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Free Energy and Equilibrium

Standard free energy and the equilibrium constant are directly linked: ΔG° = −RT ln K. So a large K (> 1) forces a negative ΔG° (products favored), and a small K forces a positive ΔG°. When ΔG° = 0, K = 1 — a balanced mixture, not a stopped reaction.

UNIT 9 TOPIC 9.5 • FREE ENERGY AND EQUILIBRIUM ΔG AND K The standard Gibbs free energy change ΔG° is tied to the equilibrium constant K at a given temperature. THE RELATIONSHIP ΔG° = −RT ln K K = e−ΔG°/RT VARIABLES ΔG° = std Gibbs free energy (J·mol⁻¹) R = gas constant (8.314 J·mol⁻¹·K⁻¹) T = temperature (K) K = equilibrium constant (unitless) UNITS CHECK R → J·mol⁻¹·K⁻¹ T → K R × T → J·mol⁻¹ ln K & e−ΔG°/RT unitless ΔG° must be in J·mol⁻¹. kJ·mol⁻¹ → J·mol⁻¹: multiply by 1000. The sign of ΔG° sets the size of K and which side is favored at equilibrium. ΔG° < 0 K > 1 (large) Products favored Equilibrium lies to the right A + B ⇌ C + D ΔG° = 0 K = 1 Neither side favored Equilibrium in the middle A + B ⇌ C + D ΔG° > 0 K < 1 (small) Reactants favored Equilibrium lies to the left A + B ⇌ C + D Large K (≫ 1) Small K (≪ 1) ΔG° negative spontaneous forward ΔG° = 0 at equilibrium (K = 1) ΔG° positive spontaneous reverse increasing ΔG° CED ANCHOR · KEY TAKEAWAY Use ΔG° = −RT ln K to link free energy to K. Negative ΔG° → products (large K); positive ΔG° → reactants (small K). REMEMBER ΔG° grows more negative as K grows larger. AP Chemistry · Unit 9 · Applications of Thermodynamics
Standard free energy and the equilibrium constant are locked together by ΔG° = −RT ln K. A large K (> 1) forces a negative ΔG°; a small K forces a positive one; ΔG° = 0 means K = 1 (a balanced mixture), not that nothing happens.
ΔG-K Linker · Open the sandbox →

The traps get the sign backward in ΔG° = −RT ln K, pair a large K with a positive ΔG° (impossible), or read ΔG° = 0 as 'no reaction' (it means K = 1). The minus sign ties a large K to a negative standard free energy.

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Lesson
Free Energy and K ›

ΔG° = −RT ln K locks the sign of ΔG° to the size of K; ΔG° = 0 means K = 1, not no reaction. The lesson applies the relationship, then closes with a ten-scenario check.

Skill check · 10 scenarios
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Diagnostic
10-item topic check ›

Ten items spanning the Topic 9.5 misconceptions: the ΔG°/K sign relationship inverted, a sign error in ΔG° = −RT ln K, and ΔG° = 0 misread as no reaction rather than K = 1.

Not started · 10 items · ~15 min
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Targeted Practice
Drill a single misconception ›

Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.

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