Solutions — NEET Notes

Types of solutions

A solution is a homogeneous mixture of two or more components — uniform in composition and properties throughout. The component in the largest quantity is the solvent, which dictates the physical state of the mixture; the remaining components are solutes. NCERT restricts the formal discussion to binary solutions: two components only. Because either component can be a solid, liquid, or gas, there are nine possible combinations — and chemistry actually realises all of them.

Air is a gaseous solution of nitrogen and oxygen; soda water is gas dissolved in liquid; ethanol-water is liquid in liquid; sugar-water is solid in liquid; brass is a copper-zinc solid solution; an amalgam of sodium with mercury is a liquid-in-solid solution. The state and properties of the resulting solution come from the solvent — sugar dissolved in water is still a liquid, copper dissolved in solid gold is still a solid.

Expressing concentration

"Dilute" and "concentrated" are vague — chemistry needs numbers. NEET expects fluency in five quantitative units, and the distinction between temperature-dependent and temperature-independent units is itself a PYQ favourite (NEET 2017 asked it directly). The five units are: mass percentage, parts per million, mole fraction, molarity, and molality.

Mass percentage (w/w) is the mass of a component divided by the total mass of the solution, expressed as a percentage. A "10% glucose in water by mass" solution contains 10 g of glucose dissolved in 90 g of water to make 100 g of solution. Commercial bleach is 3.62% sodium hypochlorite (w/w). Mass percentage is dominant in industrial use because masses are easy to weigh out.

Volume percentage (v/v) is the volume of a component divided by the total volume of solution. The 35% (v/v) ethylene glycol antifreeze in your car's coolant lowers water's freezing point to 255.4 K. Mass by volume percentage (w/V) — grams of solute per 100 mL of solution — is the unit of clinical pharmacy: a 0.9% (w/V) saline drip is 0.9 g of NaCl in 100 mL.

Parts per million (ppm) is used for trace concentrations — pollutants, fluoride in drinking water, dissolved O₂ in seawater. A litre of seawater (1030 g) carries about 5.8 ppm of dissolved oxygen. 1 ppm fluoride prevents tooth decay; 1.5 ppm mottles enamel. Ppm can be expressed as mass-to-mass, volume-to-volume, or mass-to-volume, depending on context.

Mole fraction (x) is the number of moles of one component divided by the total moles of all components. For binary mixtures, x_A + x_B = 1. Mole fractions are dimensionless and they are the natural unit for Raoult's law, Henry's law, and any quantity involving gas-mixture thermodynamics.

Molarity (M) = moles of solute per litre of solution. A 0.25 M NaOH solution contains 0.25 mol NaOH per L. Molarity is convenient because volumes are easy to measure with a pipette — but the volume of a liquid changes with temperature, so molarity changes with temperature too. Molality (m) = moles of solute per kilogram of solvent. A 1.00 m KCl solution contains 1 mol KCl (74.5 g) in 1 kg of water. Because masses do not change with temperature, molality is temperature-independent — and it is the unit of choice for all colligative-property calculations.

Solubility & Henry's law

The solubility of a substance is the maximum amount that can dissolve in a specified quantity of solvent at a specified temperature and pressure. Solubility depends on the nature of solute and solvent, on temperature, and (for gases) on pressure. The empirical rule is "like dissolves like" — polar solutes dissolve in polar solvents (NaCl in water), non-polar solutes in non-polar solvents (naphthalene in benzene). The molecular cause is that mixing is favourable when solute-solvent interactions resemble solute-solute and solvent-solvent interactions.

When solid solute is added to liquid solvent, dissolution and crystallisation reach a dynamic equilibrium. The concentration at equilibrium is the solubility; such a solution is saturated. For solids in liquids, pressure has no effect (incompressibility). Temperature affects solubility through Le Chatelier's principle: if dissolution is endothermic (Δ_solH > 0), solubility rises with temperature; if exothermic, solubility falls.

