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* 10^(-8)cm`[/tex]

Explanation :

Formula used for mean free path :

`\lambda=(1)/(√(2)\pi d^2((N)/(V)))`

where,

`\lambda` = Mean free path =
`1.51* 10^(-5)cm`

d = diameter of molecule = ?

`(N)/(V)` = number of molecules per unit volume =
`3.41* 10^(19)molecules/cm^3`

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

`1.51* 10^(-5)cm=(1)/(√(2)* (3.14) (d)^2* (3.14* 10^(19)))`

`d=2.179* 10^(-8)cm`[/tex]

Therefore, the molecular diameter is,
`2.179* 10^(-8)cm`[/tex]