1 m3 of a hydrocarbon required 2.5 m3 of oxygen for complete combustion and produced 2 m3 of CO2. Find the weight of air necessary for complete combustion of 1 kg of the hydrocarbon

To solve this problem, we need to follow these steps:

1. First, we need to find out the molecular weight of the hydrocarbon. From the problem, we know that 1 m3 of hydrocarbon produces 2 m3 of CO2. This means that the hydrocarbon must be methane (CH4), because 1 molecule of methane produces 1 molecule of CO2 when it burns.

2. The molecular weight of methane is approximately 16 g/mol (12 for the carbon and 4 for the hydrogen).

3. Now, we need to find out how much oxygen is needed to burn 1 kg of methane. From the problem, we know that 1 m3 of methane requires 2.5 m3 of oxygen. Since the molar volume of a gas at standard temperature and pressure is approximately 22.4 L/mol, this means that 1 mol of methane requires 2.5 mol of oxygen.

4. The molecular weight of oxygen is approximately 32 g/mol, so 2.5 mol of oxygen weighs 2.5 * 32 = 80 g.

5. Therefore, to burn 1 kg (or 1000 g) of methane, we need 1000 / 16 * 80 = 5000 g of oxygen.

6. Finally, we need to find out how much air is needed to provide this amount of oxygen. Air is approximately 21% oxygen by weight, so the weight of air necessary for complete combustion of 1 kg of methane is 5000 / 0.21 = approximately 23810 g, or 23.81 kg.