Question

The mean free path of nitrogen molecules at 2.3°C and 1.28 atm is 1.51 x 10-5 cm. At this temperature and pressure there are 3.41 x 1019 molecules/cm3. What is the molecular diameter?

Answer 1

Answer : The molecular diameter is, $2.179\times 10^{-8}cm$[/tex]

Explanation :

Formula used for mean free path :

$\lambda=\frac{1}{\sqrt{2}\pi d^2(\frac{N}{V})}$

where,

$\lambda$ = Mean free path = $1.51\times 10^{-5}cm$

d = diameter of molecule = ?

$\frac{N}{V}$ = number of molecules per unit volume  = $3.41\times 10^{19}molecules/cm^3$

Now put all the given values in this formula, we get:

$1.51\times 10^{-5}cm=\frac{1}{\sqrt{2}\times (3.14) (d)^2\times (3.14\times 10^{19})}$

$d=2.179\times 10^{-8}cm$[/tex]

Therefore, the molecular diameter is, $2.179\times 10^{-8}cm$[/tex]