$A$ $1 \ L$ vessel contains $2 \ moles$ of $PCl_5$ initially. If $K_c$ is found to be $1$,the degree of dissociation of $PCl_5$ for the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$ is:

Before equilibrium is set up for the chemical reaction $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$,the vapour density $d$ of the gaseous mixture was measured. If $D$ is the theoretical value of vapour density,the variation of $\alpha$ with $D/d$ is given by the graph. What is the value of $D/d$ at point $A$?

If the density of a gas at $STP$ is $0.178 \, g/L$,find its vapor density.

At temperature,$T$,a compound $AB_{2(g)}$ dissociates according to the reaction; $2AB_{2(g)} \rightleftharpoons 2AB_{(g)} + B_{2(g)}$ with a degree of dissociation $x$,which is small compared with unity. The expression for $K_p$,in terms of $x$ and the total pressure,$P$ is

For the reaction $A \rightleftharpoons \frac{1}{2} B + C$,the degree of dissociation $\alpha$ in terms of vapour density $D_t$ (theoretical) and $D_o$ (observed) is given by:

For the thermal dissociation of $PCl_5$ as $PCl_5 \rightleftharpoons PCl_3 + Cl_2$,if '$a$' moles of $PCl_5$ are taken and at equilibrium,the degree of dissociation of $PCl_5$ is $0.25$ and the total pressure is $2.0 \ atm$,then the partial pressure of $Cl_2$ at equilibrium will be: (in $atm$)