The solubility of urea in methanol is 17g urea/100ml methanol. Density of methanol is 0.792 g/ml at 293k at which vapour pressure of methanol is 96.0mmHg. Thus vapour pressure of saturated solution of urea in methanol is ____ mmHg. (nearest integer)

Wt. of urea = 17 g
vol. of methanol =100 ml
Density of methanol = 0.792 g/ml
Weight of methanol =79.2g
VP of ${\mathrm{CH}}_3\mathrm{OH}=96 \mathrm{mm}$ of Hg
VP of sol. of urea in ${\mathrm{C}}_3\mathrm{OH}=$?
For a dilute sol.

$$\begin{gathered} \frac{{\mathrm{P}}^{\mathrm{o}}-\mathrm{P}}{{\mathrm{P}}^{\mathrm{o}}}=\frac{{\mathrm{n}}_{\mathrm{s}}}{{\mathrm{n}}_{\mathrm{s}}+{\mathrm{n}}_{\mathrm{o}}} \\ \frac{96-\mathrm{P}}{96}=\frac{\left(\frac{17}{60}\right)}{\left(\frac{79.2}{32}\right)+\left(\frac{17}{60}\right)} \\ \frac{96-\mathrm{P}}{96}=0.103 \end{gathered}$$
$P=96-9.85=86.15 \mathrm{mm}\text{ of }\mathrm{Hg}$

Hence, the correct answer 86 mm.