Gibb's free energy `G` is defined as

Options

A. `G=H-TS`
B. `G=H+TS`
C. `G=U-TS`
D. `G=U+TS`

Answer

To define Gibbs free energy \( G \), we can start with its fundamental equation, which relates it to enthalpy, entropy, and temperature. The definition is as follows:

1. **Understanding the Components**:
- **Enthalpy (H)**: This is a measure of the total heat content of a system.
- **Entropy (S)**: This is a measure of the disorder or randomness in a system.
- **Temperature (T)**: This is a measure of the average kinetic energy of the particles in a substance.

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

3. **Change in Gibbs Free Energy**:
When considering changes in a system, we can express the change in Gibbs free energy (\( \Delta G \)) as:
\[ \Delta G = \Delta H - T \Delta S \]
where:
- \( \Delta G \) is the change in Gibbs free energy,
- \( \Delta H \) is the change in enthalpy,
- \( T \) is the absolute temperature,
- \( \Delta S \) is the change in entropy.

4. **Significance of Gibbs Free Energy**:
- The Gibbs free energy is a crucial parameter in thermodynamics as it helps predict the direction of chemical reactions and the equilibrium position.
- A negative change in Gibbs free energy (\( \Delta G < 0 \)) indicates that a process is spontaneous, while a positive change (\( \Delta G > 0 \)) indicates that a process is non-spontaneous.

### Summary:
Thus, the correct expression for Gibbs free energy is:
\[ G = H - TS \]
And the change in Gibbs free energy can be expressed as:
\[ \Delta G = \Delta H - T \Delta S \]