Calculate The Cell Potential for The Following Reaction Mg

The cell potential (or electromotive force) of a redox reaction measures the tendency of the reaction to occur spontaneously. For magnesium (Mg) reactions, we use the Nernst equation to calculate the cell potential under standard and non-standard conditions.

How to Calculate Cell Potential

To determine the cell potential for a magnesium redox reaction, follow these steps:

Identify the half-reactions for the oxidation and reduction processes.
Determine the standard reduction potentials (E°) for each half-reaction.
Calculate the cell potential using the Nernst equation.
Consider the effect of concentration changes on the cell potential.

The Nernst equation provides a way to calculate the cell potential under non-standard conditions, accounting for concentration differences.

Nernst Equation Formula

Nernst Equation

E = E° - (RT/nF) * ln(Q)

E = Cell potential (V)
E° = Standard cell 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 Nernst equation relates the cell potential to the standard potential and the activities or concentrations of the reactants and products.

Worked Example

Consider the reaction between magnesium and copper(II) ions:

Mg(s) + Cu²⁺(aq) → Mg²⁺(aq) + Cu(s)

Given:

E° for Mg²⁺/Mg = -2.37 V
E° for Cu²⁺/Cu = +0.34 V
Standard cell potential E° = E°_cathode - E°_anode = 0.34 - (-2.37) = 2.71 V
At equilibrium, [Mg²⁺] = [Cu²⁺] = 1 M

Using the Nernst equation at 25°C (298 K):

E = 2.71 - (0.0257) * ln(1) = 2.71 V

The cell potential is 2.71 volts under standard conditions.

Frequently Asked Questions

What is the standard cell potential for magnesium?

The standard reduction potential for Mg²⁺/Mg is -2.37 V. This means magnesium has a strong tendency to lose electrons.

How does temperature affect cell potential?

The Nernst equation shows that cell potential decreases with increasing temperature because the term (RT/nF) becomes larger.

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.