Factors affecting solubility Knowledge-Based Study

Study notes

1. What is Solubility?

   Solubility is the maximum amount of a solute that can dissolve in a given amount of solvent at a specified temperature and pressure to form a stable, saturated solution.

   A solution can be classified based on the amount of dissolved solute:

   • Unsaturated solution: Contains less solute than the solvent has the capacity to dissolve at that temperature.
   • Saturated solution: Contains the maximum amount of solute that can dissolve at dynamic equilibrium.
   • Supersaturated solution: Contains more dissolved solute than a saturated solution at the same temperature, usually prepared by cooling a saturated solution carefully without disturbance.

   Note: It is essential to distinguish between the rate of dissolution (how fast a substance dissolves) and solubility (the maximum capacity of dissolution). Factors such as stirring and particle size (surface area) change the rate of dissolution, but they do not alter the solubility value.

   Intermolecular Forces: "Like Dissolves Like"

   The primary factor determining whether a substance dissolves in a liquid is the compatibility of their intermolecular forces, summarized by the rule "like dissolves like".

   • Polar solutes dissolve in polar solvents: Substances with permanent dipole moments or hydrogen-bonding capabilities (such as ethanol, glucose, and ionic salts like NaCl) dissolve well in polar solvents like water ($H_2O$). Solvation or hydration occurs when attractive forces between solute particles and solvent molecules overcome solute-solute and solvent-solvent attractions.
   • Nonpolar solutes dissolve in nonpolar solvents: Nonpolar compounds (such as iodine, $I_2$, or hydrocarbons like octane) interact mainly via London dispersion forces and dissolve readily in nonpolar liquids like hexane ($C_6H_{14}$) or carbon tetrachloride ($CCl_4$).
   • Immiscibility: When a polar liquid (such as water) and a nonpolar liquid (such as oil or gasoline) are mixed, the strong hydrogen-bonding network among water molecules excludes the nonpolar molecules, resulting in two separate phases.

   Temperature Dependence

   The effect of temperature on solubility depends on the physical state of the solute and the enthalpy change of the dissolution process ($\Delta H_{soln}$).

   1. Solid and Liquid Solutes

   Dissolution involves breaking solute-solute and solvent-solvent interactions (endothermic) and forming solute-solvent interactions (exothermic):

   • Endothermic Dissolution ($\Delta H_{soln} > 0$): Heat is consumed during dissolution. According to Le Chatelier's principle, increasing the temperature shifts the equilibrium toward dissolving more solute. Therefore, the solubility of most solid salts (such as $KNO_3$ and $NH_4Cl$) increases with rising temperature.
   • Exothermic Dissolution ($\Delta H_{soln} < 0$): Heat is released during dissolution. Increasing the temperature decreases solubility (for example, $Ce_2(SO_4)_3$).

   2. Gaseous Solutes

   Gas dissolution in liquids is almost universally exothermic because gas molecules enter a condensed liquid state with negligible solute-solute interactions to break:

   $$\text{Gas}(g) + \text{Solvent}(l) ightleftharpoons \text{Solution}(aq) + \text{Heat}$$

   As temperature increases, the kinetic energy of dissolved gas molecules increases, allowing them to overcome weak attractive forces and escape back into the gas phase. Consequently, the solubility of all gases in liquids decreases as temperature rises (e.g., thermal pollution reducing dissolved oxygen in natural waterways).

   Pressure and Henry's Law

   Pressure changes have practically no measurable effect on the solubility of liquids and solids because liquids and solids are virtually incompressible. However, pressure profoundly affects the solubility of gases.

   Henry's Law

   Henry's Law states that at a constant temperature, the solubility ($S$) of a gas in a liquid is directly proportional to the partial pressure ($P$) of that gas above the liquid:

   $$S = k_H \cdot P$$

   where $k_H$ is the Henry's law constant specific to the gas, solvent, and temperature.

   • Increasing Pressure: Compressing the gas above the liquid increases the collision rate of gas molecules with the liquid surface, shifting equilibrium and causing more gas to dissolve.
   • Decreasing Pressure: Releasing the external pressure causes dissolved gas to come out of solution rapidly. A common real-world example is opening a carbonated beverage: the release of pressurized $CO_2$ lowers the gas solubility, causing effervescence.