In a closed vessel,$PCl_{5(g)}$ is obtained by the chemical reaction between $PCl_{3(g)}$ and $Cl_{2(g)}$. If the equilibrium concentrations in this vessel of $PCl_3$,$Cl_2$,and $PCl_5$ at $500 \ K$ are $1.59 \ M$,$1.59 \ M$,and $1.41 \ M$ respectively,then find the equilibrium constant $K_c$ for the reaction: $PCl_{3(g)} + Cl_{2(g)} \rightleftharpoons PCl_{5(g)}$

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 $M$)

If the equilibrium constant for the reaction,$2 SO_2 + O_2 \rightleftharpoons 2 SO_3$ is $64$ at $500 \ K$,then the equilibrium constant for the reaction $SO_3 \rightleftharpoons SO_2 + \frac{1}{2} O_2$ at the same temperature is

In a reaction $A + B \rightleftharpoons C + D$,the concentrations of $A$,$B$,$C$ and $D$ (in $mol/L$) are $0.5$,$0.8$,$0.4$ and $1.0$ respectively. The equilibrium constant is

(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

For the reversible reaction $2HI_{(g)} \rightleftharpoons H_{2(g)} + I_{2(g)}$, the unit of the equilibrium constant $K_c$ is: