A gas mixture consists of 2 moles of oxygen and 4 moles of argon at te

1.	A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. If we neglect all vibration modes, find the total energy of the system?
Answer» Let NA = Avogadro’s Number No. of degrees of freedom of O₂ molecule (diatomic) = 5 No. of degrees of freedom of 2 moles of oxygen = 2 N_A × 5 = 10 N_A No. of degrees of freedom of 4 moles of argon (monatomic) = 4 N_A× 3 = 12 N_A (∵ 3 = degrees of freedom) Total degrees of freedom of mixture = 10 N_A + 12 N_A = 22 N_A →1) Energy associated with each degree of freedom \| molecule = 1/2 KT Total energy of mixture = 22 NA × 1/2 KT T (∵ Using equation1) 11K N_A T 11RT(KN₄ = R)

A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. If we neglect all vibration modes, find the total energy of the system?

Answer»

Let NA = Avogadro’s Number

No. of degrees of freedom of O₂ molecule (diatomic) = 5

No. of degrees of freedom of 2 moles of oxygen = 2 N_A × 5 = 10 N_A

No. of degrees of freedom of 4 moles of argon (monatomic) = 4 N_A× 3

= 12 N_A (∵ 3 = degrees of freedom)

Total degrees of freedom of mixture = 10 N_A + 12 N_A = 22 N_A →1) Energy associated with each degree of freedom | molecule = 1/2 KT

Total energy of mixture = 22 NA × 1/2 KT T (∵ Using equation1)

11K N_A T

11RT(KN₄ = R)