The concept of free energy change in the dissolution process

Dissolution is the process where a solid, like a salt, dissolves into a solvent, forming a solution. The feasibility of this process is determined by the free energy change, denoted as ∆G°, which indicates whether the dissolution is spontaneous or not. A negative ∆G° means the process happens naturally, while a positive value suggests it does not occur under standard conditions.

Free energy change (∆G°)

Free energy change (∆G°) is a measure of the energy available to do work during a chemical process at constant temperature and pressure. In dissolution, it determines if a salt will dissolve in a solvent.

Spontaneity and equilibrium:

• If ∆G° < 0, the dissolution is spontaneous, meaning the salt will dissolve without external energy input.
• If ∆G° > 0, the process is non-spontaneous.
• At equilibrium, ∆G = 0, indicating a balance between dissolved and undissolved solute.

This free energy change ties directly to the solubility of a salt, which is the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature.

Factors affecting the free energy of dissolution

The free energy change for dissolution is influenced by several key factors at the particulate level. These factors involve interactions between particles in the solid, solvent, and solution, and they collectively determine whether a salt will dissolve.

Key factors in free energy of dissolution

• Breaking intermolecular interactions in the solid - This refers to overcoming the forces (like ionic or covalent bonds) holding the solid lattice together. Breaking these bonds requires energy, contributing positively to ∆G° (unfavorable for spontaneity).
• Reorganization of solvent molecules - When a solute dissolves, solvent molecules must rearrange to accommodate the dissolved particles. This reorganization can either increase or decrease the order of the system, affecting the energy change.
• Interaction of dissolved species with solvent - Once dissolved, solute particles interact with solvent molecules, often forming new bonds or attractions (like hydration shells around ions). These interactions typically release energy, contributing negatively to ∆G° (favorable for spontaneity).

Predicting the overall ∆G° is complex because these factors can cancel each other out or combine in unpredictable ways, making it challenging to determine if dissolution will occur just by looking at individual contributions.

The role of enthalpy and entropy in solubility

The free energy change (∆G°) is related to two fundamental thermodynamic quantities: enthalpy (∆H°) and entropy (∆S°). These components help explain why some salts dissolve easily while others do not, connecting microscopic interactions to the observable property of solubility.

Enthalpy (∆H°) in dissolution

Enthalpy change (∆H°) represents the heat absorbed or released during dissolution at constant pressure. It reflects the energy changes from breaking and forming bonds.

Types of enthalpy changes:

• Endothermic process - If ∆H° > 0, energy is absorbed to break the solid lattice, often making dissolution less favorable unless other factors compensate.
• Exothermic process - If ∆H° < 0, energy is released due to strong solute-solvent interactions, favoring dissolution.
• Estimating ∆H° - The sign of ∆H° can often be estimated by considering the strength of bonds broken in the solid versus those formed with the solvent. For example, ionic salts dissolving in water often have a negative ∆H° due to strong ion-water interactions.

Entropy (∆S°) in dissolution

Entropy change (∆S°) measures the change in disorder or randomness of the system during dissolution. It reflects how the organization of particles changes.

Changes in system disorder:

• Increase in disorder - Typically, dissolution increases entropy (∆S° > 0) because solid particles become dispersed in solution, increasing randomness. This favors spontaneity.
• Decrease in disorder - In rare cases, entropy might decrease (∆S° < 0) if solvent molecules become highly ordered around solute particles, which can oppose dissolution.
• Estimating ∆S° - The sign of ∆S° can often be predicted by considering whether the system becomes more or less ordered. For most salts, the transition from a structured solid to dispersed ions results in a positive ∆S°.

Relating ∆G°, ∆H°, and ∆S° through the Gibbs equation

The relationship between free energy, enthalpy, and entropy is given by the Gibbs free energy equation, which helps predict the spontaneity of dissolution under different conditions.

Formula for Gibbs free energy:

$\mathrm{\Delta }{G}^{\circ }=\mathrm{\Delta }{H}^{\circ }-T\mathrm{\Delta }{S}^{\circ }$

Where:

• ∆G° = Standard free energy change (kJ/mol)
• ∆H° = Standard enthalpy change (kJ/mol)
• T = Absolute temperature (K)
• ∆S° = Standard entropy change (kJ/mol·K)

This equation shows that a negative ∆H° (exothermic) and a positive ∆S° (increased disorder) both contribute to a negative ∆G°, favoring dissolution. However, the temperature (T) plays a critical role in determining how much entropy affects the overall free energy change.

Connections between particulate-level interactions and macroscopic solubility properties

The solubility of a salt, a macroscopic property, is directly linked to the particulate-level interactions discussed earlier. By analyzing these microscopic processes, we can better understand why some salts are highly soluble while others are not.

Bridging microscopic and macroscopic properties

• Lattice energy and solubility - At the particulate level, the strength of the solid lattice (lattice energy) determines how much energy is needed to break it apart. Salts with high lattice energy (strong bonds) tend to have lower solubility because breaking those bonds is energetically unfavorable.
• Solvation energy and solubility - The interaction between solute and solvent particles (solvation or hydration energy for water) influences solubility. Strong solute-solvent attractions increase solubility by lowering ∆H°, making dissolution more favorable.
• Entropy effects on solubility - The change in disorder from solid to solution impacts solubility. For instance, a significant increase in entropy (positive ∆S°) can drive dissolution even if ∆H° is positive, especially at higher temperatures.
• Temperature dependence - The Gibbs equation shows that temperature affects how entropy contributes to ∆G°. For salts with positive ∆H° and positive ∆S°, increasing temperature often enhances solubility by amplifying the -T∆S° term.

By modeling these particulate interactions, we can predict and explain the macroscopic behavior of salts in solution. However, the interplay of these factors means that solubility predictions are not always straightforward, as competing effects may balance each other out.