If the equilibrium constant of a reaction is $20.0$ at equilibrium,and the rate constant of the forward reaction is $10.0$,then the rate constant for the backward reaction is:

$A$ homogeneous ideal gaseous reaction $AB_{2(g)} \rightleftharpoons A_{(g)} + 2B_{(g)}$ is carried out in a $25 \ L$ flask at $27^{\circ}C$. The initial amount of $AB_{2}$ was $1 \ mole$ and the equilibrium pressure was $1.9 \ atm$. The value of $K_{P}$ is $x \times 10^{-2}$. The value of $x$ is $...$ (Integer answer)

Given $K_p$ for the reaction $\frac{1}{2} C_{(g)} \rightleftharpoons \frac{1}{2} A_{(g)} + \frac{1}{2} B_{(g)}$ at a fixed temperature is $0.25 \ atm$. Find the $K_p$ for the reaction $A_{(g)} + B_{(g)} \rightleftharpoons C_{(g)}$ at the same temperature.

At $T(K)$,the following gaseous equilibrium is established: $W + X \rightleftharpoons Y + Z$. The initial concentration of $W$ is two times the initial concentration of $X$. The system is heated to $T(K)$ to establish equilibrium. At equilibrium,the concentration of $Y$ is four times the concentration of $X$. What is the value of $K_c$?

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 $K_p$.

For the decomposition reaction $N_2O_4 \rightleftharpoons 2NO_2$ at constant temperature,the equilibrium constant is given by $K_p = \frac{4x^2P}{1 - x^2}$,where $P$ is the total pressure and $x$ is the degree of dissociation. Which of the following statements is correct?