Question

the rms speed of hydrogen molecules at room temperature is 2400m/s. at room temperature the rms speed of oxygen will be

Answer 1

hope it's was a Right answer

Answer 2

Answer : The rms speed of oxygen will be 600 m/s.

Solution : Given,

rms speed of hydrogen molecule = 2400 m/s

Molecular weight of $O_2$ = 32 g/mole

Molecular weight of $H_2$ = 2 g/mole

Root mean square speed : It is measured the speed of particles in a gas molecule. it is denoted as $\nu$.

Formula used :

$\nu=\sqrt{\frac{3RT}{M}}$

where,

R = Gas constant

T = temperature of gas

M = molecular weight of gas

The formula for two gas molecule will be,

$\frac{\nu (_H_2)}{\nu (_O_2)}= \sqrt{\frac{(\frac{3RT}{M_H_2})}{(\frac{3RT}{M_O_2})}}\\\frac{\nu (_H_2)}{\nu (_O_2)}= \sqrt{\frac{M_O_2}{M_H_2}}$

Now put all the given values in this expression, we get

$\frac{2400m/s}{\nu (_O_2)}= \sqrt{\frac{32g/mole}{2g/mole}}$

By rearranging the terms, we get the value for rms speed of oxygen.

$\nu (_O_2)=600m/s$

Therefore, the rms speed of oxygen will be 600 m/s.