A solution is a homogeneous mixture of two or more substances, consisting of a solute dissolved in a solvent. Solutions are classified on the basis of the physical state of the components; the most common are solid-liquid solutions such as sugar in water, but gaseous solutions like air and liquid-gas solutions like aerated drinks also exist. The chapter focuses on the concentration of solutions, colligative properties, and the laws that govern the behaviour of dilute solutions, particularly Raoult's law and the concept of ideal and non-ideal solutions.
Concentration can be expressed in several ways, including mass percentage, mole fraction, molarity, molality, and normality. Each unit has a specific use: molarity depends on temperature because it involves volume, whereas molality is temperature independent because it is based on mass. Understanding when to use each unit is critical for solving numerical problems in chemistry.
The second part of the chapter deals with the colligative properties, which depend only on the number of solute particles and not on their chemical nature. These are relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure. Each property is related to molality or molarity through a proportionality constant. The chapter also covers abnormal molar masses arising from association or dissociation of solute particles, quantified through the van't Hoff factor.
The concentration of a solution is the amount of solute present in a given quantity of solution or solvent.
$$\text{Mass percentage} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 100$$
The mole fraction of a component is the ratio of the number of moles of that component to the total number of moles of all components. $$x_A = \frac{n_A}{n_A + n_B}, \qquad x_B = \frac{n_B}{n_A + n_B}, \qquad x_A + x_B = 1$$
Molarity is the number of moles of solute present in one litre of solution. $$M = \frac{\text{moles of solute}}{\text{volume of solution in litres}}$$ Molarity decreases when temperature increases because volume of the solution expands.
Molality is the number of moles of solute present in one kilogram of solvent. $$m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}$$ Molality is independent of temperature.
Normality is the number of gram equivalents of solute present per litre of solution.
Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature. The solubility of a gas in a liquid is governed by Henry's law.
The mass of a gas dissolved in a given volume of liquid at constant temperature is directly proportional to the pressure of the gas in equilibrium with the liquid. $$p = K_H \times x$$ where $p$ is the partial pressure of the gas, $x$ is the mole fraction of the gas in solution, and $K_H$ is Henry's law constant.
Applications of Henry's law include carbonated beverages (high pressure keeps CO2 dissolved), the scuba diving danger of nitrogen narcosis, and the use of bottled oxygen for altitude climbers. The solubility of gases decreases with increase in temperature.
The solubility of most solid solutes in water increases with temperature. The solubility is affected by the nature of the solute and solvent, and by temperature.
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 the solution. $$p_A = p_A^\circ \times x_A, \qquad p_B = p_B^\circ \times x_B$$ where $p_A^\circ$ is the vapour pressure of pure component A.
The total vapour pressure of the solution is: $$p_{\text{total}} = p_A + p_B = p_A^\circ x_A + p_B^\circ x_B$$
An ideal solution obeys Raoult's law over the entire range of composition. There is no enthalpy change and no volume change on mixing. Example: benzene + toluene, n-hexane + n-heptane.
Non-ideal solutions deviate from Raoult's law: - Positive deviation: The observed vapour pressure is higher than expected. A-A and B-B interactions are stronger than A-B interactions. Example: ethanol + acetone, carbon disulphide + acetone. The enthalpy change is positive. - Negative deviation: The observed vapour pressure is lower than expected. A-B interactions are stronger than A-A and B-B interactions. Example: chloroform + acetone, nitric acid + water. The enthalpy change is negative.
Azeotropes are mixtures that boil at a constant temperature and cannot be separated by fractional distillation. Minimum boiling azeotropes arise from positive deviations, while maximum boiling azeotropes arise from negative deviations.
Colligative properties depend on the number of solute particles present in solution, not on their identity.
$$\frac{p_A^\circ - p_A}{p_A^\circ} = x_B$$ where $x_B$ is the mole fraction of the solute.
The boiling point of a solution is higher than that of the pure solvent. $$\Delta T_b = T_b - T_b^\circ = K_b \times m$$ where $K_b$ is the molal boiling point elevation constant and $m$ is the molality.
The freezing point of a solution is lower than that of the pure solvent. $$\Delta T_f = T_f^\circ - T_f = K_f \times m$$ where $K_f$ is the molal freezing point depression constant.
Osmosis is the spontaneous flow of solvent molecules through a semipermeable membrane from a less concentrated solution to a more concentrated solution. $$\pi = \frac{n_B R T}{V} = C R T$$ where $\pi$ is the osmotic pressure, $C$ is the molar concentration, and $T$ is the absolute temperature. Osmotic pressure is the colligative property best suited for determining molar masses of macromolecules and polymers because even dilute solutions produce measurable pressure.
The experimentally observed molar mass of a solute is often higher or lower than the theoretical molar mass because solute particles associate or dissociate in solution.
The van't Hoff factor, $i$, is defined as: $$i = \frac{\text{observed colligative property}}{\text{theoretical colligative property}} = \frac{\text{theoretical molar mass}}{\text{observed molar mass}}$$
The modified colligative property equations use $i$: $$\Delta T_b = i \times K_b \times m, \qquad \Delta T_f = i \times K_f \times m, \qquad \pi = i \times C \times R \times T$$
For complete dissociation of a compound forming $n$ particles from one formula unit, $i = n$. For complete association of $n$ molecules into one, $i = 1/n$.
| Unit | Definition | Formula | Temperature Dependent |
|---|---|---|---|
| Mass percentage | Mass of solute per 100 units of solution | (solute mass/solution mass) x 100 | No |
| Mole fraction | Moles of component / total moles | xA = nA/(nA+nB) | No |
| Molarity | Moles of solute per litre of solution | M = moles/volume (L) | Yes |
| Molality | Moles of solute per kg of solvent | m = moles/solvent mass (kg) | No |
| Normality | Gram equivalents per litre | N = equivalents/volume (L) | Yes |
| Property | Symbol | Relation | Best for |
|---|---|---|---|
| Relative lowering of vapour pressure | Δp/p° | = xB | Small solutes |
| Elevation of boiling point | ΔTb | = Kb x m | Small solutes |
| Depression of freezing point | ΔTf | = Kf x m | Small solutes |
| Osmotic pressure | π | = CRT | Polymers and macromolecules |
Solutions form the bridge between pure chemistry and everyday processes such as dissolving sugar in tea, carbonated drinks, and intravenous drips in hospitals. Raoult's law provides the fundamental link between vapour pressure and composition, while the deviations from it explain the behaviour of real liquid mixtures and the formation of azeotropes. The four colligative properties provide a powerful tool for determining molar masses, especially for substances that cannot easily be purified or converted to gas. The van't Hoff factor extends these concepts to handle dissociation and association, which is essential for electrolytes such as salts and acids. A solid understanding of this chapter is vital for further study of chemical equilibria, kinetics, and electrochemistry, and its numerical problems appear regularly in both board and competitive examinations.