Question

Which of the following relations about \( E^\circ_{cell} \) is false?

• A. \( E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode} \)
• B. \( E^\circ_{cell} = 0.0592 \log K \)
• C. \( E^\circ_{cell} = \frac{\Delta G^\circ}{-nF} \)
• D. \( E^\circ_{cell} = E^\circ_{anode} + E^\circ_{cathode} \)

Hint:

The cell potential is always the difference between the cathode and anode potentials, not their sum.

Answer 1

The Correct Option is D

Step 1: Review each equation.
The standard electrode potential, \( E^\circ_{cell} \), represents the overall voltage of a galvanic cell and can be derived from different relationships. Let's go through each of the options.

Step 2: Analyze each equation.
- Option \((1)\): \( E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode} \) is correct. This is the standard formula for calculating the cell potential in a galvanic cell.
- Option \((2)\): \( E^\circ_{cell} = 0.0592 \log K \) is a correct form of the Nernst equation, where \(K\) is the equilibrium constant.
- Option \((3)\): \( E^\circ_{cell} = \frac{\Delta G^\circ}{-nF} \) is a correct formula that connects the Gibbs free energy change and cell potential.
- Option \((4)\): \( E^\circ_{cell} = E^\circ_{anode} + E^\circ_{cathode} \) is incorrect. The cell potential is the difference between the cathode and anode potentials, not their sum. Thus, this equation is false.

Step 3: Identify the incorrect relation.
The relation in option \((4)\) is incorrect, so the correct answer is option \((4)\).

Step 4: Final Answer.
Thus, the false relation is \( E^\circ_{cell} = E^\circ_{anode} + E^\circ_{cathode} \), which corresponds to option \((4)\).