Question

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium
at temperature T. Assuming the gases are ideal, the correct statement(s) is(are)
(A) The average energy per mole of the gas mixture is 2RT.
(B) The ratio of speed of sound in the gas mixture to that in helium gas is ⎷6 / 5.
(C) The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/2.
(D) The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/√2.

Answer 1

Explanation:

Given A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is(are)

• Now consider the first option we have,
• Total energy of hydrogen will be 5/2 RT
• Total energy of helium will be 3/2 RT
• Therefore total energy of the mixture will be 3/2 RT + 5/2 RT
•                                                                  = 8/2 RT
•                                                                  = 4RT
• Now average energy per mole of the mixture will be 4 RT / 2 = 2 RT
• So the first option a is correct.
• Now consider the second option we have,
• To measure speed of sound and its velocity will be
• V = √γ R T / M
• We need to find γ of helium and γ of mixture
• So γ of helium is 5/3
• Now γ of mixture will be total number of moles / γ mixture  
• So  n1 + n2 / γ mix – 1 = n1 (he) / γ1 – 1 + n2 (h2) / γ2 – 1
•        2 / γ mix = 1 / 5/3 – 1 + 1/ 7/5 – 1
•      So γ mix = 3/2
• So velocity of sound in mixture / velocity of sound in helium  = √ γ mix / γ he x Molar mass of he / molar mass of mixture.
•                                                      = √3/2 x 4 / 5/3 x 3 (molar mass of mixture = (1 x 2) + (1 x 4)/2 = 3)
•                                                      = √6/5
•                 So option b is correct.
•         Now consider option c we get
•                                                    So we have V rms = √3 RT / M
•             So V rms of helium / V rms of hydrogen = √molar mass of he / molar mass of h2
•                                                                                = √2/4
•                                                                               = 1/√2
•          So option c is incorrect
•            So option d is correct.
•     So the options a, b and d are correct.                          

Reference link will be

https://brainly.in/question/14375347

Answer 2

Answer:

options ABAndD is correct hope it helps you