Questions: Gibbs Free Energy and Spontaneity

Question 1

A reaction has ΔH = +50 kJ/mol and ΔS = +200 J/(mol·K). At what temperature range is this reaction spontaneous?

• A. Never spontaneous
• B. Always spontaneous
• C. Spontaneous only at low temperatures
• D. Spontaneous only at high temperatures

Answer: (D)

ΔG = ΔH − TΔS. With ΔH > 0 and ΔS > 0, ΔG = positive − T(positive). As T increases, the −TΔS term grows more negative and eventually dominates, making ΔG < 0. The crossover temperature is T = ΔH/ΔS = 50,000 J / 200 J·K⁻¹ = 250 K; above this temperature, the reaction is spontaneous.

Question 2

A reaction is thermodynamically spontaneous (ΔG < 0), so it should proceed at a measurable rate under ordinary conditions.

• T. True
• F. False

Answer: False

Spontaneity (ΔG < 0) describes thermodynamic favorability — the direction a system would eventually reach equilibrium — but says nothing about the rate. The conversion of diamond to graphite is spontaneous under standard conditions, yet it is immeasurably slow. Kinetics and thermodynamics are independent: a reaction can be thermodynamically spontaneous yet kinetically inert due to a high activation energy barrier.

Question 3

What does it mean for a chemical reaction when ΔG = 0?

Model answer: The reaction is at equilibrium — the forward and reverse reactions proceed at equal rates, and there is no net change in the amounts of reactants or products.

ΔG = 0 is the condition for thermodynamic equilibrium. It does not mean nothing is happening; both forward and reverse reactions continue, but at equal rates. The relationship ΔG° = −RT ln K connects the standard free energy to the equilibrium constant, showing that when ΔG° = 0, K = 1 (products and reactants equally favored at standard conditions).