Question

compare the rms speed of hydrogen molecule
at 127°c with rms speed of oxygen
moleules at 27°c given that molecular
masses of hydrogen and oxygen alles
and 32 Respectively​

Answer 1

Given

• Hydrogen molecules at 127°C ( 400 K)

• Oxygen molecules at 27°C ( 300 K)

To find

Compare their RMS (root mean square speed ).

Concept

Root mean square speed of a gas of molar mass M and at temperature T is given by $\sqrt{ \frac{3RT}{M} }$

Calculation

Hence, RMS speed of hydrogen gas (M = 2 , T = 400 K )

$v (H_{2}) = \sqrt{ \frac{3R \times 400}{2} } .$

RMS speed of oxygen gas (M = 32, T = 300 K)

$v_ (O)_2 = \sqrt{ \frac{3R \times 300}{32} } \\ comparing \: \frac{v( H_{2}) }{ \: v( O_{2})\: } = \frac{ \ \sqrt{ \frac{3R \times 400}{2} } }{ \sqrt{ \frac{3R \times 300}{32} }} \\ \\ = > \frac{v( H_{2}) }{ \: v( O_{2})\: } = \frac{8}{ \sqrt{3} } \\ \\ = > \sqrt{3} v (H_{2}) = 8 v_ (O)_2.$