Question

Solute A associates in water. When $0.7\, g$ of solute A is dissolved in $42.0 \,g$ of water, it depresses the freezing point by $0.2^{\circ} C$. The percentage association of solute A in water, is
[Given : Molar mass of $A =93 \,g \,mol ^{-1}$. Molal depression constant of water is $1.86 \,K \,kg\, mol ^{-1}$ ]

• A. $50 \%$
• B. $60 \%$
• C. $70 \%$
• D. $80 \%$

Answer 1

Answer: (D)

$\Delta T = i k _{ f } \times m$
$0.2= i \times 1.86 \times \frac{0.7}{93} \times \frac{1000}{42}$
$i =\frac{0.2 \times 93 \times 6}{1.86 \times 100}$
$i =0.60$

$i =1-\alpha+\frac{\alpha}{2}$
$i =1-\frac{\alpha}{2}$
$1-\frac{\alpha}{2}=0.60$
$1-0.60=\frac{\alpha}{2}$
$\alpha=0.80$