Question

n moles of $N_2{O}_{5\left(g\right)}$ at pressure $P^o$ at 300 K are taken in a closed container of fixed volume V. $N_2{O}_5$ undergoes gas-phase decomposition at 400 K to ${NO}_{2\left(g\right)}$ and $O_{2\left(g\right)}$. The pressure of mixture (P at 400 K) when $N_2{O}_{5\left(g\right)}$ has degree of decomposition $\alpha$ can be given by :

• A. $P=P^o(1+\frac{3}{2}\alpha )$
• B. $P=\frac{4}{3}{P}^o(1+\frac{\alpha }{2})$
• C. $P=n(1-\alpha )$
• D. $P=n(1+\frac{3}{2}\alpha )$

Answer 1

Answer: (A)

$P=P^o(1+\frac{3}{2}\alpha )$

$N_2{O}_5\rightleftharpoons 2N{O}_2+\frac{1}{2}{O}_2$

Pressure $⟶P^o(1-\alpha )$ $P^o\left(2\alpha \right)P^o\left(\frac{\alpha }{2}\right)$

Total pressure of the mixture= $P^o(1-\alpha +2\alpha +\frac{\alpha }{2})$

$=P^o(1+\frac{3}{2}\alpha )$ .