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The volume of N2 gas of 0ºC and 1.013 bar required to cover a sample of silica gel with uni molecular layer is $129 {cm}^{3} g^{- 1} of gel.$ The surface area per gram of the gel if each nitrogen molecule occupies $16 .2 \times 10^{- 20} m^{2} is x \times 10^{3}$ The value of x = _____

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answer is 1.

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Detailed Solution

PV = nRT

$\Rightarrow 1.013 \times 0.129 = n \times 0.0821 \times 273 ∴ n = 0.0583 mol$
Area occupied
$= 0.00583 \times 6.023 \times 10^{23} \times 16.2 \times 10^{- 20} = 0.568 \times 10^{3} m^{2} g^{- 1} ∴ x = 0.568$

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