Pressure of 1 g of an ideal gas A at 27°C is found to be 2 bar. When 2 g of another ideal gas B is introduced in the same flask at same temperature the pressure becomes 3 bar. Find a relationship between their molecular masses.

Question

Philoid · Accepted Answer

For ideal gas A, the ideal gas equation is given by,

⇒ P_aV = n_aRT

Where, Pa and n_a represent the pressure and number of moles of gas A.

For ideal gas B, the ideal gas equation is given by,

⇒ P_bV = n_bRT

Where,P_a and n_b represent the pressure and number of moles of gas B.

[V and T are constants for gases A and B]

Therefore, we have,

⇒

Where, M_a and M_b are the molecular masses of gases A and B respectively.

Now, we have

Substituting the values

m_a = 1 g

P_a = 2 bar

m_b = 2 g

P_b = 1 bar.

Given,

(Since total pressure is 3 bar)

Substituting these values in equation we have

⇒

Thus, a relationship between the molecular masses of A and B is given by

⇒ 4M_a = M_b