$A$ schematic plot of $\ln K_{eq}$ versus inverse of temperature $(1/T)$ for a reaction is shown below. The reaction must be

$2 \ mol$ of $N_2$ is mixed with $6 \ mol$ of $H_2$ in a closed vessel of $1 \ L$ capacity. If $50\%$ of $N_2$ is converted into $NH_3$ at equilibrium,the value of $K_c$ for the reaction $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$ is

For the reaction $N_2O_{4_{(g)}} \rightleftharpoons 2NO_{2_{(g)}}$ at $298 \ K$,the equilibrium constant $K_p$ is $0.14 \ atm$. Calculate the value of $K_c$. $(R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1})$

One mole of $PCl_{5(g)}$ was heated in a $1 \ L$ closed flask at $500 \ K$. At equilibrium,$0.1 \ mole$ of $Cl_{2(g)}$ was formed. What is its $K_{p}$ (in $atm$)? (Given $R=0.082 \ L \ atm \ mol^{-1} \ K^{-1}$)

For the decomposition of the compound,represented as $NH_2COONH_{4(s)} \rightleftharpoons 2NH_{3(g)} + CO_{2(g)}$,the $K_p = 2.9 \times 10^{-5} \ atm^3$. If the reaction is started with $1 \ mol$ of the compound,the total pressure at equilibrium would be............ $\times 10^{-2} \ atm$.

For the following gaseous equilibria at $300 \ K$,find the increasing order of the ratio $\frac{K_p}{K_c}$ for $X, Y,$ and $Z$:
$X: 2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$
$Y: PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$
$Z: 2HI_{(g)} \rightleftharpoons H_{2(g)} + I_{2(g)}$