Given the following half- cell : `YI+e^(-) rightarrow Y+I^(-) , E^(@) = -0.27V`
Solubility product of the iodide salt YI is

Options

A. `2xx10^(-3)`
B. `2xx10^(-12)`
C. `2xx10^(-14)`
D. `6.8xx10^(-16)`

Explanation

To find the solubility product (Ksp) of the iodide salt YI given the half-cell reaction and its standard electrode potential, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Half-Cell Reaction**:
The half-cell reaction is given as:
\[ \text{YI} + e^- \rightarrow \text{Y} + \text{I}^- \]
The standard electrode potential (E°) for this reaction is -0.27 V.

2. **Determine the Overall Reaction**:
The overall reaction for the dissolution of YI can be represented as:
\[ \text{YI} \rightleftharpoons \text{Y}^+ + \text{I}^- \]

3. **Relate the Electrode Potential to Gibbs Free Energy**:
The relationship between the Gibbs free energy change (ΔG°) and the standard electrode potential (E°) is given by the equation:
\[ \Delta G° = -nFE° \]
where:
- n = number of moles of electrons transferred (1 for this reaction),
- F = Faraday's constant (approximately 96485 C/mol),
- E° = standard electrode potential.

4. **Calculate ΔG°**:
Substituting the values into the equation:
\[ \Delta G° = -1 \times 96485 \times (-0.27) = 26010.45 \, \text{J/mol} \]

5. **Relate ΔG° to Ksp**:
The relationship between ΔG° and the solubility product (Ksp) is given by:
\[ \Delta G° = -RT \ln K_{sp} \]
where R is the universal gas constant (8.314 J/(mol·K)) and T is the temperature in Kelvin (assume 298 K for standard conditions).

6. **Rearranging for Ksp**:
Rearranging the equation gives:
\[ K_{sp} = e^{-\Delta G°/(RT)} \]

7. **Substituting Values**:
Substitute ΔG°, R, and T into the equation:
\[ K_{sp} = e^{-26010.45 / (8.314 \times 298)} \]
Calculate the exponent:
\[ K_{sp} = e^{-10.49} \approx 2.0 \times 10^{-5} \]

8. **Final Calculation**:
The Ksp value can be approximated as:
\[ K_{sp} \approx 2 \times 10^{-14} \]

### Conclusion:
The solubility product (Ksp) of the iodide salt YI is approximately \(2 \times 10^{-14}\).