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]`

Explanation

To determine which expression is correct regarding the relationship between Gibbs free energy (ΔG), enthalpy (ΔH), and entropy (ΔS), we can use the fundamental equation derived from the second law of thermodynamics. This equation is:

\[ \Delta G = \Delta H - T\Delta S \]

Where:
- ΔG = change in Gibbs free energy
- ΔH = change in enthalpy
- T = temperature in Kelvin
- ΔS = change in entropy

### Step-by-Step Solution:

1. **Understanding the Equation**:
The equation indicates that the change in Gibbs free energy (ΔG) is equal to the change in enthalpy (ΔH) minus the product of temperature (T) and the change in entropy (ΔS).

2. **Analyzing Spontaneity**:
- A reaction is spontaneous if ΔG < 0.
- This means that for a reaction to be spontaneous, the term \( \Delta H - T\Delta S \) must be negative.

3. **Conditions for Spontaneity**:
- If ΔH is negative (exothermic reaction) and ΔS is positive (increase in disorder), ΔG will definitely be negative, indicating spontaneity.
- If ΔH is positive (endothermic reaction) and ΔS is also positive, spontaneity depends on the temperature (T). At high temperatures, \( T\Delta S \) can outweigh ΔH, making ΔG negative.
- If ΔH is negative and ΔS is negative, spontaneity is favored at low temperatures.
- If ΔH is positive and ΔS is negative, the reaction is non-spontaneous at all temperatures.

4. **Conclusion**:
Based on the above analysis, we can conclude that the correct expression relating ΔG, ΔH, and ΔS is:

\[ \Delta G = \Delta H - T\Delta S \]