In a vessel, $\mathrm{O_2}$ gas undergoes physisorption on an adsorbent surface, causing its partial pressure to decrease from $6\,\text{atm}$ to $P\,\text{atm}$ in an $8.21\,\text{L}$ vessel at $500\,\text{K}$. If the total number of sites on the adsorbent surface is $2 \times 10^{23}$ and every site accommodates effectively three $\mathrm{O_2}$ molecules, find $P$ (in atm). [$N_A = 6 \times 10^{23}$]