Calculate The Standard Cell Potential of The Following Galvanic Cell

Introduction

The standard cell potential (E°cell) is a measure of the tendency of a galvanic cell to produce an electric current. It's calculated using the standard reduction potentials of the half-reactions involved in the cell. The standard cell potential determines whether a reaction will occur spontaneously and the voltage produced by the cell.

Galvanic cells, also known as voltaic cells, convert chemical energy into electrical energy. They consist of two half-cells: an oxidation half-cell and a reduction half-cell. The standard cell potential is calculated by subtracting the standard reduction potential of the oxidation half-cell from the standard reduction potential of the reduction half-cell.

How to Calculate Standard Cell Potential

To calculate the standard cell potential of a galvanic cell, follow these steps:

1. Identify the oxidation and reduction half-reactions.
2. Look up the standard reduction potentials (E°red) for each half-reaction.
3. Multiply the standard reduction potential of the oxidation half-cell by -1 to get the standard oxidation potential (E°ox).
4. Calculate the standard cell potential using the formula:
   E°cell = E°red (reduction half-cell) - E°ox (oxidation half-cell)

The standard cell potential is expressed in volts (V). A positive value indicates a spontaneous reaction, while a negative value indicates a non-spontaneous reaction.

Standard Reduction Potentials

Standard reduction potentials are the potentials of half-cells when all reactants and products are in their standard states (1 M concentration for solutes, 1 atm pressure for gases, and pure solids or liquids). The standard reduction potentials are typically referenced to the standard hydrogen electrode (SHE), which has a potential of 0 V.

Some common standard reduction potentials include:

• F₂(g) + 2e⁻ → 2F⁻(aq): E° = +2.87 V
• Cl₂(g) + 2e⁻ → 2Cl⁻(aq): E° = +1.36 V
• Br₂(l) + 2e⁻ → 2Br⁻(aq): E° = +1.09 V
• I₂(s) + 2e⁻ → 2I⁻(aq): E° = +0.54 V
• 2H⁺(aq) + 2e⁻ → H₂(g): E° = 0 V (reference electrode)
• Cu²⁺(aq) + 2e⁻ → Cu(s): E° = +0.34 V
• Fe²⁺(aq) + 2e⁻ → Fe(s): E° = -0.44 V
• Zn²⁺(aq) + 2e⁻ → Zn(s): E° = -0.76 V
• Al³⁺(aq) + 3e⁻ → Al(s): E° = -1.66 V
• Mg²⁺(aq) + 2e⁻ → Mg(s): E° = -2.37 V

These values are essential for calculating the standard cell potential of galvanic cells.

Example Calculation

Let's calculate the standard cell potential for the following galvanic cell:

Step 1: Identify the half-reactions.

Step 2: Look up the standard reduction potentials.

• E°red for Cu²⁺/Cu: +0.34 V
• E°ox for Zn/Zn²⁺: -0.76 V (from the standard reduction potential of Zn²⁺/Zn)

Step 3: Calculate the standard cell potential.

The standard cell potential for this galvanic cell is 1.10 V, indicating a spontaneous reaction.

Interpreting the Results

The standard cell potential provides several important pieces of information about a galvanic cell:

• Spontaneity: A positive standard cell potential indicates a spontaneous reaction, while a negative value indicates a non-spontaneous reaction.
• Voltage: The standard cell potential represents the maximum voltage that can be produced by the cell under standard conditions.
• Driving Force: The larger the standard cell potential, the greater the driving force for the reaction to occur.

Understanding the standard cell potential helps in predicting the behavior of galvanic cells and designing efficient electrochemical systems.