Question

The lowest possible temperature in outer space is 3.13 K. What is the rms speed of hydrogen molecules at this temperature? (The molar mass of molecular hydrogen is 2.02 g/mol )

Answer 1

`v_(rms) =196.59 m/s`

Given:

Temperature, T = 3.13 K

molar mass of molecular hydrogen, m = 2.02 g/mol =
`2.02* 10^(-3)kg/mol`

Solution:

To calculate the root mean squarer or rms speed of hydrogen molecule, we use the given formula:

`v_(rms) = \sqrt{(3TR)/(m)}`

where

R = rydberg's constant = 8.314 J/mol-K

Putting the values in the above formula:

`v_(rms) = \sqrt{(3* 3.13* 8.314)/(2.02* 10^(-3))}`

`v_(rms) =196.59 m/s`