Question

A monolayer of N₂ molecules is adsorbed on the surface of 1.0g Al₂O₃/Fe catalyst at 77K, the boiling point of liquid nitrogen. Upon warming, the nitrogen occupies 2.86cm³ at 0 C and 1atm. What is the surface area of a catalyst? The effective size of N₂ molecule is 0.167nm² .

Answer 1

Moles of nitrogen can be calculated from PV= nRT

n= PV/RT

V= 2.86cm3= 0.00286 L

T= 0deg.c =0+273.15= 273.15K P= 1am R= 0.08206 L.atm/mole.K

moels of Nitrogen= 1*0.00286/(0.08206*273.15)=0.00013 moles

Mass of nitrogen = molecular weight* moles= 28*0.00013=0.00364 gms

1 moles of any substance contains 6.023*1023 molecules

Number of molecules in 0.00013*6.023*10²³ =7.83*10¹⁹

1nm²= 10^-18 m2

0.167 nm2= 0.167*10^-18m²

total area of Catalyst= 7.83*10¹⁹* 0.167*10^-18 m2=`14.64 m2

specific area of catalyst= 14.64/1 m2/g