Question

${SO}_3\left(g\right)$ is heated in a closed vessel. An equilibrium
$2{SO}_3\left(g\right)\rightleftharpoons 2{SO}_2\left(g\right)+O_2\left(g\right)$
is established. The vapour density of the mixture, in which ${SO}_3$ is $50$% dissociated, is:

• A. $32$
• B. $35$
• C. $42$
• D. $55$

Answer 1

The correct option is A $32$

${SO}_3\left(g\right)$ is heated in a closed vessel. An equilibrium
$2{SO}_3\left(g\right)\rightleftharpoons 2{SO}_2\left(g\right)+O_2\left(g\right)$
is established. The vapour density of the mixture, in which ${SO}_3$ is $50$% dissociated, is $32$.
Sulfur trioxide has molar mass of 80 g/mol . It's vapour density (before dissociation ) is $D=\frac{80}{2}=40$
2 molecules of $S{O}_3$ on dissociation gives 3 molecules of gaseous products.
1 molecule of $S{O}_3$ on dissociation gives $\frac{3}{2}=1.5$ molecules of gaseous products.
$n=1.5$
$\alpha =\frac{D-d}{(n-1)d}$
$0.5=\frac{40-d}{(1.5-1)d}$
$0.5=\frac{40-d}{0.5d}$
$0.25d=40-d$
$1.25d=40$
$d=32$