Chapter 1: Solutions | Summary

The concentration of a solution can be expressed qualitatively (dilute or concentrated) or quantitatively using several units. Mass percentage (w/w) is the mass of solute per 100 g of solution; volume percentage (V/V) is the volume of solute per 100 mL of solution; mass by volume percentage (w/V) is mass of solute in 100 mL of solution, commonly used in medicine. Parts per million (ppm) is used for trace quantities and equals the number of parts of a component per 10^6 parts of the solution.

Mole fraction (x) is the ratio of moles of a component to the total moles of all components; its sum for all components always equals 1. Molarity (M) is moles of solute per litre of solution, while molality (m) is moles of solute per kilogram of solvent. Crucially, mass percentage, ppm, mole fraction, and molality are temperature-independent, whereas molarity changes with temperature because volume depends on temperature.

Solubility is the maximum amount of a substance that can be dissolved in a specified amount of solvent at a given temperature and pressure. It depends on the nature of the solute and solvent — the principle 'like dissolves like' applies, meaning polar solutes dissolve in polar solvents and nonpolar solutes in nonpolar solvents. When a solute is added to a solvent, dissolution and crystallisation occur simultaneously until dynamic equilibrium is reached, giving a saturated solution.

For solids in liquids, temperature significantly affects solubility: endothermic dissolution increases with temperature while exothermic dissolution decreases. Pressure has negligible effect on solid solubility as solids and liquids are nearly incompressible. For gases in liquids, solubility increases with pressure and decreases with temperature, as dissolution of a gas is an exothermic process governed by Le Chatelier's Principle.

Henry's law states that at constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. Mathematically, p = KH x, where p is the partial pressure, x is the mole fraction of the gas in solution, and KH is Henry's law constant. A higher KH value at a given pressure means lower solubility. KH is characteristic of both the gas and the solvent, and increases with increasing temperature, confirming that gas solubility decreases as temperature rises.

Henry's law has important applications: CO2 is dissolved in soft drinks by sealing bottles under high pressure; scuba divers breathe air diluted with helium to prevent 'bends' — a painful condition caused by nitrogen bubble formation in blood when pressure decreases too rapidly on ascent; at high altitudes, reduced oxygen partial pressure leads to anoxia in climbers. Raoult's law is a special case of Henry's law where KH equals the vapour pressure of the pure component.

Raoult's law states that for a solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction in solution: p1 = x1 p1° and p2 = x2 p2°. The total vapour pressure is the sum of partial pressures: ptotal = p1° + (p2° − p1°)x2. A plot of total vapour pressure against mole fraction is linear. The vapour phase is always richer in the more volatile component.

When a non-volatile solute is dissolved in a volatile solvent, only solvent molecules contribute to vapour pressure. Solute molecules occupy part of the surface, reducing the fraction of solvent molecules escaping, thereby lowering the vapour pressure. This lowering depends only on the number of solute particles (irrespective of their nature), and the relative lowering equals the mole fraction of the solute: (p1° − p1)/p1° = x2.

Ideal solutions obey Raoult's law over the entire concentration range and have ΔmixH = 0 and ΔmixV = 0 — no heat is evolved or absorbed on mixing and the volume is additive. This occurs when A–A, B–B, and A–B intermolecular interactions are nearly equal. Examples include n-hexane and n-heptane, benzene and toluene, bromoethane and chloroethane.

Non-ideal solutions deviate from Raoult's law. Positive deviations occur when A–B interactions are weaker than A–A or B–B (e.g., ethanol-acetone, acetone-CS2); ΔmixH > 0. Negative deviations occur when A–B interactions are stronger (e.g., chloroform-acetone, phenol-aniline); ΔmixH < 0. Azeotropes are binary mixtures with identical liquid and vapour compositions that boil at constant temperature and cannot be separated by fractional distillation. Large positive deviations form minimum boiling azeotropes (e.g., ethanol-water, ~95% ethanol); large negative deviations form maximum boiling azeotropes (e.g., HNO3-water, ~68% HNO3, bp 393.5 K).

Colligative properties depend only on the number of solute particles, not their identity. The four colligative properties are: (1) relative lowering of vapour pressure, (2) elevation of boiling point, (3) depression of freezing point, and (4) osmotic pressure. Relative lowering of vapour pressure equals the mole fraction of solute. Elevation of boiling point ΔTb = Kb × m, where Kb is the ebullioscopic constant (K kg mol⁻¹). Depression of freezing point ΔTf = Kf × m, where Kf is the cryoscopic constant.

Osmotic pressure Π = CRT, where C is molarity. Osmosis is the flow of solvent through a semipermeable membrane from lower to higher solute concentration. The pressure needed to stop osmosis is the osmotic pressure. Reverse osmosis, used in seawater desalination, occurs when pressure greater than osmotic pressure is applied to the solution side. Isotonic solutions have the same osmotic pressure; hypertonic solutions cause cells to shrink (crenation); hypotonic solutions cause cells to swell. These properties are used to calculate molar masses of solutes.

Some solutes show abnormal molar masses when determined from colligative properties. Electrolytes like KCl dissociate in solution, increasing the number of particles, so the experimentally measured molar mass is lower than the true value. Conversely, solutes like acetic acid associate (dimerize) in non-polar solvents like benzene due to hydrogen bonding, reducing the number of particles, so the measured molar mass is higher than the true value.

Van't Hoff introduced the factor i = (Normal molar mass / Abnormal molar mass) = (Observed colligative property / Calculated colligative property). For dissociation, i > 1; for association, i < 1. Modified colligative property equations: ΔTb = i Kb m; ΔTf = i Kf m; Π = i n2RT/V. For dilute KCl, i approaches 2; for K2SO4, i approaches 3. For acetic acid dimerizing in benzene, i approaches 0.5.

Chapter 1 on Solutions provides a comprehensive understanding of how mixtures behave at the molecular level. Starting from the classification of solutions and methods of expressing concentration, the chapter progresses through the fundamental laws — Henry's law governing gas solubility and Raoult's law governing vapour pressure — to the four colligative properties and their applications in determining molar masses. The van't Hoff factor elegantly resolves discrepancies arising from solute dissociation or association, connecting experimental observations to theoretical predictions.

From a board examination perspective, this chapter is highly important as it integrates numerical problem-solving with conceptual understanding. Students must master the interconversion of concentration units, the application of Raoult's law to ideal and non-ideal solutions, calculations involving all four colligative properties, and the use of van't Hoff factor for electrolytes and associated solutes. Real-world examples such as desalination, scuba diving, intravenous solutions, and food preservation make this chapter both practically relevant and conceptually rich.