Question

Addition of non-volatile solute to a solvent always increases the colligative properties such as osmotic pressure, $\Delta P, \Delta T_b$ and $\Delta T_f$. All these colligative properties are directly proportional to molality if solutions are dilute. The decrease in colligative properties on addition of non-volatile solute is due to increase in number of particles.
For different aqueous solutions of $0.1 \,N$ urea, $0.1 \,N \,NaCl , 0.1 \,N \,Na _2 \,SO _4$ and $0.1\, N \,Na_3 PO _4$ solution at $27^{\circ} C$ the correct statements are :
1. The order of osmotic pressure is $NaCl > Na _2 SO _4> Na _3 PO _4>$ urea
2. $\pi=\frac{\Delta T_b}{K_b} \times S T$ for urea solution
3. Addition of salt on ice increases its melting point
4. Addition of salt on ice brings in melting of ice earlier

• A. 2, 3, 4
• B. 1, 2, 4
• C. 1, 2, 3
• D. 3, 4

Answer 1

Answer: (B)

1. Molar concentrations are $0.1 \, M \, NaCl$, $\frac{0.1}{2} \, M \, Na _2 SO _4$ and $\frac{0.1}{3} \,M \, Na _3 PO _4$
$\therefore \pi \propto C X(1-\alpha+X \alpha+Y \alpha) \propto C(X+Y)$ if $\alpha=1$
$\therefore \pi_{\text {urea }} \propto 0.1 \times 1, \pi_{ NaCl } \propto 0.1 \times 2 ; \pi_{ Na _2 SO _4}$ $\propto \frac{0.1}{2} \times 3 ; \pi_{ Na _3 PO _4} \propto \frac{0.1}{3} \times 4$
2. Also $\pi=C M \times S \times T$ and $\Delta T_b=$ Molality $\times K_b$ If Molarity $=$ Molality (for dilute solution) $\pi=\frac{\Delta T_b}{K_b} \times S \times T$
3. Addition of salt on ice lowers the freezing point.
4. Also addition of salt on ice lowers its melting point and thus, ice melts earlier