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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