3: Solubility

When dissolution releases heat, heat behaves as a product in the equilibrium description. Increasing temperature can then shift the equilibrium toward the undissolved solid, causing solubility to decrease. Therefore the observation suggests, but does not by itself rigorously prove, an exothermic dissolution. The other choices do not describe the thermodynamic reason for the trend.

On cooling, the solubility of a suitable solid decreases and the excess solute separates from solution. Slow cooling allows molecules or ions to diffuse, select the proper lattice positions and grow into relatively large, well-ordered crystals. Impurities are more likely to remain in the mother liquor. Rapid cooling can trap impurities and produce many small or poorly formed crystals.

The slope of a solubility curve represents the change in solubility per unit change in temperature over the plotted range. A steep slope therefore means that even a modest temperature change produces a relatively large change in the amount that can dissolve. This temperature sensitivity can be useful in recrystallisation. A steep curve does not imply absence of solvent or a gaseous solute.

A nearly flat solubility curve means that changing temperature produces only a small change in solubility. Consequently, cooling a hot solution will separate only a small amount of solute, giving poor recovery and weak purification by crystallisation. Effective recrystallisation generally requires a substantial difference between hot and cold solubilities. Pressure is not the controlling idea for ordinary solid crystallisation.

Fractional crystallisation separates dissolved solids because their solubilities respond differently to temperature. On cooling or concentrating the solution, one component reaches its crystallisation condition before the other, so it can be removed preferentially. If both substances have identical solubility behaviour, they crystallise together and separation is poor. Complete insolubility or a purely gaseous mixture is not the intended situation.

Pressure has a large effect when a process involves a substantial change in volume, as in dissolving or compressing a gas. Solids and liquids have particles already packed closely together, so their volumes change very little under ordinary pressure changes. Their solubility may still depend on pressure in special high-pressure situations, but the effect is usually negligible compared with that for gases.

Dissolving an ionic crystal requires separating ions from the crystal lattice and solvating them in water. Strong ion–dipole attraction between the ions and polar water molecules stabilises the separated ions and can make dissolution favourable. The final outcome also depends on lattice enthalpy and entropy, so hydration is important but not the only factor. Keeping ions away from water would oppose dissolution.

For the same mass, smaller particles expose a larger total surface area to the solvent. This increases contact and usually speeds up the approach to equilibrium. However, at a fixed temperature and pressure, the equilibrium solubility is determined mainly by the chemical nature of solute and solvent, not by ordinary particle size. Thus particle size affects rate, while it normally does not change the final equilibrium amount.

Henry's law constant depends on temperature, solvent and the convention used for defining the constant. A fair comparison therefore requires the same temperature, solvent and relevant pressure range; then a lower K_H in the same convention indicates greater solubility at a given pressure. If temperature or solvent differs, the constants themselves may differ for reasons unrelated to the gas's intrinsic comparison.

Using the form p = K_H x, at fixed gas pressure the dissolved mole fraction is x = p/K_H. Thus, if K_H increases with temperature, x decreases under otherwise identical conditions. This agrees with the usual observation that heating drives many dissolved gases out of solution. The increase in K_H does not remove pressure dependence and does not imply complete insolubility.

At constant temperature, the maximum solute-to-solvent ratio that can remain dissolved is fixed by the solubility. Evaporation reduces the amount of solvent while the dissolved solute initially remains, so the solution becomes supersaturated relative to the new solvent amount. Excess solute then crystallises or precipitates until saturation is restored. Evaporation does not make the solution unsaturated or necessarily vaporise the solute.

Suppose a solution is saturated at the initial temperature, so its dissolved amount equals the old solubility limit. If heating increases the solubility of the solid, the new limit becomes larger while the actual dissolved amount has not instantly increased. The same solution is then unsaturated and can dissolve more solute. If solubility decreases on heating, crystallisation rather than unsaturation would be expected.

