What is the relationship between the standard free-energy change, ∆G°, for a reaction and the equilibrium constant, K? What is the sign of ∆G° when: (a) K > 1? (b) K = 1? (c) K < 1?

The standard free energy change (∆G°) is a thermodynamic quantity that indicates the spontaneity of a reaction under standard conditions (1 M concentration, 1 atm pressure, and a specified temperature). A negative ∆G° suggests that a reaction is spontaneous, while a positive ∆G° indicates non-spontaneity. It is a crucial factor in predicting whether a reaction will proceed in the forward direction.

The equilibrium constant (K) is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. A K value greater than 1 indicates that products are favored at equilibrium, while a K value less than 1 suggests that reactants are favored. The value of K provides insight into the extent of a reaction's progress towards completion.

The relationship between standard free energy change (∆G°) and the equilibrium constant (K) is described by the equation ∆G° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin. This equation shows that when K > 1, ∆G° is negative, indicating a spontaneous reaction; when K = 1, ∆G° is zero, indicating equilibrium; and when K < 1, ∆G° is positive, indicating non-spontaneity.