Free Energy of Dissolution - AP Chemistry Study Guide

Getting Started

Why do some salts, like table salt, dissolve readily in water, while others, like chalk, barely dissolve at all? The answer lies in a thermodynamic tug-of-war at the molecular level. The dissolution of a solid in a liquid is a complex process governed by the interplay of energy changes (enthalpy) and changes in molecular disorder (entropy), which together determine the overall spontaneity of the process.

What You Should Be Able to Do

After completing this section, you should be able to:

• Describe the three main energetic steps involved in the dissolution of an ionic solid.

• Relate the signs of the enthalpy and entropy of solution to the molecular-level changes occurring.

• Use the Gibbs free energy equation to explain why a salt is or is not soluble under given conditions.

• Predict how a change in temperature will affect the solubility of a salt based on the thermodynamics of its dissolution.

Key Concepts & Analysis

The dissolution of an ionic compound is a process driven by changes in free energy. We can analyze this process by breaking it down into its constituent parts, examining the energy inputs required and the energy outputs released, to understand the cause of its overall spontaneity.

Inputs & Preconditions

The initial state of our system consists of two separate components:

1. The Solute: A solid ionic compound held together by strong electrostatic attractions between cations and anions in a highly ordered crystal lattice.

2. The Solvent: A pure liquid, typically water, with its own network of intermolecular forces (e.g., hydrogen bonds).

For dissolution to occur, the forces holding the solute together and the forces holding the solvent together must be overcome, and new, more favorable interactions between solute and solvent must be formed.

Key Steps / Mechanism

We can model the overall energy change of dissolution, the enthalpy of solution (ΔH_soln), as a hypothetical three-step process. The spontaneity of this process is ultimately determined by the Gibbs free energy of solution (ΔG_soln), which incorporates both this enthalpy change and the entropy of solution (ΔS_soln).

1. Breaking Solute-Solute Interactions (Endothermic)

First, energy must be supplied to break apart the ionic lattice and separate the ions. This energy input is equal in magnitude to the lattice energy of the solid. Because energy is absorbed, this step is always endothermic (ΔH₁ > 0).

• MX(s) + energy → M⁺(g) + X⁻(g)

• Stronger ionic bonds (higher charge, smaller ions) lead to a larger, more positive enthalpy change in this step.

2. Breaking Solvent-Solvent Interactions (Endothermic)

Next, space must be created within the solvent to accommodate the solute ions. This requires overcoming the intermolecular forces between solvent molecules (e.g., breaking hydrogen bonds in water). This step is also endothermic (ΔH₂ > 0).

3. Forming Solute-Solvent Interactions (Exothermic)

The gaseous ions are now introduced into the solvent. The ions form new, stabilizing ion-dipole interactions with the polar solvent molecules (a process called hydration if the solvent is water). This step always releases energy and is therefore exothermic (ΔH₃ < 0). The energy change is called the enthalpy of hydration.

• M⁺(g) + X⁻(g) → M⁺(aq) + X⁻(aq) + energy

• Stronger ion-dipole forces (higher ion charge, smaller ion radius) lead to a more negative (more exothermic) enthalpy of hydration.

The Overall Enthalpy and Entropy of Solution

The net enthalpy of solution is the sum of these three steps:

ΔH_soln = ΔH₁ + ΔH₂ + ΔH₃

• If the energy released during hydration (ΔH₃) is greater than the energy required to break the lattice and separate solvent molecules (ΔH₁ + ΔH₂), the overall process is exothermic (ΔH_soln < 0), and the solution feels warm.

• If the energy required is greater than the energy released, the process is endothermic (ΔH_soln > 0), and the solution feels cold.

The entropy of solution (ΔS_soln) is the change in disorder. Typically, a highly ordered crystal lattice breaking apart into mobile, dispersed ions in a solution leads to a significant increase in entropy (ΔS_soln > 0). However, the hydration of ions creates ordered "shells" of solvent molecules around them, which decreases entropy. The final sign of ΔS_soln is a balance between these two opposing effects, though it is positive for most salts.

Outputs & Effects

The final output is a homogeneous solution. The primary effect we observe is whether the salt is soluble, which is determined by the spontaneity of the process. A process is spontaneous if the Gibbs free energy change is negative (ΔG < 0).

The Gibbs free energy of solution (ΔG_soln) connects enthalpy and entropy:

ΔG_soln = ΔH_soln - TΔS_soln

• A negative ΔG_soln indicates a spontaneous dissolution process, meaning the salt is soluble.

• A positive ΔG_soln indicates a non-spontaneous process, meaning the salt is largely insoluble.

Controls & Limiting Factors

Temperature (T) is the key external factor controlling solubility. Its role is evident in the -TΔS_soln term of the Gibbs free energy equation.

• For endothermic dissolutions (ΔH_soln > 0): Most salts fall into this category. Since ΔS_soln is usually positive, the -TΔS_soln term is negative. Increasing the temperature makes this negative term larger, causing ΔG_soln to become more negative. Therefore, solubility increases with increasing temperature.

• For exothermic dissolutions (ΔH_soln < 0): Increasing the temperature makes the negative -TΔS_soln term larger, which counteracts the negative ΔH_soln. This can make ΔG_soln less negative or even positive. Therefore, for many exothermic salts, solubility decreases with increasing temperature.

The spontaneity of dissolution is a delicate balance. A process can be driven by enthalpy (exothermic), entropy (large increase in disorder), or a combination of both.

