9.6 Free Energy of Dissolution

When a salt dissolves in water, it involves a complex interplay of energy changes and disorder. This topic explores why some substances dissolve easily while others barely dissolve at all. Understanding dissolution requires examining both enthalpy (energy) and entropy (disorder) changes. The balance between these factors determines whether a salt will dissolve spontaneously and to what extent. By breaking down the dissolution process into its component steps, we can better predict and explain solubility trends across different compounds.

The Thermodynamics of Dissolution

Dissolution is more than just a salt "disappearing" in water. It's a process with distinct energy changes that we can analyze using thermodynamic principles.

Three Key Steps in Dissolution

When a salt dissolves, three main processes occur simultaneously:

Breaking the solid apart (lattice disruption):

• Ionic or intermolecular bonds in the solid must break

• This step requires energy (endothermic)
• This step increases disorder (positive entropy change)

Reorganizing the solvent (solvent reorganization):

• Water molecules must create spaces for the dissolved particles
• This typically requires some energy (slightly endothermic)
• This decreases disorder as water organizes (negative entropy change)

Solvating the ions/molecules (solute-solvent interaction):

• Water molecules surround and interact with dissolved particles
• This usually releases energy (exothermic)
• This can either increase or decrease disorder, depending on how structured the hydration shells are

The free energy change for the overall dissolution process combines all these factors:

ΔG°_dissolution = ΔG°_lattice + ΔG°_{reorganization} + ΔG°_solvation

Where each individual ΔG° depends on both enthalpy and entropy:

ΔG° = ΔH° - TΔS°

The table below summarizes the typical enthalpy and entropy changes for each step:

The Role of Enthalpy in Dissolution

The enthalpy change (ΔH°_dissolution) tells us whether the overall process absorbs or releases heat. It's the sum of the enthalpy changes from the three steps above.

For ionic compounds, we can think of this as:

ΔH°_dissolution = ΔH°_lattice + ΔH°_hydration

Where:

• ΔH°_lattice is the energy needed to break the ionic lattice (always positive)
• ΔH°_hydration is the energy released when ions are hydrated (always negative)

The overall enthalpy change determines whether dissolution is exothermic or endothermic:

When dissolution is exothermic (ΔH°_dissolution < 0):

• Heat is released when the substance dissolves
• The solution gets warmer
• The hydration energy outweighs the lattice energy
• Examples: NaOH, H₂SO₄, CaCl₂

When dissolution is endothermic (ΔH°_dissolution > 0):

• Heat is absorbed when the substance dissolves
• The solution gets colder
• The lattice energy outweighs the hydration energy
• Examples: NH₄NO₃, KCl, NaCl

The strength of these enthalpy effects depends on several factors:

For lattice energy (breaking the solid):

• Smaller ions form stronger lattices (harder to break)
• Higher charges form stronger lattices (harder to break)
• More closely packed crystals have stronger lattices

For hydration energy (solvating the ions):

• Smaller ions have stronger hydration (more exothermic)
• Higher charged ions have stronger hydration (more exothermic)
• The dipole nature of water is crucial for strong ion-dipole interactions

The Role of Entropy in Dissolution

Entropy change (ΔS°_dissolution) measures how disorder changes during dissolution. Like enthalpy, it reflects all three steps of the dissolution process.

For most solid-to-solution processes:

• Breaking up the orderly solid increases disorder (positive ΔS°)
• Creating organized solvent shells around ions decreases disorder (negative ΔS°)

The balance of these effects determines the overall entropy change:

For ionic and most polar compounds:

• Small, highly charged ions cause significant water organization (large negative ΔS°)
• Larger ions with distributed charge create less water organization (smaller negative ΔS° or even positive)

For dissolution of gases in water:

• Entropy change is usually negative (decreased disorder)
• Free gas molecules have more disorder than dissolved ones
• This explains why gas solubility decreases with increasing temperature

For dissolution of liquids in liquids:

• Entropy changes are typically small
• Can be either positive or negative depending on the specific interactions

Predicting Solubility Trends

Understanding the enthalpy and entropy factors helps us predict whether a salt will dissolve and how temperature will affect its solubility.

The Overall Free Energy of Dissolution

For a salt to dissolve spontaneously, the free energy change must be negative:

ΔG°_dissolution = ΔH°_dissolution - TΔS°_dissolution < 0

This gives us several possible scenarios:

This explains why:

• Most endothermic dissolution processes show increased solubility at higher temperatures
• Most exothermic dissolution processes show decreased solubility at higher temperatures
• Some compounds are practically insoluble regardless of temperature

Factors Complicating Solubility Predictions

While the thermodynamic principles are straightforward, predicting solubility can be challenging because:

Multiple factors often cancel each other out:

• Lattice energy and hydration energy are both large but opposite in sign
• Small changes in either can flip the overall enthalpy from positive to negative
• Similar cancellations occur with entropy changes

Ion size and charge create competing effects:

• Smaller ions form stronger lattices (reducing solubility)
• Smaller ions also have stronger hydration (increasing solubility)
• The net effect depends on which factor dominates

Solvent properties matter significantly:

• Polar solvents better dissolve ionic compounds
• Nonpolar solvents better dissolve nonpolar compounds
• The dielectric constant of the solvent affects how it interacts with ions

Common ion effects and other solutes change the picture:

• The presence of common ions decreases solubility
• Other dissolved substances can affect the solvent's ability to dissolve more solute
• pH can dramatically affect the solubility of some compounds

Examples and Applications

The principles of dissolution thermodynamics explain many everyday observations and important chemical processes.

Common Salt Examples

Sodium chloride (table salt, NaCl):

• Slightly endothermic dissolution (ΔH° ≈ +3.9 kJ/mol)
• Small positive entropy change (ΔS° ≈ +43 J/mol·K)
• Spontaneous dissolution at room temperature because TΔS° > ΔH°
• Solubility increases slightly with temperature (typical for endothermic dissolution)

Lithium chloride (LiCl):

• Exothermic dissolution (ΔH° ≈ -37 kJ/mol)
• The Li⁺ ion is small and forms strong hydration shells
• Hydration energy outweighs the lattice energy
• Solubility decreases with increasing temperature

Calcium sulfate (CaSO₄):

• Very low solubility in water
• Both Ca²⁺ and SO₄²⁻ are doubly charged ions
• Creates a strong ionic lattice that's difficult to break
• Hydration energy isn't enough to overcome the lattice energy
• Slightly endothermic dissolution, so solubility increases slightly with temperature

Real-World Applications

Understanding dissolution thermodynamics helps explain:

Cold packs and hot packs:

• Instant cold packs often contain NH₄NO₃, which has a strongly endothermic dissolution
• Heat packs may use CaCl₂, MgSO₄, or other salts with exothermic dissolution

Water treatment and purification:

• Selective precipitation based on solubility differences
• Temperature adjustments to optimize dissolution or precipitation
• Addition of ions to force precipitation of contaminants

Pharmaceutical development:

• Drug solubility affects bioavailability
• Designing more soluble forms of medications
• Creating controlled-release formulations based on solubility principles

The thermodynamics of dissolution provides powerful tools for predicting and controlling solubility. By analyzing the enthalpy and entropy changes associated with breaking the solid lattice, reorganizing the solvent, and creating solute-solvent interactions, we can better understand why substances dissolve as they do. Though precise predictions can be challenging due to the competing factors involved, the fundamental principles help explain solubility trends and guide practical applications across chemistry, medicine, and industry.