Calculate The Cell Potential for The Following Equation Cu Ag

This calculator helps you determine the cell potential for the Cu | Ag half-cell reaction using the Nernst equation. The cell potential is a measure of the tendency of a chemical reaction to occur spontaneously.

Introduction

The cell potential (or electromotive force) of a galvanic cell is a measure of the tendency of a chemical reaction to occur spontaneously. For the Cu | Ag half-cell reaction, we can calculate the cell potential using the Nernst equation.

The standard reduction potentials for the half-reactions are:

Cu²⁺ + 2e⁻ → Cu (E° = +0.52 V)
Ag⁺ + e⁻ → Ag (E° = +0.80 V)

The overall cell reaction is:

Cu + 2Ag⁺ → Cu²⁺ + 2Ag

Nernst Equation Formula

The Nernst equation relates the reduction potential of an electrochemical reaction to the activities or concentrations of the chemical species involved. For the Cu | Ag half-cell reaction, the Nernst equation is:

E_cell = E°_cell - (RT/nF) * ln(Q)

Where:

E_cell = cell potential (V)
E°_cell = 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

For the Cu | Ag reaction, the standard cell potential (E°_cell) is calculated as:

E°_cell = E°_cathode - E°_anode

Where E°_cathode is the standard reduction potential of the cathode reaction and E°_anode is the standard reduction potential of the anode reaction.

Worked Example

Let's calculate the cell potential for the Cu | Ag half-cell reaction with the following conditions:

Initial concentration of Cu²⁺ = 0.1 M
Initial concentration of Ag⁺ = 0.01 M
Temperature = 25°C (298 K)

The reaction quotient (Q) is given by:

Q = [Cu²⁺] / [Ag⁺]²

Substituting the values:

Q = 0.1 / (0.01)² = 100

Now, calculate the cell potential using the Nernst equation:

E_cell = E°_cell - (RT/nF) * ln(Q)

Where:

E°_cell = 0.80 V - 0.52 V = 0.28 V
R = 8.314 J/mol·K
T = 298 K
n = 2 (number of electrons transferred)
F = 96,485 C/mol
Q = 100

Substituting these values:

E_cell = 0.28 - (8.314 * 298 / (2 * 96485)) * ln(100) E_cell ≈ 0.28 - 0.0295 * 4.605 ≈ 0.28 - 0.137 ≈ 0.143 V

The calculated cell potential is approximately 0.143 V.

Interpreting Results

The cell potential calculated using the Nernst equation provides several important pieces of information:

Spontaneity: If the cell potential is positive, the reaction is spontaneous as written. If it's negative, the reaction is non-spontaneous.
Equilibrium: When the cell potential is zero, the reaction is at equilibrium.
Driving Force: The magnitude of the cell potential indicates the driving force for the reaction.

In the example above, the positive cell potential of 0.143 V indicates that the reaction is spontaneous under the given conditions.

Note: The Nernst equation assumes ideal behavior and does not account for non-ideal factors such as ion pairing or solvent effects.

FAQ

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

The standard cell potential (E°_cell) is the cell potential measured under standard conditions (1 M concentrations, 25°C, and 1 atm pressure). The cell potential (E_cell) is the potential measured under non-standard conditions and is calculated using the Nernst equation.

How does temperature affect the cell potential?

The Nernst equation shows that the cell potential depends on temperature through the RT term. As temperature increases, the cell potential tends to decrease because the entropy term becomes more significant.

What is the reaction quotient (Q) in the Nernst equation?

The reaction quotient (Q) is the ratio of the product concentrations to the reactant concentrations, each raised to the power of their stoichiometric coefficients. It indicates the direction and extent of the reaction.

Can the Nernst equation be used for non-aqueous solutions?

The Nernst equation is derived from thermodynamic principles and can be applied to any solution, including non-aqueous ones, as long as the activities or concentrations are properly defined.