferred, F is Faraday constant, and Q is reaction quotient.

Cell potential vs. reaction quotient (Q)

x: ln(Q) · y: E (V)

Try it: interactive calculator

Cell potential E

1.1V

= 1.1 - (8.314*298/(2*96485))*ln(1)

Standard potential E°1.1 VTemperature T298 KElectrons transferred n2 molReaction quotient Q1

Step-by-step worked examples

Zn–Cu cell at 25°C, n=2, E°=1.10 V. If Q=4, what is E?

E = 1.10 − (8.314×298)/(2×96485)×ln(4)
E = 1.10 − 0.02569×1.386
E = 1.10 − 0.0356 = 1.064 V

At equilibrium (Q=K), what is E?

When Q=K: ln(Q) = ln(K)
E = E° − (RT/nF)×ln(K) = 0 V
(The cell voltage is zero at equilibrium.)

Temperature doubles from 298 K to 596 K, Q=1, n=1, E°=0.5 V. New E?

E = 0.5 − (8.314×596)/(1×96485)×ln(1)
ln(1)=0 so E = 0.5 V
(At Q=1, E=E° regardless of T.)

Flashcards

Quick quiz

Q1.Nernst equation: E = E° − (RT/nF)ln(Q). At Q=1, E equals:

Correct answer: B. ln(1)=0, so E = E° − 0 = E°.

Q2.As Q increases (reaction progresses), E:

Correct answer: B. ln(Q) increases, so E° − (positive number) = decreases.

Q3.What is ln(Q) at equilibrium?

Correct answer: C. At equilibrium Q=K, so ln(Q)=ln(K).

Q4.Doubling temperature T at Q=1 does what to E?

Correct answer: C. At Q=1, ln(Q)=0, so E = E° regardless of T.

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Common mistakes

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E = E° when Q = K. — Correct: E = 0 when Q = K (at equilibrium).

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E increases as the cell discharges. — Correct: E decreases (voltage drops) as Q approaches K.

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The Nernst equation only works at 25°C. — Correct: It works at any temperature; 0.0592 simplification is only at 25°C.

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Higher temperature always increases E. — Correct: At Q=1 (standard), temperature doesn't affect E; only at other Q values.

FAQ

What is the Nernst equation formula?

E = E° − (RT/nF)ln(Q). It predicts actual cell potential from concentrations.

What does Q represent in the Nernst equation?

Q is the reaction quotient: [products]/[reactants] at current conditions.

Why does E drop as the reaction proceeds?

As Q increases toward equilibrium (K), the driving force (E) decreases to zero.

Simplified Nernst at 25°C?

E = E° − (0.0592/n)×log₁₀(Q) using base-10 log instead of natural log.