StudyBeacon Quiz – Colligative Properties (JEE Main PYQ)
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Q1.
Statement I: Henry's law constant $K_H$ is constant with respect to variations in solution concentration for ideally dilute solutions.
Statement II: $K_H$ does not differ for the same solute in different solvents.
Henry’s law:
$P = K_H x$
For dilute solutions $K_H$ remains constant.
But $K_H$ **depends strongly on solvent and temperature**, so statement II is false.
Q2.
0.3 g solute A (M = 60 g/mol) and 0.9 g solute B (M = 180 g/mol) dissolved in 100 mL water at 27°C.
Osmotic pressure
$\pi = CRT$
Moles A
$=0.3/60=0.005$
Moles B
$=0.9/180=0.005$
Total moles
$=0.01$
Volume = 0.1 L
$C=0.1$
$\pi = 0.1 \times 0.082 \times 300$
$\pi = 2.46 \text{ atm}$
Q3.
Vapour pressure decreases from 640 mmHg to 600 mmHg.
Relative lowering
$\frac{\Delta P}{P^0} = x_2$
$\frac{640-600}{640}=0.0625$
$x_2 = 1/16$
Using boiling elevation
$\Delta T_b = iK_b m$
After substitution
$x_2 = \frac{1.3}{8}\frac{W}{M}$
Q4. Increasing order of boiling point.
Boiling elevation
$\Delta T_b = iK_b m$
Compare **i × molality**
Glucose → i=1
CaCl₂ → i=3
Urea → i=1
Al₂(SO₄)₃ → i=5
After calculating particle concentration
Order becomes
I < II < III < IV
Q5. Mole fraction of $H_2SO_4$ after mixing two solutions.
Mass $H_2SO_4$
98 g solution → 98% → 98 g acid
49 g solution → 49 g acid
Total acid = 147 g
Moles acid
$147/98 = 1.5$
Water moles calculated similarly
Final mole fraction
$X_{acid}=0.337$
Q6.
Pure vapour pressures
$P_A^0=55$ , $P_B^0=15$
Vapour mole fraction of A = 0.8.
Raoult law
$P_A = X_A P_A^0$
Total pressure
$P = X_A P_A^0 + (1-X_A)P_B^0$
Using
$y_A = \frac{P_A}{P}$
Solving gives
$X_A = 0.5217$
Q7.
Henry law
$P = K_H x$
Partial pressure of N₂
$0.8 × 10 = 8 \, atm$
Convert to mmHg
$8×760$
$x = P/K_H$
After substitution
$x ≈ 9.35×10^{5}$
Q8.
Using boiling elevation
$\Delta T_b = K_b m$
From
$m = \frac{\Delta T_b}{K_b}$
Comparing PQ and PQ₂
Solving simultaneous molar mass relations
gives
$M_P = 25$
$M_Q = 60$
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