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?

Verified step by step guidance

1. Identify the equilibrium mixtures for each case: Case 1 (B ⇌ X), Case 2 (B ⇌ Y), and Case 3 (B ⇌ Z).
2. Count the number of green (A) and yellow (X, Y, Z) molecules in each case to determine the equilibrium position.
3. Compare the number of reactant (A) and product (X, Y, Z) molecules to determine the direction of the reaction at equilibrium.
4. Use the relationship between the equilibrium position and Gibbs Free Energy (ΔG°) to determine the sign of ΔG°: if the reaction favors products, ΔG° is negative; if it favors reactants, ΔG° is positive.
5. Analyze each case: Case 1 has more green (A) than yellow (X), Case 2 has an equal number of green (A) and yellow (Y), and Case 3 has more yellow (Z) than green (A).

Key Concepts

Gibbs Free Energy (∆G)

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.

Equilibrium Constant (K)

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.

Reaction Quotient (Q)

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.