Solutions

2.1 Core concepts

• A solution is a homogeneous mixture of two or more components; the component in the largest quantity is the solvent and determines the physical state of the solution, while the other components are solutes. We restrict ourselves to binary solutions (NCERT §1.1, p. 1–2).
• Nine types of solutions exist based on the physical state of solute and solvent — gaseous solutions (gas/liquid/solid in gas; e.g. O2+N2, chloroform in N2, camphor in N2), liquid solutions (gas/liquid/solid in liquid; e.g. O2 in water, ethanol in water, glucose in water), and solid solutions (gas/liquid/solid in solid; e.g. H2 in Pd, Na-amalgam, Cu in Au) (NCERT §1.1, Table 1.1, p. 2).
• Concentration can be expressed as mass % (w/w = mass of component × 100 / total mass), volume % (V/V), mass-by-volume % (w/V, mass of solute in 100 mL solution — common in medicine/pharmacy), ppm (parts × 10⁶ / total parts) for trace solutes, mole fraction x_i = n_i / Σn_i with Σx_i = 1, molarity M = moles of solute / litre of solution, and molality m = moles of solute / kg of solvent (NCERT §1.2, p. 2–4).
• Mass %, ppm, mole fraction and molality are independent of temperature; molarity depends on temperature because volume varies with temperature while mass does not (NCERT §1.2, p. 5).
• Solubility is the maximum amount of a substance that can be dissolved in a specified quantity of solvent at a specified temperature; it depends on the nature of solute and solvent, temperature, and pressure. "Like dissolves like" — polar solutes dissolve in polar solvents and non-polar in non-polar (NCERT §1.3, §1.3.1, p. 5–6).
• For a solid in a liquid, dissolution and crystallisation reach a dynamic equilibrium (Solute + Solvent ⇌ Solution); the saturated concentration equals the solubility. If dissolution is endothermic (Δ_sol H > 0) solubility increases with temperature; if exothermic (Δ_sol H < 0) it decreases. Pressure has no significant effect on solid–liquid solubility (NCERT §1.3.1, p. 6).
• For a gas in a liquid, solubility increases with pressure. Henry's law: at constant temperature, the partial pressure of the gas in vapour phase is directly proportional to its mole fraction in solution — p = K_H·x. Higher K_H ⇒ lower solubility at given pressure; K_H increases with temperature, so gas solubility decreases as temperature rises (aquatic life prefers cold water) (NCERT §1.3.2, p. 7–8, Table 1.2).
• Applications of Henry's law: CO2 sealed under high pressure in soft drinks; scuba divers' tanks use He-diluted air to prevent "bends" (N2 bubbles in blood on ascent); anoxia at high altitudes due to low partial pressure of O2 (NCERT §1.3.2, p. 8–9).
• Raoult's law (two volatile components 1 and 2): partial vapour pressure of each volatile component is proportional to its mole fraction in solution — p1 = x1·p1°, p2 = x2·p2°; total p_total = p1° + (p2° – p1°)·x2. In the vapour phase, mole fraction of component i is y_i = p_i / p_total; the vapour is always richer in the more volatile component (NCERT §1.4.1, p. 9–11).
• Raoult's law is a special case of Henry's law where the proportionality constant K_H = p1° (i.e. the gas becomes a volatile component) (NCERT §1.4.2, p. 12).
• For a non-volatile solute (solid in liquid), only solvent contributes to vapour pressure. Raoult's law in general form: partial vapour pressure of each volatile component is directly proportional to its mole fraction, p1 = x1·p1°. A plot of p_solution vs. x_solvent is linear, varying from 0 to p1° (NCERT §1.4.3, p. 12–13, Fig. 1.5).
• Ideal solutions obey Raoult's law over the entire concentration range, with Δ_mix H = 0 and Δ_mix V = 0; A-A, B-B and A-B interactions are nearly equal. Examples: n-hexane + n-heptane, bromoethane + chloroethane, benzene + toluene (NCERT §1.5.1, p. 13).
• Non-ideal solutions: positive deviation when A-B interactions are weaker than A-A and B-B (vapour pressure higher than Raoult prediction; e.g. ethanol + acetone, CS2 + acetone). Negative deviation when A-B interactions are stronger than A-A and B-B (vapour pressure lower; e.g. phenol + aniline, chloroform + acetone — H-bond between CHCl3 H and acetone O) (NCERT §1.5.2, p. 13–14, Fig. 1.6).
• Azeotropes are binary mixtures with identical composition in liquid and vapour phase that boil at constant temperature and cannot be separated by fractional distillation. Large positive deviation ⇒ minimum-boiling azeotrope (e.g. 95% v/v ethanol-water). Large negative deviation ⇒ maximum-boiling azeotrope (e.g. 68% HNO3 + 32% water, b.p. 393.5 K) (NCERT §1.5.2, p. 14–15).
• Four colligative properties (depend only on the number of solute particles, not their identity): (1) relative lowering of vapour pressure, (2) elevation of boiling point, (3) depression of freezing point, (4) osmotic pressure (NCERT §1.6, p. 15).
• Relative lowering of vapour pressure: (p1° − p1)/p1° = x2 (mole fraction of solute); for dilute solutions this equals n2/n1 = (w2·M1)/(M2·w1), used to find M2 (NCERT §1.6.1, p. 15–16, eq. 1.24–1.28).
• Elevation of boiling point: ΔT_b = T_b − T_b° = K_b·m, where K_b is the molal elevation (ebullioscopic) constant (unit K kg mol⁻¹). For water K_b = 0.52, benzene 2.53, chloroform 3.63, etc. M2 = (1000·K_b·w2)/(ΔT_b·w1) (NCERT §1.6.2, p. 16–17, eq. 1.30, 1.33, Table 1.3).
• Depression of freezing point: ΔT_f = T_f° − T_f = K_f·m, where K_f is the molal depression (cryoscopic) constant (unit K kg mol⁻¹). For water K_f = 1.86, benzene 5.12, camphor-like cyclohexane 20.00, carbon tetrachloride 31.8. M2 = (1000·K_f·w2)/(ΔT_f·w1). The values of K_f and K_b can also be calculated from K_f = R·M1·T_f²/(1000·Δ_fus H) and K_b = R·M1·T_b²/(1000·Δ_vap H) (NCERT §1.6.3, p. 18–19, eq. 1.34–1.38, Table 1.3).
• Osmosis: net flow of solvent through a semipermeable membrane from pure solvent (or dilute solution) into the more concentrated solution. The excess pressure that must be applied on the solution side to just stop this flow is osmotic pressure π. For dilute solutions π = CRT = (n2/V)·RT, so M2 = (w2·R·T)/(π·V). Isotonic solutions have equal π (e.g. 0.9% w/V NaCl = normal saline ≈ blood plasma); hypertonic causes cells to shrink, hypotonic causes them to swell. Reverse osmosis (RO, used for desalination) drives solvent out of solution when applied pressure > π; cellulose acetate is the workable porous membrane (NCERT §1.6.4 & §1.6.5, p. 20–23, eq. 1.39–1.42, Fig. 1.9–1.11).
• Abnormal molar mass: solutes that dissociate (e.g. KCl, NaCl, K2SO4) give experimental M lower than true M (more particles); solutes that associate (e.g. acetic acid dimer in benzene) give M higher than true (NCERT §1.7, p. 23–24).
• van't Hoff factor i = (normal molar mass)/(abnormal molar mass) = (observed colligative property)/(calculated colligative property) = (moles of particles after dissociation/association)/(moles before). i > 1 for dissociation, i < 1 for association. Modified equations: ΔT_b = i·K_b·m, ΔT_f = i·K_f·m, π = i·(n2/V)·RT, (p1°−p1)/p1° = i·(n2/n1). For KCl, NaCl, MgSO4 i → 2 in dilute solution; for K2SO4 i → 3 (NCERT §1.7, p. 24–25, Table 1.4).

