$28 \, g$ of $N_2$ and $6 \, g$ of $H_2$ were kept at $400 \, ^oC$ in a $1 \, L$ vessel. The equilibrium mixture contained $27.54 \, g$ of $NH_3$. The approximate value of $K_c$ for the reaction $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$ is (in $L^2 \, mol^{-2}$):

The two substances $A$ and $B$ are in equilibrium with $C$ and $D$ as $2A + B \rightleftharpoons 3C + 2D$. If the initial pressure of $A$ and $B$ are in the ratio of $4:1$ and at equilibrium,the partial pressures of $A$ and $D$ are equal,find the correct relation.

At $550 \ K$,the $K_c$ for the following reaction is $10^4 \ mol^{-1} \ L$: $X_{(g)} + Y_{(g)} \rightleftharpoons Z_{(g)}$. At equilibrium,it was observed that $[X] = \frac{1}{2}[Y] = \frac{1}{2}[Z]$. What is the value of $[Z]$ (in $mol \ L^{-1}$) at equilibrium?

At $600 \ K$,$2 \ mol$ of $NO$ are mixed with $1 \ mol$ of $O_2$.
$2 \ NO_{(g)} + O_{2(g)} \rightleftarrows 2 \ NO_{2(g)}$
The reaction occurring as above comes to equilibrium under a total pressure of $1 \ atm$. Analysis of the system shows that $0.6 \ mol$ of oxygen are present at equilibrium. The equilibrium constant for the reaction is $.........$ (Nearest integer).

In the reaction $2P_{(g)} + Q_{(g)} \rightleftharpoons 3R_{(g)} + S_{(g)}$,if $2 \text{ moles}$ of each $P$ and $Q$ are taken initially in a $1 \text{ L}$ flask,which of the following is true at equilibrium?

$5 \ \text{moles}$ of $SO_2$ and $5 \ \text{moles}$ of $O_2$ are allowed to react to form $SO_3$ in a closed vessel. At the equilibrium stage,$60\%$ of $SO_2$ is used up. The total number of moles of $SO_2$,$O_2$,and $SO_3$ in the vessel now is: