Question

What is the relation between \( \Delta G \) and \( E_{\text{cell}} \)?

• A. \( \Delta G = -nFE_{\text{cell}} \)
• B. \( \Delta G = nFE_{\text{cell}} \)
• C. \( \Delta G = nFE_{\text{cell}} \) (Positive value)
• D. \( \Delta G = -nFE_{\text{cell}} \) (Negative value)

Hint:

The equation \( \Delta G = -nFE_{\text{cell}} \) links the spontaneity of a redox reaction to the cell potential. A positive \( E_{\text{cell}} \) indicates a spontaneous reaction.

Answer 1

The Correct Option is A

Step 1: Understanding the Relationship.
The Nernst equation relates \( \Delta G \) (Gibbs free energy) and \( E_{\text{cell}} \) (electrochemical cell potential): \[ \Delta G = -nFE_{\text{cell}} \] Where: - \( n \) is the number of moles of electrons involved, - \( F \) is the Faraday constant (\( 96500 \, \text{C/mol} \)), - \( E_{\text{cell}} \) is the cell potential.
Step 2: Analyzing the Options.
- (A) \( \Delta G = -nFE_{\text{cell}} \) is correct because it is the standard equation used in electrochemistry.
- (B) \( \Delta G = nFE_{\text{cell}} \) is incorrect because the sign is wrong for the relationship.
- (C) and (D) both are variations with incorrect signs.
Step 3: Conclusion.
The correct answer is (A) \( \Delta G = -nFE_{\text{cell}} \).