Calculate The Cell Voltage for The Following Reaction

How to Calculate Cell Voltage

The cell voltage (E_cell) of an electrochemical reaction can be calculated using the Nernst equation, which accounts for the standard reduction potential (E°) and the activities or concentrations of the reactants and products.

The general form of the Nernst equation is:

For practical calculations, especially at room temperature (25°C or 298 K), the equation can be simplified to:

This simplified form uses the value of 0.0592 V at 25°C, which is derived from the constants R, T, and F.

Nernst Equation Explained

The Nernst equation is a fundamental concept in electrochemistry that relates the reduction potential of a reaction to the standard reduction potential and the activities of the species involved.

Key points about the Nernst equation:

• It predicts the potential of an electrode under non-standard conditions
• It shows how the potential changes with concentration changes
• It applies to both galvanic (spontaneous) and electrolytic (non-spontaneous) cells
• The equation is valid for any temperature, but the simplified form assumes 25°C

The Nernst equation is particularly useful for calculating the potential of a cell when the concentrations of reactants and products are not at standard state (1 M for solutes, 1 atm for gases).

Standard Reduction Potentials

Standard reduction potentials (E°) are the potentials of half-cells under standard conditions (1 M concentration, 1 atm pressure, 25°C). These values are essential for calculating cell potentials.

Some common standard reduction potentials include:

• F₂/F^-: +2.87 V
• Cl₂/Cl^-: +1.36 V
• Br₂/Br^-: +1.09 V
• I₂/I^-: +0.54 V
• Cu²⁺/Cu: +0.34 V
• Ag⁺/Ag: +0.80 V
• Zn²⁺/Zn: -0.76 V
• Fe²⁺/Fe: -0.44 V
• H⁺/H₂: 0 V (reference electrode)

When calculating cell potentials, you subtract the reduction potential of the cathode (more positive) from the reduction potential of the anode (more negative).

Example Calculation

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

Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

Given:

• E°_Zn²⁺/Zn = -0.76 V
• E°_Cu²⁺/Cu = +0.34 V
• E°_cell = E°_cathode - E°_anode = 0.34 V - (-0.76 V) = 1.10 V
• Assume [Zn²⁺] = [Cu²⁺] = 1 M (standard state)

Since the concentrations are at standard state, the cell voltage is equal to the standard cell potential:

E_cell = 1.10 V

If the concentrations change, you would use the Nernst equation to calculate the new cell voltage.