Which of the following statements about Raoult's law for a dilute solution of a non-volatile solute in a volatile solvent are CORRECT?
A: The vapour pressure of the solution is less than that of the pure solvent.
B: The relative lowering of vapour pressure equals the mole fraction of the solute.
C: Raoult's law is applicable only for volatile solvents.

Francois-Marie Raoult (1886-1887) conducted extensive experimental studies on the vapour pressure of solutions and discovered the fundamental relationship that now bears his name. For an ideal solution containing a volatile solvent (component 1) and a non-volatile solute (component 2), the partial vapour pressure of the solvent above the solution is directly proportional to the mole fraction of the solvent: P1 = x1 * P1(pure) = (1 - x2) * P1(pure). Since x2 > 0 (there is some solute), x1 < 1, and therefore P1 < P1(pure): the vapour pressure of the solution is always lower than that of the pure solvent when a non-volatile solute is present. The physical explanation is straightforward: in the pure solvent, all surface molecules are solvent molecules that can evaporate. When solute is dissolved, some surface positions are occupied by solute molecules (which do not evaporate, being non-volatile), reducing the fraction of the surface from which solvent can escape and thereby reducing the rate of evaporation. Since at equilibrium the rate of condensation must equal the rate of evaporation, the equilibrium vapour pressure is lower. The reduction in vapour pressure is directly proportional to the mole fraction of the solute: (P1(pure) - P1) / P1(pure) = x2. This quantity, the relative lowering of vapour pressure, is a colligative property — it depends only on the number of solute particles, not their chemical nature.

Colligative properties are solution properties that depend only on the number of dissolved particles (molecules or ions) per unit volume or per unit mass of solvent, and not on the chemical identity of the solute particles. This makes them extraordinarily useful for determining molecular masses of unknown solutes and for understanding the behaviour of solutions. Four major colligative properties: Lowering of vapour pressure: delta_P = P1(pure) - P1 = x2 * P1(pure). Elevation of boiling point: delta_Tb = Kb * b2, where Kb is the molal elevation constant (Ebullioscopic constant) and b2 is the molality of the solution. Kb = R * M1 * Tb^2 / (1000 * delta_vap H) where M1 = molar mass of solvent, Tb = boiling point of pure solvent, delta_vap H = enthalpy of vaporisation. For water: Kb = 0.52 K kg/mol. Depression of freezing point: delta_Tf = Kf * b2, where Kf is the molal depression constant (Cryoscopic constant). For water: Kf = 1.86 K kg/mol. This is why antifreeze (ethylene glycol or CaCl2) is added to automobile radiators and salt is spread on icy roads. Osmotic pressure: pi = M * R * T (van't Hoff equation, valid for dilute solutions). Osmotic pressure is the pressure that must be applied to a solution to prevent osmotic flow of pure solvent through a semi-permeable membrane separating the solution from the pure solvent.

One of the most powerful practical applications of colligative properties is the experimental determination of the molar mass (molecular weight) of substances — particularly large molecules like proteins, polymers, and polysaccharides — by measuring the magnitude of a colligative property depression or elevation. From boiling point elevation: M2 = Kb * w2 / (delta_Tb * w1) where w2 = mass of solute (g), w1 = mass of solvent (kg), delta_Tb = observed boiling point elevation (K). Similarly for freezing point depression. For high molecular weight substances like proteins: osmotic pressure measurement is most practical because: osmotic pressure is very sensitive (1 g/L protein in water gives about 1 mmHg osmotic pressure but only about 0.0001°C freezing point depression), measurable over a wide concentration range, and does not require the solute to be volatile. The molecular masses of proteins determined by osmotic pressure measurements historically were critical in establishing their large molecular weights (before modern mass spectrometry).

Ideal solutions obey Raoult's law over the entire composition range, but most real solutions deviate from ideal behaviour — some more than others. Positive deviation from Raoult's law occurs when the total vapour pressure exceeds that predicted by Raoult's law (P_observed > P_Raoult). This indicates that solute-solvent intermolecular interactions are weaker than the average of the solvent-solvent and solute-solute interactions, so molecules tend to escape from the liquid more readily. Examples: acetone-CS2, acetone-ethanol, ethanol-hexane, water-ethanol, chloroform-diethyl ether. Large positive deviations can result in the formation of a minimum boiling azeotrope (a mixture that boils at a lower temperature than either pure component and distils without change in composition): ethanol-water forms a minimum boiling azeotrope at 95.6% ethanol by mass and 78.1°C (lower than the boiling point of pure water at 100°C or pure ethanol at 78.4°C). Negative deviation from Raoult's law occurs when the total vapour pressure is lower than predicted (P_observed < P_Raoult), indicating stronger solute-solvent interactions than the pure component interactions: examples include acetone-chloroform (the C=O of acetone forms H-bonds with the CHCl3 hydrogen), water-H2SO4, water-HCl, water-HNO3. Large negative deviations can lead to maximum boiling azeotropes (boil at higher temperature than either component): water-HCl forms a maximum boiling azeotrope at 20.2% HCl and 108.6°C.

While Raoult's law describes the vapour pressure of the solvent component of a solution (or of solutions where both components are volatile and similar in nature), solutions containing dissolved gases obey a different empirical law discovered by William Henry (1803): Henry's law states that at constant temperature, the amount of a gas dissolved in a liquid is directly proportional to the partial pressure of that gas above the liquid: m = Kh * p, or equivalently p = KH * x (where x is the mole fraction of the dissolved gas and KH is the Henry's law constant, which depends on the gas, the solvent, and the temperature). The physical basis of Henry's law is similar to Raoult's law: at higher partial pressure, more gas molecules strike the liquid surface per unit time, driving dissolution until the rate of escape from solution equals the rate of dissolution. Henry's law is the basis of several important practical phenomena: carbonation of beverages (dissolving CO2 under pressure, released when bottle is opened and pressure drops), diving physiology (bends/decompression sickness from N2 dissolving in blood under high pressure at depth, forming bubbles on rapid ascent), gas absorption in industrial processes, and the calculation of blood oxygen content at different altitudes.

The colligative properties of electrolyte solutions are significantly larger than predicted for the same molality of a non-electrolyte solute, because electrolytes dissociate into multiple ions upon dissolution, each ion contributing independently to colligative properties. The van't Hoff factor i = (actual number of particles in solution) / (number of formula units dissolved) = observed colligative property / expected colligative property for non-electrolyte. For a strong electrolyte completely dissociating into n ions per formula unit: i_theoretical = n. NaCl (n=2): i_theoretical = 2, but experimentally i ≈ 1.87 at 0.1 m concentration. MgSO4 (n=2): i ≈ 1.21 at 0.1 m. The difference between theoretical and experimental i is due to ion-ion interactions (Debye-Huckel theory): in solution, each ion is surrounded by an ionic atmosphere of oppositely charged ions, and the behaviour of the solution deviates from the ideal of completely independent ions. As concentration decreases, i approaches its theoretical maximum value, reaching i_theoretical only at infinite dilution where interionic forces vanish. For weak electrolytes: i depends on the degree of dissociation alpha: for an electrolyte dissociating into n ions, i = 1 + (n-1)*alpha. This allows calculation of the degree of dissociation from colligative property measurements, which is how early physical chemists measured dissociation constants of weak acids before modern electrochemical and spectroscopic methods became available.