Question

The ratio of $\frac{\text{Δ}{\text{T}}_{\text{b}}}{{\text{K}}_{\text{b}}}$ of 10 g AB₂ and 14 g A₂B per 100 g of solvent in their respective solutions (AB₂ and A₂B both are non-electrolyte) in both the cases is 1 mol/kg. Hence, the atomic weight of A and B are respectively:

• A. 100, 40
• B. 60, 20
• C. 20, 60
• D. None of these

Answer 1

Answer: (B)

$\text{Δ}{\left(\text{T}\right)}_{\text{b}}={\left(\text{K}\right)}_{\text{b}}\left(\frac{{\left(\text{W}\right)}_{\text{solute}}}{{\left(\text{W}\right)}_{\text{solvent}}}\times \frac{1}{{\left(\text{M}\right)}_{\text{solute}}}\right)\times 1000$
$1=\frac{1000\times 10}{100\times {\text{M}}_{{\text{AB}}_2}}\Rightarrow {\text{M}}_{{\text{AB}}_2}=100$
Similarly, ${\text{M}}_{{\text{A}}_2\text{B}}=140$
$100={\text{M}}_{\text{A}}+2{\text{M}}_{\text{B}}$
and $140=2{\text{M}}_{\text{A}}+{\text{M}}_{\text{B}};$
${\text{M}}_{\text{A}}=60,{\text{M}}_{\text{B}}=20$
Alternative solution
$\frac{\Delta {\text{T}}_{\text{b}}}{{\text{K}}_{\text{b}}}=1=\frac{10}{\frac{{\text{M}}_{\text{A}}+2{\text{M}}_{\text{B}}}{\text{0.1}}}$
${\text{M}}_{\text{A}}+2{\text{M}}_{\text{B}}=100$ ........ (1)
$\frac{\Delta {\text{T}}_{\text{b}}}{{\text{K}}_{\text{b}}}=1=\frac{14}{\frac{{\text{2M}}_{\text{A}}+{\text{M}}_{\text{B}}}{\text{0.1}}}$
$2{\text{M}}_{\text{A}}+{\text{M}}_{\text{B}}=140$ ........ (2)
${\text{M}}_{\text{A}}={\text{60, M}}_{\text{B}}=20$