When ' $x$ ' $\times 10^{-2} \mathrm{~mL}$ methanol (molar mass $=32 \mathrm{~g}$; density $=0.792 \mathrm{~g} / \mathrm{cm}^3$) is added to $100 \mathrm{~mL}$ water (density $=1 \mathrm{~g} / \mathrm{cm}^3$), the following diagram is obtained. $x=$ ______ (nearest integer). [Given :…

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When ' $x$ ' $\times 10^{-2} \mathrm{~mL}$ methanol (molar mass $=32 \mathrm{~g}$; density $=0.792 \mathrm{~g} / \mathrm{cm}^3$) is added to $100 \mathrm{~mL}$ water (density $=1 \mathrm{~g} / \mathrm{cm}^3$), the following diagram is obtained. $x=$ ______ (nearest integer). [Given : Molal freezing point depression constant of water at $273.15 \mathrm{~K}$ is $1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$]

Aicharya · Accepted Answer

$\begin{aligned} & \Delta \mathrm{T}_{\mathrm{f}}=273.15-270.65=2.5 \mathrm{~K} \ & \Delta \mathrm{T}_{\mathrm{f}}=\mathrm{K}_{\mathrm{f}} \mathrm{m} \Rightarrow 2.5=1.86 	imes \frac{\mathrm{n}}{0.1} \ & \Rightarrow \mathrm{n}=0.1344 	ext { moles } \ & \Rightarrow \mathrm{w}=0.1344 	imes 32=4.3 \mathrm{~g} \ & 	ext { Volume }=\frac{4.3}{0.792}=5.43 \mathrm{ml}=543 	imes 10^{-2} \mathrm{ml}\end{aligned}$

When ' \(x\) ' \(\times 10^{-2} \mathrm{~mL}\) methanol (molar mass \(=32 \mathrm{~g}\); density \(=0.792…

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