If $Ag^{+} + NH_3 \rightleftharpoons [Ag(NH_3)]^+$; $K_1 = 1.6 \times 10^3$ and $[Ag(NH_3)]^+ + NH_3 \rightleftharpoons [Ag(NH_3)_2]^+$; $K_2 = 6.8 \times 10^3$. Then the formation constant of $[Ag(NH_3)_2]^+$ is:

Observe the following equilibrium in a $1 \text{ L}$ flask. $A_{(g)} \rightleftharpoons B_{(g)}$. At $T \text{ K}$,the equilibrium concentrations of $A$ and $B$ are $0.5 \text{ M}$ and $0.375 \text{ M}$ respectively. $0.1 \text{ moles}$ of $A$ is added into the flask and heated to $T \text{ K}$ to establish the equilibrium again. The new equilibrium concentrations (in $\text{M}$) of $A$ and $B$ are respectively.

The equilibrium constants for some reactions are given below:
$(1)$ $x \rightleftharpoons y ; K = 10^{-1}$
$(2)$ $y \rightleftharpoons z ; K = 2 \times 10^{-2}$
$(3)$ $p \rightleftharpoons Q ; K = 3 \times 10^{-4}$
$(4)$ $R \rightleftharpoons S ; K = 2 \times 10^{-3}$
The initial concentrations of reactants are taken to be the same for each reaction. Which of the above reactions indicate that the reaction mixture contains high concentrations of reactants and products respectively?

For the equilibrium $N_2 + 3H_2 \rightleftharpoons 2NH_3$,$K_c$ at $1000 \ K$ is $2.37 \times 10^{-3}$. If at equilibrium $[N_2] = 2 \ M$ and $[H_2] = 3 \ M$,the concentration of $NH_3$ is: (in $M$)

For the balanced reaction $A + B \rightleftharpoons 2C$,if the equilibrium concentrations of both $A$ and $B$ are $0.20 \ mol/L$,and the concentration of $C$ is $0.60 \ mol/L$,then the equilibrium constant for this reaction will be:

(i) $H_3PO_{4\text{(aq)}} \rightleftharpoons H^+{_{\text{(aq)}}} + H_2PO_4^-{_{\text{(aq)}}}$
(ii) $H_2PO_4^-{_{\text{(aq)}}} \rightleftharpoons H^+{_{\text{(aq)}}} + HPO_4^{2-}{_{\text{(aq)}}}$
(iii) $HPO_4^{2-}{_{\text{(aq)}}} \rightleftharpoons H^+{_{\text{(aq)}}} + PO_4^{3-}{_{\text{(aq)}}}$
The equilibrium constants for the above reactions at a certain temperature are $K_1$,$K_2$,and $K_3$ respectively. The equilibrium constant for the reaction $H_3PO_{4\text{(aq)}} \rightleftharpoons 3H^{+}{_{\text{(aq)}}} + PO_4^{3-}{_{\text{(aq)}}}$
$K = K_1 \times K_2 \times K_3$ is