Question

A solution contains naphthalene (C10H8) dissolved in hexane (C6H14) at a concentration of 13.06% naphthalene by mass. Calculate the vapor pressure at 25 ∘C of hexane above the solution. The vapor pressure of pure hexane at 25 ∘C is 151 torr.

Answer 1

Answer: The vapor pressure of the solution at $25^0C$ is 137 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 : 13.06 g of napthalene is present in 100 g of solution, thus (100-13.06) g = 86.94 g of hexane

moles of solute (napthalene) = $\frac{\text{Given mass}}{\text {Molar mass}}=\frac{13.06g}{128g/mol}=0.102moles$

moles of solvent (hexane) = $\frac{\text{Given mass}}{\text {Molar mass}}=\frac{86.94g}{86g/mol}=1.01moles$

Total moles = moles of solute (napthalene)  + moles of solvent (hexane) = 0.102 + 1.01 = 1.112

$x_2$ = mole fraction of solute (napthalene) =$\frac{0.102}{1.112}=0.0917$

$\frac{151-p_s}{151}=1\times 0.0917$

$p_s=137torr$

Thus the vapor pressure of the solution at $25^0C$ is 137 torr