For gases in liquids, pressure is decisive. William Henry (1803) gave the quantitative relation: at constant temperature, the partial pressure of a gas in the vapour phase is directly proportional to its mole fraction in solution. Mathematically:

p = K_H · x

Henry's law — partial pressure proportional to mole fraction

Here K_H is the Henry's law constant, characteristic of each gas-solvent pair. A higher K_H at a given pressure means lower solubility — so for N₂ in water at 293 K (K_H = 76.48 kbar) and O₂ in water (K_H = 34.86 kbar), oxygen is more soluble than nitrogen. K_H for both gases increases with temperature — which is why aquatic life prefers cold waters and why warm rivers asphyxiate fish.

Henry's law explains a clutch of biological and industrial phenomena. Sealed soda bottles trap CO₂ at high pressure to maximise dissolved CO₂; opening the bottle drops the pressure and the gas effervesces. Scuba divers breathing compressed air at depth absorb extra N₂ into their blood; if they surface too quickly, the dissolved N₂ comes out as bubbles in capillaries — a painful and dangerous condition called bends. Divers' tanks therefore use a helium-nitrogen-oxygen mix to reduce N₂ load. At high altitude, low atmospheric oxygen partial pressure lowers blood-oxygen content, producing anoxia — weakness and confused thinking — in mountaineers.

Vapour pressure & Raoult's law

A liquid in a closed container evaporates until the vapour phase reaches equilibrium with the liquid; the pressure exerted by the vapour at that point is the vapour pressure of the liquid. For a solution of two volatile liquids, both components contribute to the total vapour pressure. The French chemist François-Marie Raoult (1886) found that each contribution is proportional to that component's mole fraction in the liquid phase:

p₁ = x₁ · p₁°    p_total = p₁ + p₂

Raoult's law — the central equation of solution thermodynamics

Here p₁° is the vapour pressure of pure component 1. The total vapour pressure varies linearly with mole fraction between the two pure-component extremes: p_total = p₁° + (p₂° − p₁°) x₂. Combining Raoult with Dalton's law of partial pressures gives the vapour-phase composition: y_i = p_i / p_total. A consequence — useful in distillation theory — is that the vapour is always richer in the more volatile component.

For a non-volatile solute (sugar, urea, salt) in a volatile solvent, only the solvent appears in the vapour phase. The solute molecules occupy a fraction of the surface and reduce the number of solvent molecules that can escape — so the solution's vapour pressure is lower than the pure solvent's. The general form of Raoult's law applies: p₁ = x₁ p₁°. This single result drives every colligative property we examine below.

Raoult's law and Henry's law are not separate ideas — they are limits of the same principle. For a volatile solvent, the proportionality constant in p = (constant) × x is p°. For a dilute gaseous solute, it is K_H. Raoult's law is the special case of Henry's law where K_H equals p° of the pure component.

Ideal vs non-ideal solutions

An ideal solution obeys Raoult's law across the entire range of concentration. Ideal solutions have three molecular signatures: zero enthalpy of mixing (Δ_mixH = 0), zero volume of mixing (Δ_mixV = 0), and intermolecular forces between A-B pairs that are nearly equal to those between A-A and B-B pairs. Perfectly ideal solutions are rare in reality, but n-hexane + n-heptane, bromoethane + chloroethane, and benzene + toluene come close.

A non-ideal solution departs from Raoult's law. If the observed vapour pressure is higher than Raoult predicts, the solution shows positive deviation: A-B interactions are weaker than A-A and B-B, so molecules find it easier to escape into the vapour phase than they would in pure liquid. Ethanol + acetone is the textbook example — acetone disrupts ethanol's hydrogen-bond network, weakening solute-solvent interactions. Carbon disulphide + acetone shows the same effect. If the observed vapour pressure is lower, the solution shows negative deviation: A-B interactions are stronger than A-A and B-B, so molecules are held tighter and escape less readily. Phenol + aniline forms strong O-H···N hydrogen bonds; chloroform + acetone forms C-H···O hydrogen bonds. Both show negative deviation.

Azeotropes

Some non-ideal mixtures form azeotropes — binary mixtures with identical compositions in liquid and vapour phases that boil at a constant temperature. Because liquid and vapour have the same composition, fractional distillation cannot separate the components beyond the azeotropic point.

