$2 \times 10^6$ molecules of $N_2$ gas enter into a vessel having a volume of $400 \, mL$ at $400 \, K$ temperature. Find the pressure in $atm$ and $bar$. $[R = 0.082 \, L \, atm \, mol^{-1} \, K^{-1}]$,$[1 \, atm = 1.013 \, bar]$

(A) $1$. Calculate the number of moles $(n)$: $n = \frac{\text{Number of molecules}}{N_A} = \frac{2 \times 10^6}{6.022 \times 10^{23}} \approx 3.321 \times 10^{-18} \, mol$.
$2$. Convert volume to liters: $V = 400 \, mL = 0.4 \, L$.
$3$. Use the ideal gas equation $PV = nRT$: $P = \frac{nRT}{V}$.
$4$. Calculate pressure in $atm$: $P = \frac{3.321 \times 10^{-18} \times 0.082 \times 400}{0.4} = 2.723 \times 10^{-16} \, atm$.
$5$. Convert pressure to $bar$: $P_{bar} = 2.723 \times 10^{-16} \times 1.013 = 2.758 \times 10^{-16} \, bar$.