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 the correct relationship between Gibbs free energy change (ΔG), enthalpy change (ΔH), temperature (T), and entropy change (ΔS), we can follow these steps:

### Step-by-Step Solution:

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

2. **Analyze the Options**:
We need to evaluate each of the provided options to determine which one correctly represents the relationship stated in the Gibbs free energy equation.

3. **Evaluate Option 1**:
The first option states:
\[ -\Delta G = \Delta H - T \Delta S \]
Rearranging this gives:
\[ \Delta G = \Delta H - T \Delta S \quad \text{(which is correct)} \]
However, since it is presented as negative ΔG, this option is incorrect.

4. **Evaluate Option 2**:
The second option states:
\[ \Delta H = \Delta H - T \Delta S \]
This equation is not valid as it simplifies to \(0 = -T \Delta S\), which is not generally true. Therefore, this option is incorrect.

5. **Evaluate Option 3**:
The third option states:
\[ \Delta S = \frac{1}{T} (\Delta G - \Delta H) \]
Rearranging the Gibbs free energy equation gives:
\[ T \Delta S = \Delta H - \Delta G \quad \Rightarrow \quad \Delta S = \frac{\Delta H - \Delta G}{T} \]
This means that option 3 is also incorrect as it does not match the rearranged form.

6. **Evaluate Option 4**:
The fourth option states:
\[ \frac{1}{T} = \Delta H - \Delta G \]
Rearranging gives:
\[ \Delta S = \frac{\Delta H - \Delta G}{T} \]
This is the correct representation of the relationship between ΔS, ΔH, and ΔG.

### Conclusion:
The correct option is **Option 4**:
\[ \Delta S = \frac{\Delta H - \Delta G}{T} \]