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.

In which of the following reactions is the value of $K_p$ equal to $K_c$?

In which one of the following gaseous equilibria is $K_p$ less than $K_c$?

For the reaction $SO_{2(g)} + \frac{1}{2}O_{2(g)} \rightleftharpoons SO_{3(g)}$,the relationship is given by $K_P = K_C(RT)^x$. Find the value of $x$.

For the reaction $P + Q \rightleftharpoons R + C$,the equilibrium constant $K_c$ is $10^{-2}$ and the forward rate constant $K_f$ is $10^{-1}$. The rate constant for the backward reaction $(K_b)$ will be:

Pure $PCl_5$ is introduced into an evacuated chamber and comes to equilibrium at $247\, ^oC$ and $2.0\ atm$. The equilibrium gaseous mixture contains $40\%$ chlorine by volume. Calculate $K_p$ at $247\, ^oC$ for the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$ in $atm$.