For the reactions:
$A \rightleftharpoons B$ $K_C = 2$
$B \rightleftharpoons C$ $K_C = 3$
$C \rightleftharpoons D + E$ $K_C = 5$
$K_C$ for the reaction $A \rightleftharpoons D + E$ is:

An equilibrium mixture of the reaction $2H_2S_{(g)} \rightleftharpoons 2H_{2(g)} + S_{2(g)}$ had $0.5 mol$ $H_2S$,$0.10 mol$ $H_2$,and $0.4 mol$ $S_2$ in a $1 L$ vessel. The value of the equilibrium constant $(K_c)$ in $mol L^{-1}$ is:

The equilibrium constants for the reactions $(i)$,$(ii)$,and $(iii)$ are $K_1$,$K_2$,and $K_3$ respectively. Which of the following is the correct relationship?
$(i)$ $N_2 + 2O_2 \rightleftharpoons 2NO_2$
$(ii)$ $2NO_2 \rightleftharpoons N_2 + 2O_2$
$(iii)$ $NO_2 \rightleftharpoons 1/2 N_2 + O_2$

The equilibrium constant for the reaction $SO_{3(g)} \rightleftharpoons SO_{2(g)} + 1/2 O_{2(g)}$ is $4.9 \times 10^{-2}$. Find the equilibrium constant for the reaction $2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$.

At $298 \ K$,the $K_c$ of the reaction $Cu(s) + 2Ag^+(aq) \rightleftharpoons Cu^{2+}(aq) + 2Ag(s)$ is $3.0 \times 10^{14}$. In a reaction mixture at a certain temperature,$[Cu^{2+}] = 1.8 \times 10^{-2} \ M$ and $[Ag^+] = 3.0 \times 10^{-9} \ M$. Is this reaction in equilibrium? In which direction will the reaction proceed?

Consider the following gaseous equilibrium reactions $(I)$,$(II)$ and $(III)$ with equilibrium constants $K_1$,$K_2$ and $K_3$ respectively:
$I$) $\frac{1}{2} N_2 + \frac{3}{2} H_2 \rightleftharpoons NH_3$
$II$) $2 NO \rightleftharpoons N_2 + O_2$
$III$) $H_2 + \frac{1}{2} O_2 \rightleftharpoons H_2 O$
The correct expression for the equilibrium constant for the gaseous equilibrium reaction $2 NH_3 + \frac{5}{2} O_2 \rightleftharpoons 2 NO + 3 H_2 O$ is