MHT-CET Chemistry · Teaching notes

Solutions and Colligative Properties — MHT-CET Chemistry

Solutions and Colligative Properties is the largest chapter in MHT-CET Chemistry by past-year count and one of the cheapest: three questions a paper, and barely one in thirty of them HARD. Almost every question is one of five formulas with the numbers changed — Henry's law, Raoult's law, ΔTb = Kb·m, ΔTf = Kf·m and π = CRT — plus the van't Hoff factor that multiplies each of them for an electrolyte. The recall questions are a short list too: which solute-solvent pairing a given mixture is, which salt's solubility falls with temperature, which mixtures deviate from Raoult's law and in which direction, and which properties count as colligative. The pages below follow the textbook order, because each colligative property is the previous one's formula with a different constant, and the last page collects the van't Hoff factor that the electrolyte stems on every earlier page quietly assume. Every PYQ is tagged.

Every subtopic, worked example, formula and trap in one printable document — answers shown, ready to share.

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Subtopic notes

PYQ weightage by concept

19 concepts · 135 PYQs — where the marks actually sit, so you know what to drill first

Types of Solutions, Solubility and Henry's Law29 PYQs · 21%

Concept	PYQs	Share
Henry's Law: S = K_H · P, and Partial Pressures From Mole Fractions	13	10%
Types of Solutions by the States of Solute and Solvent	7	5%
Solubility of Solids: Like Dissolves Like, ΔH of Solution, and the Salt That Dissolves Less on Heating	7	5%
Concentration Terms: Which Ones Change With Temperature	2	1%

Vapour Pressure and Raoult's Law24 PYQs · 18%

Concept	PYQs	Share
Relative Lowering of Vapour Pressure = Mole Fraction of the Solute	14	10%
Raoult's Law for Two Volatile Liquids: P = x_A P_A° + x_B P_B°	6	4%
Ideal and Non-Ideal Solutions: Which Way a Mixture Deviates	4	3%

Elevation of Boiling Point28 PYQs · 21%

Concept	PYQs	Share
ΔTb = Kb · m: Solve for Any One of Molality, Kb, Moles or Solvent Mass	18	13%
Ranking Electrolyte Solutions: Compare i × m	6	4%
Molar Mass From ΔTb: M₂ = 1000 Kb W₂ / (ΔTb W₁)	4	3%

Depression of Freezing Point16 PYQs · 12%

Concept	PYQs	Share
ΔTf = Kf · m: Molality, Kf, or ΔTf From a Freezing Point	9	7%
Molar Mass From ΔTf: M₂ = 1000 Kf W₂ / (ΔTf W₁)	5	4%
Highest and Lowest Depression: Compare i × m	2	1%

Osmotic Pressure22 PYQs · 16%

Concept	PYQs	Share
Isotonic and Hypertonic Solutions, and π = iCRT for Electrolytes	8	6%
π = CRT: Solve for π, C, T or n	7	5%
Molar Mass From Osmotic Pressure: M = W R T / (π V)	7	5%

Van't Hoff Factor and Abnormal Molar Mass16 PYQs · 12%

Concept	PYQs	Share
The Van't Hoff Factor: i = ΔTf(observed)/(Kf · m), and the Ion Count for Complete Dissociation	12	9%
Which Properties Are Colligative, and the Statements the Exam Tests	3	2%
Degree of Dissociation From i: α = (i − 1)/(n − 1)	1	1%

Formula & revision sheet

16 formulas · 3 reference tables · 19 gotchas across all subtopics — the exam-eve cheat-sheet

Types of Solutions, Solubility and Henry's Law

Formulas (3)

Concentration Terms: Which Ones Change With Temperature · Concentration terms $M = \frac{n}{V(\text{L})} \ (\text{T-dependent}),\qquad m = \frac{n}{W_{\text{solvent}}(\text{kg})},\qquad x = \frac{n}{n_{\text{total}}}$
Solubility of Solids: Like Dissolves Like, ΔH of Solution, and the Salt That Dissolves Less on Heating · Enthalpy of solution $\Delta H_{\text{sol}} = \Delta H_{\text{lattice}} + \Delta H_{\text{hyd}}$
Henry's Law: S = K_H · P, and Partial Pressures From Mole Fractions · Henry and Dalton $S = K_H\,P \qquad K_H = \frac{S}{P} \qquad P_i = x_i\,P_{\text{total}}$

