7.14 Free Energy of Dissolution

Free energy of dissolution explains why some salts dissolve and others barely dissolve, using both enthalpy and entropy. When a salt dissolves, the solid lattice separates, some solvent attractions are disrupted, and new attractions form between ions and solvent. For AP Chemistry, connect particle-level attractions to the sign of $\Delta G$.

Why This Matters for the AP Chemistry Exam

This topic ties Unit 7 solubility ideas to the thermodynamics you will study in depth in Unit 9. You should be able to reason about how enthalpy and entropy together control whether a salt dissolves, and connect a free energy change to the equilibrium constant. On the exam, you may be asked to justify a claim about dissolution using chemical principles, interpret why a process is or is not favorable, or link the value of K to whether a reaction proceeds forward. Keeping the energy reasoning connected to particle-level behavior is what these questions reward.

more resources to help you study

practice multiple choiceFRQ practice & scoringcheatsheetsscore calculatorkey terms

Key Takeaways

• Dissolution is a reversible process that can be treated as an equilibrium, the same way you treat other reactions in Unit 7.
• Entropy (S) measures how spread out or disordered a system is; processes tend to increase entropy unless energy keeps things ordered.
• Gibbs free energy combines enthalpy and entropy: ΔG = ΔH - TΔS.
• A negative ΔG means the process is thermodynamically favorable; a positive ΔG means it is unfavorable.
• A thermodynamically favorable process has K greater than 1, so a favorable dissolution corresponds to a larger Ksp.
• Dissolving a salt requires breaking solute-solute attractions in the lattice and some solvent-solvent attractions, while forming new ion-solvent attractions releases energy.

A Quick Thermodynamics Refresher

Thermodynamics in AP Chemistry is the study of energy transfers during chemical reactions. Notice the word is energy, not just heat or temperature. Heat is only one piece of the picture.

In Unit 6 you used enthalpy (H) to describe a reaction as exothermic (heat-releasing) or endothermic (heat-absorbing). Two more measures matter here and get fuller treatment in Unit 9: entropy (S) and Gibbs free energy (G). This guide gives you enough of both to reason about dissolution.

Entropy

Entropy describes how spread out or disordered a system is. Another way to say it: entropy counts the number of possible arrangements available to a system. The more spread out and chaotic the arrangement, the higher the entropy.

A non-chemical example helps. A bedroom gets messy easily: pull the sheets off, toss clothes on the floor, and disorder goes up. Returning the room to an ordered state takes energy and effort. Systems tend toward higher entropy, and it takes energy to keep them ordered.

A common chemical example is melting and boiling:

H2O (s) ⇌ H2O (l) ⇌ H2O (g)

Moving left to right, entropy increases. Moving right to left, entropy decreases. Solids are the most ordered, liquids are in between, and gases are the most disordered.

Gibbs Free Energy and Thermodynamic Favorability

Gibbs free energy combines enthalpy and entropy into one value that describes whether a reaction is thermodynamically favorable. The change is:

$\Delta G = \Delta H - T\Delta S$

When ΔG is negative, the reaction is thermodynamically favorable (often called spontaneous). When ΔG is positive, the reaction is thermodynamically unfavorable. These terms describe how enthalpy and entropy changes work together to determine how far forward a reaction proceeds.

Gibbs free energy also connects to K, the equilibrium constant. A thermodynamically favorable process has K greater than 1, and an unfavorable one has K less than 1. You will work out this relationship in detail in Unit 9.

Gibbs Free Energy and Dissolving Substances

Salts, both soluble and sparingly soluble (what people often call insoluble), exist as crystal lattices in the solid state. For a salt to dissolve, three things happen with energy:

• The solute-solute attractions holding the lattice together must be broken. This takes energy.
• Some solvent-solvent attractions, such as hydrogen bonds between water molecules, must be broken. This also takes energy.
• New attractions form between the ions and solvent molecules. This releases energy.

The overall enthalpy change for dissolution depends on how the energy taken in to break attractions compares with the energy released when new attractions form. The entropy change matters too, since separating a packed lattice into ions moving through solution usually increases disorder.

Because ΔG = ΔH - TΔS, both enthalpy and entropy decide whether dissolution is favorable at a given temperature. If ΔG is positive, the salt does not dissolve readily and Ksp is very small. If ΔG is negative, dissolution is favorable and Ksp is larger.

How to Use This on the AP Chemistry Exam

Free Response

If you are asked to explain why a salt does or does not dissolve, connect it back to ΔG = ΔH - TΔS. State whether breaking and forming attractions makes ΔH favorable or unfavorable, then describe the entropy change, then combine them into a statement about ΔG. Finish by linking the sign of ΔG to the size of Ksp.

Justifying a Claim

When a question asks you to justify a claim about favorability, do not just label a process spontaneous. Give the reasoning: name the enthalpy contribution, name the entropy contribution, and explain how temperature affects the TΔS term. A favorable dissolution lines up with K greater than 1.

Common Trap

Temperature can flip the answer. Because ΔG depends on TΔS, a process that is unfavorable at a low temperature can become favorable at a higher temperature when the entropy term grows large enough. Always check whether temperature is part of the question before deciding the sign of ΔG.

Common Misconceptions

• Spontaneous does not mean fast. A negative ΔG tells you a process is thermodynamically favorable, not how quickly it happens. Speed is a kinetics question, not a thermodynamics one.
• Entropy is not "messiness" in a casual sense. It measures the number of available arrangements and how spread out energy and particles are, which is why a dissolved salt usually has higher entropy than the solid lattice.
• Dissolving is not always exothermic. Some salts dissolve while absorbing heat, because a favorable entropy change can drive dissolution even when ΔH is positive.
• A small Ksp does not mean nothing dissolves. It means very little dissolves, but a saturated solution still contains some dissolved ions in equilibrium with the solid.
• Insoluble is a relative term. Sparingly soluble salts still dissolve a tiny amount, which is exactly why they have a measurable Ksp.

Related AP Chemistry Guides

• 7.1 Introduction to Equilibrium
• Unit 7 Overview: Equilibrium
• 7.2 Direction of Reversible Reactions
• 7.3 Reaction Quotient and Equilibrium Constant
• 7.4 Calculating the Equilibrium Constant
• 7.11 Introduction to Solubility Equilibria