Solutions

Solutions is one of the most reliably scoring chapters in the NEET chemistry paper: almost every year there are questions on concentration terms, Henry's law, Raoult's law deviations, and one or two numericals on colligative properties. The concepts are few, but they must be paired with clean formula handling.

Types of Solutions and Ways of Stating Concentration

A solution is a homogeneous mixture of two or more substances whose composition can be varied continuously. The component present in excess (and which decides the physical state) is the solvent; the rest are solutes. A binary solution has just two components. Because each of solute and solvent can be solid, liquid or gas, nine classes exist — for example gas-in-gas (air), gas-in-liquid (dissolved oxygen in water), solid-in-liquid (sugar syrup), liquid-in-solid (mercury amalgamated with sodium), gas-in-solid (hydrogen adsorbed in palladium), solid-in-solid (brass, bronze).

Concentration tells us how much solute is present, and the exam expects fluency in switching between the standard measures. For a binary solution of solute B in solvent A:

• Mass percentage = (mass of B / total mass of solution) × 100
• Volume percentage = (volume of B / total volume of solution) × 100 — used for liquid–liquid mixtures such as 35% v/v antifreeze
• Mass by volume percentage = mass of B in gram present in 100 mL of solution — the pharmacist's unit
• Parts per million (ppm) = (number of parts of B / total parts) × 10⁶ — used for trace impurities, hardness of water, pollutants
• Mole fraction, x_B = n_B/(n_A + n_B); for any solution Σx = 1. It is dimensionless and temperature-independent.
• Molarity (M) = moles of solute per litre of solution (unit mol L⁻¹)
• Molality (m) = moles of solute per kilogram of solvent (unit mol kg⁻¹)

The single most important distinction: molarity involves a volume, and volume expands on heating, so molarity changes with temperature while molality, mole fraction and mass percentage do not. This is exactly why all colligative-property equations are written in molality, not molarity.

A useful interconversion, with d = density of solution in g mL⁻¹ and M₂ = molar mass of solute:

m = (1000 × M) / (1000d − M × M₂)

For very dilute aqueous solutions, d ≈ 1 g mL⁻¹ and molarity ≈ molality; many NEET numericals silently rely on this approximation.

Solubility: Solids in Liquids and Henry's Law for Gases

Solubility is the maximum amount of solute that dissolves in a given amount of solvent at a stated temperature and pressure. The guiding rule is "like dissolves like": polar solutes (NaCl, sugar) dissolve in polar solvents (water), while non-polar solutes (naphthalene, anthracene) dissolve in non-polar solvents (benzene, hexane), because solute–solvent interactions must be comparable in strength to the interactions being broken.

At saturation the dissolved and undissolved solute are in dynamic equilibrium. Applying Le Chatelier's principle: if dissolution is endothermic (ΔH_sol > 0), solubility rises with temperature; if exothermic (ΔH_sol < 0), solubility falls with temperature. Pressure has essentially no effect on solids and liquids, since neither is significantly compressible.

Gases are a different story. Gas solubility increases strongly with pressure and decreases with temperature (dissolution of a gas is exothermic — the gas loses translational freedom). Quantitatively, Henry's law:

p = K_H · x

where p is the partial pressure of the gas above the solution, x its mole fraction in solution, and K_H the Henry's law constant.

Key points about K_H that examiners love:

1. K_H is characteristic of the gas–solvent pair and depends on temperature.
2. Higher K_H means lower solubility at a given pressure (K_H sits with pressure on the same side, so x = p/K_H).
3. K_H increases with rising temperature, hence gases become less soluble in warm water — the reason aquatic life suffers in thermally polluted water.

Applications worth remembering: carbonated drinks are sealed under high CO₂ pressure so that enough gas stays dissolved; deep-sea divers breathe air diluted with helium because nitrogen dissolved at high pressure bubbles out during rapid ascent, causing bends; at high altitude the low partial pressure of O₂ lowers blood oxygen, producing anoxia and the weakness climbers experience.

Vapour Pressure, Raoult's Law, Ideal and Non-Ideal Solutions

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

p₁ = p₁° x₁ and p₂ = p₂° x₂, so p_total = p₁° x₁ + p₂° x₂ = p₂° + (p₁° − p₂°) x₁

A plot of p_total against x₁ is therefore a straight line lying between p₁° and p₂°. In the vapour phase, by Dalton's law, y₁ = p₁/p_total; the vapour is always richer in the more volatile component.

When the solute is non-volatile, only the solvent contributes: p = p₁° x₁. Since x₁ = 1 − x₂,

(p₁° − p)/p₁° = x₂ → relative lowering of vapour pressure equals the mole fraction of the solute.

Ideal solutions obey Raoult's law across the whole composition range and satisfy ΔH_mixing = 0 and ΔV_mixing = 0, because A–B interactions are essentially identical to A–A and B–B interactions. Standard examples: benzene + toluene, n-hexane + n-heptane, chlorobenzene + bromobenzene, bromoethane + chloroethane.

Non-ideal solutions deviate:

• Positive deviation: A–B attractions are weaker than A–A and B–B, so molecules escape more readily. Observed vapour pressure > Raoult's prediction; ΔH_mix > 0 (endothermic), ΔV_mix > 0. Examples: ethanol + water, acetone + carbon disulphide, acetone + benzene.
• Negative deviation: A–B attractions are stronger (often new hydrogen bonding). Observed vapour pressure < predicted; ΔH_mix < 0, ΔV_mix < 0. Examples: chloroform + acetone (H-bond between CHCl₃ H and acetone O), nitric acid + water, phenol + aniline.

Solutions with large deviations form azeotropes — constant-boiling mixtures that distil unchanged, so their components cannot be separated by fractional distillation.

