The temperature coefficient of a given cell , `((delE)/(delT))_P` is `1.5xx10^(-4) VK^(-1)` at 300 K. The change in entropy of cell during the cource of reaction,
`Pb((s))+ HgCl_(2)((aq))rightarrowPbCl_(2) (aq)+ Hg(1)`

Options

A. (28.95J/K)
B. (14.47J/K)
C. (57.9J/K)
D. (27.70J/K)

Explanation

To solve the problem, we need to calculate the change in entropy (\( \Delta S \)) of the cell reaction given the temperature coefficient of the cell and the number of electrons involved in the reaction.

### Step-by-Step Solution:

1. **Identify the Reaction and Oxidation States:**
The given reaction is:
\[ \text{Pb(s)} + \text{HgCl}_2(\text{aq}) \rightarrow \text{PbCl}_2(\text{aq}) + \text{Hg(l)} \]
- In this reaction, lead (Pb) goes from an oxidation state of 0 to +2 (losing 2 electrons).
- Mercury (Hg) goes from +2 in HgCl2 to 0 (gaining 2 electrons).

2. **Determine the Number of Electrons Transferred (n):**
From the oxidation and reduction processes:
- Pb loses 2 electrons: \( n = 2 \)
- Hg gains 2 electrons: \( n = 2 \)

Therefore, the total number of electrons transferred in the reaction is:
\[ n = 2 \]

3. **Use the Formula for Change in Entropy:**
The change in entropy (\( \Delta S \)) can be calculated using the formula:
\[ \Delta S = nF \left( \frac{\Delta E}{\Delta T} \right)_P \]
Where:
- \( n \) = number of electrons transferred (2 in this case)
- \( F \) = Faraday's constant (\( 96500 \, \text{C/mol} \))
- \( \left( \frac{\Delta E}{\Delta T} \right)_P \) = temperature coefficient of the cell (\( 1.5 \times 10^{-4} \, \text{V/K} \))

4. **Substituting the Values:**
Now, substituting the values into the formula:
\[ \Delta S = 2 \times 96500 \, \text{C/mol} \times 1.5 \times 10^{-4} \, \text{V/K} \]

5. **Calculating \( \Delta S \):**
Performing the calculation:
\[ \Delta S = 2 \times 96500 \times 1.5 \times 10^{-4} \]
\[ \Delta S = 2 \times 96500 \times 0.00015 \]
\[ \Delta S = 28.95 \, \text{J/K} \]

### Final Answer:
The change in entropy (\( \Delta S \)) of the cell during the course of the reaction is approximately:
\[ \Delta S \approx 28.95 \, \text{J/K} \]