Calculate The Cell Emf for The Following Reaction

Determine the electromotive force (EMF) of a galvanic cell using the Nernst equation. This calculator helps you calculate the cell potential for redox reactions based on standard reduction potentials and concentrations of reactants and products.

How to Calculate Cell EMF

The electromotive force (EMF) of a galvanic cell is the maximum potential difference between the two electrodes when no current flows. The Nernst equation allows us to calculate the cell potential under non-standard conditions.

Key Concepts

Standard reduction potential (E°) - the potential of a half-cell under standard conditions (1 M concentration, 298 K, 1 atm)
Activity coefficients (γ) - account for deviations from ideal behavior
Concentration of reactants and products - affect the cell potential

Calculation Steps

Write the balanced redox reaction
Identify the standard reduction potentials for each half-reaction
Calculate the standard cell potential (E°cell)
Apply the Nernst equation to find the cell potential under non-standard conditions

Note: The Nernst equation assumes ideal conditions and doesn't account for kinetic factors or concentration polarization.

Nernst Equation Formula

The Nernst equation relates the reduction potential of a reaction to the activities of the chemical species involved:

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 activities of products divided by reactants)

For dilute solutions, activities can be approximated by concentrations.

Worked Example

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

Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

E°Zn²⁺/Zn = +0.76 V

E°Cu²⁺/Cu = +0.34 V

[Cu²⁺] = 0.1 M

[Zn²⁺] = 1 M (standard state)

Solution

Calculate E°cell: E°cell = E°Cu²⁺/Cu - E°Zn²⁺/Zn = 0.34 V - 0.76 V = -0.42 V
Calculate Q: Q = [Zn²⁺]/[Cu²⁺] = 1/0.1 = 10
Apply Nernst equation: E = E°cell - (RT/nF) * ln(Q)
Calculate (RT/nF): (8.314 × 298)/(2 × 96,485) ≈ 0.0257 V
Final calculation: E = -0.42 - (0.0257 × ln(10)) ≈ -0.42 - 0.057 ≈ -0.477 V

The cell potential is approximately -0.48 V.

Frequently Asked Questions

What is the difference between standard cell potential and cell potential?: The standard cell potential (E°cell) is the potential measured under standard conditions (1 M concentrations, 298 K, 1 atm). The cell potential (E) is the potential under non-standard conditions, calculated using the Nernst equation.
How does temperature affect cell potential?: The Nernst equation includes temperature (T) in the calculation. Higher temperatures increase the cell potential, but this effect is usually small for most reactions.
What is the reaction quotient (Q)?: The reaction quotient (Q) is the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, each raised to the power of their stoichiometric coefficients.
When is the Nernst equation not applicable?: The Nernst equation assumes ideal conditions and doesn't account for kinetic factors, concentration polarization, or deviations from ideal behavior in concentrated solutions.