At $298 \ K$,for the reaction $Ag^{+} + 2NH_3 \rightleftharpoons Ag(NH_3)_2^{+}$,the concentrations of $Ag^{+}$,$Ag(NH_3)_2^{+}$,and $NH_3$ are $10^{-1} \ M$,$10^{-1} \ M$,and $10^3 \ M$ respectively. The value of $K_c$ at $298 \ K$ for this equilibrium is ...... .

For the reaction $x \rightleftharpoons y$,which of the following factors will affect the value of $[\text{Product}] / [\text{Reactant}]^{-1}$ at equilibrium?

For the reaction $A_{(g)} + B_{(g)} \rightleftharpoons 2 C_{(g)}$; $K_{c} = 4$. If equilibrium concentration of $A_{(g)}$ and $B_{(g)}$ are found to be $0.1 \ M$ and $0.4 \ M$ respectively. Determine equilibrium concentration of $C_{(g)}$. (in $M$)

In the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,the equilibrium concentrations of $PCl_5$ and $PCl_3$ are $0.4 \ mol/L$ and $0.2 \ mol/L$ respectively. If the value of $K_c$ is $0.5$,what is the concentration of $Cl_2$ in $mol/L$?

If the reaction $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$ at $720 \ K$ has $K = 48$,then for the reaction $2HI_{(g)} \rightleftharpoons H_{2(g)} + I_{2(g)}$,find its equilibrium constant.

Consider the following reactions in which all the reactants and products are in gaseous state:
$2PQ \rightleftharpoons P_2 + Q_2\,;\,K_1 = 2.5 \times 10^5$
$PQ + \frac{1}{2}R_2 \rightleftharpoons PQR\,;\,K_2 = 5 \times 10^{-3}$
The value of the equilibrium constant for the reaction:
$\frac{1}{2}P_2 + \frac{1}{2}Q_2 + \frac{1}{2}R_2 \rightleftharpoons PQR$ is