Which is/are correct?

Options

A. (a) `2.303 log K=-DeltaH^(ɵ)//RT+DeltaS^(ɵ)//R`
B. (b) `DeltaG^(ɵ)=-2.303RT log K`
C. (c) `-2.303 log K=-DeltaH^(ɵ)//RT^(2)+DeltaS^(ɵ)//R`
D. (d) `2.303 log K=(1//RT)(DeltaH^(ɵ)+DeltaS^(ɵ))`

Explanation

To determine which statements are correct regarding the relationship between the equilibrium constant (K), Gibbs free energy change (ΔG), enthalpy change (ΔH), and entropy change (ΔS), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship between ΔG and K**:
The fundamental equation connecting Gibbs free energy change (ΔG) and the equilibrium constant (K) is given by:
\[ \Delta G = \Delta G^0 + RT \ln Q \]
At equilibrium, the reaction quotient (Q) is equal to the equilibrium constant (K), and ΔG becomes zero. Therefore, we can rewrite the equation as:
\[ 0 = \Delta G^0 + RT \ln K \]
Rearranging this gives:
\[ \Delta G^0 = -RT \ln K \]

2. **Converting Natural Log to Base 10 Log**:
To convert the natural logarithm to base 10 logarithm, we use the relationship:
\[ \ln K = 2.303 \log K \]
Substituting this into the equation for ΔG^0 gives:
\[ \Delta G^0 = -RT (2.303 \log K) \]
Thus, we have:
\[ \Delta G^0 = -2.303RT \log K \]

3. **Connecting ΔG^0 to ΔH and ΔS**:
Another important thermodynamic relation is:
\[ \Delta G^0 = \Delta H - T \Delta S \]
By equating the two expressions for ΔG^0, we have:
\[ -2.303RT \log K = \Delta H - T \Delta S \]

4. **Rearranging the Equation**:
Dividing the entire equation by RT gives:
\[ -2.303 \log K = \frac{\Delta H}{RT} - \frac{\Delta S}{R} \]

5. **Identifying the Correct Statements**:
Now, we can analyze the options provided in the question. Based on our derivations:
- The second option is correct as it relates ΔG^0 to K.
- The first option is also correct as it establishes a relationship involving ΔH and ΔS.
- The third option is incorrect because it mentions RT² instead of RT.
- The fourth option is irrelevant as it does not relate to the derivations we made.

### Conclusion:
The correct options are the first and second statements.