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Gibbs free energy (ΔG°) is a thermodynamic potential that measures the maximum or reversible work that may be done by a system at constant temperature T and pressure P. A negative ΔG° value implies that the reaction is spontaneous, while a positive ΔG° value indicates that the reaction is non-spontaneous. When ΔG° = 0, the reaction is at equilibrium.

The equilibrium constant (K) is a measure of the concentration of reaction products and reactants in the equilibrium state. If K > 1, the reaction favors the formation of products, while if K < 1, the reaction favors the formation of reactants. At equilibrium, both reactants and products are present in a ratio governed by K.

Since we know that a negative ΔG° corresponds to a spontaneous reaction, which means that products are favored (K > 1), and a positive ΔG° corresponds to a non-spontaneous reaction, which means reactants are favored (K < 1), we can deduce the correct relationship between ΔG° and K. If ΔG° = RT ln(K): - For K > 1 (products favored), ln(K) > 0, and RT > 0, so ΔG° would be positive, which contradicts our understanding of spontaneity (ΔG° should be negative). - For K < 1 (reactants favored), ln(K) < 0, and RT > 0, so ΔG° would be negative, which also contradicts our understanding of spontaneity (ΔG° should be positive). If ΔG° = -RT ln(K): - For K > 1 (products favored), ln(K) > 0, and RT > 0, so ΔG° would be negative, which is consistent with our understanding of spontaneity. - For K < 1 (reactants favored), ln(K) < 0, and RT > 0, so ΔG° would be positive, which is also consistent with our understanding of spontaneity. Based on this analysis, the correct relationship between ΔG° and K must be:

ΔG° = -RT ln(K)