Question

A mixture of 2 moles of helium gas (atomic mass = 4 amu), and 1 mole of argon gas (atomic mass = 40amu) is kept at 300K in a container. The ratio of the rms speeds  [{ѵ_rms(helium)}/{ѵ_rms(argon)}] is

(A) 0.45 

(B) 2.24 

(C) 3.16 

(D) 0.32

Answer 1

The correct option (C) 3.16 

Explanation:

He gas: n₁ = 2

Ar gas: n₂ = 1

T = 300K

V_rms = √(3RT/M_o)

At constant temp, V_rms ∝ (1/√M_o)

∴ [{V_rms(He)}/{V_rms(Ar)}] = √{(M_oAr)/(M_oHe)}

 Molar mass of He = M_oHe = 4

Molar mass of Ar = M_oAr = 40

∴ ratio = √(40/4)

= √10

= 3.16