Question 478: Thermodynamics & KTG

Question

A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds $$\left[ {{{{V_{rms}}\,(helium)} \over {{V_{rms}}\,(\arg on)}}} \right],$$ is close to :

Accepted Answer

We know,
V
rms
= $$\sqrt {{{3RT} \over M}} $$
Where M = molar mass of  the gas.
Here temperature is 300 K for both the gas. So  temperature is constant. R is also a constant.
$$ 	herefore $$   V
rms
$$ \propto \,\,\sqrt {{1 \over M}} $$
$$ 	herefore $$    $${{{V_{rms}}(helium|)} \over {{V_{rms}}\left( {\arg an)} ight)}} = \sqrt {{{{M_{Ar}}} \over {{M_{He}}}}} $$
= $$\sqrt {{{40} \over 4}} $$
= $$\sqrt {10} $$
= 3.16

Answer

3.16

Answer

0.32

Answer

0.45

Answer

2.24

Thermodynamics & KTG

A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds $\left[ {{{{V_{rms}}\,(helium)} \over {{V_{rms}}\,(\arg on)}}} \right],$ is close to :

Choose the correct answer: