Solutions

A solution is a homogeneous mixture of two or more components; the substance present in larger amount is usually the solvent and the others are solutes. To describe 'how much' solute is present we use several measures of concentration, and choosing the right one — and converting between them — is a guaranteed NEET skill.

The common measures are: mass percentage (mass of solute per 100 g of solution); parts per million (ppm) for very dilute solutions; mole fraction $x$ (moles of a component divided by total moles, so all mole fractions sum to $1$); molarity $M$ (moles of solute per litre of solution); and molality $m$ (moles of solute per kilogram of solvent). A key NEET point is that molarity depends on temperature (because volume changes with temperature) whereas molality and mole fraction do not — so molality is preferred when temperature varies, as in colligative measurements.

The solubility of a substance is the maximum amount that dissolves in a given amount of solvent at a particular temperature. For solids in liquids, solubility usually increases with temperature for endothermic dissolution and decreases for exothermic dissolution (following Le Chatelier's principle). The general guideline 'like dissolves like' holds — polar solutes dissolve in polar solvents and non-polar in non-polar.

For gases dissolving in liquids, solubility is governed by Henry's law: at constant temperature, the solubility of a gas is directly proportional to the partial pressure of the gas above the liquid, written $p = K_H\, x$, where $K_H$ is the Henry's law constant and $x$ the mole fraction of the gas. A higher $K_H$ means lower solubility. Gas solubility decreases with rising temperature — which is why warm water holds less dissolved oxygen, and why fizzy drinks go flat. Henry's law also explains the painful 'bends' in deep-sea divers and the use of helium–oxygen mixtures, biological links NEET sometimes draws on.

The vapour pressure of a solution is described by Raoult's law. For a solution of two volatile liquids, the partial vapour pressure of each component equals its vapour pressure in the pure state multiplied by its mole fraction in the solution: $p_A = p_A^{\circ} x_A$ and $p_B = p_B^{\circ} x_B$, so the total vapour pressure is $p = p_A^{\circ} x_A + p_B^{\circ} x_B$. This linear relationship is the foundation for the rest of the chapter.

When the solute is non-volatile, it contributes no vapour, so the solution's vapour pressure is simply $p = p_A^{\circ} x_A$ (where A is the solvent). Because $x_A < 1$, the vapour pressure is always lowered by adding a non-volatile solute — the origin of the colligative properties studied later. NEET often gives a numerical asking for this lowering.

An ideal solution is one that obeys Raoult's law over the entire range of composition, with zero enthalpy of mixing ($\Delta H_{mix} = 0$) and zero volume change ($\Delta V_{mix} = 0$). This happens when the solute–solvent interactions are essentially the same as the interactions in the pure components — for example, benzene with toluene, or n-hexane with n-heptane.

Most real solutions are non-ideal and deviate from Raoult's law. In a positive deviation, the components interact more weakly with each other than with themselves, so vapour pressure is higher than predicted ($\Delta H_{mix} > 0$); ethanol with water is an example, and such mixtures form minimum-boiling azeotropes. In a negative deviation, the components attract each other more strongly (e.g. by hydrogen bonding), so vapour pressure is lower than predicted ($\Delta H_{mix} < 0$); nitric acid with water is an example, forming a maximum-boiling azeotrope. Azeotropes are constant-boiling mixtures that cannot be separated by simple distillation — a recurring NEET fact.

Adding a non-volatile solute to a solvent changes four measurable properties that depend only on the number of solute particles, not on their chemical nature. These are the colligative properties, and they are a cornerstone of NEET physical chemistry because they let us determine the molar mass of an unknown solute.

The first is the relative lowering of vapour pressure. From Raoult's law, the lowering divided by the pure solvent's vapour pressure equals the mole fraction of the solute: $\dfrac{p_A^{\circ} - p}{p_A^{\circ}} = x_B$. The second is the elevation of boiling point: a solution boils at a higher temperature than the pure solvent, with $\Delta T_b = K_b\, m$, where $K_b$ is the molal elevation (ebullioscopic) constant and $m$ the molality. The third is the depression of freezing point: a solution freezes lower than the pure solvent, with $\Delta T_f = K_f\, m$, where $K_f$ is the molal depression (cryoscopic) constant. This is why salt is spread on icy roads and why antifreeze is added to car radiators — everyday links NEET often uses.

The fourth and most important is osmotic pressure. Osmosis is the net flow of solvent through a semipermeable membrane from a dilute to a concentrated solution; the pressure needed to just stop this flow is the osmotic pressure $\Pi$, given by $\Pi = CRT$ (the van't Hoff equation), where $C$ is the molar concentration. Osmotic pressure is especially valued for finding the molar mass of macromolecules like proteins and polymers, because it is sizeable and can be measured accurately at room temperature, unlike the other three effects.

All four properties can be rearranged to give the solute's molar mass, since each links a measurable change to the number of moles dissolved. NEET problems typically supply $K_b$ or $K_f$, the masses of solute and solvent, and the measured temperature change, and ask for the molar mass — so being fluent with $\Delta T_b = K_b m$, $\Delta T_f = K_f m$, and $\Pi = CRT$, and rearranging them, covers the bulk of this topic.

The colligative-property formulas assume that the number of dissolved particles equals the number of solute formula units. But some solutes dissociate into ions and others associate into larger aggregates, so the actual number of particles differs from what was dissolved. When this happens, the molar mass calculated from a colligative property comes out wrong — an abnormal molar mass. NEET frequently builds questions around this idea.

To correct for it, van't Hoff introduced the van't Hoff factor $i$, defined as the ratio of the observed (actual) number of particles in solution to the number of formula units initially dissolved. Equivalently, $i = \dfrac{\text{normal molar mass}}{\text{observed molar mass}}$, or the ratio of the observed colligative effect to the calculated (normal) effect.

For a solute that dissociates, more particles are produced, so $i > 1$. For example, NaCl gives two ions ($\text{Na}^+$ and $\text{Cl}^-$), so its ideal $i = 2$; $\text{BaCl}_2$ gives three ions, so ideal $i = 3$ (the real value is a little less because dissociation is not always complete). For a solute that associates, the number of particles falls, so $i < 1$; benzoic acid dimerises in benzene through hydrogen bonding, giving $i \approx 0.5$. For a solute that neither dissociates nor associates (a normal non-electrolyte like glucose or urea), $i = 1$.

The colligative formulas are modified by inserting $i$: $\Delta T_b = i K_b\, m$, $\Delta T_f = i K_f\, m$, $\Pi = i\,CRT$, and $\dfrac{p_A^{\circ}-p}{p_A^{\circ}} = i\, x_B$. NEET problems often ask you to compare the freezing-point depression of equimolar solutions of different solutes — the one that dissociates most (largest $i$) shows the greatest effect. Mastering the meaning of $i$ and these modified equations completes the chapter and turns 'abnormal' colligative problems into routine calculations.