The vapour density of undecomposed ${\mathrm{N}}_2{\mathrm{O}}_4$ is 46. When heated, vapour density decreases to 24.5 due to its dissociation to ${\mathrm{NO}}_2$. The % dissociation of ${\mathrm{N}}_2{\mathrm{O}}_4$ at the final temperature is

${\mathrm{N}}_2{\mathrm{O}}_4 \rightleftharpoons 2{\mathrm{NO}}_2$

1                 0                        at initial

$1-\mathrm{\alpha }$           $2\mathrm{\alpha }$                    at equilibrium

$\therefore \frac{{\mathrm{VD}}_{\mathrm{initial}}}{{\mathrm{VD}}_{\mathrm{final}}} = \frac{{\mathrm{n}}_{\mathrm{final}}}{{\mathrm{n}}_{\mathrm{initial}}}$

$\frac{46}{25.4} = \frac{25.4}{46}= \frac{1+\mathrm{\alpha }}{1}$

$1.8=1 + \mathrm{\alpha } \Rightarrow \mathrm{\alpha } = 0.8$

or      80%