Reference tables (1)

Types of Solutions by the States of Solute and Solvent9 rows

Solute	Solvent	Example
Gas	Liquid	Carbonated water ( $\text{CO}_2$ in water), oxygen in water The gas is the solute even though it is what the drink is named for.
Liquid	Liquid	Ethanol in water; gasoline (a liquid-in-liquid mixture of hydrocarbons)
Solid	Liquid	Sea water (salt in water), sugar in water
Solid	Gas	Iodine vapour in air; camphor in nitrogen Iodine in air is solid-in-GAS — air is the solvent, whatever the amount of iodine.
Liquid	Gas	Chloroform mixed with nitrogen; water vapour in air (humidity)
Gas	Gas	Air (oxygen in nitrogen)
Solid	Solid	Alloys — brass (zinc in copper), bronze (tin in copper) An alloy is a solid solution; bronze is NOT solid-in-liquid.
Gas	Solid	Hydrogen adsorbed in palladium
Liquid	Solid	Amalgam — mercury in sodium or in silver

Name the solute first, then the solvent: 'solid in gas' means a solid solute in a gaseous solvent.

Watch out for (4)

Naming the solvent first
→ Types of Solutions by the States of Solute and Solvent
Ignoring the water of crystallisation
→ Concentration Terms: Which Ones Change With Temperature
Subtracting the hydration enthalpy
→ Solubility of Solids: Like Dissolves Like, ΔH of Solution, and the Salt That Dissolves Less on Heating
Dividing by the pressure
→ Henry's Law: S = K_H · P, and Partial Pressures From Mole Fractions

Vapour Pressure and Raoult's Law

Formulas (2)

Raoult's Law for Two Volatile Liquids: P = x_A P_A° + x_B P_B° · Raoult's law $P_{\text{total}} = x_A P_A^\circ + x_B P_B^\circ \qquad y_A = \frac{x_A P_A^\circ}{P_{\text{total}}}$
Relative Lowering of Vapour Pressure = Mole Fraction of the Solute · Relative lowering $\frac{P^\circ - P}{P^\circ} = x_2 = \frac{n_2}{n_1 + n_2} \approx \frac{W_2\,M_1}{M_2\,W_1}$

Reference tables (1)

Ideal and Non-Ideal Solutions: Which Way a Mixture Deviates3 rows

Type	Raoult's law	ΔH mix, ΔV mix	Examples
Ideal	Obeyed at every composition	Both zero	Benzene + toluene; hexane + heptane The exam's default 'obeys Raoult's law' answer is benzene + toluene.
Positive deviation	P above Raoult	Both positive	Ethanol + acetone; CS₂ + acetone; ethanol + water Acetone breaks ethanol's hydrogen bonds — weaker A–B attraction, higher vapour pressure.
Negative deviation	P below Raoult	Both negative	Chloroform + acetone; phenol + aniline; HNO₃ + water Chloroform's H bonds to acetone's oxygen — a NEW attraction, lower vapour pressure.

Deviation follows the strength of the A–B attraction relative to A–A and B–B.

Watch out for (3)

Using the given mole fraction for the wrong component
→ Raoult's Law for Two Volatile Liquids: P = x_A P_A° + x_B P_B°
Dividing by the solution's pressure, or reporting the solvent's mole fraction
→ Relative Lowering of Vapour Pressure = Mole Fraction of the Solute
Calling chloroform + acetone positive
→ Ideal and Non-Ideal Solutions: Which Way a Mixture Deviates

Elevation of Boiling Point

Formulas (3)

ΔTb = Kb · m: Solve for Any One of Molality, Kb, Moles or Solvent Mass · Boiling point elevation $\Delta T_b = K_b\,m = K_b\,\frac{n_2}{W_1(\text{kg})} \qquad T_b = T_b^\circ + \Delta T_b$
Molar Mass From ΔTb: M₂ = 1000 Kb W₂ / (ΔTb W₁) · Molar mass $M_2 = \frac{1000\,K_b\,W_2}{\Delta T_b\,W_1}$
Ranking Electrolyte Solutions: Compare i × m · Electrolyte elevation $\Delta T_b = i\,K_b\,m \qquad \text{rank by } i \times m$

Watch out for (3)

