Chemistry Final: Gibbs, Entropy, and Spontaneity Key Concepts

Boiling point relation

T_b = ∆H_vap / ∆S_vap

∆G° and K

∆G° = −RT ln K

Non-standard ∆G

∆G = ∆H − T∆S; ∆G = ∆G° + RT ln Q

Spontaneity by ∆G

∆G < 0 spontaneous; ∆G > 0 non-spontaneous

Equilibrium value of ∆G

∆G = 0

Second Law condition

∆S_univ = ∆S_sys + ∆S_surr > 0 for spontaneous

Surroundings entropy formula

∆S_surr = −∆H_sys / T

Exothermic effect on surroundings

∆H < 0 → ∆S_surr > 0 (helps spontaneity)

Endothermic effect on surroundings

∆H > 0 → ∆S_surr < 0 (hurts spontaneity)

Temperature switch (T*)

T* = ∆H / ∆S (use J and K)

Always spontaneous combo

∆H < 0 and ∆S > 0

Never spontaneous combo

∆H > 0 and ∆S < 0

Low-T spontaneous combo

∆H < 0 and ∆S < 0

High-T spontaneous combo

∆H > 0 and ∆S > 0

Entropy: phase ↑ disorder

solid → liquid → gas gives +∆S

Entropy: phase ↓ disorder

gas → liquid/solid gives −∆S

More gas moles in products

∆S > 0 (entropy increases)

Compressing gases

∆S < 0 (entropy decreases)

Dissolving crystalline solid

Usually ∆S > 0

Unit rule for calculations

Convert kJ→J; use T in Kelvin

At T* what is ∆G?

∆G = 0 (equilibrium threshold)

Why engines aren't 100% efficient

Some energy disperses; ∆S_univ must increase

"Hot loves chaos" meaning

High temperature favors processes with +∆S

Quick ∆S_surr tip

Bigger |∆H| or lower T → larger |∆S_surr| magnitude