Ratio of $\Delta \mathrm{T}_{\mathrm{b}} / \mathrm{K}_{\mathrm{b}}$ of $6 \% \mathrm{~AB}_{2}$ and $9 \%…

Ratio of $\Delta \mathrm{T}_{\mathrm{b}} / \mathrm{K}_{\mathrm{b}}$ of $6 \% \mathrm{~AB}_{2}$ and $9 \% \mathrm{~A}_{2} \mathrm{~B}$ $\left(\mathrm{AB}_{2}ight.$ and $\mathrm{A}_{2} \mathrm{~B}$ both are non-electrolytes) is $1 \mathrm{~mol} / \mathrm{kg}$ in both cases. Hence, atomic masses of $\mathrm{A}$ and $\mathrm{B}$ are respectively:
  1. $60,90$
  2. $40,40$
  3. $40,10$
  4. $10,40$

Solution

$\Delta T=\frac{1000 K_{b} w_{1}}{m_{1} w_{2}}$
$\frac{\Delta T}{K_{b}}\left(A B_{2}ight)=\frac{1000 \times 6}{m_{1} w_{2}}=1$
$\frac{1000 \times 6}{m_{1} \times 100}=1$
$\therefore m_{1}\left(A B_{2}ight)=60=A+2 B$
$\frac{\Delta T}{K_{b}}\left(A_{2} Bight)=\frac{1000 \times 9}{m_{1} \times 100}=1$
$\therefore m_{1}\left(A_{2} Bight)=90=2 A+B$
$\therefore \mathrm{A}=40, \mathrm{~B}=10$ .

Asked in: JEE-TOPICTESTS-CHEMISTRY

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