For the reaction $cis-C_2H_2Cl_2 \rightleftharpoons trans-C_2H_2Cl_2$,the equilibrium constant at $500 \ K$ is $0.6$. The equilibrium constant for the reaction $trans-C_2H_2Cl_2 \rightleftharpoons cis-C_2H_2Cl_2$ at the same temperature will be ...............

The reaction,$CO_{(g)} + 3H_{2(g)} \longleftrightarrow CH_{4(g)} + H_{2}O_{(g)}$ is at equilibrium at $1300 \, K$ in a $1 \, L$ flask. It also contains $0.30 \, mol$ of $CO$,$0.10 \, mol$ of $H_{2}$,and $0.02 \, mol$ of $H_{2}O$ and an unknown amount of $CH_{4}$ in the flask. Determine the concentration of $CH_{4}$ in the mixture. The equilibrium constant,$K_{c}$ for the reaction at the given temperature is $3.90$.

$3.1 \ mol$ of $FeCl_3$ and $3.2 \ mol$ of $NH_4SCN$ are added to $1 \ L$ of water. At equilibrium,$3.0 \ mol$ of $FeSCN^{2+}$ is formed. The equilibrium constant $K_c$ for the reaction is:
$Fe^{3+} + SCN^{-} \rightleftharpoons FeSCN^{2+}$

$4.5 \ mol$ 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:

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?

$A$ reaction with reaction quotient $Q_C$ and equilibrium constant $K_C$ will proceed in the direction of the products when: