For the following three equilibria $X, Y$,and $Z$ in the gaseous state at $300 \ K$,the increasing order of the ratio of $K_p$ to $K_c$ is:
$X: 2SO_2 + O_2 \rightleftharpoons 2SO_3$
$Y: PCl_5 \rightleftharpoons PCl_3 + Cl_2$
$Z: 2HI \rightleftharpoons H_2 + I_2$

For the reaction $PCl_{3(g)} + Cl_{2(g)} \rightleftharpoons PCl_{5(g)}$ at $250 \ ^\circ C$,the value of $K_c$ is $26$. The value of $K_p$ at the same temperature will be:

For the reaction in equilibrium $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$,the equilibrium concentrations of $N_2O_4$ and $NO_2$ are $4.8 \times 10^{-2} \ mol/L$ and $1.2 \times 10^{-2} \ mol/L$,then $K_C$ is

$40\%$ of $HI$ undergoes decomposition to $H_2$ and $I_2$ at $300 \ K$. $\Delta G^{\ominus}$ for this decomposition reaction at one atmosphere pressure is $... \ J \ mol^{-1}$. [nearest integer]
(Use $R = 8.31 \ J \ K^{-1} \ mol^{-1}$; $\log 2 = 0.3010$; $\ln 10 = 2.3$; $\log 3 = 0.477$)

In the synthesis of $HI$,the amounts of $H_{2(g)}$,$I_{2(g)}$,and $HI_{(g)}$ at equilibrium were found to be $0.8 \ mol$,$0.8 \ mol$,and $2.4 \ mol$ respectively in a $10 \ L$ vessel. Calculate the equilibrium constant $(K_c)$ for the reaction $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$ and the equilibrium constant for the reverse reaction.

For the reaction $NH_4HS_{(s)} \rightleftharpoons NH_{3(g)} + H_2S_{(g)}$,the observed total pressure of the reaction mixture at equilibrium is $1.12 \ atm$ at $106 \ ^\circ C$. The value of $K_P$ for the reaction is: (in $atm^2$)