20% of surface sites are occupied by $N_{2}$ molecules. The density of surface site is $6.023 imes

Question

20% of surface sites are occupied by $N_{2}$ molecules. The density of surface site is $6.023 	imes 10^{14}~cm^{-2}$ and total surface area is $1000~cm^{2}$. The catalyst is heated to 300 K while $N_{2}$ is completely desorbed into a pressure of 0.001 atm and volume of 2.46 $cm^{3}$. Find the number of active sites occupied by each $N_{2}$ molecule.

Professor PC Thomas Classes · Answer

Total surface sites = $6.023 	imes 10^{14} 	imes 1000 = 6.023 	imes 10^{17}$. Sites occupied by $N_2$ = $20\% 	ext{ of } 6.023 	imes 10^{17} = 1.204 	imes 10^{17}$. Moles of $N_2$ desorbed = $\frac{PV}{RT} = \frac{0.001 	imes 2.46 	imes 10^{-3}}{0.082 	imes 300} = 10^{-7}~mol$. Molecules of $N_2$ = $10^{-7} 	imes 6.023 	imes 10^{23} = 6.023 	imes 10^{16}$. Sites per molecule = $\frac{1.204 	imes 10^{17}}{6.023 	imes 10^{16}} = 2$.