Question

A solution containing $8.44g$ of sucrose in $100g$ of water has a vapour pressure $4.56mm$ of $Hg$ at $273K$. If the vapour pressure of pure water is $4.58mm$ of $Hg$ at the same temperature, calculate the molecular weight of sucrose.

Answer 1

Let M g/mol be the molecular weight of sucrose. The number of moles of sucrose $=\frac{8.44}{M}$.
The molecular weight of water is 18 g/mol. The number of moles of water $=\frac{100}{18}=5.56$.
The mole fraction of sucrose $=\frac{\frac{8.44}{M}}{\frac{8.44}{M}+5.56}\simeq \frac{8.44}{M\times 5.56}\simeq \frac{1.52}{M}$
The relative lowering of vapour pressure is equal to the mole fraction of solute.

$\frac{P^0-P}{P^0}={\chi }_{solute}$
$\frac{4.58-4.56}{4.58}=\frac{1.52}{M}$

$M=348$ g/mol.

Hence, the molecular weight of sucrose is $348g/mol$.