2.2 Definitions to memorise

2.3 Diagrams / processes to remember

• Fig. 1.1 (p. 7): Effect of pressure on the solubility of a gas — gas particles compressed above the solution increase dissolution rate.
• Fig. 1.2 (p. 7): Linear plot of partial pressure vs. mole fraction of HCl in cyclohexane at 293 K; slope = K_H.
• Fig. 1.3 (p. 10): Vapour pressure vs. mole fraction for an ideal binary liquid solution — lines I (p1 vs x1), II (p2 vs x2) and III (p_total vs x2) all linear.
• Fig. 1.4 (p. 12): Lowering of vapour pressure when a non-volatile solute is added — fraction of surface available for solvent escape is reduced.
• Fig. 1.5 (p. 13): Linear plot of solution vapour pressure vs. mole fraction of solvent (Raoult's law plot for non-volatile solute).
• Fig. 1.6 (p. 14): Vapour pressure plots showing (a) positive deviation, (b) negative deviation from Raoult's law.
• Fig. 1.7 (p. 17): Vapour-pressure-vs-temperature curves of pure solvent and solution — ΔT_b is the horizontal gap at 1.013 bar.
• Fig. 1.8 (p. 18): Same diagram showing ΔT_f as the gap between the freezing points of pure solvent and solution.
• Fig. 1.9 / 1.10 (p. 20–21): Thistle funnel and U-tube setups demonstrating osmosis and the definition of osmotic pressure.
• Fig. 1.11 (p. 23): Reverse osmosis schematic — applied pressure > π forces pure water through a cellulose acetate membrane.
• Table 1.2 (p. 8): K_H values; e.g. He = 144.97 kbar at 293 K, CO2 = 1.67 kbar at 298 K, N2 = 76.48 kbar at 293 K.
• Table 1.3 (p. 19): K_b and K_f for water (0.52, 1.86), benzene (2.53, 5.12), chloroform (3.63, 4.79), CCl4 (5.03, 31.8), camphor-like cyclohexane (2.79, 20.00).
• Table 1.4 (p. 25): van't Hoff factor i values for NaCl, KCl, MgSO4, K2SO4 at 0.1 m, 0.01 m, 0.001 m — approach the integer ideal value on dilution.

2.4 Common confusions / NTA trap points

• Confusing molarity (per litre of solution, T-dependent) with molality (per kg of solvent, T-independent). NTA often gives density to convert one to the other.
• Forgetting that K_H increases with temperature, so a higher K_H means lower solubility — students misread the trend.
• Mixing up positive and negative deviation: positive deviation ⇒ weaker A-B forces ⇒ minimum-boiling azeotrope; negative deviation ⇒ stronger A-B forces ⇒ maximum-boiling azeotrope.
• Forgetting to include the van't Hoff factor i for electrolytes (i = 2 for NaCl/KCl, i = 3 for K2SO4) when computing colligative properties.
• For association (e.g. benzoic acid dimer in benzene), i < 1 and observed molar mass is higher than the true molecular mass — the opposite of dissociation.
• Confusing isotonic / hypertonic / hypotonic — recall that 0.9% w/V NaCl is isotonic with blood; cells in hypertonic solutions shrink (water leaves), in hypotonic solutions swell.