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: Understanding the Question:
We need to identify the incorrect formula relating standard cell potential to other thermodynamic variables.
Step 2: Detailed Explanation:
(A) \( \text{E}^\circ_{\text{cell}} = \text{E}^\circ_{\text{(cathode)}} - \text{E}^\circ_{\text{(anode)}} \): True (where both are reduction potentials).
(B) \( \text{E}^\circ_{\text{cell}} = \frac{0.0592}{n} \log \text{K} \): True (derived from Nernst equation at equilibrium at 298 K).
(C) \( \Delta\text{G}^\circ = -n\text{F}\text{E}^\circ_{\text{cell}} \): This is the correct fundamental relation. Rearranging gives \( \text{E}^\circ_{\text{cell}} = -\frac{\Delta\text{G}^\circ}{n\text{F}} \). The negative sign is missing in option (C).
(D) \( \text{E}^\circ_{\text{cell}} = \text{E}^\circ_{\text{oxidation (anode)}} + \text{E}^\circ_{\text{reduction (cathode)}} \): True.
Step 3: Final Answer:
Relationship (C) is false because of the missing negative sign.