Which one of the following is correct?

Options

A. `-triangleG=triangleH-TtriangleS`
B. `triangleH=triangleH-T triangleS`
C. `triangleS=1/T [triangleG-triangleH]`
D. `triangleS=1/T [triangleH-triangleG]`

Answer

To solve the question regarding which thermodynamic relation is correct, we will analyze the given options based on the fundamental thermodynamic equations.

### Step-by-Step Solution:

1. **Understanding Gibbs Free Energy Relation**:
The Gibbs free energy (G) is related to enthalpy (H) and entropy (S) through the equation:
\[ \Delta G = \Delta H - T \Delta S \]
This equation is crucial for determining the spontaneity of a reaction.

2. **Analyzing the First Option**:
The first option states:
\[ -\Delta G = \Delta H - T \Delta S \]
If we multiply both sides by -1, we get:
\[ \Delta G = -\Delta H + T \Delta S \]
This does not match the standard Gibbs free energy equation. Thus, this option is incorrect.

3. **Analyzing the Second Option**:
The second option states:
\[ \Delta H = \Delta H - T \Delta S \]
Rearranging gives:
\[ 0 = -T \Delta S \]
This implies either \(T = 0\) or \(\Delta S = 0\), which is not a valid thermodynamic relation. Therefore, this option is also incorrect.

4. **Analyzing the Third Option**:
The third option states:
\[ \Delta S = \Delta H - \Delta G \]
Rearranging this gives:
\[ \Delta S = \frac{\Delta H - \Delta G}{T} \]
This is a rearrangement of the Gibbs free energy equation and is a valid expression.

5. **Conclusion**:
The only correct relation derived from the options is:
\[ \Delta S = \frac{\Delta H - \Delta G}{T} \]
Thus, the correct answer is option D.

### Final Answer:
The correct thermodynamic relation is:
\[ \Delta S = \frac{\Delta H - \Delta G}{T} \]
So, the answer is option D.