Physics

Calculate the excluded volume for the gas having molecular diameter $1A$?

SOLUTION

Solution:-
As we know that,
Excluded volume of a gas $= 4 \times$ actual volume of gas
Actual volume of a gas $= \cfrac{4}{3} \pi {r}^{3}$
Given that diameter of molecule $\left( d \right) = 1 \mathring{A} = {10}^{-8} cm$
$\therefore$ radius of molecule $= \cfrac{d}{2} = \cfrac{{10}^{-8}}{2} cm$
$\therefore$ Actual volume of gas $=$ No. of molecules $\left( {N}_{A} \right) \times$ volume of one molecule
$\because {N}_{A} = 6.023 \times {10}^{23}$
$\therefore$ Actual volume of gas $= 6.023 \times {10}^{23} \times \cfrac{4}{3} \times 3.14 \times {\left( \cfrac{{10}^{-8}}{2} \right)}^{3} = 0.31 \; {cm}^{3}$
$\therefore$ Excluded volume of gas $= 4 \times 0.31 = 1.24 \; {cm}^{3}$
Hence the excluded volume for the gas having molecular diameter $1 \mathring{A}$ is $1.24 {cm}^{3}$.

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Subjective Medium Published on 18th 08, 2020
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