Solutions with large positive deviation form a minimum boiling azeotrope — boiling point lower than either pure component. Ethanol-water is the most famous: fractional distillation of fermented sugar can purify ethanol up to roughly 95% by volume, beyond which the azeotrope locks the composition. Solutions with large negative deviation form a maximum boiling azeotrope — boiling point higher than either pure component. Nitric acid + water forms an azeotrope at 68% HNO₃ by mass, boiling at 393.5 K (120.4 °C). This is the practical upper limit of concentrated nitric acid produced by distillation.

Colligative properties

The word colligative comes from the Latin co (together) and ligare (to bind). A colligative property is one that depends only on the number of solute particles in solution and not on their chemical nature. There are exactly four colligative properties — and NCERT treats each in turn. All four arise from a single underlying cause: the lowering of the solvent's vapour pressure by a non-volatile solute, predicted by Raoult's law.

Relative lowering of vapour pressure

Start from Raoult's law for a non-volatile solute: p₁ = x₁ p₁°. The lowering Δp₁ = p₁° − p₁ = p₁°(1 − x₁) = x₂ p₁°. Dividing both sides by p₁° gives the relative lowering of vapour pressure:

(p₁° − p₁) / p₁° = x₂ = n₂ / (n₁ + n₂)

Relative lowering of vapour pressure = mole fraction of solute

For dilute solutions, n₂ ≪ n₁, so the denominator simplifies to n₁. Substituting n = w/M for both solvent and solute, the equation becomes (p₁° − p₁)/p₁° = (w₂ M₁) / (M₂ w₁), from which the molar mass M₂ of the solute can be calculated if all other quantities are known. NCERT's worked example: 0.5 g of an unknown non-volatile solute dissolved in 39 g benzene lowers the vapour pressure from 0.850 bar to 0.845 bar, giving M₂ = 170 g mol⁻¹.

Elevation of boiling point

A liquid boils at the temperature at which its vapour pressure equals atmospheric pressure (1.013 bar at sea level). When a non-volatile solute lowers the solvent's vapour pressure at every temperature, the solution's vapour-pressure curve sits below the pure solvent's. To make it reach 1.013 bar, the solution must be heated higher than the pure solvent's boiling point. The difference ΔT_b = T_b − T_b° is the elevation of boiling point, and experiment shows it is proportional to molality:

NCERT's worked illustration: 1.80 g of an unknown non-volatile solute in 90 g benzene raises the b.p. from 353.23 K to 354.11 K (ΔT_b = 0.88 K). With K_b = 2.53 K kg mol⁻¹, the molar mass works out to 58 g mol⁻¹. K_b is a property of the solvent alone — adding twice as much solute doubles the molality and doubles ΔT_b, but K_b stays the same. NEET 2017 tested this exact reasoning for the freezing-point constant.

Depression of freezing point

The freezing point of a liquid is the temperature at which its vapour pressure equals that of the solid phase. A non-volatile solute lowers the liquid solution's vapour pressure but does not affect the solid solvent (it crystallises out as pure ice, salt-free). The solid- and liquid-curve intersection — the freezing point — therefore shifts to a lower temperature for the solution. The drop ΔT_f = T_f° − T_f is the depression of freezing point:

This is the chemistry of salted roads and antifreeze. Sprinkling NaCl on icy pavement depresses water's freezing point and melts the ice (with dissociation pushing the effect further — see van't Hoff factor below). 35% v/v ethylene glycol depresses water's freezing point to about 255 K, protecting car radiators from freezing in winter. NCERT's worked example: 45 g of ethylene glycol in 600 g water gives a molality of 1.2 m, hence ΔT_f = 1.86 × 1.2 = 2.23 K, lowering the freezing point from 273.15 K to 270.95 K. NEET 2020 used the same logic for benzene + non-electrolyte solute.

Osmotic pressure & reverse osmosis

A semipermeable membrane contains pores small enough to let solvent molecules pass but block solute molecules. When such a membrane separates a solution from pure solvent, solvent molecules flow spontaneously from solvent to solution — a process called osmosis. The flow continues until the hydrostatic pressure on the solution side rises enough to stop it. That pressure — the excess pressure that must be applied to the solution to prevent osmosis — is the osmotic pressure (π) of the solution.

