What is the relationship between the standard free-energy change, ΔG^∘, for a reaction and the e

step 1 So let's look at the relationship between the equilibrium constant and our Gibbs free energy. So

What is the relationship between the standard free-energy...

What is the relationship between the standard free-energy change, $\Delta G^{\circ},$ for a reaction and the equilibrium constant, $K ?$ What is the sign of $\Delta G^{\circ}$ when:
(a) $K>1 \qquad$ (b) $K=1 \quad$ (c) $K<1$

Key Concepts

Standard Free Energy Change (?G°)

This concept refers to the change in Gibbs free energy for a reaction under standard conditions (typically 1 bar or 1 atm for gases, 1 M for solutions, and a specified temperature, usually 298 K). It provides a quantitative measure of the energy available to do work during a chemical reaction under these defined conditions, and it indicates whether a reaction is thermodynamically favorable.

Equilibrium Constant (K)

The equilibrium constant quantifies the ratio of the concentrations (or pressures) of products to reactants at equilibrium. It is a central concept in chemical thermodynamics that indicates the extent to which a reaction will proceed; a high K value favors products while a low K value favors reactants.

Thermodynamic Relationship between ?G° and K

The relationship between standard free-energy change and the equilibrium constant is given by the equation ?G° = -RT ln K, where R is the universal gas constant and T is the temperature in Kelvin. This equation links the thermodynamics of a reaction with its equilibrium behavior, showing that the magnitude and sign of ?G° directly depend on the value of K.

Interpretation of ?G° Based on K Values

The sign of ?G° reveals the spontaneity of a reaction under standard conditions: if K > 1, the natural logarithm of K is positive, making ?G° negative and indicating a spontaneous reaction; if K = 1, ln K equals zero, which makes ?G° zero and signifies that the reaction is at equilibrium; if K < 1, ln K is negative, resulting in a positive ?G° and a non-spontaneous reaction in the forward direction under standard conditions.

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