Give the relation between Kc and Delta G

Answer

To establish the relationship between the equilibrium constant (Kc) and the change in Gibbs free energy (ΔG), we can follow these steps:

### Step 1: Understand the Definitions
- **Kc**: The equilibrium constant for a reaction at equilibrium, expressed in terms of the concentrations of the products and reactants.
- **ΔG**: The change in Gibbs free energy, which indicates the spontaneity of a reaction. A negative ΔG suggests that the reaction is spontaneous.

### Step 2: Write the Fundamental Equation
The relationship between ΔG and Kc is given by the equation:
\[ \Delta G^\circ = -RT \ln K_c \]

Where:
- \( \Delta G^\circ \) is the standard change in Gibbs free energy.
- \( R \) is the universal gas constant (approximately 8.314 J/(mol·K)).
- \( T \) is the absolute temperature in Kelvin.
- \( K_c \) is the equilibrium constant.

### Step 3: Analyze the Equation
- The equation shows that ΔG is directly related to the natural logarithm of Kc.
- If Kc > 1, then ΔG < 0 (the reaction is spontaneous).
- If Kc < 1, then ΔG > 0 (the reaction is non-spontaneous).
- If Kc = 1, then ΔG = 0 (the system is at equilibrium).

### Step 4: Conclusion
Thus, the relationship between Kc and ΔG can be summarized as:
- A larger Kc indicates a more favorable reaction (more products at equilibrium), resulting in a more negative ΔG.
- Conversely, a smaller Kc indicates a less favorable reaction (more reactants at equilibrium), resulting in a more positive ΔG.

### Final Relation
The final relation can be expressed as:
\[ \Delta G^\circ = -RT \ln K_c \]

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