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 $0.001atm$ and volume of $2.46c{m}^3$. Find the number of active sites occupied by each $N_2$ molecule.

Answer 1

$P_{N_2}=0.001atm;T=300K;V=2.46c{m}^3$

$\therefore \text{Number of}{N}_2\text{molecules}=\frac{PV}{RT}\times N_A=\frac{0.001\times 2.46\times {10}^{-3}}{0.082\times 300}\times 6.023\times {10}^{23}=6.023\times {10}^{16}$

$\text{Total number of surface sites}=\text{Density}\times \text{Total surface area}=6.023\times {10}^{14}\times 1000=6.023\times {10}^{17}$

$\text{Site occupied by}{N}_2\text{molecules}=\frac{20}{100}\times 6.023\times {10}^{17}=12.04\times {10}^{16}$

$\therefore \text{Number of sites occupied by each}{N}_2\text{molecule}=\frac{12.04\times {10}^{16}}{6.023\times {10}^{16}}=2$