3: Solubility

If dissolution releases heat, heat behaves like a product in the equilibrium description. Increasing temperature can therefore favour the reverse process, causing some dissolved material to leave the solution and lowering solubility. The result is not an absolute rule for every solid, but it is the thermodynamically consistent possible trend described here.

At fixed temperature and for a dilute solution, Henry’s law gives x proportional to p, where x is the dissolved mole fraction and p is the gas partial pressure. Therefore doubling p doubles x and the dissolved amount, provided the system remains in the range where Henry’s law applies. Heating usually has the opposite effect for gases.

In a gas mixture, total pressure is the sum of the partial pressures of all gases. Henry’s law for one selected gas uses that gas’s own partial pressure because it measures the molecules of that gas available at the liquid surface. The total pressure alone cannot show how much of the pressure belongs to the gas being considered.

Gas solubility is generally reduced by high temperature and increased by pressure. Low pressure therefore removes one favourable factor, while warm temperature adds an unfavourable one. Together they can produce especially low dissolved oxygen, making respiration harder for aquatic organisms. Actual oxygen levels also depend on mixing, photosynthesis, and consumption.

If solubility decreases on heating, the reverse trend may occur on cooling: solubility may increase. The cooled solution could then dissolve more solute rather than expel it, so crystallization is not necessary. The curve and actual conditions must be examined; the other choices make physically unjustified absolute claims.

At constant temperature, increasing pressure favours dissolution of a gas. For most gases, increasing temperature favours escape from the liquid and lowers solubility. When both variables change, the net result depends on the magnitudes and the gas–solvent system; it cannot be decided by considering only one effect or by claiming both act in the same direction.

These five pieces of information identify which solubility principle applies. Solute and solvent determine interactions; temperature changes many solubilities; pressure is central for gases; and saturation state tells whether more solute can dissolve or must separate. Organising the conditions before calculating prevents use of the wrong formula or trend.

At constant temperature, Henry’s law makes the dissolved mole fraction directly proportional to partial pressure. The pressure ratio is 2.0/0.5 = 4. Therefore, the new mole fraction is x₂ = x₁ × 4 = 0.01 × 4 = 0.04. Option B would correspond to only doubling the original mole fraction, while option C represents a decrease; neither matches the fourfold pressure increase.

High pressure at depth increases the amount of gas that can dissolve in blood and tissues. During a rapid ascent, ambient pressure falls before the excess gas can be removed safely. The dissolved gas can then nucleate and expand into bubbles, producing decompression sickness. Controlled ascent and decompression stops reduce this risk.

If dissolution is exothermic, heat appears as a product in the equilibrium description. Increasing temperature can therefore favour the reverse process and reduce the amount dissolved, giving a downward solubility trend. This is a consistency argument rather than an absolute rule for every solid, because lattice and hydration changes can also affect solubility.

Solubility is 30 g solute for every 100 g water. For 250 g water, use direct proportion: required solute = 30 × (250/100) = 30 × 2.5 = 75 g. Thus 75 g is needed for saturation, assuming the stated temperature remains unchanged and no volume or density correction is required.

Solubility is being expressed as grams of solute dissolved in 100 g of solvent. Since 36 g solute dissolves in 120 g water, use a direct proportion: solubility per 100 g water = (36/120) × 100 = 30 g. Thus, 30 g is the correct value. The value 36 g incorrectly keeps the original solvent mass, while 43.2 g reverses the scaling factor.

Pressure and temperature can produce opposite effects for a dissolved gas: increasing pressure generally increases solubility, whereas increasing temperature generally decreases it. Therefore, neither factor should be ignored. Their magnitudes or the wording of the question must be considered before deciding the net effect. Hence option C is safest.

Common salt is an ionic solid, so its positive and negative ions are held in a crystal lattice. Water is polar: its partially charged ends attract the ions and surround them, forming hydrated ions. This hydration stabilizes separated ions and can compensate sufficiently for the energy needed to break the lattice. Thus, hydration by polar water is the key reason, although the exact solubility also depends on lattice energy.

Dissolution of an ionic solid requires separation of its ions from the crystal lattice. Polar water can then surround and stabilize those ions through hydration. If the hydration energy and resulting stabilization are sufficiently favourable compared with the lattice forces, dissolution is more likely and solubility increases. A non-polar solvent or absence of solvent does not provide this ionic stabilization, so the other choices are unsuitable.

A steep upward curve means the substance is much more soluble at high temperature than at low temperature. A hot solvent can therefore dissolve a relatively large amount, while cooling sharply lowers the solubility and causes crystals to separate. This large hot–cold difference is desirable in recrystallization and improves recovery of crystals.

At constant temperature, increasing pressure generally increases gas solubility. However, heating generally decreases the solubility of a gas because dissolution is often exothermic. Since these changes act in opposite directions, the net result cannot be decided from only one factor. The relative size of the changes or additional data must be examined.

A supersaturated solution contains more dissolved solute than is stable at equilibrium, but crystallization may not begin spontaneously because a suitable starting surface is absent. The added crystal acts as a seed or nucleation centre. Solute particles attach to its orderly lattice and growth proceeds rapidly. It does not remove solvent or create infinite pressure.

Henry's law gives a simple proportional relation between the partial pressure of a gas and its dissolved concentration or mole fraction. Such relations work best when the solution is dilute and interactions are close to ideal. At high concentrations or with strong chemical reaction between gas and solvent, the simple law may fail or require modification. Hence A is correct.

Using the Class 12 form of Henry’s law, p = K_H x, the mole fraction of dissolved gas is x = p/K_H. At the same pressure, increasing K_H therefore decreases x, which means lower solubility. A high Henry’s constant indicates that comparatively greater pressure is required to dissolve the same amount of gas. It does not make solubility zero or depend on liquid colour.

For many solid solutes, dissolution absorbs heat from the surroundings. According to Le Chatelier's principle, increasing temperature favours the endothermic direction, so the equilibrium shifts toward more dissolved solute. This is a general trend, not an exceptionless rule: some solids dissolve exothermically and may become less soluble on heating. Thus A is the best answer.

For each gas, Henry’s law in this convention is p = K_H x, where p is the partial pressure and x is the mole fraction dissolved in the liquid. Since both gases have the same K_H, x is directly proportional to p. Thus, p₁ = 2p₂ gives x₁ = p₁/K_H = 2p₂/K_H = 2x₂. Therefore, the first gas has twice the mole fraction of the second.

With the convention p = K_H x, the dissolved mole fraction is x = p/K_H. At the same pressure, reducing K_H increases x, meaning more gas is dissolved. Thus a lower Henry's law constant corresponds to higher solubility in this chapter's convention. Other answer choices either reverse the relation or do not describe a meaningful gas-solubility quantity.

For an exothermic dissolution, heat is released when solute enters the solution. Treating heat as a product, an increase in temperature shifts equilibrium toward the undissolved solid according to Le Chatelier's principle. Consequently, solubility may decrease. The word may is important because real systems can involve additional effects, but the stated thermodynamic trend supports option A.

The temperature effect depends on the enthalpy change of dissolution. If dissolution is exothermic, heat behaves like a product; increasing temperature shifts the equilibrium toward the undissolved solid, so solubility can decrease. For an endothermic process, heating generally favours dissolution instead. Pressure of a liquid-solid system and solvent colour do not provide the relevant explanation here, so option A is correct.