Calculate The Cell Potential for The Following Cell

The cell potential (or electromotive force) of an electrochemical cell is a fundamental concept in chemistry that describes the tendency of a cell to do work. This calculator helps you determine the cell potential for a given half-cell reaction using the Nernst equation.

How to Calculate Cell Potential

The cell potential is calculated using the Nernst equation, which relates the reduction potential of a half-cell reaction to the activities or concentrations of the species involved. The standard cell potential (E°) is the potential when all reactants and products are at standard state (1 M concentration for solutes, 1 atm pressure for gases, and pure solids or liquids).

Note: The Nernst equation assumes ideal behavior and does not account for non-idealities in real solutions.

Key Concepts

The Nernst equation is temperature-dependent, with the standard potential (E°) changing with temperature.
For a spontaneous reaction, the cell potential is positive.
The Nernst equation can be used to calculate equilibrium concentrations.

Nernst Equation Formula

Nernst Equation:

E = E° - (RT/nF) * ln(Q)

Where:

E = cell potential (V)
E° = standard cell potential (V)
R = gas constant (8.314 J/mol·K)
T = temperature (K)
n = number of moles of electrons transferred
F = Faraday constant (96,485 C/mol)
Q = reaction quotient (product of concentrations of products divided by reactants)

The Nernst equation shows how the cell potential changes with the reaction quotient Q. At equilibrium, Q = K (equilibrium constant), and E = 0.

Worked Example

Example Calculation

For the reaction:

Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

Given:

E° = +0.76 V
[Cu²⁺] = 0.01 M
[Zn²⁺] = 0.01 M (standard state)
T = 298 K
n = 2

Calculation:

Q = [Zn²⁺]/[Cu²⁺] = 0.01/0.01 = 1

E = 0.76 - (8.314 × 298 / (2 × 96,485)) × ln(1) = 0.76 V

Result: The cell potential is 0.76 V.

Interpreting Results

The cell potential tells you:

If the reaction is spontaneous (positive E)
The direction of electron flow
How much work the cell can do per mole of electrons transferred

For a galvanic cell, the positive electrode is the cathode (reduction occurs), and the negative electrode is the anode (oxidation occurs).

Frequently Asked Questions

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

Standard cell potential (E°) is the potential when all reactants and products are at standard state (1 M concentration). Cell potential (E) is the actual potential under non-standard conditions, calculated using the Nernst equation.

How does temperature affect cell potential?

The Nernst equation shows that cell potential decreases with increasing temperature because the term (RT/nF) increases. However, the standard potential (E°) itself changes with temperature.

Can the Nernst equation be used for gases?

Yes, the Nernst equation can be applied to gas-phase reactions by using partial pressures instead of concentrations. The reaction quotient Q would then be the product of partial pressures of products divided by reactants.