Ratio of $\frac{Δ T}{K_{b}} of 10 g A B_{2} and 14 g A_{2} B$ per $100 g$ of solvent in their respective solution ( $A B_{2} and A_{2} B$ both are non-electrolytes) is $1$ mol/kg in both cases. Hence, relative atomic mass of $A$ and $B$ are respectively:

60, 20

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20, 60

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100, 40

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None of these

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Solution

The correct option is A $60, 20$
We know that,
$Δ T = K_{b} = (\frac{W_{s o l u t e}}{W_{s o l v e n t}} \times \frac{1}{M_{s o l u t e}}) \times 1000$
For $A B_{2}$
$1 = \frac{10 \times 1000}{100 \times M_{A B_{2}}} \Rightarrow M_{A B_{2}} = 100$
For $A_{2} B$
$1 = \frac{14 \times 1000}{100 \times M_{A_{2} B}} \Rightarrow M_{A_{2} B} = 140$
So,
$M_{A} + 2 M_{B} = 100 . . . (1)$
$2 M_{A} + M_{B} = 140 . . . (2)$
Multipling equation $(1)$ by $(2)$
$2 M_{A} + 4 M_{B} = 200 . . . (3)$
$(3) - (2) \Rightarrow 3 M_{B} = 60 \Rightarrow M_{B} = 20$
So, $M_{A} = 60$
Hence relative atomic mass of $A$ is 60 and $B$ is 20.

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