For the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,$1 mol$ of $PCl_5$ is taken at $5 atm$ pressure. If $50\%$ of $PCl_5$ dissociates at equilibrium,calculate $K_p$.

Consider the following reversible chemical reactions:
$A_{2(g)} + B_{2(g)} \overset {K_1} \leftrightarrows 2AB_{(g)} ......(1)$
$6AB_{(g)} \overset {K_2} \leftrightarrows 3A_{2(g)} + 3B_{2(g)} ......(2)$
The relation between $K_1$ and $K_2$ is:

For the reaction $2A_{(g)} \rightleftharpoons B_{(g)} + 3C_{(g)}$,at a given temperature $K_c = 16$,what must be the volume of the flask if a mixture of $2 \ mol$ each of $A, B, C$ exists at equilibrium?

For the reaction $A_{(g)} \rightleftharpoons B_{(g)}$ at $495 \ K$,$\Delta_{r}G^{\circ} = -9.478 \ kJ \ mol^{-1}$. If we start the reaction in a closed container at $495 \ K$ with $22 \ mmol$ of $A$,the amount of $B$ in the equilibrium mixture is $x \ mmol$. Find $x$ (Round off to the nearest integer). $[R = 8.314 \ J \ mol^{-1} \ K^{-1}; \ln 10 = 2.303]$

One mole of $N_2O_4$ in a $1 \ L$ flask decomposes to attain the equilibrium $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$. At the equilibrium the mole fraction of $NO_2$ is $1/2$. Hence $K_C$ will be:

At $1100 \ K$ temperature,$CaCO_{3(s)}$ and $CaO_{(s)}$ are in equilibrium. The pressure of $CO_{2(g)}$ is $2.0 \times 10^5 \ Pa$.
Find the equilibrium constant $(K_p)$ for the reaction: $CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$