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Liquid Solution & Colligative Properties formulas

Master Liquid Solution & Colligative Properties through 22 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Liquid Solution & Colligative Properties, every formula

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Molarity
$M = \frac{moles of solute}{volume (L)}$
Molality
$m = \frac{moles of solute}{mass of solvent (kg)}$
Mole fraction
$x_{A} = \frac{n _{A}}{n _{A} + n _{B}}$
Raoult's law
$P = x_{so l v e n t} P^{\circ}$
Q1MCQRaoult's law
Raoult's law for a solution with a non-volatile solute is:
- A
  $P=x_{solvent}P^{\circ}$
- B
  $P=x_{solute}P^{\circ}$
- C
  $P=P^{\circ}$
- D
  $P=x_{solvent}$
Raoult's law (two volatile)
$P = x_{A} P_{A}^{\circ} + x_{B} P_{B}^{\circ}$
Q1MCQTwo volatile
For two volatile liquids, the total vapour pressure is:
- A
  $x_A P_A^{\circ}+x_B P_B^{\circ}$
- B
  $x_A P_A^{\circ}$
- C
  $P_A^{\circ}+P_B^{\circ}$
- D
  $x_A x_B$
Relative lowering of vapour pressure
$\frac{P ^{\circ} - P}{P ^{\circ}} = x_{so l u t e}$
Q1MCQRLVP
The relative lowering of vapour pressure equals:
- A
  $x_{solute}$
- B
  $x_{solvent}$
- C
  $P^{\circ}$
- D
  $1$
Elevation in boiling point
$Δ T_{b} = K_{b} m$
Q1MCQBoiling point
The elevation in boiling point is:
- A
  $K_b m$
- B
  $K_f m$
- C
  $\dfrac{m}{K_b}$
- D
  $K_b$
Depression in freezing point
$Δ T_{f} = K_{f} m$
Q1MCQFreezing point
The depression in freezing point is:
- A
  $K_f m$
- B
  $K_b m$
- C
  $\dfrac{m}{K_f}$
- D
  $K_f$
Osmotic pressure
$π = C R T = \frac{n}{V} R T$
Q1MCQOsmotic pressure
The osmotic pressure of a dilute solution is:
- A
  $CRT$
- B
  $\dfrac{C}{RT}$
- C
  $CR$
- D
  $\dfrac{RT}{C}$
van't Hoff factor
$i = \frac{observed colligative property}{normal value}$
Q1MCQvan't Hoff factor
The van't Hoff factor $i$ for a solute that dissociates is:
- A
  greater than 1
- B
  less than 1
- C
  equal to 1
- D
  zero
Colligative property with i
$Δ T_{b} = i K_{b} m, π = i C R T$
Q1MCQColligative with i
The osmotic pressure with dissociation is:
- A
  $iCRT$
- B
  $\dfrac{CRT}{i}$
- C
  $CRT$
- D
  $iC$
Degree of dissociation (from i)
$α = \frac{i - 1}{n - 1}$
Q1MCQDissociation from i
The degree of dissociation from $i$ is:
- A
  $\dfrac{i-1}{n-1}$
- B
  $\dfrac{1-i}{n-1}$
- C
  $i-1$
- D
  $\dfrac{i}{n}$
Degree of association (from i)
$α = \frac{1 - i}{1 - \frac{1}{n}}$
Q1MCQAssociation from i
The degree of association from $i$ is:
- A
  $\dfrac{1-i}{1-\tfrac1n}$
- B
  $\dfrac{i-1}{n-1}$
- C
  $1-i$
- D
  $\dfrac{i}{n}$
Molar mass from ΔTb
$M = \frac{K _{b} \times w \times 1000}{Δ T _{b} \times W}$
Q1MCQMolar mass (ΔTb)
The molar mass from boiling-point elevation is:
- A
  $\dfrac{K_b\,w\times1000}{\Delta T_b\,W}$
- B
  $\dfrac{\Delta T_b\,W}{K_b\,w}$
- C
  $K_b\,w$
- D
  $\dfrac{K_b}{\Delta T_b}$
Molar mass from π
$M = \frac{w R T}{π V}$
Q1MCQMolar mass (π)
The molar mass from osmotic pressure is:
- A
  $\dfrac{wRT}{\pi V}$
- B
  $\dfrac{\pi V}{wRT}$
- C
  $\pi V$
- D
  $\dfrac{w}{\pi}$
Henry's law
$p = K_{H} x$
Q1MCQHenry's law
Henry's law states the solubility of a gas is:
- A
  $p=K_H x$
- B
  $p=\dfrac{K_H}{x}$
- C
  $p=K_H$
- D
  $x=K_H$
Isotonic solutions
$π_{1} = π_{2} \Rightarrow C_{1} = C_{2}$
Q1MCQIsotonic
Two isotonic solutions have equal:
- A
  osmotic pressures
- B
  masses
- C
  volumes
- D
  densities
Ideal solution
$Δ H_{mi x} = 0, Δ V_{mi x} = 0$
Q1MCQIdeal solution
For an ideal solution:
- A
  $\Delta H_{mix}=0$ and $\Delta V_{mix}=0$
- B
  $\Delta H_{mix}>0$
- C
  $\Delta V_{mix}>0$
- D
  $\Delta H_{mix}<0$
Positive deviation
$P > P_{R a o u l t} (Δ H_{mi x} > 0)$
Q1MCQPositive deviation
A solution shows positive deviation from Raoult's law when:
- A
  $\Delta H_{mix}>0$
- B
  $\Delta H_{mix}<0$
- C
  $\Delta H_{mix}=0$
- D
  $\Delta V_{mix}=0$
Negative deviation
$P < P_{R a o u l t} (Δ H_{mi x} < 0)$
Q1MCQNegative deviation
A solution shows negative deviation when:
- A
  $\Delta H_{mix}<0$
- B
  $\Delta H_{mix}>0$
- C
  $\Delta H_{mix}=0$
- D
  $\Delta V_{mix}>0$
ppm
$ppm = \frac{mass of solute}{mass of solution} \times 1 0^{6}$
Q1MCQppm
The concentration in ppm is:
- A
  $\dfrac{\text{mass of solute}}{\text{mass of solution}}\times10^{6}$
- B
  $\dfrac{\text{mass of solute}}{\text{mass of solution}}\times100$
- C
  $\dfrac{\text{moles}}{\text{volume}}$
- D
  $\dfrac{\text{mass}}{\text{volume}}$
Colligative property nature
$depends on number of particles, not identity$
Q1MCQColligative nature
Colligative properties depend on:
- A
  the number of solute particles
- B
  the nature of the solute
- C
  the size of particles
- D
  the colour

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Liquid Solution & Colligative Properties formulas

Liquid Solution & Colligative Properties, every formula

Molarity

Molality

Mole fraction

Raoult's law

Raoult's law (two volatile)

Relative lowering of vapour pressure

Elevation in boiling point

Depression in freezing point

Osmotic pressure

van't Hoff factor

Colligative property with i

Degree of dissociation (from i)

Degree of association (from i)

Molar mass from ΔTb

Molar mass from π

Henry's law

Isotonic solutions

Ideal solution

Positive deviation

Negative deviation

ppm

Colligative property nature

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