Nernst Equation

The Nernst equation calculates the cell potential under non-standard conditions. It relates electrode potential to temperature, concentration, and the number of electrons transferred.

The Nernst Equation

E = E° - (RT/nF) ln Q

At 25°C (298 K), simplified form:

E = E° - (0.0592/n) log Q

Variable Definitions

E = Cell Potential

Units: Volts (V)

Cell potential under actual conditions

E° = Standard Cell Potential

Units: Volts (V)

Cell potential at standard conditions (1 M, 1 atm, 25°C)

Calculated from E°(cathode) - E°(anode)

R = Gas Constant

Value: 8.314 J/(mol·K)

T = Temperature

Units: Kelvin (K)

Usually 298 K (25°C) for standard temperature

n = Moles of Electrons

Units: mol e⁻

Number of electrons transferred in the balanced redox reaction

F = Faraday's Constant

Value: 96,485 C/mol

Charge per mole of electrons

Q = Reaction Quotient

Formula: Q = [products] / [reactants]

Ratio of concentrations at non-standard conditions

💡 At equilibrium, Q = K and E = 0

Common Forms of the Equation

Natural Logarithm Form

E = E° - (RT/nF) ln Q

General form valid at any temperature

At 25°C (298 K) with log₁₀

E = E° - (0.0592 V / n) log Q

Most commonly used form. 0.0592 = (RT ln 10)/F at 298 K

At 25°C with ln

E = E° - (0.0257 V / n) ln Q

Using natural log. 0.0257 = RT/F at 298 K

Step-by-Step Example

Problem: Calculate cell potential for Zn²⁺ + Cu → Zn + Cu²⁺ when [Zn²⁺] = 0.10 M and [Cu²⁺] = 2.0 M at 25°C. E° = 1.10 V.

Given:

  • E° = 1.10 V
  • [Zn²⁺] = 0.10 M
  • [Cu²⁺] = 2.0 M
  • n = 2 (2 electrons transferred)
  • T = 298 K (25°C)

Step 1: Determine n

Balanced half-reactions:

Oxidation: Zn → Zn²⁺ + 2e⁻
Reduction: Cu²⁺ + 2e⁻ → Cu
n = 2 electrons

Step 2: Calculate Q

Q = [products]/[reactants] = [Zn²⁺]/[Cu²⁺]

Q = 0.10 / 2.0 = 0.05

Step 3: Use Nernst equation at 25°C

E = E° - (0.0592/n) log Q
E = 1.10 - (0.0592/2) log(0.05)
E = 1.10 - (0.0296) × (-1.30)
E = 1.10 + 0.038 = 1.14 V

Answer: E = 1.14 V

Cell potential is higher than E° because [products] < [reactants], favoring forward reaction.

Common Mistakes

❌ Wrong Q calculation

Q uses products over reactants (like equilibrium). Make sure to balance coefficients as exponents!

❌ Forgetting electrons (n)

Must balance the redox equation to find n. Missing or wrong n completely changes the answer.

❌ Mixing ln and log

Use ln with 0.0257 V or log with 0.0592 V at 25°C. Don't mix them!

❌ Using wrong temperature constant

0.0592 and 0.0257 are only valid at 25°C (298 K). At other temperatures, use E = E° - (RT/nF) ln Q.

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Frequently Asked Questions

What is the Nernst equation?

E = E° - (RT/nF) ln Q. It calculates cell potential at non-standard conditions based on concentration and temperature.

When do I use 0.0592?

Use E = E° - (0.0592/n) log Q at 25°C (298 K) when using log₁₀. This is the most common simplified form.

How do I find n (electrons transferred)?

Balance the redox equation by separating into half-reactions. n equals the electrons in each balanced half-reaction.

What happens when E = 0?

When E = 0, the cell is at equilibrium. No current flows, and Q = K (equilibrium constant).

What if concentrations increase?

If product concentrations increase, Q increases, making E smaller. If reactant concentrations increase, Q decreases, making E larger.

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