The decomposition of ${\text{HNO}}_{\text{3}}$ represented below attains equilibrium at a given  ${\text{P}}_{\text{eq}}$ and T. If we

start ${\text{4NHO}}_{\text{3}}\rightleftharpoons {\text{\hspace{0.17em}4NO}}_{\text{2}\left(\text{g}\right)}{\text{+2H}}_{\text{2}}{\text{O}}_{\left(\text{g}\right)}{\text{\hspace{0.17em}+\hspace{0.17em}O}}_{\text{2}\left(\text{g}\right)}$ with pure ${\text{HNO}}_{\text{3}}$ having initial pressure ${\text{P}}_P$ then at

equilibrium. Select the correct statements :

${\text{4HNO}}_{\text{3}\left(\text{g}\right)}\rightleftharpoons {\text{\hspace{0.17em}4NO}}_{\text{2}\left(\text{g}\right)}{\text{\hspace{0.17em}+\hspace{0.17em}2H}}_{\text{2}}{\text{O}}_{\left(\text{g}\right)}{\text{\hspace{0.17em}+\hspace{0.17em}O}}_{\text{2}\left(\text{g}\right)}\text{;}$

${\text{P}}_{\text{i}}\text{ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}0 \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}0\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}0}$

${\text{P}}_{\text{i}}\text{\hspace{0.17em}-\hspace{0.17em}4 \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}4P\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}2P\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}P}$

Pressure at equilibrium is ${\text{P}}_{\text{eq}}$.

${\text{P}}_{\text{eq}}{\text{.\hspace{0.17em}=\hspace{0.17em}P}}_{\text{i}}-\text{\hspace{0.17em}4P\hspace{0.17em}+\hspace{0.17em}4P\hspace{0.17em}}+\text{2P\hspace{0.17em}+\hspace{0.17em}P}$

$\therefore {\text{\hspace{0.17em}P}}_{\text{i}}-{\text{\hspace{0.17em}4P\hspace{0.17em}=\hspace{0.17em}P}}_{\text{eq}}-{\text{\hspace{0.17em}7P\hspace{0.17em}=\hspace{0.17em}P}}_{\text{eq}}-{\text{\hspace{0.17em}7P}}_{{\text{O}}_{\text{2}}}{\text{;\hspace{0.17em}P\hspace{0.17em}=\hspace{0.17em}P}}_{{\text{O}}_{\text{2}}}$

${\text{K}}_{\text{P}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{{\left({\text{P}}_{{\text{NO}}_{\text{2}}}\right)}^{\text{4}}{\left({\text{P}}_{{\text{H}}_{\text{2}}\text{O}}\right)}^{\text{2}}{\text{P}}_{{\text{O}}_{\text{2}}}}{{\left({\text{P}}_{{\text{HNO}}_{\text{3}}}\right)}^{\text{4}}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{\text{1024\hspace{0.17em}}{\left({\text{P}}_{{\text{O}}_{\text{2}}}\right)}^{\text{7}}}{{\left({\text{P}}_{\text{eq}}{\text{\hspace{0.17em}-\hspace{0.17em}7P}}_{{\text{O}}_{\text{2}}}\right)}^{\text{4}}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{\text{1024}{\left({\text{P}}_{{\text{O}}_{\text{2}}}\right)}^{\text{7}}}{{\left({\text{P}}_{\text{1}}{\text{\hspace{0.17em}-\hspace{0.17em}4P}}_{{\text{O}}_{\text{2}}}\right)}^{\text{4}}}\text{\hspace{0.17em}and}$

${\text{K}}_{\text{p}}^{\text{0}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{{\left({\text{P}}_{{\text{NO}}_{\text{2}}}\right)}^{\text{4}}{\left({\text{P}}_{{\text{H}}_{\text{2}}\text{O}}\right)}^{\text{2}}{\text{P}}_{{\text{O}}_{\text{2}}}}{\left({\text{P}}_{{\text{NHO}}_{\text{3}}}\right)}\text{\hspace{0.17em}×\hspace{0.17em}}\frac{\text{1}}{{\left(\text{P°}\right)}^{\text{3}}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{{\left(\text{4P}\right)}^{\text{21}}\text{\hspace{0.17em}×\hspace{0.17em}}{\left(\text{2P}\right)}^{\text{2}}{\text{\hspace{0.17em}×\hspace{0.17em}P}}_{{\text{O}}_{\text{2}}}}{{\left({\text{P}}_{\text{eq}}{\text{\hspace{0.17em}-\hspace{0.17em}7P}}_{{\text{O}}_{\text{2}}}\right)}^{\text{4}}}\text{\hspace{0.17em}×\hspace{0.17em}}\frac{\text{1}}{{\left(\text{P°}\right)}^{\text{3}}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{\text{1024\hspace{0.17em}}{\left({\text{P}}_{{\text{O}}_{\text{2}}}\right)}^{\text{7}}}{{\left({\text{P}}_{\text{eq}}{\text{\hspace{0.17em}-\hspace{0.17em}7P}}_{{\text{O}}_{\text{2}}}\right)}^{\text{4}}}\text{\hspace{0.17em}×\hspace{0.17em}}\frac{\text{1}}{{\left({\text{P}}^{\text{0}}\right)}^{\text{3}}}$