5: Colligative Properties

Seawater contains dissolved salts and other solutes. These particles lower the vapour pressure of water, so the liquid must be heated to a slightly higher temperature before its vapour pressure equals atmospheric pressure. Consequently its boiling point is elevated. Seawater still produces vapour; it simply requires a higher temperature to boil.

For dilute solutions, colligative changes such as ΔTf, ΔTb, and π are proportional to effective particle concentration when solvent and temperature conditions are fixed. Therefore doubling the effective number of particles ideally doubles the corresponding effect. This proportional statement assumes the same solvent and no significant non-ideal interactions.

Every colligative calculation begins by identifying the effective number of dissolved particles. First determine the solute moles and then check whether dissociation or association changes the count; the van’t Hoff factor represents that correction. Once particle concentration is known, the appropriate formula can be applied.

Colligative properties are governed primarily by the number of effective solute particles in a given amount of solvent. The chemical identity matters only insofar as it determines whether particles dissociate or associate. Colour, smell, and container shape do not control vapour-pressure lowering, boiling-point elevation, freezing-point depression, or osmotic pressure.

Colligative properties depend mainly on the number of dissolved particles relative to the amount of solvent, not on the chemical identity of those particles. Osmotic pressure is one of the four standard colligative properties, along with relative lowering of vapour pressure, elevation of boiling point and depression of freezing point. Colour, shine and container thickness are not colligative properties.

Elevation in boiling point means that the boiling temperature of a solution is higher than that of the pure solvent under the same external pressure. A non-volatile solute lowers the solvent vapour pressure. Since boiling occurs when vapour pressure equals external pressure, the solution must be heated more to reach that condition. Thus the correct choice is A.

For a solution containing a suitable dissolved solute, the freezing point is lower than the freezing point of the pure solvent. Solute particles disturb the formation of the ordered solid structure and lower the solvent vapour pressure. Therefore the solution must be cooled to a lower temperature before solidification begins. This temperature difference is called depression in freezing point.

For a dilute solution, elevation in boiling point is expressed as ΔT_b = K_b m, or ΔT_b = iK_bm when the van't Hoff factor is needed. The symbol m denotes molality: moles of solute per kilogram of solvent. Because it uses solvent mass rather than solution volume, molality is not changed directly by temperature-related volume expansion and is preferred here.

The depression in freezing point is calculated from ΔT_f = K_f m for a non-electrolyte and from ΔT_f = iK_fm when particle dissociation or association is considered. K_f is the cryoscopic constant of the solvent, with units commonly expressed as K kg mol⁻¹. K_b belongs to boiling point elevation, while R and π have different meanings.

The relation for boiling point elevation is ΔT_b = K_bm for a non-electrolyte and ΔT_b = iK_bm when the effective number of particles differs from the expected number. K_b is the ebullioscopic constant of the solvent. K_f is used for freezing point depression; i is a correction factor, not the solvent constant itself.

Osmosis is the net movement of solvent through a semipermeable membrane toward the solution with higher effective solute concentration. The minimum external pressure that must be applied on the solution side to stop this net movement is called osmotic pressure. Vapour and partial pressures describe gases, not membrane flow.

Isotonic solutions have equal osmotic pressure at the same temperature. Across a membrane permeable to solvent but not solute, solvent molecules may move in both directions, but the two opposite flows balance each other. Therefore there is no net solvent flow and no volume change caused by osmosis. Isotonicity does not mean that the solutions boil or freeze.

For dilute solutions at the same temperature, osmotic pressure follows π = CRT, or π = iCRT when the van't Hoff factor is included. Thus, for comparable solutes and equal temperature, a higher osmotic pressure indicates a higher effective concentration of dissolved particles. It does not indicate a pure or particle-free solution; the temperature and particle factor must be considered in exact comparisons.

The van't Hoff factor is represented by i. It measures the ratio of the actual number of solute particles in solution to the number expected from the formula units initially dissolved. Dissociation generally makes i greater than 1, whereas association can make it less than 1. The symbols m, R and T represent molality, gas constant and temperature, respectively.

When sodium chloride dissolves in water, it separates substantially into Na+ and Cl− ions. One formula unit can therefore produce approximately two solute particles, increasing the effective particle concentration and the colligative effect. The exact factor may be below two in real solutions because dissociation is not perfectly ideal at all concentrations.

For a dilute solution, freezing point depression is ΔT_f = K_fm, or ΔT_f = iK_fm when the van't Hoff factor is included. If the amount of solvent is fixed and more solute is added, molality m and usually the number of dissolved particles increase. Therefore the magnitude of the depression increases and the solution freezes at a lower temperature. The change is not automatically zero or constant.

Osmosis requires a semipermeable membrane that permits solvent molecules to pass but restricts the relevant solute particles. This selective permeability creates a difference in solvent chemical potential and allows a net solvent flow. A solid metal sheet or wooden strip does not provide the required selective passage, and ordinary paper is not automatically semipermeable.

Across a semipermeable membrane, solvent generally moves from the side with higher solvent activity, usually the dilute solution, toward the side with lower solvent activity, usually the more concentrated solution. This net flow tends to dilute the concentrated side. Direction is determined by composition, not by whether the container is above or below.

Salt dissolves in the thin liquid layer on ice and produces a solution whose freezing point is lower than that of pure water. At a temperature between these two freezing points, pure water would remain solid, but the salt solution cannot freeze and existing ice melts to form more solution. This is freezing point depression, not a decrease in boiling point or merely a colour change.

An antifreeze solute, commonly used in a water-based coolant, lowers the freezing point of the liquid through a colligative effect. Thus the coolant can remain liquid at temperatures below the freezing point of pure water, helping prevent expansion-related damage. Its practical formulation can also address corrosion and heat transfer, but lowering freezing point is the concept tested here.

For a non-electrolyte solution, the elevation in boiling point is calculated using ΔT_b = K_bm. Substituting K_b = 0.52 and m = 1 gives ΔT_b = 0.52 × 1 = 0.52. The value is a temperature difference, not the final boiling temperature. The van't Hoff factor would multiply the result only if dissociation or association were specified.

The depression in freezing point is given by ΔT_f = K_fm for a non-electrolyte. Inserting the values gives ΔT_f = 1.86 × 0.5 = 0.93. Thus the solution's freezing point is 0.93 temperature unit lower than the pure solvent's freezing point. The answer is not 1.86 because the molality is one-half, and it is not a sum or double product.

Elevation in boiling point means that the solution's boiling point is higher than the pure solvent's value. Therefore use T_b(solution) = T_b°(solvent) + ΔT_b. Substitution gives 80 °C + 1.2 °C = 81.2 °C. Subtracting would describe the direction of freezing point depression, not boiling point elevation, while 1.2 °C alone is only the increase.

Depression in freezing point means that the solution freezes at a lower temperature. Hence T_f(solution) = T_f°(solvent) − ΔT_f. Using the given values, 5 °C − 2 °C = 3 °C. The value 7 °C would incorrectly add the depression, while 2 °C is only the magnitude of the change and not the final freezing point.

Two solutions are isotonic when they have equal osmotic pressure at the same temperature, so there is no net solvent flow across a suitable semipermeable membrane. Hypertonic and hypotonic describe solutions with respectively higher and lower osmotic pressure relative to a reference solution. Non-volatile refers to vapour behaviour, not osmotic equality.