$2 \ mol$ of $N_2O_{4(g)}$ is kept in a closed container at $298 \ K$ and under $1 \ atm$ pressure. It is heated to $596 \ K$ when $20 \%$ by mass of $N_2O_{4(g)}$ decomposes to $NO_2$. The resulting pressure is (in $atm$)

Reaction between $N_{2}$ and $O_{2}$ takes place as follows:
$2 N_{2(g)} + O_{2(g)} \longleftrightarrow 2 N_{2}O_{(g)}$
If a mixture of $0.482 \ mol$ of $N_{2}$ and $0.933 \ mol$ of $O_{2}$ is placed in a $10 \ L$ reaction vessel and allowed to form $N_{2}O$ at a temperature for which $K_{c} = 2.0 \times 10^{-37}$,determine the composition of the equilibrium mixture.

For the reaction $2SO_3 \rightleftharpoons 2SO_2 + O_2$,if $K_c = 100$ and the degree of dissociation $\alpha = 1$,determine the concentration of $O_2$ when the concentration of $SO_3$ is equal to the concentration of $SO_2$.

For the reaction $C_{(s)} + CO_{2(g)} \rightleftharpoons 2CO_{(g)}$,if $25\%$ of $CO_2$ is converted to $CO$ at equilibrium and the total equilibrium pressure is $12 \ atm$,then the partial pressure of $CO_2$ at equilibrium will be............$atm$.

For the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,at equilibrium,the mole fraction of $PCl_5$ is $0.4$ and the mole fraction of $Cl_2$ is $0.3$. What will be the mole fraction of $PCl_3$?

Two equilibria,$AB \rightleftharpoons A^{+} + B^{-}$ and $AB + B^{-} \rightleftharpoons AB_2^-$,are simultaneously maintained in a solution with equilibrium constants $K_1$ and $K_2$ respectively. The ratio of $[A^{+}]$ to $[AB_2^-]$ in the solution is