Multiple choice

Assuming that $O_2$ molecule is spherical in shape with radius $2 \mathring {A} $, the percentage of the volume of $O_2$ moleculesto the total volume of gas at $STP$ is:

  1. 0.09 %

  2. 0.9 %

  3. 0.009 %

  4. 0.045 %
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A Correct answer
Explanation

The volume of one spherical O2 molecule with radius 2 angstroms is about 3.35 x 10^-23 cm^3. Multiplying by Avogadro's number and comparing with the molar gas volume at STP gives approximately 0.09%.

AI explanation

At STP, one mole of gas occupies 22400 cubic cm, so the fraction of the volume occupied by the spherical molecules is the number of molecules times the molecular volume divided by the molar volume. The volume of one molecule with radius 2 Angstroms is (4/3) * pi * (2 * 10^-8)^3 = 3.35 * 10^-23 cubic cm. Multiplying by Avogadro's number gives a total molecular volume per mole of 6.022 * 10^23 * 3.35 * 10^-23 = 20.17 cubic cm. The percentage is therefore (20.17 / 22400) * 100 = 0.09 percent.

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