Question

The vapour pressure of a solution having $2.0g$ of solute $X$ (molar atomic mass $=32gmo{l}^{-1}$ ) in $100g$ of $C{S}_2$ (vapour) pressure $=854$ torr) is $848.9$ torr. The molecular formula of the solute is

• A. $X$
• B. $X_2$
• C. $X_4$
• D. $X_8$

Answer 1

Answer: (D)

$\frac{p^{\circ }-p}{p^{\circ }}=\underset{(\text{ Solute })}{x_A},$
$x_A=\frac{n_A}{n_A+n_B}\simeq \frac{n_A}{n_B}$ (For dilute solution)
$\Rightarrow \frac{854-848.9}{854}=\frac{n_A}{n_B}=\frac{W_A\times M_B}{M_A\times W_B};$
$W_A=$ weight of solute,
$W_B=$ molar mass of solute
$\Rightarrow \frac{5.1}{854}=\frac{2\times 76}{M_A\times 100};$
$M_B=$ molar mass of solvent
$=C{S}_2=12+32\times 2$
$\Rightarrow 76g$
$\underset{\text{(Molar mass of solute)}}{M_A}=\frac{2\times 76\times 854}{100\times 5.1}=253$
Number of atoms $=\frac{\text{ molar mass }}{\text{ atomic mass }}=\frac{253}{32}=7.90\approx 8$
So formula of solute is $X_8$