VKC Notes · Solutions · Civil Services P-I · IFoS P-I · Geo-Scientist Prelims and P-II

7.2 Solutions: Raoult’s and Henry’s Laws, Non-ideal Solutions, Colligative Properties, van ’t Hoff Factor and Activity

★★★ 2021–2026: 42 Geo-Scientist Prelims questions, six to nine every year, the largest single Prelims block in physical chemistry; and 1 IFoS Mains part (10 marks) on activity coefficients. Mains asks the same ideas inside phase equilibria (7.1) and electrochemistry (8.3).

Syllabus lines. Civil Services and IFoS (Phase equilibria and solutions): “phase equilibria in binary systems, partially miscible liquids …; partial molar quantities, their significance and determination; excess thermodynamic functions and their determination”. Geo-Scientist Prelims asks Raoult’s and Henry’s laws, colligative properties and the van ’t Hoff factor every year; Mains Paper II has activity and activity coefficients.

Two-page short notes for revision All VKC notes

Download PDF PLAN

PDF edition, print-ready. It opens with the VKC plan, together with every locked answer, note and test on the site.

CSE 2024 Q7(a) = asked there; tap to open the solved answerSN = line kept in the short notes

7.2.1 Raoult’s law and ideal solutions ★★★

(7.2.1)

Ideal solution: every component obeys Raoult’s law at all compositions; A–B interactions equal the average of A–A and B–B, so Δ_mixH = 0 and Δ_mixV = 0 (benzene–toluene, hexane–heptane). In terms of chemical potential, μ_A = μ_A* + RT ln x_A (6.2).SN
Total pressure is linear in the liquid composition Geo Pre 2022 Q65, while 1/p is linear in the vapour composition Geo Pre 2021 Q68. The vapour is richer in the more volatile component: pure pressures 1 : 6 and x_A : x_B = 1 : 4 give y_B = 24/25 = 0.96 Geo Pre 2023 Q61.SN
1 mol benzene (6.0 kPa) + 2 mol toluene (4.8 kPa): p = (1/3)(6.0) + (2/3)(4.8) = 5.2 kPa; y_benzene = 2.0/5.2 = 0.385, not 1/3 Geo Pre 2026 Q64.SN

Fig. 7.2.1 An ideal pair at 25 °C (benzene 12.7, toluene 3.8 kPa, computed): straight liquid line, vapour curve below; at x_A = 0.50, y_A = 0.77.

Draw it in 60 s: two dashed lines from zero to p_A* and p_B*, a straight line joining p_B* to p_A* (sum), a sagging curve under it (vapour); a tie-line from x to y.

7.2.2 Henry’s law and the solubility of gases ★★★

(7.2.2)

For a dilute solute the partial pressure is proportional to its mole fraction, but the constant K_B is not p_B*: a solute molecule is surrounded by solvent, not by its own kind. An ideal-dilute solution: solvent obeys Raoult, solute obeys Henry. Labels for a vapour-pressure plot: the straight line from the origin to K is Henry, the straight line to p* is Raoult, the curve is the real solution Geo Pre 2026 Q65.SN
Units follow the composition scale: Pa with mole fraction Geo Pre 2026 Q69. Large K means low solubility. H₂ in water, K = 7.03 × 10⁹ Pa, p = 1.00 × 10⁶ Pa: x = 1.42 × 10⁻⁴ Geo Pre 2021 Q69. O₂, K = 8.0 × 10⁴ kPa kg mol⁻¹, p = 20 kPa: b = 2.5 × 10⁻⁴ mol kg⁻¹ ≈ 0.25 mmol dm⁻³ Geo Pre 2024 Q65. Acetone in chloroform, K = 20 kPa, x = 0.30: p = 6.0 kPa Geo Pre 2025 Q70.SN
Ratio of dissolved O₂ and N₂ from air (y = 0.2 and 0.8) with K = 880 and 440: (p_O₂/K_O₂)/(p_N₂/K_N₂) = (0.2/880)/(0.8/440) = 0.125 Geo Pre 2022 Q68.
K depends on the gas, the solvent and the temperature; CO₂ (reacts with water) is far more soluble than O₂, and O₂ more than N₂ Geo Pre 2024 Q64 Geo Pre 2023 Q66. Gases that liquefy easily (strong attractions) or ionise in water are more soluble; solubility of most gases falls on heating (dissolution is exothermic) Geo Pre 2022 Q69.SN

7.2.3 Non-ideal solutions: positive and negative deviations ★★

Positive deviation (A–B weaker than A–A and B–B): molecules escape more easily, p above Raoult, Δ_mixH > 0, Δ_mixV > 0. Ethanol–water, acetone–CS₂, ethanol–cyclohexane. A large deviation gives a pressure maximum: a minimum-boiling azeotrope (ethanol–water, 95.6% ethanol by mass).SN
Negative deviation (A–B stronger, often a new H-bond): p below Raoult, Δ_mixH < 0, volume contracts. Acetone–chloroform (C–H···O), HNO₃–water, HCl–water; a pressure minimum gives a maximum-boiling azeotrope. Distillation of azeotropes and partially miscible pairs: 7.1.7.SN
In either case each component approaches Raoult as x → 1 and Henry as x → 0; the Duhem–Margules equation links the two partial pressures (6.2.4), so if one component deviates positively the other must too.

Fig. 7.2.2 Positive and negative deviations (computed from a regular-solution model, ξ = ±1.4): total pressure through a maximum or a minimum.

Draw it in 60 s: two boxes: dashed straight Raoult lines; in one the three curves bow upward with a peak in the top curve, in the other they sag with a dip.

7.2.4 Thermodynamics of mixing and excess functions ★★

(7.2.3)

Ideal mixing is driven only by entropy (Δ_mixH = 0, Δ_mixV = 0); Δ_mixG < 0 at all compositions, most negative at x = 0.5.SN
Excess functions: X^E = Δ_mixX(real) − Δ_mixX(ideal). Determination: G^E from vapour pressures (γ_i = p_i/x_ip_i*), H^E from calorimetry (heat of mixing), V^E from densities (dilatometry), S^E = (H^E − G^E)/T.SN
Regular solution: H^E = ξnRTx_Ax_B with S^E = 0, so ln γ_A = ξx_B². For ξ > 2, Δ_mixG has two minima and the liquids separate into two phases: the origin of partial miscibility and of the upper critical solution temperature (7.1.7).SN

Fig. 7.2.3 Gibbs energy of mixing of a regular solution (computed) for ξ = 0 to 3.

Draw it in 60 s: a deep U for ξ = 0; flatter curves as ξ grows; for ξ = 3 a W with two dips (two liquid phases).

Part of VKC Basic

Read all 11 sections of this topic, its short notes and the PDF with VKC Basic

VKC Basic (₹999 for 6 months) opens every solved answer, the notes, the handbook and the daily answer archive. Every Mains test series includes it.

See what is included Already a member? Sign in

Solved PYQs, short notes and books: vkcscience.comTelegram: t.me/upsc_chemistry_vkc