Factors Affecting Solubility

The extent to which a substance dissolves in a solvent varies greatly with different substances. It depends on the nature of solute and solvent, temperature and pressure.

i. Nature of solute and solvent : Generally the compounds with similar chemical character are more readily soluble in each other than those with entirely different chemical characters. The saying that 'like dissolves like' guides us in predicting the solubility of a solute in a given solvent. Thus, substances having similar intermolecular forces are likely to be soluble in each other. Generally polar solutes dissolve in polar solvents: in these, the solute-solute, solute-solvent and solvent-solvent interactions are all of similar magnitude. For example, NaCl dissolves in water -- the strong ion-dipole interactions of $\mathrm{Na^+}$ and $\mathrm{Cl^-}$ ions with water molecules, the hydrogen bonding between water molecules, and the ion-ion attractions between $\mathrm{Na^+}$ and $\mathrm{Cl^-}$ ions are all comparable. (The textbook prints these ionic charges in its circled style, as Na$^{\oplus}$ and Cl$^{\ominus}$.) Nonpolar organic compounds like cholesterol dissolve in nonpolar solvents such as benzene. Sugar dissolves in water! The dissolution of sugar in water is due to intermolecular hydrogen bonding between sugar and water.

ii. Effect of temperature on solubility : How the solubility of a substance changes with temperature depends on the enthalpy of solution. Many solids, for example KCl, dissolve in water by an endothermic process, that is, with the absorption of heat. When temperature is increased by adding heat to the system, the solubility of the substance increases according to the Le-Chatelier principle: the addition of heat causes a stress on the saturated solution, and this stress favours the endothermic process. On the other hand, when a substance dissolves in water by an exothermic process, its solubility decreases with an increase of temperature. Substances such as $\mathrm{CaCl_2}$ and $\mathrm{Li_2SO_4{\cdot}H_2O}$ dissolve in water releasing heat.

It is important to understand that there is no direct correlation between solubility and exothermicity or endothermicity. For example, the dissolution of $\mathrm{CaCl_2}$ in water is exothermic and that of $\mathrm{NH_4NO_3}$ is endothermic -- yet the solubility of these increases with the temperature.

Figure 2.1 shows the result of experimental determination of solubilities of some ionic solids in water at various temperatures. Following are some experimental observations from Fig. 2.1:

i. Solubilities of NaBr, NaCl and KCl change slightly with temperature.

ii. Solubilities of $\mathrm{KNO_3}$, $\mathrm{NaNO_3}$ and KBr increase appreciably with increasing temperature.

iii. Solubility of $\mathrm{Na_2SO_4}$ decreases with increase of temperature.

The solubility of gases in water usually decreases with an increase of temperature. When gases are dissolved in water, the gas molecules in the liquid phase are condensed. Condensation is an exothermic process, so the solubility of gases in water must decrease as temperature is raised.

iii. Effect of pressure on solubility : Pressure has no effect on the solubilities of solids and liquids, as they are incompressible. However, pressure greatly affects the solubility of gases in liquids: the solubility of a gas increases with increasing pressure. The quantitative relationship between gas solubility in a liquid and pressure is given by Henry's law.

Henry's law : It states that the solubility of a gas in a liquid is directly proportional to the pressure of the gas over the solution. Thus,

where $S$ is the solubility of the gas in $\mathrm{mol\,L^{-1}}$, $P$ is the pressure of the gas in bar over the solution, and $K_H$, the proportionality constant, is called Henry's law constant.

Units of $K_H$ : $K_H = \dfrac{S}{P} = \dfrac{\mathrm{mol\,L^{-1}}}{\mathrm{bar}} = \mathrm{mol\,L^{-1}\,bar^{-1}}$

When $P = 1$ bar, $K_H = S$. Thus, $K_H$ is the solubility of the gas in a liquid when its pressure over the solution is 1 bar.