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:

Consider the partial decomposition of $A$ as:
$2A_{(g)} \rightleftharpoons 2B_{(g)} + C_{(g)}$
At equilibrium,a $700 \ mL$ gaseous mixture contains $100 \ mL$ of gas $C$ at $10 \ atm$ and $300 \ K$. What is the value of $K_P$ for the reaction?

For the reactions $(1)$ and $(2)$ :
$A \rightleftharpoons B + C \dots (1)$
$D \rightleftharpoons 2E \dots (2)$
Given $K_{P_1} : K_{P_2} = 9 : 1$.
If the degree of dissociation of $A$ and $D$ is the same,then the total pressure at equilibria $(1)$ and $(2)$ are in the ratio (Assume reactions are started with equal number of moles of $A$ and $D$). (in $: 1$)

In the reversible reaction $A + B \rightleftharpoons C + D$,the concentration of each $C$ and $D$ at equilibrium was $0.8 \ mol/L$. If the initial concentration of $A$ and $B$ was $1 \ mol/L$ each,then the equilibrium constant $K_c$ will be:

For the reaction $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$ at $25^o C$,the value of $K_c$ is $6.10 \times 10^{-3}$. What is the value of $K_c$ for the equilibrium reaction $NO_{2(g)} \rightleftharpoons 1/2 N_2O_{4(g)}$?

Match List-$I$ (Hypothetical reaction) with List-$II$ (Ratio of $K_p/K_c$ for the given reaction) and select the correct answer using the options given below.

$(1)$ $A_{2(g)} + 3B_{2(g)} \rightleftharpoons 2AB_{3(g)}$	$(i)$ $(RT)^{-2}$
$(2)$ $A_{2(g)} + B_{2(g)} \rightleftharpoons 2AB_{(g)}$	$(ii)$ $(RT)^0$
$(3)$ $A_{(s)} + 1.5B_{2(g)} \rightleftharpoons AB_{3(g)}$	$(iii)$ $(RT)^{1/2}$
$(4)$ $AB_{2(g)} \rightleftharpoons AB_{(g)} + 0.5B_{2(g)}$	$(iv)$ $(RT)^{-1/2}$