Two cylinders, both fitted with frictionless pistons, are filled with mixtures of He and Ar gases. In the first cylinder, the masses of He and Ar are m₁ and m₂ , respectively. In the second cylinder, the masses of He and Ar are m₂ and m₁ , respectively. The molar mass of Ar is 10 times the molar mass of He. The external pressure applied by the piston on the first cylinder needs to be 5 times that on the second cylind

Step-by-step solution

Let the molar mass of He be M . Then the molar mass of Ar is 10M . In the first cylinder, the total number of moles is given by: n₁ = m₁ M + m₂ 10M = 10m₁ + m₂ 10M In the second cylinder, the total number of moles is given by: n₂ = m₂ M + m₁ 10M = 10m₂ + m₁ 10M Using the ideal gas equation PV = nRT , since the volume and temperature are the same for both cylinders, the pressure is directly proportional to the number of moles. Thus, P₁ P₂ = n₁ n₂ . Given that P₁ = 5P₂ , we have: n₁ n₂ = 5 Substituting the expression