Question

Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be `3 Å`.

Answer 1

As is known, one mole of a gas at STP contains `6.023 xx 10^(23)` molecules and occupies a volume of `22400 c.c.`
Molecular volume = `4/3 pi r^(3) xx 6.023 xx 10^(23)`
`= 4/3 xx 3.14 (1.5 xx 10^(-10))^(3) xx 6.023 xx 10^(23)`
`= 8.51 xx 10^(-6) m^(3) = 8.51 cm^(3)`
`(M o l e c u l ar "volume")/("Actual volume") = (8.51 cm^(3))/(22400 cm^(3)) = 3.8 xx 10^(-4)`.