Key Models & Representations

The relationship between the signs of enthalpy and entropy changes and the resulting spontaneity of dissolution can be summarized in the following matrix.

Key Terms, Quantities, & Concepts

• Dissolution: The process in which a solute (solid, liquid, or gas) forms a solution in a solvent.

• Solubility: A measure of the maximum amount of a solute that can dissolve in a given amount of solvent at a specific temperature to form a saturated solution.

• Lattice Energy: The energy required to completely separate one mole of a solid ionic compound into its gaseous constituent ions. It is a measure of the strength of the ionic bonds.

• Enthalpy of Hydration (ΔH_hyd): The enthalpy change that occurs when one mole of gaseous ions is dissolved in water. It is always exothermic.

• Enthalpy of Solution (ΔH_soln): The net amount of heat energy absorbed or released when a solute is dissolved in a solvent.

• Entropy of Solution (ΔS_soln): The change in disorder or randomness of the system when a solute dissolves in a solvent.

• Gibbs Free Energy of Solution (ΔG_soln): The thermodynamic potential that measures the maximum reversible work that may be performed by a system. A negative value indicates a spontaneous process.

• Spontaneous Process: A process that proceeds without any ongoing external influence. Spontaneity is determined by a negative change in Gibbs free energy.

Skill Snapshots

Causation

• A high lattice energy (strong ionic bonds) causes a large positive enthalpy contribution, which disfavors dissolution.

• A large increase in disorder upon dissolving (ΔS_soln > 0) causes the -TΔS term to be highly negative, which favors dissolution, especially at higher temperatures.

• Strong ion-dipole interactions with the solvent cause a highly exothermic enthalpy of hydration, which favors dissolution by making the overall ΔH_soln more negative.

Comparison

• Endothermic dissolution (ΔH > 0) becomes more spontaneous as temperature increases, whereas exothermic dissolution (ΔH < 0) generally becomes less spontaneous as temperature increases.

• The dissolution of NaCl is enthalpy-driven at a small scale (slightly endothermic) but primarily entropy-driven, whereas the dissolution of NaOH is strongly enthalpy-driven (very exothermic).

• A substance is considered "soluble" if its dissolution has a negative ΔG under standard conditions, whereas it is "insoluble" if its ΔG is significantly positive.

Change Over Time & Conditions (CCOT)

• Baseline: A solid crystal of ammonium nitrate (NH₄NO₃) and a beaker of room-temperature water exist as separate, stable phases.

• Change 1: When the solid is added to the water, the dissolution process begins. It is highly endothermic (ΔH_soln > 0), absorbing a large amount of heat from the surroundings and causing the water temperature to drop significantly.

• Change 2: Despite the unfavorable enthalpy change, the process is spontaneous because the breakup of the crystal into three mobile ions (NH₄⁺ and NO₃⁻) creates a large increase in entropy (ΔS_soln > 0), making ΔG negative.

• Continuity: Throughout the process, the total mass and the number of atoms of nitrogen, hydrogen, and oxygen are conserved.

Common Misconceptions & Clarifications

1. Misconception: If a dissolution process feels cold (is endothermic), it cannot be spontaneous.

   Clarification: This is incorrect. Many spontaneous processes are endothermic. The dissolution of ammonium nitrate in a chemical cold pack is a prime example. The process is driven by a large positive change in entropy (ΔS > 0), which makes the -TΔS term sufficiently negative to overcome the positive ΔH, resulting in an overall negative ΔG.

2. Misconception: Dissolving a solid in a liquid always increases the entropy of the system.

   Clarification: While breaking up an ordered crystal into mobile ions increases entropy, the subsequent hydration of those ions creates order in the surrounding solvent molecules. For small, highly charged ions (like F⁻ or Al³⁺), this ordering effect can be so significant that the overall entropy change (ΔS_soln) is small or even negative.

3. Misconception: "Insoluble" salts do not dissolve at all.

   Clarification: "Insoluble" is a relative term indicating very low solubility. All ionic compounds dissolve to some extent, establishing an equilibrium between the solid and its dissolved ions. For an "insoluble" salt like silver chloride (AgCl), the ΔG° of dissolution is positive, meaning the process is non-spontaneous and the equilibrium lies far to the left, favoring the solid state.

4. Misconception: Any process that releases heat (exothermic) is always spontaneous.

   Clarification: Spontaneity depends on Gibbs free energy (ΔG), not just enthalpy (ΔH). An exothermic process (ΔH < 0) can be non-spontaneous if it is accompanied by a large decrease in entropy (ΔS < 0). At high enough temperatures, the positive -TΔS term can overwhelm the negative ΔH, making ΔG positive and the process non-spontaneous.

One-Paragraph Summary

The solubility of a salt is a direct consequence of the thermodynamics governing its dissolution. This process is not dictated by a single factor but by the overall change in Gibbs free energy (ΔG), which balances the change in enthalpy (ΔH) and the change in entropy (ΔS). The enthalpy of solution is the net result of the energy required to break the solute's crystal lattice versus the energy released when ions are hydrated by the solvent. Simultaneously, the entropy of solution reflects the balance between the increased disorder of the ions and the increased order of the solvent molecules that surround them. A salt dissolves spontaneously (is soluble) when the combination of these enthalpy and entropy effects yields a negative ΔG, a condition that is often dependent on temperature.