Class 12 Chemistry · Chapter 1 NotesSolutions

A solution is a homogeneous mixture of two or more components whose composition and properties are uniform throughout. The component present in the largest quantity is called the solvent, and it decides the physical state of the solution. The other components are called solutes. In this chapter we deal mainly with binary solutions, that is, solutions having two components. Depending on the physical states of the solute and the solvent, solutions are classified as gaseous, liquid and solid solutions. For example, a mixture of oxygen and nitrogen gases is a gaseous solution, oxygen dissolved in water is a liquid solution, and a solution of hydrogen in palladium is a solid solution.

• Gaseous solutiongas in gas (oxygen and nitrogen), liquid in gas (chloroform in nitrogen gas), solid in gas (camphor in nitrogen gas)
• Liquid solutiongas in liquid (oxygen in water), liquid in liquid (ethanol in water), solid in liquid (glucose in water)
• Solid solutiongas in solid (hydrogen in palladium), liquid in solid (amalgam of mercury with sodium), solid in solid (copper in gold)

The concentration of a solution can be described qualitatively as dilute or concentrated, but a quantitative description is more useful. Mass percentage (w/w) gives the mass of the component in 100 g of solution. Volume percentage (v/v) gives the volume of the component in 100 mL of solution. Mass by volume percentage (w/V) gives the mass of solute in 100 mL of solution. Parts per million (ppm) is used for trace quantities. Mole fraction is the ratio of the number of moles of a component to the total number of moles of all components, and the sum of all mole fractions in a solution is unity. Molarity is the number of moles of solute per litre of solution, while molality is the number of moles of solute per kilogram of solvent. Mass percentage, ppm, mole fraction and molality do not depend on temperature, but molarity does because volume changes with temperature.

• Mass % = (mass of component / total mass of solution) × 100
• Volume % = (volume of component / total volume of solution) × 100
• ppm = (number of parts of component / total number of parts of all components) × 10⁶
• Mole fraction xᵢ = nᵢ / (n₁ + n₂ + ... + nᵢ) and x₁ + x₂ + ... + xᵢ = 1
• Molarity (M) = moles of solute / volume of solution in litre
• Molality (m) = moles of solute / mass of solvent in kg

Solubility is the maximum amount of a substance that can dissolve in a specified amount of solvent at a given temperature. Polar solutes dissolve in polar solvents and non-polar solutes in non-polar solvents — like dissolves like. When a solid solute is added to a solvent, dissolution and crystallisation occur simultaneously, and at equilibrium a saturated solution is formed. For solids in liquids, solubility generally increases with temperature if dissolution is endothermic and decreases if it is exothermic; pressure has no significant effect. For gases in liquids, solubility increases with pressure and decreases with temperature. Henry's law states that at constant temperature the partial pressure of the gas in the vapour phase (p) is proportional to the mole fraction of the gas (x) in the solution: p = K_H x. Higher the value of K_H at a given pressure, lower is the solubility of the gas.

• Henry's lawp = K_H x, where K_H is the Henry's law constant
• Applicationssealing soft drinks under high pressure, scuba diving and bends, anoxia at high altitudes
• Solubility of gases decreases with rise in temperature because dissolution is exothermic

For a binary solution of two volatile liquids, Raoult's law states that the partial vapour pressure of each component is directly proportional to its mole fraction in the solution. For component 1, p₁ = p₁⁰ x₁, and for component 2, p₂ = p₂⁰ x₂, where p₁⁰ and p₂⁰ are the vapour pressures of the pure components. By Dalton's law, the total vapour pressure is p_total = p₁ + p₂ = p₁⁰ + (p₂⁰ − p₁⁰) x₂. The vapour phase is always richer in the more volatile component. When a non-volatile solute is dissolved in a solvent, the vapour pressure of the solution is lower than that of the pure solvent because the surface is partly occupied by solute particles. Raoult's law in this case gives p₁ = x₁ p₁⁰, and the relative lowering of vapour pressure equals the mole fraction of the solute.

