Solutions and Their Concentration — Notes

A solution is a homogeneous mixture of two or more substances. The component in larger amount is the solvent; the others are solutes. By the states of solvent and solute there are nine types: gaseous (air; humid air; camphor in air), liquid (soda water; ethanol in water; salt solution) and solid solutions (hydrogen in palladium; sodium amalgam; alloys such as brass, bronze and carat gold). A binary solution has two components.

• Mass % $= \dfrac{\text{mass of component}}{\text{mass of solution}} \times 100$; volume %; w/v % (g per 100 mL).
• ppm $= \dfrac{\text{mass of component}}{\text{mass of solution}} \times 10^{6}$ (1 ppm = 1 mg per kg).
• Mole fraction $x_\text{B} = n_\text{B}/(n_\text{A} + n_\text{B})$; $\sum x = 1$.
• Molarity $M$ = mol of solute per L of solution; molality $m$ = mol of solute per kg of solvent.
• Normality $N$ = gram equivalents of solute per L of solution; equivalent mass = molar mass ÷ n-factor (basicity, acidity, electrons transferred), so $N = n \times M$. At an end point, $N_1V_1 = N_2V_2$.
• Mass %, ppm, mole fraction and molality are independent of temperature; molarity and normality fall slightly on heating because the volume of solution increases.
• Conversions: assume 100 g of solution for a percentage; use density to get volume; molarity ↔ molality: $m = \dfrac{1000M}{1000d - M M_\text{B}}$ (d in g mL⁻¹, $M_\text{B}$ = molar mass of solute).

Solubility of a gas in a liquid increases with pressure and decreases with temperature (dissolving is usually exothermic).

Henry’s law: at constant temperature, the solubility of a gas is proportional to its partial pressure; $p = K_\text{H}\,x$. Larger $K_\text{H}$ → less soluble; $K_\text{H}$ increases with temperature.

Applications: soft drinks bottled under high CO₂ pressure; the bends in divers (tanks use air diluted with helium); anoxia at high altitude; low oxygen in warm water.

Limitations: holds for low pressures, gases that do not react with or dissociate in the solvent (not NH₃ or HCl in water), and dilute solutions.

Raoult’s law: for a solution of volatile liquids, the partial vapour pressure of each component equals its pure vapour pressure times its mole fraction: $p_\text{A} = p^\circ_\text{A}x_\text{A}$; $p_\text{total} = p_\text{A} + p_\text{B}$ (Dalton). Vapour composition: $y_\text{A} = p_\text{A}/p_\text{total}$; the vapour is richer in the more volatile component. For a non-volatile solute, $p = p^\circ_1 x_1$ (vapour pressure lowered). Raoult’s law is a special case of Henry’s law with $K_\text{H} = p^\circ$.

An azeotrope is a liquid mixture that boils at constant temperature and distils with unchanged composition (liquid and vapour have the same composition).

• Minimum-boiling azeotrope: from large positive deviation; e.g. ethanol + water (about 95% ethanol by volume, about 351 K).
• Maximum-boiling azeotrope: from large negative deviation; e.g. nitric acid + water (about 68% HNO₃, about 393.5 K), HCl + water (about 20% HCl, about 383 K).

Boiling point–composition diagrams: the liquid and vapour curves meet at the azeotrope (minimum or maximum). Fractional distillation of a mixture gives one pure component and the azeotrope — never both pure components — because at the azeotrope the vapour has the same composition as the liquid.