Grams where kilograms belong
→ ΔTb = Kb · m: Solve for Any One of Molality, Kb, Moles or Solvent Mass
Swapping W₁ and W₂
→ Molar Mass From ΔTb: M₂ = 1000 Kb W₂ / (ΔTb W₁)
Counting AlPO₄ as five ions
→ Ranking Electrolyte Solutions: Compare i × m

Depression of Freezing Point

Formulas (3)

ΔTf = Kf · m: Molality, Kf, or ΔTf From a Freezing Point · Freezing point depression $\Delta T_f = K_f\,m,\qquad \Delta T_f = T_f^\circ - T_f \qquad (K_f^{\text{water}} = 1.86\ \text{K kg mol}^{-1})$
Molar Mass From ΔTf: M₂ = 1000 Kf W₂ / (ΔTf W₁) · Molar mass $M_2 = \frac{1000\,K_f\,W_2}{\Delta T_f\,W_1}$
Highest and Lowest Depression: Compare i × m · Electrolyte depression $\Delta T_f = i\,K_f\,m \qquad \text{rank by } i \times m$

Watch out for (3)

Reading a freezing point as the depression
→ ΔTf = Kf · m: Molality, Kf, or ΔTf From a Freezing Point
Choosing the formula with W₁ on top
→ Molar Mass From ΔTf: M₂ = 1000 Kf W₂ / (ΔTf W₁)
Ranking by molality alone
→ Highest and Lowest Depression: Compare i × m

Osmotic Pressure

Formulas (3)

π = CRT: Solve for π, C, T or n · Van't Hoff equation $\pi = CRT = \frac{n}{V}RT \qquad (R = 0.082\ \text{dm}^3\,\text{atm K}^{-1}\text{mol}^{-1})$
Molar Mass From Osmotic Pressure: M = W R T / (π V) · Molar mass $M = \frac{W\,R\,T}{\pi\,V}$
Isotonic and Hypertonic Solutions, and π = iCRT for Electrolytes · Electrolytes and isotonicity $\pi = i\,C\,R\,T \qquad \text{isotonic} \iff \pi_1 = \pi_2 \iff (iC)_1 = (iC)_2$

Watch out for (3)

Volume in millilitres
→ π = CRT: Solve for π, C, T or n
Leaving V in millilitres
→ Molar Mass From Osmotic Pressure: M = W R T / (π V)
Comparing grams per litre directly
→ Isotonic and Hypertonic Solutions, and π = iCRT for Electrolytes

Van't Hoff Factor and Abnormal Molar Mass

Formulas (2)

The Van't Hoff Factor: i = ΔTf(observed)/(Kf · m), and the Ion Count for Complete Dissociation · Van't Hoff factor $i = \frac{\text{observed}}{\text{calculated}} = \frac{\Delta T_f^{\text{obs}}}{K_f\,m} = \frac{M_{\text{calc}}}{M_{\text{obs}}}$
Degree of Dissociation From i: α = (i − 1)/(n − 1) · Degree of dissociation $i = 1 + (n - 1)\alpha \ \Rightarrow\ \alpha = \frac{i - 1}{n - 1} \qquad \text{association: } i = 1 - \alpha + \frac{\alpha}{n}$

Reference tables (1)

Which Properties Are Colligative, and the Statements the Exam Tests6 rows

Property	Colligative?	Formula
Relative lowering of vapour pressure	Yes	$\dfrac{P^\circ - P}{P^\circ} = x_2$
Elevation of boiling point	Yes	$\Delta T_b = i K_b m$
Depression of freezing point	Yes	$\Delta T_f = i K_f m$
Osmotic pressure	Yes	$\pi = i C R T$
Boiling point (of the solution)	No	An intensive property of the liquid; its CHANGE is colligative 'Boiling point' alone is the standard wrong answer to 'which is not colligative'.
Osmosis	No	A process; osmotic PRESSURE is the property 'Osmosis is a colligative property' is a planted false statement.

Four properties, all proportional to particle count; the quantities they change are not themselves colligative.

Watch out for (3)

Using the calculated ΔTf as the observed one
→ The Van't Hoff Factor: i = ΔTf(observed)/(Kf · m), and the Ion Count for Complete Dissociation
Dividing by n instead of n − 1
→ Degree of Dissociation From i: α = (i − 1)/(n − 1)
Marking 'boiling point elevation' as the non-colligative one
→ Which Properties Are Colligative, and the Statements the Exam Tests