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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 3Å.
Solution 1
Diameter of an oxygen molecule, d = 3 A = 3 x 10-10 m. Consider one mole of oxygen gas at STP, which contain total NA = 6.023 x 1023 molecules.
Actual molecular volume of `6.023 xx 10^23` oxygen molecules
`V_"actual" = 4/3 pir^3 . N_A`
`= 4/3 xx 3.14 xx (1.5)^3 xx 10^(-3) xx 6.02 xx 10^23 m^3`
`= 8.51 xx 10^(-6) m^3`
`= 8.51 xx 10^(-3) litre` [∵ `1 m^3 = 10^3 litre`]
:. Molecular volume of one mole of oxygen
`V_"actual" = 8.51 xx 10^(-3) litre`
At STP, the volume of one mole of oxygen
`V_"molar" = 22.4 litre`
`V_"actual"/"V_"molar" = 8.51 xx 10^(-3)/22.4" = 3.8 xx 10^(-4) ~~ 4 xx 10^(-4)`
Solution 2
Diameter of an oxygen molecule, d = 3Å
Radius, r = `d/2 = 3/2 ` = 1.5 Å = 1.5 × 10–8 cm
Actual volume occupied by 1 mole of oxygen gas at STP = 22400 cm3
Molecular volume of oxygen gas, `V = 4/3 pir^3. N`
Where, N is Avogadro’s number = 6.023 × 1023 molecules/mole
`:. V = 4/3 xx 3.14 xx (1.5 xx 10^(-8))^3 xx 6.023 xx 10^23 = 8.51 cm^3`
Ratio of the molecular volume to the actual volume of oxygen = `8.51/22400`
`= 3.8 xx 10^(-4)`
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