Question

Which from following formulae is used to obtain value of $\text{E}^\circ_{\text{cell}}$ for a reaction taking place in Dry cell?

• A. $\frac{-\Delta\text{G}^\circ}{\text{F}}$
• B. $\frac{-\Delta\text{G}^\circ}{2F}$
• C. $\frac{-\Delta\text{G}^\circ}{3 \text{F}}$
• D. $\frac{-\Delta\text{G}^\circ}{4F}$

Hint:

In these formulas, "n" is the key. Since Zinc is divalent ($Zn^{2+}$), 2 electrons are involved, making $n=2$.

Answer 1

The Correct Option is B

Step 1: Concept
The relationship between the standard Gibbs free energy change ($\Delta G^\circ$) and the standard cell potential ($E^\circ_{cell}$) is $\Delta G^\circ = -nFE^\circ_{cell}$.

Step 2: Meaning
$n$ represents the number of moles of electrons transferred in the balanced redox reaction.

Step 3: Analysis
In a typical Dry cell (Leclanché cell), the primary reaction involves the oxidation of Zinc: $\text{Zn} \rightarrow \text{Zn}^{2+} + 2\text{e}^-$. Thus, $n = 2$. Rearranging the formula: $E^\circ_{cell} = -\Delta G^\circ / (2F)$.

Step 4: Conclusion
The correct formula for $n=2$ is $\frac{-\Delta\text{G}^\circ}{2F}$. Final Answer: (B)