Solutions and Colligative Properties — MHT-CET Formulas and Traps

Types of Solutions, Solubility and Henry's Law

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}}

Types of Solutions by the States of Solute and Solvent

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.

Common traps

Naming the solvent first

'Solid in gas' is a solid solute in a gas solvent. Iodine in air is solid-in-gas, not gas-in-solid; the reversed option is always offered.

Ignoring the water of crystallisation

\text{BaCl}_2\cdot2\text{H}_2\text{O}

brings its own water; the water to ADD is

50 - 7.04

, not

50 - 6

. Option (D)

50.0

g is the version that forgot the hydrate entirely.

Subtracting the hydration enthalpy

\Delta H_{\text{hyd}}

is already negative; ADD it.

699 - (-681.8)

gives

1380

, not on the list, but a sign slip in the NaCl stem gives

+786

, which is option (A).

Dividing by the pressure

In the CET form

S = K_H P

; solubility is

K_H

TIMES

P

. Dividing gives

8.56 \times 10^{-4}

, and the un-multiplied

K_H

itself is offered as option (C).

Vapour Pressure and Raoult's Law

Learn this subtopic in the notes

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}

Ideal and Non-Ideal Solutions: Which Way a Mixture Deviates

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.

Common traps

Using the given mole fraction for the wrong component

If

x_B = 0.4

is given,

x_A = 0.6

multiplies

P_A^\circ

. Swapping them turns

400

into a value that is also on the list.

Dividing by the solution's pressure, or reporting the solvent's mole fraction

\dfrac{2}{30}

gives

0.067

, and

0.9375

is

x_1

, the SOLVENT's mole fraction — both are options on the

32/30

stem. The relative lowering divides by

P^\circ

and equals the SOLUTE's mole fraction.

Calling chloroform + acetone positive

Chloroform's C–H hydrogen-bonds to acetone's C=O, a new attraction that LOWERS the vapour pressure: negative deviation. Ethanol + acetone is the positive one.

Elevation of Boiling Point

Learn this subtopic in the notes

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

Common traps

Grams where kilograms belong

Molality is per KILOGRAM of solvent.

30

g is

0.03

kg; leaving it as

30

drops the answer by a factor of

1000

, and the option list is built around that.

Swapping W₁ and W₂

W_2

(solute) is on top,

W_1

(solvent) below. The swap changes

200

to

2

— not on the list — but on the formula-recognition stem the swapped option is (B).

Counting AlPO₄ as five ions

AlPO

_4

gives Al

^{3+}

and PO

_4^{3-}

: TWO ions,

i = 2

, like MgSO

_4

. Al

_2

(SO

_4

)

_3

is the one with five.

Depression of Freezing Point

Learn this subtopic in the notes

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

Common traps

Reading a freezing point as the depression

-0.95^\circ

C is the freezing POINT; the depression is

+0.95

K. A stem in kelvin that says 'freezes at

-0.7

K' is using the same convention — take the magnitude.

Choosing the formula with W₁ on top

On the formula-recognition stem the four options permute

W_1

,

W_2

,

K_f

and

\Delta T_f

. Check with units:

K_f

(K kg mol

^{-1}

)

\times

g

\times 1000

, over K

\times

g, leaves g mol

^{-1}

.

Ranking by molality alone

1

m AlPO

_4

beats

0.05

m Al

_2

(SO

_4

)

_3

only after the ion count:

2

against

0.25

. Without

i

, the highest molality still wins here — but the LOWEST-depression stem is decided by

i

.

Osmotic Pressure

Learn this subtopic in the notes

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

Common traps

Volume in millilitres

0.025

mol in

100

mL is

0.25

M, not

0.00025

M. Convert to dm

^3

first; the mL version gives

0.00615

atm and a wrong pick.

Leaving V in millilitres

300

mL is

0.3

dm

^3

; with

300

in the denominator the molar mass comes out

1000

times too small. The options are spaced to catch a factor-of-ten slip, not this one — so the mistake shows as 'none of the options', a sign to recheck units.

Comparing grams per litre directly

6

g of urea and

34.2

g of sucrose are the SAME number of moles. Isotonicity is about molarity; the mass-matched pair (

6

and

6

) is never the answer.

Van't Hoff Factor and Abnormal Molar Mass

Learn this subtopic in the notes

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}

Which Properties Are Colligative, and the Statements the Exam Tests

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.

Common traps

Using the calculated ΔTf as the observed one

K_f m = 0.372

is the EXPECTED depression for

0.2

m; the observed

0.68

goes on top. Inverting gives

0.55

, option (D) on the

-0.660

K stem.

Dividing by n instead of n − 1

\alpha = \dfrac{i - 1}{n - 1}

; for

n = 2

that is simply

i - 1

. Dividing

0.236

by

2

gives

11.8\%

, close to option (A).

Marking 'boiling point elevation' as the non-colligative one

The option list mixes 'boiling point' with 'freezing point depression'. The bare property is the odd one out; anything with 'elevation', 'depression' or 'lowering' in its name is colligative.

Solutions and Colligative Properties formulas

Types of Solutions, Solubility and Henry's Law

Concentration Terms: Which Ones Change With Temperature

Solubility of Solids: Like Dissolves Like, ΔH of Solution, and the Salt That Dissolves Less on Heating

Henry's Law: S = K_H · P, and Partial Pressures From Mole Fractions

Types of Solutions by the States of Solute and Solvent

Common traps

Vapour Pressure and Raoult's Law

Raoult's Law for Two Volatile Liquids: P = x_A P_A° + x_B P_B°

Relative Lowering of Vapour Pressure = Mole Fraction of the Solute

Ideal and Non-Ideal Solutions: Which Way a Mixture Deviates

Common traps

Elevation of Boiling Point

ΔTb = Kb · m: Solve for Any One of Molality, Kb, Moles or Solvent Mass

Molar Mass From ΔTb: M₂ = 1000 Kb W₂ / (ΔTb W₁)

Ranking Electrolyte Solutions: Compare i × m

Common traps

Depression of Freezing Point

ΔTf = Kf · m: Molality, Kf, or ΔTf From a Freezing Point

Molar Mass From ΔTf: M₂ = 1000 Kf W₂ / (ΔTf W₁)

Highest and Lowest Depression: Compare i × m

Common traps

Osmotic Pressure

π = CRT: Solve for π, C, T or n

Molar Mass From Osmotic Pressure: M = W R T / (π V)

Isotonic and Hypertonic Solutions, and π = iCRT for Electrolytes

Common traps

Van't Hoff Factor and Abnormal Molar Mass

The Van't Hoff Factor: i = ΔTf(observed)/(Kf · m), and the Ion Count for Complete Dissociation

Degree of Dissociation From i: α = (i − 1)/(n − 1)

Which Properties Are Colligative, and the Statements the Exam Tests

Common traps

More MHT-CET Chemistry formula sheets