A mixture of carbon dioxide and oxygen has volume 8310 cm ^3 , temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are _______. (Assume both carbon dioxide and oxygen gases behave like ideal gases) [R = 8.31 J/mol.K ]

Step-by-step solution

Using the ideal gas equation, the total number of moles of the mixture is given by: n = PV RT Substituting the given values: P = 100 kPa = 10^5 Pa V = 8310 cm ^3 = 8.31 10⁻³ m ^3 T = 300 K R = 8.31 J/(mol K) n = 10^5 8.31 10⁻³ 8.31 300 = 100 300 = 1 3 mol Let n₁ and n₂ be the number of moles of CO₂ and O₂ respectively. n₁ + n₂ = 1 3 The total mass of the mixture is 13.2 g . Using the molar masses of CO₂ ( 44 g/mol ) and O₂ ( 32 g/mol ): 44n₁ + 32n₂ = 13.2 Substituting n₂ = 1 3 - n₁ into the mass equation: 44n₁ + 32