Question

The rms speeds of the molecules of Hydrogen, Oxygen, and Carbon dioxide at the same temperature are V_H, V_O, and `V_{CO_2}` respectively then ______.

Options

• `V_H = V_O > V_{CO_2}`

• `V_{CO_2} > V_O > V_H`

• `V_H > V_O > V_{CO_2}`

• `V_H = V_O = V_{CO_2}`

Answer 1

The rms speeds of the molecules of Hydrogen, Oxygen, and Carbon dioxide at the same temperature are V_H, V_O, and V_CO2 respectively then `bbunderline(V_H > V_O > V_{CO_2})`.

Explanation:

Root mean square velocity,

`V_{rms} = sqrt((3RT)/M)`

The temperature is the same for everyone. So, `V_{rms} ∝ 1/sqrtM`

Hence, the lighter gas has a faster r.m.s.

`V_H : V_O : V_{CO_2} = 1/sqrt(M_H) : 1/sqrt(M_O) : 1/sqrt(M_{CO_2})`

= `1/1 : 1/sqrt16 : 1/sqrt44`

= `1/1 : 1/4 : 1/(2sqrt11)`

`V_H > V_O > V_{CO_2}`.