The following pictures represent equilibrium mixtures for the interconversion of A molecules (red) and X, Y, or Z molecules (blue):
What is the sign of ∆G° for each of the three reactions?

Gibbs Free Energy (∆G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. A negative ∆G indicates that a reaction is spontaneous, while a positive ∆G suggests non-spontaneity. The sign of ∆G is crucial for predicting the direction of a chemical reaction and its equilibrium position.

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction. It is related to the Gibbs Free Energy change by the equation ∆G° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin. A larger K value (greater than 1) indicates a reaction that favors products, while a smaller K value (less than 1) favors reactants.

The reaction quotient (Q) is a measure of the relative amounts of products and reactants present in a reaction at any point in time. It is calculated using the same formula as the equilibrium constant but with the current concentrations. Comparing Q to K helps determine the direction in which a reaction will proceed to reach equilibrium: if Q < K, the reaction will shift towards products, and if Q > K, it will shift towards reactants.