Free Energy of Dissolution
Later connection: combine lattice, solvent and hydration contributions to dissolution free energy.
Before this connection: Chemical equilibrium: dissolution equations, Q versus K, and molar solubility; Energy transfer and enthalpy; Entropy and standard free energy.
AP Chemistry Topic 9.6 · CED printed p. 172 / PDF p. 179. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Dissolving an ionic solid has several competing pieces. Pulling its ions apart disrupts attractive lattice interactions and costs energy. Separating or reorganizing solvent molecules to make room also has an energy cost. New ion–water interactions can release energy. The net dissolution enthalpy is their sum, so it can be positive or negative. At the particle level, draw both the ions separating from the lattice and water reorienting around them; leaving out the solvent tells only half the story.
Entropy also has competing contributions. Dispersing ions can increase accessible arrangements, but ordered hydration shells can restrict nearby water arrangements and reduce their contribution. Do not assume the total dissolution entropy is always positive. Free energy combines the overall values, ΔG° = ΔH° − TΔS°. Small differences among large opposing contributions make simple solubility predictions difficult. An endothermic salt can dissolve favorably if entropy wins, and exothermicity alone does not guarantee a large equilibrium constant. The standard free-energy comparison relates to Ksp; the actual driving force also depends on dissolved-ion activities. At saturation with the solid present, Qsp = Ksp and net dissolution stops even though microscopic dissolution/precipitation continues.
You can examine a dissolution through a hypothetical bookkeeping path: separate the solid particles, reorganize the solvent, then form solute–solvent interactions. Disrupting attractions costs enthalpy; forming attractions releases it. Entropy contributions depend on the modeled arrangements: freeing particles can increase accessible arrangements, while a constrained hydration shell can reduce them. These are not universally fixed solvent-entropy signs. For each specified step, estimate both ΔH and ΔS, compare their sizes in ΔG = ΔH − TΔS, and only then sum. Large positive and negative terms can nearly cancel, so a small uncertainty can change a prediction. An exothermic hydration term alone does not establish net solubility.
Let's work through it
- A model salt has net ΔH°diss = +8.00 kJ mol−1 and ΔS°diss = +40.0 J mol−1 K−1 at 298 K.
- The enthalpy cost opposes dissolution; the entropy contribution TΔS° = 11.9 kJ mol−1 favors it.
- ΔG° = 8.00 − 11.92 = −3.92 kJ mol−1. The favorable entropy contribution outweighs the net endothermic cost.
- Explain with both components: lattice/solvent disruption costs energy, hydration releases some energy, and total dispersal exceeds any solvent-ordering entropy penalty in this supplied-data model. The final saturated mixture still has zero actual net driving force.
Try it from memory
Pause & retrieve
Try it before you peek.
Write your answer and the reason from memory. Then compare with the worked answer. Your self-assessment is a study decision, not an automatically graded score.
Question 1
Why can hydration lower entropy?
See every recall question with its answer
These references preserve each prompt and its answer for direct evidence links. Try the interactive questions above before opening the worked reasoning.
Retrieval 1
Why can hydration lower entropy?
Worked answer and reason
Reoriented water near ions can have fewer accessible arrangements.
Solvent organization contributes to the overall entropy change.
Retrieval 2
Does a positive standard dissolution ΔG° mean zero solubility?
Worked answer and reason
No. It corresponds to an equilibrium constant below one; an initially ion-poor solution can still gain dissolved ions.
Actual driving force depends on Q as well as the standard-state value.
Catch the tempting mistake
- Breaking a lattice is exothermic because ions separate.
- Separating oppositely charged lattice ions requires energy; new hydration interactions can release it.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 9 problem 8 · ap application · multiple
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For the teacher
- Look for a solvent contribution in both enthalpy and entropy reasoning. Use data when competing trends prevent a reliable sign prediction.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 9.6.A
- Explain the relationship between the solubility of a salt and changes in the enthalpy and entropy that occur in the dissolution process.
- 9.6.A.1
- The free energy change (ΔG°) for dissolution of a substance reflects a number of factors: the breaking of the intermolecular interactions that hold the solid together, the reorganization of the solvent around the dissolved species, and the interaction of the dissolved species with the solvent. It is possible to estimate the sign and relative magnitude of the enthalpic and entropic contributions to each of these factors. However, making predictions for the total change in free energy of dissolution can be challenging due to the cancellations among the free energies associated with the three factors cited.
Science references for this teaching
- AP Chemistry Course and Exam Description, effective Fall 2024 — Required topic-numbered learning objectives and essential knowledge, all continuations and AP exclusions; supplied PDF SHA256 b5dfe8677ef3d88c613865d2e2a3e8d6125d652e2b24c71ef1e8ce4e011094f0.
- OpenStax Chemistry 2e §16.4, Free Energy — Enthalpy–entropy competition and ΔG°/equilibrium connection.
Glossary and deeper reading · 11 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Enthalpy
Enthalpy is a state function defined from internal energy, pressure, and volume. At constant pressure with only pressure–volume work, an enthalpy change equals the heat transferred to the system. For example, a negative reaction enthalpy indicates heat release for the written reaction under those conditions.
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Entropy
Entropy is a state function related to the number of microscopic arrangements compatible with a macroscopic state. Changes depend on both matter and energy distribution, so visual messiness alone is not a reliable measure. For example, an ideal gas expanding at fixed temperature has more accessible positional arrangements and increased entropy.
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Solubility product
A solubility product is an equilibrium constant for a specified dissolution reaction. Its expression includes dissolved-species activities and omits the pure solid. For example, dissolving one formula unit that releases two anions gives an anion activity squared in the expression.
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Solute
A solute is a component dispersed in a solvent to form a solution. It need not be a solid, and a solution need not be liquid. For example, carbon dioxide is a gaseous solute in carbonated water.
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Chemical equilibrium
Chemical equilibrium is a dynamic state in which forward and reverse reaction rates are equal. Macroscopic composition remains constant in a closed system under fixed conditions, but reactant and product concentrations need not be equal. For example, a reversible reaction can reach equilibrium with much more reactant than product.
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Ion
An ion is an atom or group of atoms with a net electric charge. Ordinary ion formation changes electron count without changing the element's proton count. For example, a sodium atom losing one electron becomes a sodium ion with charge +1.
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Crystal lattice
A crystal lattice describes the repeating arrangement of structural sites in a crystalline solid. The occupants can be ions, atoms, or molecules depending on the material. For example, an ionic lattice places opposite charges near one another throughout a sodium chloride crystal.
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Solvation
Solvation is the interaction of solvent particles with dispersed solute particles. When the solvent is water, the process is called hydration. For example, oriented water molecules form hydration shells around dissolved ions.
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Gibbs free energy
Gibbs free energy combines enthalpy and entropy contributions to a system at specified temperature and pressure. For a reaction at constant temperature and pressure, a negative actual reaction free-energy change favors its forward direction, while standard and actual values must be distinguished. For example, a favorable reaction can still be slow if its pathway has a large activation barrier.
Read more: Gibbs Free Energy and Thermodynamic Favorability →
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Solvent
A solvent is the component used as the dissolving medium in a solution. It is often present in the greater amount, though the designation also depends on the mixture's context. For example, water is the solvent in a dilute aqueous sugar solution.
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Exothermic process
An exothermic process transfers heat from the chosen system to its surroundings. Under constant-pressure conditions with only pressure–volume work, its enthalpy change is negative. For example, freezing water releases heat to the surroundings.