Answer to Question #244991 in Physics for Diane

Question

one mole of ideal gas (avogadro number: 6.02*10^23 molecules) occupies the 22.4 litres under normal condition. What fraction of this volume is actually occupied by the ideal gas molecules? Treat the molecules of gas as sphere of radius of 1 angstroms.

state your answer to the nearest 0.00001

Answer 1

The volume of one molecule

$$V_0=\frac{4}{3}\pi R^3\\=\frac{4}{3}*3.14*(1*10^{-10}\rm \:m)^3=4.19*10^{-30}\:m^3$$

So

$$\frac{V_N}{V}=\frac{NV_0}{V}\\=\frac{6.02*10^{23}*4.19*10^{-30}\:\rm m^3}{22.4*10^{-3}\:\rm m^3}=0.00011$$