Introduction:
The equilibrium constant (K) is a fundamental concept in chemical thermodynamics that quantifies the extent of a chemical reaction at equilibrium. It relates the concentrations (or partial pressures) of reactants and products in a reaction system. The equilibrium constant is related to the standard free energy change (ΔG°) and not the free energy change (ΔG) due to several reasons.

Explanation:
1. Standard conditions:
The standard free energy change (ΔG°) is the free energy change that occurs when reactants in their standard states are converted to products in their standard states, all at a specified temperature and pressure. It is determined under standard conditions, which include a temperature of 298 K (25°C), a pressure of 1 atm, and concentrations of 1 M for solutes. These standard conditions allow for easy comparison of thermodynamic properties between different reactions.

2. Consistency and reproducibility:
The standard free energy change provides a consistent and reproducible measure of the thermodynamic driving force for a reaction. By using standard conditions, the ΔG° values can be compared between different reactions and allow for the prediction of reaction spontaneity. This consistency is crucial for developing a reliable and universally applicable equilibrium constant.

3. Relationship between ΔG° and K:
The relationship between the equilibrium constant (K) and the standard free energy change (ΔG°) is given by the equation:

ΔG° = -RT ln(K)

where R is the gas constant and T is the temperature in Kelvin. This equation shows that the standard free energy change and the equilibrium constant are directly related logarithmically. The negative sign indicates that ΔG° and K have opposite signs.

4. Link to reaction spontaneity:
The standard free energy change (ΔG°) provides information about the spontaneity of a reaction. If ΔG° is negative, the reaction is thermodynamically favorable and spontaneous. In contrast, if ΔG° is positive, the reaction is non-spontaneous. The equilibrium constant (K) is a quantitative measure of the extent to which a reaction proceeds towards equilibrium, with larger values of K indicating a greater extent of product formation.

Conclusion:
The equilibrium constant is related to the standard free energy change (ΔG°) and not the free energy change (ΔG) because the standard conditions provide consistency and reproducibility for comparing reactions. The relationship between ΔG° and K allows for the prediction of reaction spontaneity and quantification of the extent of a reaction at equilibrium. Understanding this relationship is crucial in thermodynamics and chemical kinetics for studying and predicting chemical reactions.

Equlibrium:- the state of reaction in which rate of forward reaction is equal to the rate of backward reaction .