Question

The common laboratory solvent benzene is often used to purify substances dissolved in it. The vapor pressure of benzene , C6H6, is 73.03 mm Hg at 25 degrees Celsius.
In a laboratory experiment, students synthesized a new compound and found that when 18.16 grams of the compound were dissolved in 228.6 grams of benzene, the vapor pressure of the solution was 71.88 mm Hg. The compound was also found to be nonvolatile and a non-electrolyte.

What is the molecular weight of this compound ?

Answer 1

Answer: Molecular weight of this compound is 387.3g/mol

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 : 18.16 g of compound is present in 228.6 g of benzene

moles of solute = $\frac{\text{Given mass}}{\text {Molar mass}}=\frac{18.16g}{Mg/mol}$

moles of solvent (benzene) = $\frac{\text{Given mass}}{\text {Molar mass}}=\frac{228.6g}{78g/mol}=2.93moles$

$x_2$ = mole fraction of solute  =$\frac{\frac{18.16g}{Mg/mol}}{\frac{18.16g}{Mg/mol}+2.93}$

$\frac{73.03-71.88}{73.03}=1\times \frac{\frac{18.16g}{Mg/mol}}{\frac{18.16g}{Mg/mol}+2.93}$

$M=387.3g/mol$

The molecular weight of this compound is 387.3g/mol