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

Options

A. `1.335xx10^(-10)cm`
B. `1.335xx10^(-8)cm`
C. `2.67xx10^(-8)cm`
D. `4.34xx10^(-8)cm`

Answer

C

Explanation

b = 4 `xx` volume occupied by molecules of 1 mol of a gas,
or `b=4N_(a)(4/3pir^(3))`
or `r=((3b)/(16N_(A)pi))^(1//3)`
`=[(3xx24)/(16xx6.023xx10^(23)xx3.14)]^(1//3)` cm
`=1.355xx10^(-8)cm`
Now, molecular diameter, d = 2r
`=2.67xx10^(-8)` cm