3: Solubility

Crystallization relies on a substantial difference between solubility in hot and cold solvent. A solid whose solubility changes greatly can be dissolved in a small amount of hot solvent and then recovered efficiently on cooling. If solubility hardly changes, little material separates. Complete insolubility also prevents preparation of a suitable solution for crystallization.

For the convention p = K_H x, the dissolved mole fraction is x = p/K_H. At the same pressure, a gas with a larger x, meaning greater solubility, must have a smaller K_H. Thus, if the first gas is more soluble than the second under identical conditions, its Henry’s law constant is lower. The constants need not be zero, and they are directly related to solubility in this comparison.

A saturated solution contains the maximum amount of solute that can remain dissolved in its present amount of solvent at that temperature. When solvent evaporates, the solvent capacity decreases while the dissolved solute initially remains, so the solution becomes supersaturated temporarily. Excess solute may then crystallize or precipitate until the remaining solution is saturated again.

Fractional crystallisation separates solids by exploiting their different solubilities, especially the different changes in solubility with temperature. A mixture is dissolved, often hot, and then cooled so that the component whose solubility falls more sharply crystallises preferentially. Filtration alone cannot separate two substances that are both dissolved, and boiling into gas is not the general principle here.

At depth, elevated pressure allows more nitrogen and other gases to dissolve in body fluids. A rapid ascent produces a sudden pressure decrease, reducing gas solubility and allowing bubbles to form in tissues and blood. A slow ascent, often with planned decompression stops, gives gases time to leave gradually and reduces the risk of decompression sickness.

Dissolution of an ionic solid requires separation of its ions from the crystal lattice and stabilization of those ions by water molecules. Because water is polar, its molecules can surround and hydrate cations and anions. Strong ion-water attraction favours this step, although the final solubility also depends on lattice energy and the overall energy balance.

Consider a sparingly soluble salt AB in equilibrium with its ions: AB(s) ⇌ A⁺ + B⁻. Adding a soluble electrolyte that supplies A⁺ or B⁻ increases the concentration of that ion. The equilibrium shifts left to oppose the increase, causing more solid AB to remain and reducing its dissolution. Therefore, the common-ion effect decreases solubility, although other complexation or acid–base reactions can modify a specific case.

Adding one of the ions already produced by the salt increases a product concentration in its dissolution equilibrium. For example, adding A+ to AB(s) ⇌ A+ + B− causes the equilibrium to shift left according to Le Chatelier's principle. Some dissolved ions combine to form solid salt, so the equilibrium solubility decreases rather than increases.

The solubility product, Ksp, is the equilibrium constant for dissolution of a sparingly soluble ionic solid, with each ion concentration raised to its stoichiometric power. It describes the ion concentrations in a saturated solution and helps predict precipitation by comparing the ionic product Q with Ksp. It is not a colour, pressure, or container-size measurement.

For a sparingly soluble salt, the ionic product Q is calculated from the current ion concentrations, with powers given by the balanced dissolution equation. If Q exceeds K_sp, the solution contains more dissolved ions than equilibrium permits. The excess ions combine to form solid until the ion product falls to K_sp. Thus precipitation occurs. The solution does not become entirely gaseous, and ions do not all disappear.

When Q, the actual ionic product, is smaller than Ksp, the ion concentrations have not reached the equilibrium limit for precipitation. The solution is therefore unsaturated with respect to the solid and can dissolve more salt, if solid is available. Some ions may still be present; Q < Ksp does not mean that the solution contains no ions.

The ionic product Q compares the present ion concentrations with the equilibrium limit represented by K_sp. When Q = K_sp, the solution is at equilibrium with the solid phase and contains the maximum equilibrium amount of dissolved salt. It is therefore saturated. If Q is less than K_sp, the solution is unsaturated; if Q is greater than K_sp, precipitation is expected. Hence option A is correct.

