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IAT IISER2026PhysicsKinetic Theory of Gases

A jar is filled with two monoatomic non-interacting gases A and B with total masses M_A and M_B , respectively. The molar mass of A is double the molar mass of B . If the jar is kept at temperature T , what is the ratio of the total pressure of the combined gas to the partial pressure due to the gas A ?

Options

  1. A1 + 1 2 M_B M_A
  2. B1 + 2 M_B M_A
  3. C1 + 1 2 M_A M_B
  4. D1 + 2 M_A M_B

Correct answer

B. 1 + 2 M_B M_A

Step-by-step solution

Let m_A and m_B be the molar masses of gases A and B respectively. Given m_A = 2m_B . Number of moles of gas A , n_A = M_A m_A Number of moles of gas B , n_B = M_B m_B According to Dalton's law of partial pressures, the partial pressure of a gas is proportional to its number of moles. Partial pressure of A , P_A = n_A RT V Total pressure, P = (n_A + n_B) RT V The ratio of the total pressure to the partial pressure of A is: P P_A = n_A + n_B n_A = 1 + n_B n_A Substituting the values of n_A and n_B : P P_A = 1 + M_B

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