Which one of the following is correct -

Options

A. `-DeltaG=DeltaH-TDeltaS`
B. `DeltaH=DeltaG-TDeltaS`
C. `DeltaS=1/T[DeltaG-DeltaH]`
D. `DeltaS=1/T[DeltaH-DeltaG]`

Answer

To solve the question regarding which statement about Gibbs free energy is correct, we will analyze each option based on the fundamental equation for Gibbs free energy.

### Step-by-Step Solution:

1. **Write the Gibbs Free Energy Equation**:
The fundamental equation for Gibbs free energy (ΔG) is given by:
\[ \Delta G = \Delta H - T \Delta S \]
where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.

2. **Analyze Each Statement**:
- **Statement 1**: \( \Delta G = -\Delta H + T \Delta S \)
- Rearranging this gives us:
\[ \Delta G = T \Delta S - \Delta H \]
This does not match the original equation, so this statement is incorrect.

- **Statement 2**: \( \Delta G = \Delta H + T \Delta S \)
- Rearranging this gives us:
\[ \Delta G - \Delta H = T \Delta S \]
This also does not match the original equation, so this statement is incorrect.

- **Statement 3**: \( T \Delta S = \Delta G - \Delta H \)
- Rearranging this gives us:
\[ T \Delta S + \Delta H = \Delta G \]
This does not match the original equation, so this statement is incorrect.

- **Statement 4**: \( T \Delta S = \Delta H - \Delta G \)
- Rearranging this gives us:
\[ \Delta G = \Delta H - T \Delta S \]
This matches the original equation, so this statement is correct.

3. **Conclusion**:
The correct statement among the four options is:
\[ T \Delta S = \Delta H - \Delta G \]

### Final Answer:
The correct option is **Statement 4**: \( T \Delta S = \Delta H - \Delta G \).

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