Dissolution requires solute particles to leave their original lattice or intermolecular environment and become dispersed in the solvent. If solvent molecules interact strongly and favourably with those particles, they stabilise the separated state and lower the tendency to return to the pure solute phase. This usually increases solubility, although lattice energy and entropy also contribute. Particles do not cease to exist or make the solvent gaseous.

Crystallisation on cooling requires a substantial decrease in solubility between the hot and cold temperatures. If the solubility curve is nearly flat, the cooled solution can still hold almost the same amount of solute, so little or no excess separates as crystals. A steep temperature increase in solubility would normally favour crystallisation, not explain its absence. Supersaturation is not forced by the observation.

At constant temperature, Henry's law gives a direct relationship between gas pressure and dissolved amount, so increasing pressure generally increases gas solubility. For most gases, increasing temperature makes escape from the liquid more favourable and reduces solubility. The two effects should be analysed separately and then combined. Exact behaviour can depend on the gas and range, so “generally” is appropriate for temperature.

At considerable depth, increased pressure allows more nitrogen and other gases to dissolve in body fluids. During a rapid ascent, pressure decreases before the dissolved gases can be safely removed through respiration. The gases may then come out of solution as bubbles, causing decompression sickness. The other options do not follow from pressure changes.

Treat dissolution as an equilibrium between the solid and dissolved particles. If heating increases the amount dissolved, heat acts like a factor that favours the forward dissolution process. This is consistent with an endothermic dissolution, for which heat is absorbed. The conclusion is general rather than absolute because some solids show different behaviour.

If dissolution releases heat, heating adds a product-like factor to the equilibrium and can shift it toward the undissolved solid. As a result, the solubility may decrease with temperature, indicating an exothermic dissolution. This is not determined by whether the solute is a metal or by the physical state of the solvent; those options provide no valid general explanation.

A supersaturated solution contains more dissolved solute than is normally stable at that temperature, so it is metastable. A disturbance or a seed crystal supplies a surface on which ordered particles can begin arranging. The excess solute then crystallises or precipitates until the ordinary saturation condition is approached. The solvent does not simply vanish and solubility does not become infinite.

A hot saturated solution can contain more solute than a cold solution can hold. During slow cooling, the excess solute leaves the solution gradually and its particles have time to arrange into an ordered crystal lattice. Many impurities remain in the mother liquor because their amounts are small or their solubility is different. Sudden evaporation, zero pressure, or destruction of solute is not the basis of crystallisation.

Crystallisation by cooling works best when the solute is much more soluble at high temperature than at low temperature. An almost flat solubility curve means that cooling produces only a small decrease in solubility, so only a small amount separates as crystals. Consequently, recovery and purification are difficult. Pressure is not the main controlling factor for ordinary solid solubility.

Fractional crystallisation separates components by exploiting differences in their solubilities, especially how those solubilities change with temperature. On cooling a solution, the component whose solubility falls more or is lower can crystallise preferentially, while the other remains relatively enriched in the mother liquor. If both components behave identically, this separation principle provides no useful selectivity.

Pressure significantly affects a process when the volume changes substantially. Solids and liquids are nearly incompressible, so their volumes and the volume change on mixing are usually small. Consequently, pressure produces only a minor change in their solubility. Gases are much more compressible, which is why pressure has a pronounced effect on gas solubility.

For a sparingly soluble salt such as AB, the equilibrium is AB(s) ⇌ A⁺ + B⁻. Adding a soluble compound that supplies A⁺ or B⁻ increases the concentration of a product ion. By Le Chatelier’s principle, the equilibrium shifts toward solid AB, so less salt dissolves. Hence, the common-ion effect generally decreases solubility.

For a sparingly soluble ionic salt, Ksp is the equilibrium product of the ion concentrations in its saturated solution. A small Ksp generally means that only small equilibrium concentrations of the ions are present, so the salt has low solubility. The exact comparison must account for the salt’s stoichiometry, because Ksp values of differently composed salts cannot always be compared directly.