Value of $K_p$ in the reaction $MgCO_{3(s)} \rightleftharpoons MgO_{(s)} + CO_{2(g)}$ is

At $298 \, K$,for which of the following reactions will the value of $\frac{K_p}{K_c}$ be maximum and minimum,respectively?
$(a) N_2O_4 \rightleftharpoons 2NO_2$
$(b) 2SO_2 + O_2 \rightleftharpoons 2SO_3$
$(c) X + Y \rightleftharpoons 4Z$
$(d) A + 3B \rightleftharpoons 7C$

The half-life of forward and reverse reactions are $400 \, sec$ and $100 \, sec$ respectively. If these half-lives are independent of the concentration of the reactant,find the equilibrium constant of the reaction.

For the reaction $CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$,the value of $K_p$ at $800 \ ^oC$ is $1.16 \ atm$. If $1 \ mol$ of $CaCO_{3(s)}$ is taken in a $1 \ L$ container to start the reaction,what will be the partial pressure of $CO_2$ at equilibrium in $atm$?

For the reactions $N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$ and $\frac{1}{2}N_{2(g)} + \frac{1}{2}O_{2(g)} \rightleftharpoons NO_{(g)}$,if the equilibrium constants are $K_1$ and $K_2$ respectively,then their relationship is:

In the reaction $PCl_5 \rightleftharpoons PCl_3 + Cl_2$,the partial pressures of $PCl_3$,$Cl_2$,and $PCl_5$ are $0.3 \ atm$,$0.2 \ atm$,and $0.6 \ atm$ respectively. If the partial pressures of $PCl_3$ and $Cl_2$ are doubled,what will be the partial pressure of $PCl_5$ in $atm$?