Calculate Cell Potential for The Following Reaction

This calculator helps you determine the cell potential (voltage) for a given redox reaction using the Nernst equation. The cell potential is a measure of the tendency of a chemical reaction to occur spontaneously.

How to Calculate Cell Potential

The cell potential is calculated using the Nernst equation, which relates the reduction potential of the half-reactions to the concentrations of the reactants and products. The standard reduction potential (E°) values are used as a reference point.

Nernst Equation:

E = E° - (RT/nF) * ln(Q)

Where:

E = Cell potential (V)
E° = Standard reduction potential (V)
R = Gas constant (8.314 J/mol·K)
T = Temperature (K)
n = Number of electrons transferred
F = Faraday constant (96,485 C/mol)
Q = Reaction quotient

The reaction quotient (Q) is calculated as the product of the concentrations of the products divided by the product of the concentrations of the reactants, each raised to the power of their stoichiometric coefficients.

Nernst Equation Formula

The Nernst equation is derived from the Gibbs free energy change of a reaction and provides a way to calculate the cell potential under non-standard conditions. The equation accounts for the effect of concentration changes on the cell potential.

Key Points:

The Nernst equation is valid for any temperature.
At standard conditions (1 M concentrations), the cell potential equals the standard reduction potential.
The equation shows that the cell potential decreases as the reaction proceeds (Q increases).

Worked Example

Let's calculate the cell potential for the following reaction at 25°C:

Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

Given:

E° = 1.10 V
[Cu²⁺] = 0.01 M
[Zn²⁺] = 0.01 M
n = 2 electrons
T = 298 K

Calculation:

Calculate Q: Q = [Zn²⁺]/[Cu²⁺] = 0.01/0.01 = 1
Calculate the term (RT/nF): (8.314 × 298)/(2 × 96,485) ≈ 0.0257 V
Calculate ln(Q): ln(1) = 0
E = E° - (RT/nF) * ln(Q) = 1.10 - (0.0257 × 0) = 1.10 V

The cell potential is 1.10 V, which matches the standard reduction potential since the concentrations are equal.

Interpreting Results

The cell potential tells you whether a reaction will occur spontaneously:

If E > 0, the reaction is spontaneous (favored).
If E = 0, the reaction is at equilibrium.
If E < 0, the reaction is non-spontaneous (not favored).

Changes in concentration or temperature can affect the cell potential. Higher concentrations of reactants or lower temperatures can make the reaction less favorable.

Frequently Asked Questions

What is the difference between standard and non-standard cell potential?

Standard cell potential (E°) is measured under standard conditions (1 M concentrations, 25°C). Non-standard cell potential (E) accounts for actual concentrations and temperature using the Nernst equation.

How does temperature affect cell potential?

The Nernst equation shows that temperature affects the term (RT/nF). Higher temperatures increase this term, making the cell potential less negative (more positive) for exothermic reactions and more negative for endothermic reactions.

Can the Nernst equation be used for any reaction?

The Nernst equation applies to any redox reaction where the standard reduction potential is known. It's most useful for reactions involving aqueous solutions.

What happens to cell potential as the reaction proceeds?

As the reaction proceeds, the reaction quotient (Q) increases, making the term (RT/nF) * ln(Q) more negative. This decreases the cell potential, making the reaction less favorable.