van der Waals constant b of helium is 24 mL `mol^(-1)`. Find molecular diameter of helium.

Options

A. `1.335 xx 10^(-10)cm`
B. `1.335 xx 10^(-8)cm`
C. `2.67 xx 10^(-8)cm`
D. `4.34 xx 10^(-8)cm`

Answer

C

Explanation

`b = 4 xx` volume occuoied by molecules of `1mol` of a gas.
or `b = 4N_(A) ((4)/(3)pir^(3))` or `r = ((3b)/(16N_(A^(pi))))^(1//3)`
`= [(3xx24)/(16xx6.023 xx 10^(23)xx3.14)]^(1//3)cm`
`= 1.355 xx 10^(-8)cm`
Now, molecular diameter, `d = 2r = 2.67 xx 10^(-8)cm`