Question

$20\%$ of surface sites are occupied by $N_{2}$ molecules. The density of surface site is $6.023 \times 10^{14}\, cm^{-2}$ 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

• A. $4$
• B. $2$
• C. $0$
• D. $6$

Answer 1

Answer: (B)

Pressure of $N_{2}=0.001\,atm$; $T=300\,K; V = 2.46\,cm^{3}$
$\therefore $ Number of $N_{2}$ molecules $=\frac{PV}{RT}\times N_{0}$
$=\frac{0.001 \times 2.46 \times 10^{-3}}{0.082 \times 300}\times 6.023\times 10^{23} $
$=6.016 \times 10^{16}$
Now total number of surface sites
= Density $\times$ Total surface area
$=6.023 \times 10^{14} \times 1000 =6.023 \times 10^{17}$
Site occupied by $N_{2}$ molecules $=\frac{20}{100} \times 6.023\times 10^{17}$
$=12.04 \times 10^{16}$
$\therefore $ Number of sites occupied by each $N_{2}$ molecule
$=\frac{12.04 \times 10^{16}}{6.016 \times 10^{16}}=2$