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Free energy of dissolution

Why does a cold pack get cold as it dissolves — absorbing heat — yet dissolve anyway? Because dissolving is a free-energy decision, and entropy can outvote an unfavorable enthalpy.

§1

Dissolution as a free-energy balance.

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Whether a substance dissolves is a free-energy question: ΔG = ΔH − TΔS for the dissolution. It dissolves spontaneously when ΔG < 0.

The solution enthalpy (ΔH) is the sum of two opposing pieces: the endothermic cost of separating the lattice (breaking ion-ion attractions) and the exothermic release from hydrating the ions (attracting them to water).

Because entropy usually rises when an ordered lattice disperses into solution, an endothermic dissolution can still be favorable: if TΔS is large enough, ΔG is negative even though ΔH > 0.

UNIT 9 TOPIC 9.6 • FREE ENERGY OF DISSOLUTION DISSOLUTION AND ΔG ΔG = ΔH − TΔS decides whether dissolving is favorable. Gibbs free energy ΔG = ΔH − T ΔS ΔG < 0 favorable (spontaneous) ΔG = 0 equilibrium ΔG > 0 unfavorable (nonspontaneous) Dissolution of NaCl (s → aq) ionic solid (s) H₂O + − Na⁺ Cl⁻ hydrated ions (aq) grey ring = water shell Na⁺ Cl⁻ Temperature dependence of favorability Sign of ΔG = ΔH − TΔS determines whether the process is thermodynamically favorable. ΔH ΔS ΔG = ΔH − TΔS Favorable when ΔH < 0 ΔS > 0 (−) − T(+) → always < 0 ALL temperatures ΔH < 0 ΔS < 0 low T: |ΔH| > |TΔS| LOW temperature ΔH > 0 ΔS > 0 high T: TΔS > ΔH HIGH temperature ΔH > 0 ΔS < 0 (+) − T(−) → always > 0 NEVER favorable CED ANCHOR Endothermic dissolving (ΔH > 0) can still be spontaneous when TΔS > ΔH — entropy of mixing drives it. A large positive ΔS makes the −TΔS term outweigh a positive ΔH, giving ΔG < 0. AP Chemistry · Unit 9 · Applications of Thermodynamics
Fig. 9.6.1 Dissolving is set by ΔG = ΔH − TΔS. The solution enthalpy combines the endothermic cost of separating the lattice and the exothermic release of hydration. Entropy gain can make an endothermic dissolution favorable.
§2

Weighing the terms.

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Build ΔH from its parts, then weigh against TΔS.

  1. Separate the lattice. Breaking the ionic lattice costs energy — this part is endothermic.
  2. Hydrate the ions. Surrounding ions with water releases energy — this part is exothermic.
  3. Get the solution enthalpy. ΔH_solution = lattice cost + hydration release (net sign depends on their sizes).
  4. Compare with entropy. Even if ΔH > 0, a large TΔS can make ΔG < 0 — it still dissolves.
§3

The pieces you'll meet.

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The pieces of dissolving.

ΔG
Free energy
ΔH − TΔS; dissolves when negative.
lattice
Lattice separation
Endothermic — costs energy.
hydration
Hydration
Exothermic — releases energy.
ΔH_sol
Solution enthalpy
Lattice cost + hydration release.
ΔS
Entropy gain
Dispersing the lattice usually raises S.
endo ok
Endothermic can dissolve
If TΔS outweighs ΔH.
§4

Worked example: an endothermic dissolution that happens.

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Observation. A salt dissolves while the solution gets colder — it absorbs heat, so ΔH_solution > 0 (endothermic).

Enthalpy parts. The endothermic lattice-separation cost slightly exceeds the exothermic hydration release, so the net ΔH is positive.

Entropy. The ordered lattice disperses into freely moving hydrated ions, so ΔS > 0 and TΔS is a positive, favorable term.

Verdict. ΔG = ΔH − TΔS can be negative because TΔS outweighs the positive ΔH — the salt dissolves despite being endothermic.

§5

Mistakes that cost real points.

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Pitfall · 01

"Separating the ionic lattice releases energy."

Breaking the lattice pulls oppositely charged ions apart against their attraction, which costs energy — it is endothermic. Only the hydration step (attracting ions to water) releases energy. Treating lattice separation as exothermic mis-signs the solution enthalpy.

Fix. Count lattice separation as an endothermic cost and hydration as the exothermic release.

Pitfall · 02

"An endothermic dissolution is impossible."

Many salts dissolve endothermically. Dissolution is governed by ΔG = ΔH − TΔS, so a favorable entropy increase (dispersing the lattice) can make ΔG negative even when ΔH > 0. Endothermic dissolving is common (cold packs).

Fix. Judge dissolving by ΔG, not ΔH alone; entropy can drive an endothermic dissolution.

Pitfall · 03

"The solution enthalpy is just the hydration energy."

The solution enthalpy is the sum of the endothermic lattice-separation cost and the exothermic hydration release, not hydration alone. Leaving out the lattice term (or the hydration term) gives the wrong net ΔH and the wrong prediction.

Fix. Add both pieces — lattice cost and hydration release — to get the solution enthalpy.

§6

Skill Check.

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