Solutions

1. Types & Concentration Units

A solution is a homogeneous mixture. The solvent (largest amount) decides the physical state; everything else is a solute. Nine binary types exist (gas/liquid/solid in gas/liquid/solid), e.g. air (gas in gas), ethanol in water (liquid in liquid), H₂ in palladium (gas in solid), Hg in Na amalgam (liquid in solid), Cu in gold (solid in solid).

Shortcut: $M = \dfrac{10\times d\times(\text{mass \%})}{M_2}$ (density $d$ in g mL⁻¹). Example: 68% HNO₃, $d = 1.504$ gives $M = 16.2$.

Why does molarity change with temperature but molality does not? Heating expands the solution, so the same moles sit in a larger volume and molarity falls. Mass does not change with temperature, so anything built on mass (molality, mass %, ppm) stays fixed.

2. Solubility & Henry's Law

• Like dissolves like: polar solutes dissolve in polar solvents (NaCl in water); non-polar in non-polar (naphthalene in benzene).
• Solids in liquids: dissolution is a dynamic equilibrium. If dissolving is endothermic, solubility rises with temperature; if exothermic, it falls. Pressure has almost no effect.
• Henry's law: at constant temperature, the solubility of a gas in a liquid is directly proportional to its partial pressure above the liquid.

  $$p = K_H\,x$$

• Gas solubility falls as temperature rises ($K_H$ increases), because dissolving a gas is exothermic.

The tricky part, $K_H$ versus solubility. Rearranging, $x = p/K_H$. So at a given pressure, the bigger $K_H$ is, the smaller the amount dissolved. Think of $K_H$ as the gas's "reluctance to dissolve". CO₂ ($K_H$ about 1.67 kbar) is far more soluble than O₂ ($K_H$ about 34.9 kbar), so O₂ has the higher $K_H$. This is a favourite 1-2 mark question.

Applications (name any, with reason):

• Soft drinks: CO₂ is sealed under high pressure to dissolve more.
• Scuba divers, bends: at depth more N₂ dissolves in blood; on fast ascent it bubbles out and blocks capillaries. Divers use He–O₂ mixtures because He is much less soluble.
• High altitude, anoxia: low pressure means low partial pressure of O₂, so less oxygen in blood, and climbers feel weak and confused.

3. Raoult's Law

For two volatile liquids, each component's partial vapour pressure is proportional to its mole fraction in the liquid:

$$p_1 = x_1p_1^0,\qquad p_2 = x_2p_2^0,\qquad p_{total} = p_1 + p_2 = p_1^0 + (p_2^0-p_1^0)x_2$$

The vapour composition is $y_i = p_i/p_{total}$, and the vapour is always richer in the more volatile component.

For a non-volatile solute: only the solvent evaporates, so $p_1 = x_1p_1^0$, and the relative lowering of vapour pressure equals the solute's mole fraction:

$$\frac{p_1^0-p_1}{p_1^0} = x_2 \approx \frac{n_2}{n_1}\ \text{(dilute)}$$

Why does a solute lower the vapour pressure? Solute particles take up room on the liquid's surface, so fewer solvent molecules can escape. It depends only on how many solute particles there are, not what they are. That is exactly what "colligative" means.

Link to Henry's law: both say $p \propto x$. Raoult's law is the special case of Henry's law where $K_H = p_1^0$.

4. Ideal, Non-ideal & Azeotropes

Making sense of it. If A–B attraction is weaker than A–A and B–B, molecules escape into the vapour more easily, so vapour pressure goes up (positive) and less heat is released than absorbed (endothermic). If A–B attraction is stronger, molecules are held back, so vapour pressure drops (negative) and heat is released (exothermic).

Azeotrope memory hook: high vapour pressure means the liquid boils easily, so a minimum boiling point. Low vapour pressure means it is hard to boil, so a maximum boiling point. At the azeotrope the liquid and vapour have the same composition, so distillation cannot separate them.

5. Colligative Properties

Properties that depend only on the number of solute particles, not their nature, for a non-volatile solute in dilute solution. There are four: relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure.

($w_2$ = grams of solute, $w_1$ = grams of solvent, $K_b, K_f$ in K kg mol⁻¹. For water $K_b = 0.52$ and $K_f = 1.86$.)

Why does the boiling point rise and the freezing point fall? A liquid boils when its vapour pressure reaches the outside pressure. The solute lowered the vapour pressure, so you must heat more to reach it: boiling point up. Freezing needs the liquid's vapour pressure to match the solid's, and the solute lowered the liquid's, so the two meet only at a lower temperature: freezing point down. Both shifts are proportional to molality.

Pressure cooker (2025 board): higher pressure raises the boiling point of water above 100°C, so food cooks faster.

6. Osmosis & Osmotic Pressure

• Osmosis: solvent flows through a semipermeable membrane from lower to higher solute concentration.
• Osmotic pressure ($\Pi$): the extra pressure on the solution that just stops osmosis.

  $$\Pi = iCRT,\qquad M_2 = \frac{w_2RT}{\Pi V}$$

  Use $R = 0.0821$ L atm K⁻¹ mol⁻¹, $V$ in litres, $T$ in kelvin.
• Best method for polymers and proteins (2023 board): it works at room temperature so biomolecules do not decompose, uses molarity, and gives a measurable value even for very dilute solutions.
• Isotonic: same $\Pi$ (0.9% NaCl matches blood). Hypertonic (over 0.9%): cells lose water and shrink. Hypotonic (under 0.9%): cells take in water and swell.
• Reverse osmosis: applying pressure greater than $\Pi$ on the solution side pushes the solvent out, which is used to desalinate sea water.

7. van't Hoff Factor (i)

Colligative formulas assume the solute stays as it is. If it dissociates (more particles) or associates (fewer particles), the observed effect changes, and $i$ corrects for that:

$$i = \frac{\text{observed colligative property}}{\text{calculated colligative property}} = \frac{M_{normal}}{M_{abnormal}} = \frac{\text{moles of particles after}}{\text{moles of particles before}}$$

• Dissociation into $n$ ions: $i = 1+(n-1)\alpha$. (For complete dissociation, $i = n$: NaCl 2, CaCl₂ 3, K₂SO₄ 3.)
• Association of $n$ molecules: $i = 1-\alpha\left(1-\dfrac1n\right)$. (Dimer: $i = 1-\alpha/2$.)

Lucid check: same molality, but CaCl₂ gives 3 particles and glucose gives 1, so CaCl₂ has three times the effect. Among 0.1 M glucose, KCl and CaCl₂, CaCl₂ has the lowest freezing point (2026 board) and the highest boiling point and osmotic pressure. For association, fewer particles means a smaller colligative effect, so the molar mass you calculate from it comes out too large.

Solved (2024 board): 1 molal A₂B₃ is 60% ionised. It gives 5 ions, so $i = 1+4(0.6) = 3.4$, $\Delta T_b = 3.4\times0.52\times1 = 1.77$ K, and $T_b = 101.77$°C.

8. Numerical Toolkit

Five steps for any colligative numerical: (1) identify the property and solvent, and pick $K_b$ or $K_f$; (2) decide $i$ (electrolyte or not); (3) convert units (g to mol, g to kg, mL to L, °C to K); (4) substitute with $i$ included; (5) give the answer with unit and correct sign.

Last 4 years at a glance: electrolytes and $i$ (CaCl₂ versus KCl), association and dissociation, deviation types with reasons, azeotropes, Henry's law applications, osmosis in daily life, and $\Delta T_b/\Delta T_f$ numericals. Practise the 10 PYQ and 20 flashcards on this page to lock these in.