$A$ $1 \ L$ 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:

For the equilibrium $PCl_{5_{(g)}} \rightleftharpoons PCl_{3_{(g)}} + Cl_{2_{(g)}}$,the observed vapour density of the mixture is $80$. Given atomic masses $P = 31$ and $Cl = 35.5$,the degree of dissociation of $PCl_{5_{(g)}}$ is approximately....$\%$

For the reaction $A \rightleftharpoons nB$,if $a$ moles of $A$ are taken initially and $x$ moles of $A$ dissociate at equilibrium,find the value of the degree of dissociation.

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:

At temperature $T$,the dissociation equilibrium of $AB_{2(g)}$ is given as: $2AB_{2(g)} \rightleftharpoons 2AB_{(g)} + B_{2(g)}$. If the degree of dissociation $x$ is very small compared to $1$,then the expression for the equilibrium constant $K_p$ in terms of $x$ and total pressure $P$ is:

For the equilibrium reaction $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$,the value of $K_p$ is $2$. Calculate the percentage dissociation of $N_2O_{4(g)}$ at a total pressure of $0.5 \ atm$. (in $\%$)