Question

The vapor pressure of the solution of a solute in benzene is 631.9 mm of Hg at any particular temperature. If the molality of the solution is $m$ , then find the value of $1000m$ (nearest integer) (The vapor pressure of pure benzene is 639.70 mm of Hg)

Answer 1

Answer: 158

According to Raoult's law:
$\frac{\Delta \text{P}}{{\text{P}}_{\text{A}}^{\text{o}}}=\frac{639\cdot 7-631\cdot 9}{639\cdot 7}=\frac{\text{7.8}}{\text{639.7}}=\text{0.0122}$
${\text{X}}_{\text{B}}=\text{0.0122}$
Let the total number of moles in the solution $=1$
Therefore, the number of moles of solvent $=1-0.0122$
$\text{m =}\frac{\text{moles of solute}}{\text{1 Kg of solvent}}$
$=\frac{\text{0.0122}}{\frac{\left(\text{1-0.0122}\right)\times \text{78}}{1000}}=\frac{\text{0.0122}}{\frac{\text{77.05}}{\text{1000}}}$
$=\frac{\text{0.0122}\times \text{1000}}{\text{77.05}}=\frac{\text{12.2}}{\text{77.05}}$

$=\text{0.158 m}$