3: Solubility

For a component of a gas mixture, Henry’s law uses that component’s partial pressure, not automatically the total pressure of the mixture: p_i = K_H x_i. At constant temperature and with other relevant conditions unchanged, increasing p_i increases the equilibrium mole fraction x_i of that gas in the liquid. Thus, the gas with higher partial pressure is more soluble in the stated comparison.

Henry’s law gives a proportional relation between the partial pressure of a gas and its dissolved concentration or mole fraction for a specified gas–solvent system. The Henry constant changes with temperature, so comparisons using one constant require constant temperature. Container shape, colour, and absence of molecules are irrelevant.

Solubility is determined by the balance of interactions between solute particles and solvent molecules. Changing the solvent changes polarity, hydrogen bonding, dispersion forces, and other interactions. Thus a substance may be poorly soluble in water but soluble in another solvent. Insolubility in one solvent is not universal insolubility.

When undissolved solute remains in contact with a solution and equilibrium has been reached, dissolution and crystallization occur at equal rates. The liquid therefore contains the maximum equilibrium amount of solute at that temperature. The clear appearance does not mean pure solvent; it means the undissolved particles have settled or are absent from the sampled layer.

An unsaturated solution contains less dissolved solute than the equilibrium limit at its current temperature. Adding the same solute allows more particles to dissolve until the saturation concentration is reached. Any excess added after that point remains undissolved. Changing colour or container orientation does not define saturation.

Before opening, carbon dioxide is held at high pressure above the liquid, which favours its dissolution. Opening the bottle lowers the gas pressure and disturbs the equilibrium. The liquid is then supersaturated relative to the new pressure, so carbon dioxide escapes as bubbles until a lower dissolved concentration is reached. This loss of gas reduces fizz.

Solubility is an equilibrium property: it tells how much solute can dissolve under specified conditions. Rate of dissolving is a kinetic property: it tells how quickly the process occurs. Stirring and smaller particles can increase rate by improving contact, but they do not necessarily increase the final equilibrium solubility.

The observation directly compares the equilibrium amount of gas in water at two temperatures. The higher amount in cold water and lower amount in hot water show that, for this gas over the stated range, solubility decreases on heating. Gas particles gain enough energy to escape more readily; this differs from the common trend for many solids.

The stated solubility is the maximum equilibrium amount: 40 g solute can dissolve in 100 g water at that temperature. Since only 30 g is present in solution, the amount is 10 g below the limit and more solute could dissolve. A solution containing less than the limit is unsaturated, not saturated or supersaturated.

At that temperature, 40 g per 100 g water is the normal saturation limit. If 45 g remains dissolved, the solution contains 5 g more than the ordinary equilibrium amount. This can occur in a carefully prepared, undisturbed supersaturated solution. It is unstable and may crystallize when seeded or disturbed.

A solubility value is meaningful only with its conditions. It depends on the identity and amount of solute, the solvent, and usually temperature. For gases, pressure or partial pressure is especially important. Stating temperature and solvent prevents ambiguity, while pressure should also be included whenever the substance is a gas.

At constant temperature, Henry’s law gives p = K_H x. Since K_H remains constant, x is directly proportional to the partial pressure p. If the pressure changes from p to 4p, the corresponding mole fraction changes from x to 4x. Therefore, the dissolved gas mole fraction becomes four times its original value, provided the solution remains within the range where Henry’s law applies.

A supersaturated solution contains more dissolved solute than the equilibrium saturation limit at a specified temperature. It is usually prepared by dissolving extra solute at higher temperature and cooling carefully without nucleation. Because the state is metastable, a seed crystal or disturbance can cause rapid crystallization and return the solution toward saturation.

Solubility tells us the maximum mass of solute that can dissolve in a fixed mass of solvent at a specified temperature. For 80 g water, the maximum is 40 × 80/100 = 32 g. Only 28 g is present, which is less than 32 g, so more solute could still dissolve. Therefore, the solution is unsaturated; it is neither saturated nor supersaturated.

At a fixed temperature, the solubility ratio remains constant. The new water mass, 75 g, is half of the original 150 g. Therefore, the amount of solute needed for saturation is also half: 45 × 75/150 = 22.5 g. Thus, 22.5 g will produce saturation. The other values ignore the direct proportionality between solvent mass and saturated solute mass.

Recrystallization works because the desired substance is usually much less soluble in the cold solvent and separates as crystals on cooling. An impurity that remains highly soluble at low temperature does not crystallize readily; it stays dissolved in the liquid surrounding the crystals. This residual liquid is called the mother liquor. Hence, option B is correct.

Dissolving a gas in a liquid is generally favoured by lower temperature because the process is commonly exothermic. On heating, the equilibrium tends to release dissolved gas, so less oxygen remains in water. The water itself remains present; oxygen does not become an ionic solid, and pressure need not increase.

For most gases, dissolving in a liquid is favoured by increased pressure, as described by Henry’s law, because more gas molecules are forced into contact with the liquid. Gas dissolution is also generally favoured by lower temperature when the process is exothermic, which is the usual school-level case. Therefore, low temperature and high pressure give the highest likely solubility among these choices.

Solubility is an equilibrium property: at specified temperature and pressure, it indicates the maximum amount that can dissolve in a given amount of solvent. The rate of dissolving is a kinetic property and describes how quickly that process occurs. Stirring and smaller particles usually increase rate, but do not necessarily change equilibrium solubility.

Grinding sugar produces smaller particles and increases the total surface area exposed to water. More water molecules can contact the sugar at the same time, so the sugar dissolves faster. This changes the rate of reaching equilibrium, not necessarily the final equilibrium solubility at a fixed temperature. Therefore, the claim of an automatic tenfold solubility increase is incorrect, and option B is correct.

Powdering increases surface area and therefore increases the frequency of contact between the solid and solvent. The powdered sample will dissolve more rapidly than a large lump under otherwise identical conditions. However, because both substances have the same solubility, their final maximum dissolved amounts at equilibrium are not necessarily different. Thus B is correct.

Water is strongly polar, whereas most oils are non-polar. Polar water therefore does not provide sufficiently favourable interactions with oil molecules. A non-polar organic solvent can interact more suitably with oil, so the oil dissolves better there. This is summarized by the principle “like dissolves like”; it is not an absolute rule for every substance.

On a solubility-versus-temperature graph, a nearly horizontal curve has a very small slope. This means that a substantial temperature change produces only a small change in the amount dissolved. It does not mean the solubility is zero; it means the solubility is relatively insensitive to temperature. Therefore, option C is correct.

Solids and liquids have particles packed relatively closely and are generally very slightly compressible. Changing external pressure therefore produces little change in their volumes and usually has only a negligible effect on the solubility of a solid in a liquid. Gas solubility is different because gases are highly compressible and respond strongly to pressure.

A suitable recrystallization solvent dissolves the desired compound well when hot, so a concentrated solution can be prepared. On cooling, its solubility should fall substantially, allowing the compound to crystallize. Ideally, impurities either remain dissolved or can be removed by hot filtration. Colour and complete insolubility are not selection criteria.