Question

$20\%$ of surface sites are occupied by $N_2$ molecules. The density of surface site is $6.023\times 10^{14}c{m}^{-2}$ and total surface area is $1000c{m}^2$ . The catalyst is heated to $300K$ while $N_2$ is completely desorbed into a pressure of $0.001$ atm and volume of $2.46c{m}^3$. 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 $N_2=0.001atm$; $T=300K;V=2.46c{m}^3$
$\therefore$ 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
$=\frac{12.04\times 10^{16}}{6.016\times 10^{16}}=2$