Part of PC-05 — Solutions & Colligative Properties

Error Analysis — Common Calculation Traps

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Trap 1: Using Molarity Instead of Molality

Wrong: ΔTb\Delta Tb = Kb × C (molarity) Right: ΔTb\Delta Tb = Kb × m (molality = mol/kg of solvent, not solution) Why it matters: Density ≠ 1 for all solutions; for dilute aqueous solutions they are approximately equal but not in numericals.

Trap 2: Using °C Instead of Kelvin in Osmotic Pressure

Wrong: π = CRT with T = 27°C Right: T = 27 + 273 = 300 K. Always convert to Kelvin for π = CRT.

Trap 3: Forgetting the Van't Hoff Factor for Electrolytes

Wrong: ΔTf\Delta Tf (0.1 m NaCl) = 1.86 × 0.1 = 0.186 K Right: ΔTf\Delta Tf = i × Kf × m = 2 × 1.86 × 0.1 = 0.372 K (approximately) Rule: Any time you see NaCl, KCl, CaCl2CaCl_{2}, K2SO4K_{2}SO_{4}, AlCl3AlCl_{3} — multiply by i.

Trap 4: Direction of Apparent Molar Mass for Association

Wrong: "Association gives lower apparent molar mass" Right: Association (i < 1) → fewer particles → smaller ΔT\Delta TM2M_{2} formula gives LARGER M (since ΔT\Delta T is in denominator). Apparent M > True M for associating solutes.

Trap 5: Confusing Minimum and Maximum Boiling Azeotropes

Wrong: "Positive deviation forms maximum boiling azeotrope" Right: Positive deviation → HIGHER P → LOWER boiling point → MINIMUM boiling azeotrope. Negative deviation → LOWER P → HIGHER boiling point → MAXIMUM boiling azeotrope.

Trap 6: Applying Molality to Osmotic Pressure

Wrong: π = i × m × R × T (using molality) Right: π = i × C × R × T, where C is molar concentration (mol/L). Use molarity for osmotic pressure, molality for ΔTb\Delta Tb and ΔTf\Delta Tf.

Trap 7: Wrong Formula for Association Degree

Wrong: i = 1 + (n−1)α (this is for dissociation!) Right for association (dimerization n=2): i = 1 − α/2 (i.e., i = 1 + (1/2 − 1)α = 1 − α/2) Memory: For association — particles DECREASE, so "1 minus something".

Trap 8: Forgetting That K_H Increases With Temperature

Wrong: "K_H decreases with temperature (like Kb), so gas solubility increases" Right: K_H INCREASES with temperature → since x = p/K_H, mole fraction (solubility) DECREASES with increasing temperature. Gas behaviour is opposite to solid solute behaviour (most solid solutes become MORE soluble with temperature).

Trap 9: Mole Fraction in Vapour vs Liquid Phase

Wrong: Assuming mole fraction in vapour phase equals mole fraction in liquid phase Right: y_A(vapour) = P_A/P_total = x_A·P°_A/(x_A·P°_A + x_B·P°_B). The more volatile component (higher P°) is enriched in the vapour phase.

Trap 10: Using Mass Fraction Instead of Mole Fraction in Raoult's Law

Wrong: Using weight percentage directly as x_solute in ΔP\Delta P/P° formula Right: Always convert mass to moles first, then calculate mole fraction. ΔP\Delta P/P° = n_solute/(n_solute + n_solvent).

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