Question

Assume the cell reaction,

\[ \mathrm{A}_{(\mathrm{s})}+\mathrm{B}_{(\mathrm{aq})}^{+2} \longrightarrow \mathrm{~A}_{(\mathrm{aq})}^{+2}+\mathrm{B}_{(\mathrm{s})} \]

if \(\Delta \mathrm{G}^{\circ}=-386 \mathrm{~kJ}\) at 298 K . What is \(\mathrm{E}_{\mathrm{Cell}}^0\) ?

• A. 1 V
• B. 1.5 V
• C. 2 V
• D. 2.5 V

Hint:

Use the relation between standard Gibbs energy and cell potential after finding the electrons transferred.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
\( \Delta G^{\circ}=-nFE^{\circ}_{cell} \).

Step 2: Find n
In \( \text{A}+\text{B}^{2+}\rightarrow\text{A}^{2+}+\text{B} \), two electrons are transferred, so \( n=2 \).

Step 3: Calculation
\( E^{\circ}_{cell}=\dfrac{386\times10^{3}}{2\times96500}=2.0 \text{ V} \)

Step 4: Compare the options
This matches option (C).

Final Answer:
The standard cell potential is 2 V. \[ \boxed{\text{(C) }\text{2 V}} \]