Question

Two containers are at the same temperature. The first

containsgas with pressure p1,molecular
mass m1,and
root-mean-square speed vrms1.The
second contains gas with pressure 4p1,molecular
mass m2,and
average speed vavg2=
5vrms1.Find
the mass ratio m1/m2.

Answer 1

From Maxwell-Boltzmann distribution of molecules and their speeds,

average speed, Vavg = √(
`(8RT)/(πM)`)

and Root mean speed, Vrms = √(
`(3RT)/(M)`)

Given Vavg2 = 5Vrms1

Vavg2 = √(
`(8RT)/(πM2)`) ................ eqn 1

Vrms1 = √(
`(3RT)/(M1)`) --------------eqn 2

To find m1/m2, we divide eqn 1 by eqn 2,

we have, Vavg2/Vrms1 = √(
`(8m1)/(3πm2)`)

since Vavg2 = 5Vrms1, it becomes, 5 = √(
`(8m1)/(3πm2)`)

Therfore, m1/m2 = 25 * 3π/8 = 29.45

the mass ratio m1/m2 = 29.45.