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 cm³ g^-1 of the gel. The area occupied by a nitrogen molecule is 0. 16 nm². What is the surface area per gram of silica gel?
[Given: N_A = 6 x l0²³mol^-l]

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1.6 m² g^-1

3.48 m² g^-1

5.568 m² g^-1

None of these

answer is A.

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Detailed Solution

No. of molecules per gram of N₂ in monolayer = $\frac{6 \times 10^{23}}{22, 400} \times 1 .30 = 3 .48 \times 10^{19}$
Cross-sectional area of a molecule = $1.6 \times 10^{- 19} m^{2}$
$∴$ Area covered by molecules per gram $= 3 .48 \times 10^{19} \times 1 .6 \times 10^{- 19} = 5 .568 m^{2}$
$∴ Surface area = 5 .568 m^{2} g^{- 1}$