The volume of nitrogen gas Um (measured at STP) required to cover a sample of silica get with a mono-molecular layer is `129 cm^(3) g^(-1)` of gel. Calculate the surface area per gram of the gel if each nitrogen molecule occupies `16.2 xx 10^(-20) m^(2).`

Answer

`561.8cm^(3)`

Explanation

`22400 cm^(3)` of `N_(2)` at STP contain `= 6.022 xx 10^(23)` molecules
`therefore` `129 cm^(3)` of `N_(2)` at STP will contain `= (6.022 xx 10^(23) xx 129)/(22400) = 3.468 xx 10^(21)` molecules
Area occupied by a single molecule `= 16.2 xx 10^(-20) m^(2)`
`therefore` Area occupied by `3.468 xx 10^(21)` molecules of nitrogen
`= (16.2 xx 10^(-20)) xx (3.468 xx 10^(21)) m^(2) = 561.8 m^(2).`