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Question

(C) The van der Waals constant $b$ represents the excluded volume per mole of gas molecules.The excluded volume for a pair of molecules is $4 	imes \

Vedclass · Accepted Answer

$v = \frac{b}{4N_{A}}$

Vedclass · Answer

(C) The van der Waals constant $b$ represents the excluded volume per mole of gas molecules.The excluded volume for a pair of molecules is $4 	imes 	ext{volume of one molecule}$.For $1 \ 	ext{mole}$ of gas,$b = N_{A} 	imes (2 	imes 	ext{excluded volume per molecule}) = N_{A} 	imes 2 	imes (4 	imes \frac{4}{3} \pi r^{3}) / 2 = 4 	imes N_{A} 	imes 	ext{volume of one molecule}$.Since the volume of one molecule is $v = \frac{4}{3} \pi r^{3}$,we have $b = 4 N_{A} v$.Therefore,the excluded volume per molecule is $v = \frac{b}{4 N_{A}}$.

Excluded volume $(v)$ per molecule is related to the van der Waals constant $'b'$ in the following way:

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