Gibbs free energy G, enthalpy H and entropy S are related as

Options

A. G = H + TS
B. G = H - TS
C. G - TS = H
D. S = H - G .

Explanation

To relate Gibbs free energy (G), enthalpy (H), and entropy (S), we can use the fundamental equation in thermodynamics. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Understanding the Variables**:
- **G**: Gibbs free energy
- **H**: Enthalpy
- **S**: Entropy
- **T**: Temperature in Kelvin

2. **Using the Gibbs Free Energy Equation**:
The relationship between Gibbs free energy, enthalpy, and entropy is given by the equation:
\[ G = H - TS \]
where \( G \) is the Gibbs free energy, \( H \) is the change in enthalpy, \( T \) is the absolute temperature in Kelvin, and \( S \) is the entropy.

3. **Understanding the Change in Values**:
For a chemical reaction, we often refer to the changes in these values, which can be represented as:
\[ \Delta G = \Delta H - T \Delta S \]
Here, \( \Delta G \) is the change in Gibbs free energy, \( \Delta H \) is the change in enthalpy, and \( \Delta S \) is the change in entropy for the reaction.

4. **Interpreting the Equation**:
- If \( \Delta G < 0 \): The reaction is spontaneous.
- If \( \Delta G > 0 \): The reaction is non-spontaneous.
- If \( \Delta G = 0 \): The system is at equilibrium.

5. **Conclusion**:
The relationship between Gibbs free energy, enthalpy, and entropy is crucial for understanding the spontaneity of chemical reactions. The correct relationship is:
\[ \Delta G = \Delta H - T \Delta S \]