Twenty precent of the surface sites of a catalyst is occupied by nitrogen molecules. The density of surface sites is `6.023xx10^(14)cm^(-2)` . The total sarface area is `1000cm^(2)` . The catalyst is is henced to `300K` and nitrogen is completely desorbed a pressure of `0.001` atm and volume of `2.46cm^(3)` . Calculate the number of sites occupied by niitrogen molecules.

Explanation

Step I. Calculation of total no. of surface sites
Density of surface sites `=6.023xx10^(14)cm^(-2)`
Total surface area `=1000 cm^(2)=10^(3)cm^(2)`
`therefore` Total no. of surface sites `=(6.023xx10^(14))xx(10^(3))=6.023xx10^(17)`
Step 2. Calculation of surface sites occupied by `N_(2)` moolecules.
Surface sites occupied by `N_(2)` molecules `=20/100xx6.023xx10^(17)=1.2046xx10^(17)`
Step 3. Calculation of total no of `N_(2)` molecules
`P=0.001atm, V=2.46cm^(3)=2.46xx10^(-3)L, T=300K`
`PV=nRT orn=(10^(-3)atm xx2.46xx10^(-3)L)/(0.0821L atm K^(-1)mol^(-1)xx300K)=10^(-7)`mole
`therefore` No. of molecules `=(10^(-7))xx(6.023xx10^(23))=6.023xx10^(16)`
Step 4. Calculation of no. of sites occupied by each `N_(2)` molecule
`=("No. of sites occupied")/("No. of"N_(2)"molecules")=(1.2046xx10^(17))/(6.023xx10^(16))=2`