Questions: Entropy and Gibbs Free Energy

Question 1

A reaction has ΔH = +80 kJ/mol and ΔS = +200 J/(mol·K). At which temperature range does this reaction become spontaneous?

• A. Below 400 K
• B. Above 400 K
• C. At any temperature
• D. Never — a positive ΔH makes it always non-spontaneous

Answer: (B)

For spontaneity, ΔG = ΔH - TΔS < 0. With positive ΔH and positive ΔS, ΔG < 0 when TΔS > ΔH, i.e., T > ΔH/ΔS. Converting units: 80,000 J/mol ÷ 200 J/(mol·K) = 400 K. Above 400 K, the entropy term dominates and ΔG becomes negative. This is a temperature-dependent case — endothermic but entropy-driven.

Question 2

A reaction with ΔG < 0 will occur quickly at room temperature because the negative free energy drives the reaction forward rapidly.

• T. True
• F. False

Answer: False

ΔG predicts whether a reaction is thermodynamically favorable — whether it can release free energy — but says nothing about how fast it proceeds. Reaction rates are governed by kinetics, specifically the activation energy barrier. Diamond converting to graphite has ΔG < 0 at room temperature but proceeds at an immeasurably slow rate because the activation energy is enormous. Spontaneous and fast are independent properties.

Question 3

What does the equation ΔG° = −RT ln K reveal about the relationship between thermodynamics and chemical equilibrium?

Model answer: It shows that the standard free energy change directly determines the equilibrium constant: a large negative ΔG° corresponds to a large K (products strongly favored), while a positive ΔG° gives K < 1 (reactants favored). Thermodynamic spontaneity and equilibrium position are the same phenomenon viewed from different angles.

At equilibrium, ΔG = 0 — there is no net free energy available to drive further change. The standard value ΔG° tells you where equilibrium lies under standard conditions. If ΔG° = −20 kJ/mol, then K is large (around 3000 at 298 K), meaning the reaction runs strongly toward products. This bridges thermodynamics with the equilibrium constant you studied in chemical equilibrium, and it reappears in electrochemistry via ΔG° = −nFE°.