Final answer:
To produce 77.4 g of CO2, the calculation based on stoichiometry of the combustion reaction of butane indicates that 25.55 g of butane is required.
Step-by-step explanation:
To calculate the mass of butane needed to produce 77.4 g of carbon dioxide (CO2), we first need the balanced chemical equation of the combustion of butane (C4H10):
2 C4H10 + 13 O2 → 8 CO2 + 10 H2O
Next, we calculate the number of moles of CO2:
Number of moles = mass (g) / molar mass (g/mol)
For CO2, molar mass is 44.01 g/mol, so:
Number of moles of CO2 = 77.4 g / 44.01 g/mol = 1.759 mol
From the balanced equation, we see that 8 moles of CO2 are produced from 2 moles of C4H10, which means:
Number of moles of C4H10 needed = (1.759 mol CO2) * (2 mol C4H10/8 mol CO2) = 0.43975 mol C4H10
The molar mass of C4H10 is 58.12 g/mol, so:
Mass of C4H10 needed = 0.43975 mol * 58.12 g/mol = 25.55 g
Therefore, to produce 77.4 g of CO2, 25.55 g of butane is needed.