Solutions

In this chapter: types of solutions, ways of expressing concentration, solubility of solids and gases, Henry's law, vapour pressure and Raoult's law, ideal and non-ideal solutions, azeotropes, the four colligative properties, reverse osmosis, abnormal molar masses and the van't Hoff factor.

Types of solutions

A solution is a homogeneous mixture of two or more components. The component present in the larger amount is usually called the solvent; the others are solutes. This chapter deals mostly with binary solutions (two components). Depending on the physical state of solute and solvent there are nine types, for example oxygen dissolved in water (gas in liquid), ethanol in water (liquid in liquid), glucose in water (solid in liquid), and copper dissolved in gold (solid in solid). A solution of hydrogen in palladium is a gas in a solid.

Expressing concentration

Anything based on volume changes with temperature because liquids expand on heating. Mass does not change, so mass percentage, ppm by mass, mole fraction and molality are temperature independent. This is exactly why molality, and not molarity, is used in the boiling point and freezing point formulas.

Solubility

Solids in liquids

"Like dissolves like": ionic and polar solids dissolve in polar solvents, non-polar solids in non-polar solvents. A solution in which no more solute can dissolve at a given temperature and pressure is saturated; there is a dynamic equilibrium between dissolved and undissolved solute. If dissolution is endothermic, solubility rises with temperature; if it is exothermic, solubility falls (Le Chatelier's principle). Pressure has almost no effect on the solubility of solids in liquids because solids and liquids are nearly incompressible.

Gases in liquids and Henry's law

The solubility of a gas increases with pressure. Henry's law: the partial pressure of a gas in the vapour phase is proportional to its mole fraction in the solution.

• The higher the value of K_H at a given pressure, the lower the solubility of the gas.
• K_H increases with temperature, so gases become less soluble in warm water. Aquatic life is more comfortable in cold water for this reason.
• Applications: soft drink bottles are sealed under high CO₂ pressure; scuba divers breathing compressed air can suffer bends when they rise quickly and dissolved N₂ forms bubbles in the blood, so their tanks use air diluted with helium; at high altitudes the low partial pressure of O₂ gives low blood oxygen (anoxia).

Vapour pressure and Raoult's law

For a solution of two volatile liquids, Raoult's law says that the partial vapour pressure of each component is proportional to its mole fraction in the solution.

The total vapour pressure varies linearly with mole fraction. In the vapour phase, the mole fraction of a component is y₁ = p₁ ÷ p_total; the vapour is always richer in the more volatile component. Raoult's law is a special case of Henry's law in which K_H becomes equal to p°.

Worked example: Liquids A and B form an ideal solution. At a certain temperature p_A° = 80 kPa and p_B° = 40 kPa. Find the total vapour pressure of a solution made from 1 mol A and 3 mol B, and the mole fraction of A in the vapour.
Solution: x_A = 1/4 = 0.25 and x_B = 0.75. p_A = 0.25 × 80 = 20 kPa; p_B = 0.75 × 40 = 30 kPa; p_total = 50 kPa. In the vapour, y_A = 20/50 = 0.40. The liquid had only 0.25 mole fraction of A, so the vapour is richer in A, the more volatile liquid.

Ideal and non-ideal solutions

An ideal solution obeys Raoult's law over the entire range of concentration, with Δ_mixH = 0 and Δ_mixV = 0. This happens when A-B attractions are nearly the same as A-A and B-B attractions. Examples: n-hexane + n-heptane, bromoethane + chloroethane, benzene + toluene.

Azeotropes are binary mixtures that boil at a constant temperature and have the same composition in liquid and vapour phases. They cannot be separated by fractional distillation. This is why rectified spirit (about 95% ethanol) is the best that fractional distillation of an ethanol-water mixture can give.

Colligative properties

Colligative properties depend only on the number of solute particles in a given amount of solvent, and not on their nature. For a non-volatile, non-electrolyte solute in a dilute solution there are four of them.

1. Relative lowering of vapour pressure

The relative lowering equals the mole fraction of the solute. The solute particles occupy part of the surface, so fewer solvent molecules escape.

2. Elevation of boiling point

A liquid boils when its vapour pressure equals the atmospheric pressure. The solution has a lower vapour pressure, so it must be heated to a higher temperature to reach 1.013 bar.

3. Depression of freezing point

At the freezing point, the vapour pressure of the liquid equals that of the solid. Because the solution has a lower vapour pressure, this equality is reached at a lower temperature.

Ethylene glycol is added to water in car radiators as an antifreeze for this reason, and salt is spread on icy roads.

Worked example: 2.0 g of a non-volatile non-electrolyte dissolved in 100 g of benzene lowers its freezing point by 0.64 K. Find the molar mass of the solute (K_f for benzene = 5.12 K kg mol⁻¹).
Solution: M₂ = (1000 × 5.12 × 2.0) ÷ (0.64 × 100) = 10240 ÷ 64 = 160 g mol⁻¹.

4. Osmotic pressure

When a solution and pure solvent are separated by a semipermeable membrane (SPM), solvent molecules flow through the membrane into the solution. This flow is osmosis. The extra pressure that must be applied on the solution to just stop osmosis is the osmotic pressure (π).

• Osmotic pressure is the preferred method for finding the molar mass of proteins and polymers: it is measured at room temperature, and even very dilute solutions give a measurable pressure, whereas their ΔT_b or ΔT_f would be too small.
• Isotonic solutions have the same osmotic pressure at a given temperature. The fluid inside blood cells is isotonic with 0.9% (mass/volume) NaCl, called normal saline. In a more concentrated (hypertonic) NaCl solution the cells shrink; in a less concentrated (hypotonic) one they swell.
• Reverse osmosis: if a pressure larger than π is applied on the solution side, pure solvent flows out of the solution through the membrane. It is used to desalinate sea water; cellulose acetate membranes are commonly used.

Abnormal molar masses and the van't Hoff factor

Electrolytes dissociate into more particles than the formula suggests, and some solutes associate. Ethanoic acid, for example, forms dimers in benzene through hydrogen bonding. The molar mass worked out from a colligative property is then abnormal. The van't Hoff factor corrects for this.

• Dissociation gives i > 1; for complete dissociation, i = number of ions (NaCl 2, K₂SO₄ 3, K₄[Fe(CN)₆] 5).
• Association gives i < 1; ethanoic acid dimerising completely in benzene gives i = 0.5.
• Degree of dissociation: α = (i − 1) ÷ (n − 1), where n is the number of ions from one formula unit. Degree of association: α = (1 − i) ÷ (1 − 1/n), where n molecules join to form one associated unit.

Common mistakes: (1) Using molarity instead of molality in ΔT_b and ΔT_f, or grams of solution instead of grams of solvent. (2) Forgetting the van't Hoff factor for salts: 0.1 m NaCl lowers the freezing point about twice as much as 0.1 m glucose. (3) Writing the positive deviation azeotrope as maximum boiling. Positive deviation means higher vapour pressure, so the mixture boils at a lower temperature. (4) Reading a larger K_H as higher solubility; it is the other way round. (5) Taking T in °C in π = CRT.

JEE and NEET focus

• Conversions between molarity, molality and mole fraction using density; which terms change with temperature.
• Henry's law and the meaning of K_H; everyday applications.
• Raoult's law calculations for liquid and vapour composition; ideal vs non-ideal with signs of Δ_mixH and Δ_mixV; examples of each deviation and the type of azeotrope.
• All four colligative property formulas, molar mass determination, and the reason osmotic pressure suits macromolecules.
• van't Hoff factor for dissociation and association; comparing boiling or freezing points of different 0.1 m solutions.

Practice questions