Solutions

Solutions

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

A solution is a homogeneous mixture of two or more substances. The component present in smaller amount is the solute; the one in larger amount is the solvent. Concentration can be expressed as molarity (M), molality (m), mole fraction (x), or mass percent.

Must-know equations for CUET UG:

• Molarity M = n_solute / V_solution(L)
• Molality m = n_solute / m_solvent(kg)
• Raoult’s Law p_A = p_A°·x_A
• Boiling point elevation ΔT_b = K_b·m
• Freezing point depression ΔT_f = K_f·m
• Osmotic pressure π = CRT
• van’t Hoff factor i = observed colligative property / calculated colligative property

High-yield pointers: Henry’s law (p = K_H·x) governs gas solubility; colligative properties depend on particle NUMBER, not identity; electrolytes give i > 1 due to dissociation, while associating solutes give i < 1.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Concentration Terms

Four concentration units dominate CUET questions. Molarity (M) = moles of solute per litre of solution (volume-dependent, temperature-sensitive). Molality (m) = moles of solute per kilogram of solvent (temperature-independent, preferred for colligative calculations). Mole fraction (x_A) = n_A / (n_A + n_B); dimensionless and useful in Raoult’s law. Mass percent = (mass of solute / mass of solution) × 100; ppm = (mass of solute / mass of solution) × 10⁶ for trace components.

Raoult’s Law

For a volatile solute-solvent pair, the partial vapour pressure of each component equals its pure vapour pressure multiplied by its mole fraction: p_A = p_A°·x_A. For a non-volatile solute, p_total = p_A°·x_A (the solute’s contribution is zero), giving the relative lowering of vapour pressure: (p_A° − p_A)/p_A° = x_B.

Colligative Properties

These depend solely on the number (not nature) of solute particles:

Property	Formula	Constant
Relative lowering of VP	Δp/p° = x_B	—
Boiling point elevation	ΔT_b = K_b·m	K_b (kg·K·mol⁻¹)
Freezing point depression	ΔT_f = K_f·m	K_f (kg·K·mol⁻¹)
Osmotic pressure	π = CRT	R = 0.0821 L·atm·K⁻¹·mol⁻¹

van’t Hoff Factor (i)

Electrolytes like NaCl dissociate (i ≈ 2 for NaCl, ≈3 for CaCl₂), while solutes like benzoic acid in benzene associate (i < 1). The degree of dissociation α = (i − 1)/(n − 1), where n is the number of ions per formula unit.

Henry’s Law

The solubility of a gas in a liquid at a given temperature is proportional to its partial pressure: p = K_H·x. Higher K_H means lower solubility; gases with stronger interaction with the solvent have smaller K_H.

Exam Pattern Tip

CUET UG Chemistry carries ~3% weight from this chapter, typically 1–2 MCQs. Common question types: numerical conversion between M and m using density, identifying Raoult’s-law deviation graphs (positive/negative), and calculating i from M_obs/M_calc or ΔT_obs/ΔT_calc.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Ideal vs Non-Ideal Solutions

Ideal solutions obey Raoult’s law at all concentrations and obey ΔH_mix = 0, ΔV_mix = 0 (e.g., benzene + toluene, n-hexane + n-heptane). Positive deviations occur when A–B interactions are weaker than A–A and B–B (e.g., acetone + CS₂, ethanol + cyclohexane), giving p_total > p_Raoult and minimum-boiling azeotropes. Negative deviations occur when A–B interactions are stronger (e.g., chloroform + acetone, HNO₃ + water), giving p_total < p_Raoult and maximum-boiling azeotropes. Azeotropes cannot be separated by simple distillation.

Osmosis in Practice

Osmotic pressure π = CRT applies to dilute solutions. Isotonic solutions have equal π; hypertonic solutions cause cell shrinkage (plasmolysis); hypotonic solutions cause cell swelling. Reverse osmosis applies pressure > π to purify seawater (typically π_seawater ≈ 25 atm), forcing water through a semipermeable membrane — a direct application tested in CUET general knowledge links.

Edge Cases and Numerical Traps

• Molarity changes with temperature (volume expands); molality does not. CUET problems often give density to interconvert.
• For π = CRT, use R = 0.0821 L·atm·K⁻¹·mol⁻¹ with C in mol·L⁻¹, OR R = 0.083 bar·L·K⁻¹·mol⁻¹. Mixing units is a frequent error.
• For solutes that dissociate fully (strong electrolytes), α → 1 and i = n; for partial dissociation, use α = (i − 1)/(n − 1).
• The abnormal molar mass M_obs = M_calc / i reveals association (M_obs > M_calc) or dissociation (M_obs < M_calc).

Common Mistakes

• Treating mass% and volume% as interchangeable.
• Using molality in Raoult’s law (Raoult’s law uses mole fraction, not molality).
• Forgetting that ΔT_f and ΔT_b are elevations/depressions of solvent’s transition temperatures, not absolute temperatures.
• Assuming i = 1 for all solutes — non-electrolytes only.

Practice Prompts

1. A 5% aqueous solution of glucose (M = 180 g·mol⁻¹) has density 1.02 g·mL⁻¹. Find its molarity and molality. (Answer key: M ≈ 0.283 mol·L⁻¹; m ≈ 0.293 mol·kg⁻¹)
2. 0.5 g of CaCl₂ (i = 2.75) in 100 mL water raises the boiling point by how much, given K_b(water) = 0.52 K·kg·mol⁻¹? (Apply ΔT_b = i·K_b·m with m computed from 4.5 g CaCl₂ in 0.1 kg solvent ≈ 0.4054 molal → ΔT_b ≈ 0.580 K)

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