$A$ mixture of $NO_2$ and $N_2O_4$ has a vapour density of $38.3$ at $300 \ K$. What is the number of moles of $NO_2$ in $100 \ g$ of the mixture?

The degree of dissociation of $PCl_5$ $(\alpha)$ obeying the equilibrium,$PCl_5 \rightleftharpoons PCl_3 + Cl_2$,is approximately related to the pressure at equilibrium by (given $\alpha << 1$):

At $200 \, ^\circ C$,the observed vapour density $(V.D.)$ of $PCl_5$ is $60$. The degree of dissociation $(\alpha)$ of $PCl_5$ is ..........$\%$ (Given: Molar mass of $PCl_5 = 208.5 \, g/mol$).

At $444\,^oC$,the equilibrium constant $K$ for the reaction $2AB_{(g)} \rightleftharpoons A_{2(g)} + B_{2(g)}$ is $\frac{1}{64}$. The degree of dissociation of $AB$ will be .....$\%$

For a reaction at equilibrium $A_{(g)} \rightleftharpoons B_{(g)} + \frac{1}{2} C_{(g)}$,the relation between dissociation constant $(K)$,degree of dissociation $(\alpha)$ and equilibrium pressure $(p)$ is given by?

Consider the following gas phase dissociation, $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$ with equilibrium constant $K_P$ at a particular temperature and at pressure $P$. The degree of dissociation $(\alpha)$ for $PCl_{5(g)}$ is