At 1 atm and 273 K the volume of nitrogen gas required to cover a sample of silica gel, assuming Langmuir monolayer adsorption , is found to be `1.30 cm^(3)g^(-1)` of the gel. The area occupied by a nitrogen molecule is `0.16nm^(2)`. Find out the no. of surface sites occupied per molecule of `N_(2)`.

Options

A. `5.568 m^(2)g^(-1)`
B. `3.48 m^(2)g^(-1)`
C. `1.6 m^(2) g^(-1)`
D. None of these

Answer

A

Explanation

No. of molecules per gram of `N_(2)` in monolayer
`=(6xx10^(23))/(22,400)xx1.30=3.488xx10^(19)`
Cross-sectional area of a molecule `= 1.6 xx10^(-19)m^(2)`
:.Area covered by molecules per gram
`= 3.48 xx 10^(19)xx 1.6 xx10^(-19)=5.568 m^(2)`
Surface area `= 5.568 m^(2)g^(-1)`