$(i) X(g) \rightleftharpoons Y(g) + Z(g), K_{p1} = 3$
$(ii) A(g) \rightleftharpoons 2B(g), K_{p2} = 1$
If the degree of dissociation and initial concentration of both the reactants $X(g)$ and $A(g)$ are equal,then the ratio of the total pressure at equilibrium $\left( \frac{p_1}{p_2} \right)$ is equal to $x : 1$. The value of $x$ is $......$ (Nearest integer)

Dissociation of a gas $A_2$ takes place according to the following chemical reaction. At equilibrium, the total pressure is $1 \ bar$ at $300 \ K$.
$A_{2(g)} \rightleftharpoons 2A_{(g)}$
The standard Gibbs energy of formation of the involved substances has been provided below:

Substance	$\Delta G_f^{\circ} / kJ \ mol^{-1}$
$A_2$	$-100.00$
$A$	$-50.832$

The degree of dissociation of $A_{2(g)}$ is given by $(x \times 10^{-2})^{1/2}$ where $x =$ . . . . . . . (Nearest integer).
[Given: $R = 8.3 \ J \ mol^{-1} \ K^{-1}$, $\ln 2 = 0.693$]

$2$ moles each of $A$ and $B$ were taken in a container and the following reaction takes place: $2 \ A_{(g)} + B_{(g)} \rightleftharpoons 2 \ C_{(g)} + D_{(g)}$. When the system attains equilibrium,which of the following is true?

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

Which of the following statements is correct?

In a $1.0 \, L$ vessel at $90 \, ^\circ C$,$0.2 \, mol$ of $H_{2(g)}$ and $2.0 \, mol$ of $S_{(s)}$ are mixed. For the reaction $H_{2(g)} + S_{(s)} \rightleftharpoons H_2S_{(g)}$; $K_p = 6.8 \times 10^{-2}$,the partial pressure of $H_2S_{(g)}$ at equilibrium will be ............ $atm$.