Which of the following relation represents correct relation between standard electrode potential and equilibrium constant?
I. `logK = (nFE^(@))/(2.303RT)`
II. `K = e^((nFE)/(RT))`
III. `log K = (-nFE^(@))/(2.303 RT)`
IV. `log K = 0.4342 (-nFE^(@))/(RT)`
Choose the correct statement(s).

Options

A. I, II and III are correct
B. II and III are correct
C. I, II and IV are correct
D. I and IV are correct

Explanation

To solve the problem, we need to analyze the relationships provided in the options and determine which ones correctly represent the relationship between standard electrode potential (E°) and the equilibrium constant (K).

### Step-by-Step Solution:

1. **Understand the Relationship Between Gibbs Free Energy and Electrode Potential**:
The relationship between Gibbs free energy (ΔG) and standard electrode potential (E°) is given by:
\[ \Delta G = -nFE^{\circ} \]
where:
- \( n \) = number of moles of electrons transferred
- \( F \) = Faraday's constant (approximately 96485 C/mol)
- \( E^{\circ} \) = standard electrode potential

2. **Understand the Relationship Between Gibbs Free Energy and Equilibrium Constant**:
The relationship between Gibbs free energy and the equilibrium constant (K) is given by:
\[ \Delta G = -2.303RT \log K \]
where:
- \( R \) = universal gas constant (approximately 8.314 J/(mol·K))
- \( T \) = temperature in Kelvin

3. **Equate the Two Expressions for Gibbs Free Energy**:
Since both expressions represent ΔG, we can set them equal to each other:
\[ -nFE^{\circ} = -2.303RT \log K \]
By canceling the negative signs, we get:
\[ nFE^{\circ} = 2.303RT \log K \]

4. **Rearranging the Equation**:
Now, rearranging this equation gives us:
\[ \log K = \frac{nFE^{\circ}}{2.303RT} \]
This matches with option I:
- **I.** \( \log K = \frac{nFE^{\circ}}{2.303RT} \) (Correct)

5. **Natural Log Relation**:
We can also express K in terms of the natural logarithm:
\[ K = e^{\left(\frac{nFE^{\circ}}{RT}\right)} \]
This matches with option II:
- **II.** \( K = e^{\left(\frac{nFE^{\circ}}{RT}\right)} \) (Correct)

6. **Analyzing Option III**:
Option III states:
- **III.** \( \log K = \frac{-nFE^{\circ}}{2.303RT} \)
This is incorrect because we derived that \( \log K \) should be positive when \( E^{\circ} \) is positive.

7. **Analyzing Option IV**:
Option IV states:
- **IV.** \( \log K = 0.4342 \left(\frac{-nFE^{\circ}}{RT}\right) \)
This is also incorrect because the negative sign is not consistent with our derived positive relationship.

### Conclusion:
The correct statements are:
- **I** and **II** are correct.