Nernst Equation

Introduction

The Nernst equation relates the electrode potential under non-standard conditions to the standard electrode potential, temperature, and activities (or concentrations) of the involved species. It’s essential for predicting cell voltages in real systems.

Compute cell potentials under non-standard conditions — formula, variables, simplified form at 25°C, and applications.

Mathematical Form

For a general redox reaction: aA + ne⁻ → bB, the Nernst equation is:

E = E° − (RT / nF) · ln Q

Where:

• E = electrode potential (V)
• E° = standard electrode potential (V)
• R = 8.314 J·mol⁻¹·K⁻¹
• T = temperature (K)
• n = number of electrons transferred
• F = 96485 C·mol⁻¹ (Faraday constant)
• Q = reaction quotient

Simplified Nernst Equation at 25°C

At 298 K (25°C) the equation simplifies to:

E = E° − (0.0592 / n) · log₁₀ Q

Understanding the Terms

• Reaction quotient Q: Q = [Products]^b / [Reactants]^a (activities or concentrations).
• Concentration effect: Changing concentrations alters Q and therefore E.
• Temperature effect: Full equation shows explicit temperature dependence via RT/nF.

Applications

• Calculating cell potential under non-standard conditions.
• Determining equilibrium constants from cell potentials.
• Explaining pH meter (ion-selective electrode) response.
• Predicting how concentration changes affect battery voltage.

Quiz

1. What does the Nernst equation calculate in an electrochemical cell?
2. Write the simplified Nernst equation at 25°C.
3. What is the significance of the reaction quotient Q?
4. How does increasing product concentration affect the cell potential?
5. Why is the Nernst equation important for pH meters?

Answers and Explanation

1. It calculates the electrode potential (E) under non-standard conditions.
2. E = E° − (0.0592 / n) log₁₀ Q
3. Q reflects the instantaneous ratio of products to reactants and influences E.
4. Increasing product concentration increases Q, which generally decreases E (for reductions written as products on top of Q).
5. pH meters rely on the Nernst relationship between potential and hydrogen ion concentration to read pH from measured voltage.

FAQ

How do you calculate Q?

Q is calculated from current concentrations (or activities) as the product concentration terms divided by reactant concentration terms, each raised to their stoichiometric powers.

Does temperature make a big difference?

Yes — the full Nernst equation includes RT/nF, so temperature changes alter the slope; the simplified constant 0.0592 is valid only at 298 K.

References & Links

• Nernst equation — Wikipedia
• Electrochemical Cells — CHEMASH