First slide

Kinetic theory of ideal gases

Question

A flask contains hydrogen and helium in the ratio 2 : 1 by mass. The temperature of the mixture is 27^oC. Obtain the ratio of rms speeds of the molecules of the two gases. Molecular mass of hydrogen = 2, molecular mass of helium = 4.

Easy

A

2 : 1
B

$\sqrt{2} : 1$
C

1 : 2
D

1 : 3

Solution

Average KE of the molecule $= \frac{1}{2} m v_{r m s}^{2}$
For hydrogen, $\frac{1}{2} m_{H} v_{H}^{2} = (\frac{3}{2}) k T$ …(1)
For helium, $\frac{1}{2} m_{H e} v_{H e}^{2} = \frac{3}{2} k T$ …(2)
So, $\frac{v_{H}^{2}}{v_{H e}^{2}} = \frac{M_{H e}}{M_{H}} = \frac{4}{2} = 2$
Or, $\frac{v_{H}}{v_{H e}} = \sqrt{2} : 1$ .

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App