At $1000 \ K$,the equilibrium constant for the reaction $CO_{2(g)} + H_{2(g)} \rightleftharpoons CO_{(g)} + H_2O_{(g)}$ is $0.53$. In a one litre vessel,at equilibrium the mixture contains $0.25 \ mole$ of $CO$,$0.5 \ mole$ of $CO_2$,$0.6 \ mole$ of $H_2$ and $x \ moles$ of $H_2O$. The value of $x$ is

$A$ mixture of $1.57 \ mol$ of $N_2$,$1.92 \ mol$ of $H_2$ and $8.13 \ mol$ of $NH_3$ is introduced into a $20 \ L$ reaction vessel at $500 \ K$. At this temperature,the equilibrium constant,$K_c$ for the reaction $N_{2(g)} + 3H_{2(g)} \longleftrightarrow 2NH_{3(g)}$ is $1.7 \times 10^2$. Is the reaction mixture at equilibrium? If not,what is the direction of the net reaction?

The number of correct statement$(s)$ involving equilibria in physical processes from the following is:
$A$. Equilibrium is possible only in a closed system at a given temperature.
$B$. Both the opposing processes occur at the same rate.
$C$. When equilibrium is attained at a given temperature,the value of all its parameters becomes constant.
$D$. For dissolution of solids in liquids,the solubility is constant at a given temperature.

When $1 \ mol$ of $H_2$ and $1 \ mol$ of $N_2$ are enclosed in a $5 \ L$ vessel and the reaction is allowed to attain equilibrium,it is found that at equilibrium there is $x \ mol$ of $H_2$. The number of moles of $NH_3$ would be

Match the items in List-$X$ with List-$Y$ and select the correct option.

List-$X$	List-$Y$
$(A)$ $A_{(g)} \rightleftharpoons B_{(g)} + \text{Heat}$	$(i)$ Equilibrium constant
$(B)$ $r_b/r_f$	$(ii)$ Favored at low temperature
$(C)$ $r_f/r_b$	$(iii)$ [Equilibrium constant]$^{-1}$
$(D)$ $2A_{(g)} + B_{(g)} \rightleftharpoons C_{(g)}$	$(iv)$ $A_{(g)} + B_{(g)} \rightleftharpoons C_{(g)} + D_{(g)}$
$(E)$ Effect of pressure	$(V)$ $\Delta n < 0$

In a $0.25 \ L$ tube,$4 \ mol$ of $NO$ undergoes dissociation. If the degree of dissociation is $10\%$,then the value of $K_c$ for the reaction $2NO \rightleftharpoons N_2 + O_2$ will be: