Question

Calculate the vapor pressure (in torr) at 298 K in a solution prepared by dissolving 38.5 g of the non-volatile non-electrolye urea {CO(NH2)2} in 142 g of methanol. The vapor pressure of methanol at 298 K is 122.7 torr. Give your answer to 2 decimal places.

Answer 1

Answer: The vapor pressure of methanol solution at 298K is 107.12 torr

Explanation:

As the relative lowering of vapor pressure is directly proportional to the amount of dissolved solute.

The formula for relative lowering of vapor pressure will be,

$\frac{p^o-p_s}{p^o}=i\times x_2$

where,

$\frac{p^o-p_s}{p^o}$= relative lowering in vapor pressure

i = Van'T Hoff factor = 1 (for non electrolytes)

$x_2$ = mole fraction of solute  =$\frac{\text {moles of solute}}{\text {total moles}}$

Given : 38.5 g of urea is present in 142 g of methanol

moles of solute (urea) = $\frac{\text{Given mass}}{\text {Molar mass}}=\frac{38.5g}{60g/mol}=0.64moles$

moles of solvent (methanol) = $\frac{\text{Given mass}}{\text {Molar mass}}=\frac{142g}{32g/mol}=4.4moles$

Total moles = moles of solute  + moles of solvent  = 0.64 + 4.4 = 5.04

$x_2$ = mole fraction of solute  =$\frac{0.64}{5.04}=0.127$

$\frac{122.7-p_s}{122.7}=1\times 0.127$

$p_s=107.12torr$

Thus the vapor pressure of methanol solution at 298K is 107.12 torr