Question

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 $0.16{nm}^2$. What is the surface area per gram of silica gel?
$[Given{N}_A=6X{10}^{23}]$

• A. $5.568m^2{g}^{-1}$
• B. $3.48m^2{g}^{-1}$
• C. $1.6m^2{g}^{-1}$
• D. None of these

Answer 1

The correct option is A $5.568m^2{g}^{-1}$

No. of molecules per gram of $N_2$ in monolayer
$=\frac{6\times {10}^{23}}{22,400}\times 1.30$
$=3.48\times {10}^{19}$
Cross-sectional area of a molecule
$=1.6\times {10}^{-19}{m}^2$
$\therefore$ Area covered by molecules per gram
$=3.48\times {10}^{19}\times 1.6\times {10}^{-19}=5.568m^2$
$\therefore$ Surface area $=5.568m^2{g}^{-1}$