A mixture of carbon dioxide and oxygen occupies 8310 cm³ at 300 K and 100 kPa. The total mass of the mixture is 13.2 g. Assuming ideal-gas behaviour and taking R = 8.31 J·mol⁻¹·K⁻¹, what are the numbers of moles of CO₂ and O₂, respectively?
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Question

A mixture of carbon dioxide and oxygen occupies 8310 cm³ at 300 K and 100 kPa. The total mass of the mixture is 13.2 g. Assuming ideal-gas behaviour and taking R = 8.31 J·mol⁻¹·K⁻¹, what are the numbers of moles of CO₂ and O₂, respectively?

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G1 Physics · Accepted Answer

First find the total number of moles using the ideal-gas equation: PV = nRT. Convert the volume: V = 8310 cm³ = 8.31×10⁻³ m³. Pressure: P = 100 kPa = 1.00×10⁵ Pa. Therefore, n(total) = PV ÷ (RT) = [1.00×10⁵×8.31×10⁻³] ÷ [8.31×300] = 1 ÷ 3 ≈ 0.333 mol. Let n(CO₂) = n₁, n(O₂) = n₂. Then, n₁+n₂ = 0.333. (1) Using molar masses 44 g·mol⁻¹ and 32 g·mol⁻¹, 44n₁+32n₂ = 13.2. (2) From equation (1), n₂ = 0.333-n₁. Substitute into equation (2): 44n₁+32(0.333-n₁) = 13.2. Thus, 12n₁ ≈ 2.533, n₁ ≈ 0.211 mol.…