If the reaction shown in a chemical equation is spontaneous, what can we infer about the value of K?

• A. K is greater than 1
• B. K is equal to ΔG
• C. K is less than 1
• D. K is equal to zero

Answer: (A)

In a spontaneous reaction, the Gibbs free energy change (ΔG) is negative. The relationship between the Gibbs free energy change and the equilibrium constant (K) is given by the equation:

ΔG = ΔG° + RT ln(Q)

At equilibrium, Q equals K, and ΔG becomes zero. Thus, when a reaction is spontaneous and we consider its equilibrium state, we can derive the formula:

ΔG° = -RT ln(K)

From this equation, if ΔG° is negative (indicating that the reaction is spontaneous), then the term -RT ln(K) also must be negative. To satisfy this condition, ln(K) must be positive, which occurs when K is greater than 1. Therefore, we can infer that a spontaneous reaction corresponds to an equilibrium constant greater than 1, indicating that products are favored over reactants at equilibrium. This relationship highlights why the correct answer points out that K must be greater than 1 for a spontaneous reaction.