3: Solubility

For most gases, increasing temperature decreases solubility because dissolved gas molecules escape more readily from the liquid. Increasing pressure generally increases gas solubility, as described by Henry’s law. Therefore, the combination of high temperature and low pressure produces both unfavorable effects and is most likely to give the lowest aqueous solubility. The other choices include lower temperature or higher pressure.

At constant temperature, Henry's law gives p = KHx, where x is the mole fraction of dissolved gas and KH remains constant. Therefore x is directly proportional to pressure. If the original x is 0.02, doubling the pressure gives x = 2 × 0.02 = 0.04, under the ideal proportionality assumed in the question.

Recrystallization uses the difference in solubility between hot and cold solvent. The impure solid is dissolved in a minimum amount of hot solvent, and cooling lowers the solubility so the desired compound crystallizes. Suitable impurities may remain in the mother liquor or be removed earlier. Simple filtration alone cannot purify a dissolved solid.

Gas particles are far apart and gases are highly compressible. Changing pressure therefore changes the gas concentration in contact with a liquid and strongly affects how much gas dissolves. Solids and liquids are much less compressible, so their solubilities usually show a comparatively small pressure effect under ordinary conditions. Solids of course do contain particles.

Represent gas dissolution as gas + liquid ⇌ dissolved gas + heat. When temperature is increased, heat behaves like an added product. By Le Chatelier’s principle, the equilibrium shifts in the direction that consumes some of this added heat, namely toward the reverse process. Consequently, less gas remains dissolved. The system does not convert all gas to a solid, and a shift does occur.

At constant temperature, increasing partial pressure tends to increase gas solubility according to Henry's law. However, increasing temperature generally decreases gas solubility. When both variables change in opposite directions, the net result depends on the magnitudes of the two effects and cannot be stated with certainty without more data.

Using the mole-fraction form of Henry’s law, p = KHx, rearrange to x = p/KH. At fixed pressure, a larger Henry’s law constant gives a smaller dissolved-gas mole fraction x. Therefore, the gas is less soluble. The constant is not a direct measure that rises with solubility; in this convention, a large KH indicates lower solubility, while an infinite solubility is impossible.

At depth, high pressure can cause more inert gas, especially nitrogen, to dissolve in body tissues and fluids. If a diver rises too rapidly, the pressure falls quickly and dissolved gas can form bubbles, causing decompression sickness. A controlled, gradual ascent and appropriate decompression procedures allow gas to leave more safely.

For an endothermic dissolution, heat behaves like a reactant in the dissolution equilibrium. Raising the temperature supplies heat and generally favors the forward process, allowing more solute to dissolve. Therefore solubility tends to increase. The exact behavior can depend on the system, but under the stated idealized condition option A is the correct trend.

In an exothermic dissolution, heat is released as the solute dissolves. Increasing temperature adds heat to the system, so Le Chatelier's principle predicts a possible shift toward undissolved solute and a decrease in solubility. The word ‘may’ is important because real solubility curves can depend on additional factors and are not identical for every solid.

Recrystallization by cooling depends on a large difference between solubility in hot and cold solvent. If solubility changes only slightly, cooling removes only a small amount of solute, so the crystal yield is low. Choosing a suitable solvent, filtration, and impurity removal are general purification steps, but the specific cooling method is least effective here.

A useful crystallization solvent dissolves a substantial amount of the substance when hot but only a small amount when cold. On cooling, the solubility falls and excess solute separates as crystals, while suitable impurities remain dissolved or can be removed by filtration. Colour, name length, and gaseous state are not selection criteria.

Dissolution requires separation of solute particles and solvent particles followed by formation of solute–solvent attractions. Polar molecules possess partial charges and can form dipole–dipole attractions, hydrogen bonds, or ion–dipole interactions with suitable polar molecules. These favorable interactions support mixing. Colour, equal mass, and physical state do not explain the general trend.

Molecular iodine, I2, is non-polar because the two identical iodine atoms share electrons symmetrically. Carbon tetrachloride is also non-polar, so iodine can interact with it through suitable dispersion forces. Water is strongly polar and does not solvate non-polar iodine efficiently. Thus the statement that water is non-polar or carbon tetrachloride is polar is incorrect.

An ionic solid contains positive and negative ions held in a crystal lattice. Polar water molecules orient their partial charges around these ions and form ion–dipole attractions, often called hydration interactions. If these interactions sufficiently compensate for separating the lattice, ions enter the solution. Ion–ion and water–water attractions exist, but by themselves they do not promote dissolution.

Dissolution of an ionic solid involves separating ions from the crystal lattice and stabilizing them in water. Strong hydration or ion–dipole interactions favour separation, while strong lattice attraction opposes it. The actual result depends on the overall energy and entropy changes, so merely being ionic does not guarantee high solubility. Colour and absence of water cannot increase dissolution.

Solubility is an equilibrium property: at specified conditions, it indicates the maximum amount that can remain dissolved. The rate of dissolving is a kinetic property and describes how quickly that state is approached. Stirring and smaller particles usually increase the rate by improving contact, but they do not necessarily change the equilibrium solubility at fixed temperature and pressure.

Grinding divides a solid into smaller particles and increases its total surface area. More surface is available for solvent molecules to collide with, so the solute reaches equilibrium more quickly. However, at the same temperature, pressure, and solvent composition, the equilibrium amount that can dissolve is generally unchanged. Thus particle size affects speed, not the final solubility limit.

Saturation is defined relative to a particular amount of solvent at a particular temperature. When extra solvent is added, the total solvent mass increases, so its capacity to dissolve solute also increases. If no extra solute is supplied, the original amount is now below the new saturation limit; therefore the solution becomes unsaturated. No automatic disappearance or pressure doubling is involved.

Evaporation removes solvent while the amount of dissolved solute initially remains nearly the same. Consequently, the solute-to-solvent ratio rises above the saturation limit for the remaining solvent. The excess solute can then crystallize or precipitate until the remaining solution is saturated again. The solution does not become unsaturated, and its intrinsic solubility need not increase at constant temperature.

Pressure has its clearest effect on gases because gases are highly compressible and their dissolution is related to the gas’s partial pressure. Solids and liquids are much less compressible, so changing pressure usually produces only a small effect on their solubility under ordinary conditions. Thus pressure is not irrelevant, but its effect is not equally large for every solute and solvent system.

Mole fraction is the number of moles of a component divided by the total number of moles of all components. Expressing dissolved gas in this form directly indicates its proportion in the solution and makes it convenient to use Henry’s law, commonly written as p = K_H x. It does not describe colour, taste, or container size.

Dissolution requires disruption of attractions within the solute and solvent and formation of new attractions between them. If the new solute–solvent interactions are sufficiently strong or favourable, the energetic cost of separation can be compensated and mixing becomes more likely. This comparison is a useful qualitative guide; entropy and the complete energy balance also influence the actual solubility.

Two liquids are completely miscible when they can mix in all proportions to form one homogeneous phase. This is favoured when interactions between unlike molecules are comparable to, or sufficiently compatible with, the interactions in each pure liquid. Molecular polarity and hydrogen bonding can be important. Equal colour, container, or solid state has no bearing on miscibility.

Water is polar and ethanol contains a polar hydroxyl group, –OH. The hydrogen attached to oxygen and the oxygen’s lone pairs allow water and ethanol molecules to form hydrogen bonds with one another. These favourable interactions support extensive mixing, so they are miscible. Ethanol also has a non-polar ethyl group, but that does not make the whole molecule non-polar or prevent mixing with water.