Question

A gaseous molecule has radius of about 0.4 nm. Assuming that this molecule is spherical in shape, calculate. 

(i) Volume of single molecule of gas 

(ii) The percentage of empty space in one mole of gas at STP.

Answer 1

(i) Radius (r) = 0.4 nm

= 0.4 x 10^-9 m = 0.4 × 10^-7 cm

= 4 x 10^-8 cm

\(\therefore\) Volume of a sphere = \(\frac{4}{3}\pi r^3\)

= \(\frac{4}{3}\times\frac{22}{7}\) x (4 x 10^-8)³ cm³

= 2.68 x 10^-22 cm³

(ii) Volume of 6.022 x 10²³ molecules of gas = 268 x 10^-22 x 6.022 × 10²³ = 161.39 cm³

^{\(\therefore\)} Volume occupied by 1 mole of gas at STP

= 22.4 L = 22400 cm³

Empty volume = Total volume of gas – Volume occupied by molecules

= 22400 - 161.39 = 22238.61 cm³

^{\(\therefore\)} Percentage empty space

= \(\frac{empty\,space}{total\,volume}\) x 100

= \(\frac{22238.61}{22400}\) x 100 = 99.28%

Hence, 99.28% of space of 1 mole of gas at STP in empty.