Calculate the volume of carbon dioxide at [tex]20.0^\circ C[/tex] and [tex]0.906 \, \text{atm}[/tex] produced from the complete combustion of [tex]5.00 \, \text{kg}[/tex] of methane. Compare your result with the volume of [tex]\text{CO}_2[/tex] produced from the complete combustion of [tex]5.00 \, \text{kg}[/tex] of propane ([tex]\text{C}_3\text{H}_8[/tex]).

Part 1: Volume of [tex]\text{CO}_2[/tex] from [tex]5.00 \, \text{kg}[/tex] methane.

The volume of carbon dioxide produced from the combustion of 5.00 kg of methane is 6.96 L, while the volume of carbon dioxide produced from the combustion of 5.00 kg of propane is 2.53 L.

Explanation:

To calculate the volume of carbon dioxide produced from the complete combustion of 5.00 kg of methane, we need to use the stoichiometry of the reaction. From the balanced equation, we know that 1 mole of methane produces 1 mole of carbon dioxide. The molar mass of methane is 16.04 g/mol, so 5.00 kg of methane is 5.00/16.04 = 0.311 mol. Since 1 mole of gas occupies a volume of about 22.4 L at standard temperature and pressure, the volume of carbon dioxide produced is 0.311 mol x 22.4 L/mol = 6.96 L.

To compare this with the volume of carbon dioxide produced from the complete combustion of 5.00 kg of propane, we can use the ratio from the balanced equation. The equation shows that 1 mole of propane produces 3 moles of carbon dioxide. The molar mass of propane is 44.10 g/mol, so 5.00 kg of propane is 5.00/44.10 = 0.113 mol. Therefore, the volume of carbon dioxide produced from the combustion of 5.00 kg of propane is 0.113 mol x 22.4 L/mol = 2.53 L.

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