The standard emf for the cell reaction,
`2Cu^(+)(aq)toCu(s)+Cu^(2+)(aq)`
is `0.36V` at `298K`. The equilibrium constant of the reaction is

Options

A. `1.2xx10^6`
B. `7.4xx10^12`
C. `2.4xx10^6`
D. `5.5xx10^8`

Explanation

To find the equilibrium constant (K) for the given cell reaction, we can use the relationship between the standard cell potential (E°) and the equilibrium constant (K) as described by the Nernst equation. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Identify the Standard EMF (E°)**:
The standard EMF for the cell reaction is given as:
\[ E° = 0.36 \, V \]

2. **Use the Nernst Equation**:
At equilibrium, the cell potential (E) is 0, and we can use the Nernst equation:
\[ E = E° - \frac{0.0591}{n} \log(Q) \]
At equilibrium, \(E = 0\), so we can rearrange the equation:
\[ E° = \frac{0.0591}{n} \log(K) \]

3. **Determine the Number of Electrons Transferred (n)**:
In the given reaction:
\[ 2Cu^+(aq) \rightarrow Cu(s) + Cu^{2+}(aq) \]
Each \(Cu^+\) ion is reduced to \(Cu\) by gaining one electron. Therefore, for the overall reaction, 2 moles of \(Cu^+\) transfer 2 electrons. Thus, \(n = 2\).

4. **Substitute Values into the Equation**:
Now, substituting the known values into the rearranged Nernst equation:
\[ 0.36 = \frac{0.0591}{2} \log(K) \]

5. **Solve for \(\log(K)\)**:
Rearranging gives:
\[ \log(K) = \frac{0.36 \times 2}{0.0591} \]
\[ \log(K) = \frac{0.72}{0.0591} \approx 12.18 \]

6. **Calculate K**:
To find K, we take the antilog:
\[ K = 10^{12.18} \approx 1.5 \times 10^{12} \]

### Final Answer:
The equilibrium constant \(K\) for the reaction is approximately:
\[ K \approx 1.5 \times 10^{12} \]