What is the relationship between the equilibrium constant (K) and the Gibbs free energy change (ΔG) for a reaction?

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Q: What is the relationship between the equilibrium constant (K) and the Gibbs free energy change (ΔG) for a reaction?

Solution: The relationship is given by the equation ΔG = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin.

Steps: 7

Step 1: Understand that K is the equilibrium constant, which tells us the ratio of products to reactants at equilibrium.
Step 2: Know that ΔG is the change in Gibbs free energy, which indicates whether a reaction is spontaneous or not.
Step 3: Learn the equation that connects K and ΔG: ΔG = -RT ln(K).
Step 4: Identify R as the gas constant, which is approximately 8.314 J/(mol·K).
Step 5: Recognize that T is the temperature in Kelvin, which is important for the calculation.
Step 6: Realize that if K is greater than 1, ΔG is negative, meaning the reaction is spontaneous in the forward direction.
Step 7: Conversely, if K is less than 1, ΔG is positive, indicating the reaction is not spontaneous in the forward direction.