Question

In the cell reaction
P⁺(𝑎𝑞)+Q(𝑠)→P(𝑠)+Q⁺(𝑎𝑞) 
the EMF of the cell, 𝐸_{𝑐𝑒𝑙𝑙} is zero. The standard EMF of the cell, 𝐸^𝑜_{𝑐𝑒𝑙𝑙} is 
[Given: 
Activities of all solids are unity. 
Activity of P⁺(𝑎𝑞) is 2 M. Activity of Q⁺(𝑎𝑞) is 1 M. 
𝑅 = universal gas constant; 𝑇 = temperature; 𝐹 = Faraday constant]

• A. $\frac{RT}{F}$
• B. $\frac{RT}{2F}$
• C. $-\frac{RT}{F}In(2)$
• D. $\frac{RT}{F}In(2)$

Answer 1

The Correct Option is C

The Nernst equation for the standard EMF of the cell is given by:

$E^\circ_{\text{cell}} = \frac{RT}{nF} \ln \frac{\text{activity of P}^+}{\text{activity of Q}^+}$

Given the activities of the solids are unity and the activity of P⁺ is 2M, and the activity of Q⁺ is 1M, the standard EMF simplifies as follows:

$E^\circ_{\text{cell}} = \frac{RT}{F} \ln \frac{2}{1} = \frac{RT}{F} \ln(2)$