JEE MAIN - Chemistry (2022 - 27th July Morning Shift - No. 5)
Boiling point of a $$2 \%$$ aqueous solution of a non-volatile solute A is equal to the boiling point of $$8 \%$$ aqueous solution of a non-volatile solute B. The relation between molecular weights of A and B is
$$\mathrm{M}_{\mathrm{A}}=4 \mathrm{M}_{\mathrm{B}}$$
$$\mathrm{M}_{\mathrm{B}}=4 \mathrm{M}_{\mathrm{A}}$$
$$\mathrm{M}_{\mathrm{A}}=8 \mathrm{M}_{\mathrm{B}}$$
$$\mathrm{M}_{\mathrm{B}}=8 \mathrm{M}_{\mathrm{A}}$$
Explanation
For $\mathbf{A}: 100 \,\mathrm{gm}$ solution $\rightarrow 2 \,\mathrm{gm}$ solute $\mathrm{A}$
$\therefore$ Molality $=\frac{2 / \mathrm{M}_{\mathrm{A}}}{0.098}$
For B : $100 \,\mathrm{gm}$ solution $\rightarrow 8 \,\mathrm{gm}$ solute $\mathrm{B}$
$$ \begin{aligned} &\therefore \text { Molality }=\frac{8 / \mathrm{M}_{\mathrm{B}}}{0.092} \\\\ &\because\left(\Delta \mathrm{T}_{\mathrm{B}}\right)_{\mathrm{A}}=\left(\Delta \mathrm{T}_{\mathrm{B}}\right)_{\mathrm{B}} \end{aligned} $$
$\therefore$ Molality of $\mathrm{A}=$ Molality of $\mathrm{B}$
$$ \therefore \frac{2}{0.098 \mathrm{M}_{\mathrm{A}}}=\frac{8}{0.092 \mathrm{M}_{\mathrm{B}}} $$
$$ \frac{2}{98} \times \frac{92}{8}=\frac{M_A}{M_B} $$
$$ \frac{1}{4.261}=\frac{\mathrm{M}_{\mathrm{A}}}{\mathrm{M}_{\mathrm{B}}} $$
$$ \therefore \mathrm{M}_{\mathrm{B}}=4.261 \times \mathrm{M}_{\mathrm{A}} $$
$\therefore$ Molality $=\frac{2 / \mathrm{M}_{\mathrm{A}}}{0.098}$
For B : $100 \,\mathrm{gm}$ solution $\rightarrow 8 \,\mathrm{gm}$ solute $\mathrm{B}$
$$ \begin{aligned} &\therefore \text { Molality }=\frac{8 / \mathrm{M}_{\mathrm{B}}}{0.092} \\\\ &\because\left(\Delta \mathrm{T}_{\mathrm{B}}\right)_{\mathrm{A}}=\left(\Delta \mathrm{T}_{\mathrm{B}}\right)_{\mathrm{B}} \end{aligned} $$
$\therefore$ Molality of $\mathrm{A}=$ Molality of $\mathrm{B}$
$$ \therefore \frac{2}{0.098 \mathrm{M}_{\mathrm{A}}}=\frac{8}{0.092 \mathrm{M}_{\mathrm{B}}} $$
$$ \frac{2}{98} \times \frac{92}{8}=\frac{M_A}{M_B} $$
$$ \frac{1}{4.261}=\frac{\mathrm{M}_{\mathrm{A}}}{\mathrm{M}_{\mathrm{B}}} $$
$$ \therefore \mathrm{M}_{\mathrm{B}}=4.261 \times \mathrm{M}_{\mathrm{A}} $$
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