$1 \ mol$ of $N_2$ and $2 \ mol$ of $H_2$ are allowed to react in a $1 \ dm^3$ vessel. At equilibrium,$0.8 \ mol$ of $NH_3$ is formed. What is the concentration of $H_2$ at equilibrium (in $M$)?

In the reaction $A + 2B \rightleftharpoons 2C$,if $2$ moles of $A$,$3.0$ moles of $B$ and $2.0$ moles of $C$ are placed in a $2.0 \ L$ flask and the equilibrium concentration of $C$ is $0.5 \ mol/L$. The equilibrium constant $K_c$ for the reaction is:

The following reaction is performed at $298 \, K$.
$2 NO_{(g)} + O_{2(g)} \rightleftharpoons 2 NO_{2(g)}$
The standard free energy of formation of $NO_{(g)}$ is $86.6 \, kJ/mol$ at $298 \, K$. What is the standard free energy of formation of $NO_{2(g)}$ at $298 \, K$? $(K_p = 1.6 \times 10^{12})$

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: $R = 8.3 \ J \ mol^{-1} \ K^{-1}$, $\ln 2 = 0.693$]

For the equilibrium $2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$,the partial pressures of $SO_2$,$O_2$,and $SO_3$ are $0.662 \ atm$,$0.101 \ atm$,and $0.331 \ atm$ respectively. If the equilibrium concentrations of $SO_2$ and $SO_3$ are made equal,the partial pressure of $O_2$ will be ..... $atm$.

For the reactions $X \rightleftharpoons 2Y$ and $Z \rightleftharpoons P + Q$,the equilibrium constants $K_p$ and $K_q$ are in the ratio $1:9$. If the degree of dissociation of $X$ and $Z$ is the same,then the ratio of their total pressures is: