For the reaction,$A_{(g)} + 2B_{(g)} \rightleftharpoons 2C_{(g)}$ at $25 \, ^oC$,$2 \, moles$ of $A$,$1 \, mole$ of $B$ and $1 \, mole$ of $C$ are present in a $1 \, L$ vessel. If $K_c$ for the reaction is $2$,then the reaction will proceed in:

At $T(K)$, the equilibrium constant of $A_{2}(g) + B_{2}(g) \rightleftharpoons C(g)$ is $2.7 \times 10^{-5}$. What is the equilibrium constant for $\frac{1}{3}A_{2}(g) + \frac{1}{3}B_{2}(g) \rightleftharpoons \frac{1}{3}C(g)$ at the same temperature?

The figure shows the change in concentration of species $A$ and $B$ as a function of time. The equilibrium constant $K_C$ for the reaction $2A_{(g)} \rightleftharpoons B_{(g)}$ is

The equilibrium constant $(K_c)$ for the reaction,$CaSO_4 \cdot 5H_2O_{(s)} \rightleftharpoons CaSO_4 \cdot 3H_2O_{(s)} + 2H_2O_{(g)}$ is equal to

$4.5 \ mol$ each of hydrogen and iodine are heated in a $10 \ L$ closed vessel. At equilibrium,$3 \ mol$ of $HI$ is formed. The equilibrium constant for the reaction $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$ will be:

For the reaction ${N_2}_{(g)} + 2{O_2}_{(g)} \rightleftharpoons 2{NO_2}_{(g)}$,the equilibrium constant is $100$. Find the equilibrium constant for the following reactions:
$(1)$ $2{NO_2}_{(g)} \rightleftharpoons {N_2}_{(g)} + 2{O_2}_{(g)}$
$(2)$ ${NO_2}_{(g)} \rightleftharpoons \frac{1}{2}{N_2}_{(g)} + {O_2}_{(g)}$