For a cell involving one electron `E_(cell)^(0)=0.59V` and 298K, the equilibrium constant for the cell reaction is:
[Given that `(2.303RT)/(F)=0.059V` at `T=298K`]

Options

A. `1.0xx10^(30)`
B. `1.0xx10^(2)`
C. `1.0xx10^(5)`
D. `1.0xx10^(10)`

Explanation

To find the equilibrium constant for the cell reaction given the standard cell potential \( E_{cell}^{0} = 0.59 \, V \) and the fact that it involves one electron (n = 1), we can use the Nernst equation.

### Step-by-Step Solution:

1. **Write the Nernst Equation**:
The Nernst equation relates the standard cell potential to the equilibrium constant:
\[ E_{cell} = E_{cell}^{0} - \frac{0.059}{n} \log K \]
At equilibrium, \( E_{cell} = 0 \), so we can rewrite the equation as:
\[ 0 = E_{cell}^{0} - \frac{0.059}{n} \log K \]

2. **Substitute Known Values**:
Since \( n = 1 \) (one electron is involved), we can substitute \( E_{cell}^{0} = 0.59 \, V \) and \( n = 1 \) into the equation:
\[ 0 = 0.59 - 0.059 \log K \]

3. **Rearrange the Equation**:
Rearranging gives:
\[ 0.059 \log K = 0.59 \]
Now, divide both sides by \( 0.059 \):
\[ \log K = \frac{0.59}{0.059} \]

4. **Calculate the Right Side**:
Performing the division:
\[ \log K = 10 \]

5. **Convert Logarithm to Exponential Form**:
To find \( K \), we take the antilogarithm:
\[ K = 10^{10} \]

### Final Answer:
The equilibrium constant \( K \) for the cell reaction is:
\[ K = 10^{10} \]