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

Answer:

$v_{rms} =196.59 m/s$

Given:

Temperature, T = 3.13 K

molar mass of molecular hydrogen, m = 2.02 g/mol = $2.02\times 10^{-3}kg/mol$

Solution:

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

$v_{rms} = \sqrt{\frac{3TR}{m}}$

where

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

Putting the values in the above formula:

$v_{rms} = \sqrt{\frac{3\times 3.13\times 8.314}{2.02\times 10^{-3}}}$

$v_{rms} =196.59 m/s$