For dilute solutions, van't Hoff (1886) found that osmotic pressure obeys an equation strikingly similar to the ideal gas law:

π = C R T = (n₂/V) R T

Van't Hoff equation for osmotic pressure

Here C is the molarity, R is the gas constant, T is absolute temperature, n₂ is moles of solute and V is volume of solution. Two solutions with the same osmotic pressure at the same temperature are isotonic — placed across a semipermeable membrane, no net flow occurs. Blood is isotonic with 0.9% (w/V) NaCl ("normal saline"), which is why intravenous drips use exactly that concentration. A hypertonic solution (higher π than blood) draws water out of cells, shrinking them; a hypotonic solution (lower π) drives water in and swells them.

Osmosis explains a clutch of everyday phenomena. Raw mangoes shrivel when pickled in brine — water flows out by osmosis. Wilted flowers revive in fresh water — water flows in. Eating too much salt causes water retention (edema). Bacteria on salted meat or sugared fruit lose water and die — the basis of food preservation. Plants pull water from soil into root cells partly by osmosis.

Osmotic pressure is the colligative method of choice for biomolecules. It is measurable even at very low concentrations (where ΔT_b and ΔT_f would be too small to detect), it uses room-temperature measurements (heat-sensitive proteins survive), and it uses molarity rather than molality (convenient for dilute biological samples). NCERT's worked example: 1.26 g of a protein in 200 cm³ of water at 300 K gives π = 2.57 × 10⁻³ bar, hence M_protein ≈ 61,000 g mol⁻¹.

If a pressure greater than the osmotic pressure is applied to the solution side, the flow reverses — pure solvent is squeezed out of the solution through the membrane. This reverse osmosis is the industrial workhorse of desalination: sea water is forced through cellulose-acetate membranes (or modern polyamide composites) at pressures of tens of bar, yielding fresh water. Many coastal cities now meet potable-water demand by reverse osmosis.

Van't Hoff factor & abnormal molar mass

Colligative formulas as written assume the solute particles are independent — neither dissociating into ions nor associating into clusters. Reality often defies this. When KCl (74.5 g, 1 mol) dissolves in water, it splits into K⁺ + Cl⁻ — so 1 mol of formula units gives 2 mol of particles. The boiling-point elevation is therefore twice what the simple equation predicts. Run the calculation in reverse — measure ΔT_b and back-calculate molar mass without accounting for dissociation — and you would get a value of about 37.25 g mol⁻¹ for KCl, half the real molar mass. This is an abnormal molar mass.

The opposite happens when solutes associate. Acetic acid in benzene dimerises through hydrogen bonding: 2 CH₃COOH ⇌ (CH₃COOH)₂. Two molecules become one particle, ΔT_f drops by half, and the apparent molar mass comes out twice the real value (120 g mol⁻¹ instead of 60).

In 1880 Jacobus van't Hoff introduced the factor i to correct for this:

Three useful rules of thumb: for non-electrolytes (glucose, urea, sucrose) that neither dissociate nor associate, i = 1 and the simple colligative formulas apply directly. For electrolytes that dissociate, i > 1 — KCl ≈ 2, BaCl₂ ≈ 3, K₄[Fe(CN)₆] ≈ 5 (assuming full dissociation). For associating solutes in low-polarity solvents (acetic acid or benzoic acid dimerising in benzene), i < 1 — typically near 0.5 for complete dimerisation. Real values lie between these limits depending on the degree of dissociation or association.

NCERT's example: 2 g of benzoic acid in 25 g benzene produces ΔT_f = 1.62 K. Substituting into M₂ = (K_f × w₂ × 1000) / (ΔT_f × w₁) with K_f = 4.9 gives an observed molar mass of 242 g mol⁻¹ — almost exactly twice the real molar mass of benzoic acid (122 g mol⁻¹), confirming nearly complete dimerisation, with i ≈ 0.5. The dimers form through carboxylic-acid hydrogen bonding, which is favoured in low-dielectric solvents like benzene where the C=O···H-O bridges are not disrupted by polar solvent molecules.