• p₁ = p₁⁰ x₁ and p₂ = p₂⁰ x₂ for volatile components
• p_total = p₁⁰ + (p₂⁰ − p₁⁰) x₂
• Relative lowering of vapour pressure(p₁⁰ − p₁) / p₁⁰ = x₂

Ideal solutions obey Raoult's law over the entire range of concentration, with enthalpy of mixing and volume of mixing both equal to zero. In such solutions, A-A, B-B and A-B intermolecular interactions are nearly equal. Examples include n-hexane and n-heptane, bromoethane and chloroethane, and benzene and toluene. Non-ideal solutions do not obey Raoult's law over the entire range. If the vapour pressure is higher than predicted, the solution shows positive deviation; this happens when A-B interactions are weaker than A-A or B-B interactions, as in ethanol and acetone. If the vapour pressure is lower than predicted, the solution shows negative deviation; this happens when A-B interactions are stronger, as in phenol and aniline, or chloroform and acetone. Azeotropes are binary mixtures having the same composition in liquid and vapour phase and boiling at a constant temperature. Large positive deviations give minimum boiling azeotropes such as ethanol-water, while large negative deviations give maximum boiling azeotropes such as nitric acid-water.

• Ideal solutionΔH_mix = 0, ΔV_mix = 0, obeys Raoult's law
• Positive deviationA-B interactions weaker than A-A or B-B; example ethanol + acetone
• Negative deviationA-B interactions stronger than A-A or B-B; example chloroform + acetone
• Minimum boiling azeotropeethanol-water (about 95% ethanol by volume)
• Maximum boiling azeotropenitric acid-water (about 68% nitric acid by mass, b.p. 393.5 K)

Colligative properties depend only on the number of solute particles and not on their nature. They are relative lowering of vapour pressure, elevation of boiling point, depression of freezing point and osmotic pressure. The elevation of boiling point is ΔT_b = K_b m, where K_b is the molal elevation constant (ebullioscopic constant). The depression of freezing point is ΔT_f = K_f m, where K_f is the molal depression constant (cryoscopic constant). Both K_b and K_f depend on the nature of the solvent. These relations allow the molar mass of a solute to be calculated from measured values of ΔT_b or ΔT_f. For example, M₂ = (1000 × w₂ × K_b) / (ΔT_b × w₁) and M₂ = (1000 × w₂ × K_f) / (ΔT_f × w₁).

• ΔT_b = K_b m and ΔT_f = K_f m
• M₂ = (1000 × w₂ × K_b) / (ΔT_b × w₁)
• M₂ = (1000 × w₂ × K_f) / (ΔT_f × w₁)
• K_b and K_f depend on the solvent; values are listed for water, benzene, ethanol, etc.

Osmosis is the flow of solvent molecules through a semipermeable membrane from the pure solvent side to the solution side, or from a dilute solution to a concentrated solution. The pressure that just stops this flow is called osmotic pressure (Π). Osmotic pressure is a colligative property and for dilute solutions it is given by Π = C R T, where C is the molarity of the solution. It can also be written as Π = (n₂ / V) R T or Π V = (w₂ / M₂) R T, which allows calculation of molar mass. Two solutions having the same osmotic pressure at a given temperature are called isotonic solutions. A solution with higher osmotic pressure than another is hypertonic, and one with lower osmotic pressure is hypotonic. Reverse osmosis occurs when a pressure larger than the osmotic pressure is applied to the solution side, forcing pure solvent out; it is used in desalination of sea water.

• Π = C R T = (n₂ / V) R T
• M₂ = (w₂ R T) / (Π V)
• Isotonic solutions have equal osmotic pressure; 0.9% (mass/volume) NaCl is normal saline
• Hypertonic solutioncells shrink; hypotonic solution: cells swell
• Reverse osmosis is used for water purification and desalination

When solutes dissociate or associate in solution, the observed colligative property does not match the value calculated assuming no change in the number of particles. This gives an abnormal molar mass — lower than normal for dissociation and higher than normal for association. Van't Hoff introduced the factor i to account for this: i = normal molar mass / abnormal molar mass = observed colligative property / calculated colligative property = total number of moles of particles after association or dissociation / number of moles of particles before association or dissociation. For dissociation, i is greater than 1 (for example, i ≈ 2 for aqueous KCl); for association, i is less than 1 (for example, i ≈ 0.5 for ethanoic acid in benzene). The colligative property equations become ΔT_b = i K_b m, ΔT_f = i K_f m, Π = i n₂ R T / V, and relative lowering of vapour pressure = i x₂.

• i = normal molar mass / abnormal molar mass
• i > 1 for dissociation, i < 1 for association
• ΔT_b = i K_b m, ΔT_f = i K_f m, Π = i n₂ R T / V
• Examplebenzoic acid dimerises in benzene, i ≈ 0.5