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 $1000$ $c{m}^2$. The catalyst is heated to $300$ $K$ while $N_2$ is completely desorbed into a pressure of $0.001$ atm and volume $2.46$ $c{m}^3$. Find the number of active sites occupied by each $N_2$ molecule.

• A. $2$
• B. $3$
• C. $1$
• D. $4$

Answer 1

The correct option is A $2$

Total number of moles of nitrogen $n=\frac{PV}{RT}=\frac{0.001\times 2.46\times {10}^{-3}}{0.08206\times 300}=9.99\times {10}^{-8}$ moles

Total number of nitrogen molecules $=6.023\times {10}^{23}\times 9.99\times {10}^{-8}=6.02\times {10}^{16}$

Total number of sites present on the surface of the catalyst $=6.023\times {10}^{14}\times 1000=6.023\times {10}^{17}$

Total number of active sites $=0.2\times 6.023\times {10}^{17}=1.2\times {10}^{17}$

Number of active sites occupied by each nitrogen molecule $=\frac{1.2\times {10}^{17}}{6.02\times {10}^{16}}=2$