Question

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is ______.

Options

• 15

• 13

• 20

• 11

Answer 1

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is 15.

Explanation:

Given: Number of moles of oxygen in a gas mixture is n₁ = 3, number of moles of argon in the same gas mixture is n₂ = 5, the temperature of gas mixture is T, the oxygen bond is rigid, the total internal energy of the mixture of gas is U = xRT.

To find: The value of x.

Number of degrees of freedom for diatomic oxygen considering the oxygen bond is rigid:

f₁ = 5

Number of degrees of freedom for monoatomic argon:

f₂ = 3

Total internal energy of the mixture of gas :

U = `1/2"n"_1"f"_1"RT"+1/2"n"_2"f"_2"RT"`

U = `(1/2xx3xx5+1/2xx5xx3)"RT"`

= 15RT

x = 15