The equilibrium constant for the reaction,$N_2 + 3H_2 \rightleftharpoons 2NH_3$ at $400 \ K$ is $41$. The equilibrium constant for the reaction,$\frac{1}{2} N_2 + \frac{3}{2} H_2 \rightleftharpoons NH_3$ at the same temperature will be closest to

Assertion: Reaction quotient is defined in the same way as equilibrium constant at any stage of the reaction.
Reason: If $Q_c < K_c$,the reaction moves in the direction of reactants.

The equilibrium constants for three reactions are given as:
$(I) \, CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2_{(g)}} + H_{2_{(g)}} ; \, k_1$
$(II) \, CH_{4_{(g)}} + H_2O_{(g)} \rightleftharpoons CO_{(g)} + 3H_{2_{(g)}} ; \, k_2$
$(III) \, CH_{4_{(g)}} + 2H_2O_{(g)} \rightleftharpoons CO_{2_{(g)}} + 4H_{2_{(g)}} ; \, k_3$
The correct relationship between their equilibrium constants is:

For the reaction $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$,the concentrations of $N_2O_4$ and $NO_2$ at equilibrium are $4.8 \times 10^{-2} \, mol \, L^{-1}$ and $1.2 \times 10^{-2} \, mol \, L^{-1}$ respectively. Calculate the value of $K_c$.

$PCl_5$,$PCl_3$,and $Cl_2$ are at equilibrium at $500 \ K$ with concentrations $[PCl_3] = 1.59 \ M$,$[Cl_2] = 1.59 \ M$,and $[PCl_5] = 1.41 \ M$. Calculate $K_c$ for the reaction:
$PCl_5 \rightleftharpoons PCl_3 + Cl_2$

At $273 \, K$,which of the following oxides is the most stable?