Twenty per cent of the surface sites of a catalyst is occupied by nitrogen molecules. The density of surface sites is `6.023 xx 10^(14) g cm^(-3)`. The total surface area is 1000 `cm^2`. The catalyst is heated to 300 K and nitrogen is completely adsorbed into a pressure of 0.001 atm and volume of 2.46 cmo. Calculate the number of sites occupied by nitrogen molecules.

Explanation

Density of sites `= 6.023 xx 10^(14) g cm^(-3)`
Total sites` =6.023 xx 10^(14) xx1000 = 6.023 xx 10^(17)`
20% sites are occupied.
So, sites occupied =`(20 )/(100 ) xx 6.023 xx 10^(17) = 12.04 xx 10^(16)`
`pV = n RT `
` or n= ( 0.001 xx 2.46 xx 10^(-3))/( 0.821 xx 300 ) = 9.98 xx 10^(-8)`
Number of molecules `= 9.98 xx 10^(-8) xx 6.023 xx 10^(23)`
` = 6.02 xx 10^(16)`
Sites occupied per molecule of nitrogen is
`("Number of sites ")/("Number of molecules ") = (12.04 xx 10^(16))/(6.02 xx 10^(16 )= 2`