• Large positive deviation → minimum boiling azeotrope, e.g. ethanol–water at about 95% ethanol by volume (why absolute alcohol cannot be obtained by simple distillation).
• Large negative deviation → maximum boiling azeotrope, e.g. nitric acid–water at about 68% HNO₃ by mass, boiling near 393.5 K.

Colligative Properties and Determination of Molar Mass

Colligative properties depend only on the number of solute particles, not on their identity. There are four.

1. Relative lowering of vapour pressure. (p₁° − p)/p₁° = x₂. For dilute solutions this leads to (p₁° − p)/p₁° = (w₂ M₁)/(M₂ w₁), from which M₂ can be found.

2. Elevation of boiling point. A non-volatile solute lowers vapour pressure, so a higher temperature is needed to reach 1 atm: ΔT_b = K_b · m, where K_b is the molal elevation (ebullioscopic) constant, unit K kg mol⁻¹. For water K_b = 0.52 K kg mol⁻¹. Hence M₂ = (1000 · K_b · w₂)/(ΔT_b · w₁), with w₁ in gram.

3. Depression of freezing point. Freezing occurs when solid solvent and solution have equal vapour pressure; lowered vapour pressure means a lower freezing temperature: ΔT_f = K_f · m, with K_f the molal depression (cryoscopic) constant (for water 1.86 K kg mol⁻¹). M₂ = (1000 · K_f · w₂)/(ΔT_f · w₁). This is the principle behind spreading salt on icy roads and using antifreeze (ethylene glycol) in car radiators — both work by lowering the freezing point of the liquid below the ambient temperature.

4. Osmotic pressure. When a solution is separated from pure solvent by a semipermeable membrane (one that lets solvent molecules pass but blocks solute particles), solvent moves spontaneously into the solution by osmosis, and the excess pressure that must be applied on the solution side to just stop this net flow is the osmotic pressure, π. Van't Hoff showed that dilute solutions obey a gas-law-like relation:

πV = n₂RT, i.e. π = CRT, where C = n₂/V is the molar concentration of solute.

Osmotic pressure is the most sensitive colligative property because even very dilute solutions give an easily measurable π, which is why it is the method of choice for determining the molar mass of macromolecules (proteins, polymers) whose solutions are necessarily dilute and whose ΔT_b or ΔT_f would otherwise be too small to measure accurately. Two solutions with equal π at a given temperature are isotonic; if one solution has higher π than another, it is hypertonic to it, and the more dilute one is hypotonic. A red blood cell placed in a hypotonic solution swells and may burst (haemolysis), while in a hypertonic solution it shrinks (crenation) — osmotic pressure differences across the cell membrane are exactly what drive both effects, which is why intravenous fluids must be prepared isotonic with blood plasma.

Reverse osmosis applies pressure greater than π on the solution side, forcing solvent to flow against its natural direction, from solution into pure solvent — the working principle of desalination plants that purify seawater using membranes.

Abnormal Molar Masses and the van't Hoff Factor

All four colligative-property formulas above assume the solute neither associates nor dissociates in solution. Real solutes often do, and the molar mass calculated by blindly applying the formula then comes out wrong — abnormally high or abnormally low. Van't Hoff introduced a correction factor, i, defined as:

i = (observed colligative property) / (calculated colligative property, assuming no association/dissociation) = (normal molar mass) / (observed/abnormal molar mass) = (actual number of particles after equilibrium) / (number of formula units initially dissolved)

Every colligative-property formula is simply multiplied by i to correct it: π = iCRT, ΔT_b = iK_bm, ΔT_f = iK_fm, and relative lowering of vapour pressure = i·x₂.

• Dissociation (electrolytes: NaCl, KCl, MgSO₄, K₂SO₄, ...) increases the effective number of particles, so i > 1. For a strong electrolyte dissociating into ν ions with degree of dissociation α, i = 1 + (ν − 1)α; for complete dissociation of NaCl, i → 2, and for K₂SO₄ (3 ions), i → 3. Because the observed molar mass = normal molar mass / i, dissociating solutes give an abnormally low observed molar mass.
• Association (solutes that pair up via hydrogen bonding, such as acetic acid or benzoic acid dimerising in a non-polar solvent like benzene) decreases the effective number of particles, so i < 1, typically approaching ½ for complete dimerisation. The observed molar mass in such cases comes out abnormally high — famously, benzoic acid in benzene gives a molar mass close to double its true value because it exists almost entirely as a hydrogen-bonded dimer in that solvent.

Common Mistakes and Exam Traps

• Forgetting the van't Hoff factor for ionic solutes in colligative-property numericals. Any question involving NaCl, K₂SO₄, CaCl₂ or similar strong electrolytes needs i built into the formula; using the plain formula (as if for a non-electrolyte like glucose or urea) is one of the most common numerical errors in this chapter.
• Mixing up which observed molar mass goes with dissociation versus association. Dissociation raises the effective particle count and therefore lowers the apparent molar mass calculated from the data (i > 1); association does the opposite, raising the apparent molar mass (i < 1) — students often flip this pairing under time pressure.
• Using molarity in colligative-property formulas. ΔT_b, ΔT_f and Raoult's law calculations are written in molality or mole fraction specifically because these do not change with temperature, unlike molarity, which depends on solution volume; substituting molarity directly gives a subtly wrong answer whenever temperature is not exactly 298 K or density is not exactly 1 g mL⁻¹.
• Assuming K_H (Henry's law constant) behaves like Raoult's law's p°. A higher K_H means lower gas solubility at a given pressure, the opposite sense of how p° works in Raoult's law for a volatile liquid component — conflating the two is a frequent source of sign confusion in gas-solubility questions.