For salts with the same ion ratio and comparable conditions, a larger Ksp indicates a larger equilibrium product of ion concentrations. This generally corresponds to a greater molar solubility, so that salt is more soluble. The qualification “similar type” matters: for salts with different stoichiometry, Ksp values cannot be compared directly without calculating solubility from the correct expression.

For a salt, precipitation is expected when the actual ionic product Q becomes greater than Ksp. Keeping Q below Ksp keeps the solution unsaturated with respect to that solid, so precipitation is not thermodynamically required. At Q = Ksp the solution is just saturated; keeping Q much greater would favour precipitation rather than prevent it.

Slow cooling lowers solubility gradually and gives solute particles enough time to arrange into a regular crystal lattice. Many impurities remain in the mother liquor instead of being trapped inside rapidly growing crystals. Rapid cooling can cause sudden nucleation, producing numerous small crystals that may retain impurities. Thus slow cooling usually improves crystal size and purity.

A solubility curve plots solubility against temperature. Its slope represents the change in solubility per unit change in temperature. A steep slope therefore means that a small temperature change produces a relatively large change in solubility. Such a substance may be suitable for recrystallisation by cooling. A flat curve would indicate little temperature dependence.

A nearly flat solubility curve means that changing temperature produces only a small change in the amount that dissolves. On cooling a hot solution, little solute will separate, so recovery by crystallisation is poor and purification becomes difficult. Good recrystallisation generally requires a large solubility at high temperature and a much smaller solubility at low temperature.

Reducing particle size increases surface area, so solvent can contact more solid and the material usually dissolves faster. However, once equilibrium is reached at a specified temperature and pressure, the final solubility is governed mainly by the chemical nature of the solute and solvent. Particle size does not make solubility infinite; it affects kinetics rather than the equilibrium amount.

Stirring continually brings fresh solvent into contact with the solid surface and removes the concentration boundary layer around dissolving particles. This usually increases the rate at which the system approaches equilibrium. It does not change the equilibrium solubility at fixed temperature and pressure, so the final maximum dissolved amount is not automatically doubled.

Henry's law constant is not universal; it depends on temperature, the gas, and the solvent. If the same solvent and temperature are used, comparing constants for different gases is straightforward at the same pressure: the lower K_H generally corresponds to greater solubility. If temperature or solvent changes, the constants themselves may change, so a direct comparison can be misleading.

Using p = K_H x, at a fixed gas pressure a larger K_H produces a smaller dissolved mole fraction x. Therefore, if K_H increases as temperature rises, the gas becomes less soluble at that higher temperature. This agrees with the usual behaviour of gases, whose dissolution in liquids is generally less favourable on heating. Pressure still affects solubility; its effect does not disappear.

A hot saturated solution can contain more dissolved solute than is normally stable at a lower temperature. If it is cooled carefully without shaking or introducing impurities, crystallisation may not start immediately, allowing the excess solute to remain temporarily dissolved. This metastable state is supersaturation. Removing all solvent cannot produce a solution, and zero pressure is not the defining condition.

A supersaturated solution contains more dissolved solute than the stable equilibrium amount at its current temperature. It is metastable, so a small disturbance can provide nucleation sites or initiate crystal growth. The excess solute then separates as crystals, bringing the solution closer to saturation. The disturbance does not destroy the solvent or necessarily increase pressure; crystallisation is the expected change.

At depth, increased pressure causes more gases, especially nitrogen, to dissolve in body fluids. A rapid ascent produces a rapid pressure drop, reducing gas solubility and allowing bubbles to form in tissues or blood. A slow ascent gives the body time to remove the gas gradually. The advice is therefore about controlled decompression, not temperature or loss of mass.

If heating allows more of a solid to dissolve, heat acts like a reactant that favours the dissolution equilibrium. This observation is therefore generally associated with an endothermic dissolution process. It is a useful qualitative inference, although the exact behaviour of a substance depends on its enthalpy and other solution effects. Pressure control or insolubility does not explain the temperature trend.