A gaseous mixture of methane ( CH ₄ ) and propane ( C ₃ H ₈ ) has a total volume of 44.8 L at 273 K and 1 atm . On complete combustion, the mixture evolves 3780 kJ of heat. The volume of CO ₂ gas produced at 273 K and 1 atm is ________ L . Given: H_c ( CH ₄) = -900 kJ mol ⁻¹ H_c ( C ₃ H ₈) = -2220 kJ mol ⁻¹ Molar volume of an ideal gas at 273 K and 1 atm is 22.4 L mol ⁻¹ .

Step-by-step solution

Let the total moles of the mixture be n . n = 44.8 22.4 = 2 moles Let the moles of CH ₄ be x and the moles of C ₃ H ₈ be (2 - x) . The total heat evolved is the sum of the heat evolved by the combustion of each gas: 900x + 2220(2 - x) = 3780 900x + 4440 - 2220x = 3780 1320x = 660 x = 0.5 mol Moles of CH ₄ = 0.5 mol Moles of C ₃ H ₈ = 1.5 mol The combustion reactions are: CH ₄ + 2 O ₂ CO ₂ + 2 H ₂ O C ₃ H ₈ + 5 O ₂ 3 CO ₂ + 4 H ₂ O Total moles of CO ₂ produced = 1 n_ CH ₄ + 3 n_ C ₃ H ₈ n_ CO ₂ = 1(0.5) + 3(1.5) = 5