At $298 \, K$ temperature,$4 \, g$ of $H_2$ gas is filled in a $500 \, mL$ vessel. Due to a small hole in the vessel,after some time,the pressure in the vessel becomes $50 \, bar$. Find the number of $H_2$ molecules that have escaped from the vessel? $(R = 8.314 \times 10^{-2} \, L \, bar \, mol^{-1} \, K^{-1})$

(A) $1$. Initial moles of $H_2$ $(n_1)$ = $\frac{\text{mass}}{\text{molar mass}} = \frac{4 \, g}{2 \, g/mol} = 2 \, mol$.
$2$. Final moles of $H_2$ $(n_2)$ remaining in the vessel can be calculated using the ideal gas equation $PV = nRT$:
$n_2 = \frac{PV}{RT} = \frac{50 \, bar \times 0.5 \, L}{8.314 \times 10^{-2} \, L \, bar \, mol^{-1} \, K^{-1} \times 298 \, K} \approx 1.0086 \, mol$.
$3$. Moles of $H_2$ escaped = $n_1 - n_2 = 2 - 1.0086 = 0.9914 \, mol$.
$4$. Number of molecules escaped = $\text{moles} \times N_A = 0.9914 \times 6.022 \times 10^{23} \approx 5.97 \times 10^{23}$ molecules.