Answer: 29.2
Step-by-step explanation:
To determine the mass of butane needed to produce 88.5 g of carbon dioxide, we need to consider the balanced chemical equation for the combustion of butane:
C₄H₁₀ + 13/2 O₂ → 4 CO₂ + 5 H₂O
From the equation, we can see that for every 1 mole of butane (C₄H₁₀) burned, we produce 4 moles of carbon dioxide (CO₂).
To calculate the mass of butane needed, we will follow these steps:
1. Find the molar mass of carbon dioxide (CO₂) and butane (C₄H₁₀). The molar mass of CO₂ is 44.01 g/mol, and the molar mass of C₄H₁₀ is 58.12 g/mol.
2. Calculate the number of moles of carbon dioxide (CO₂) produced. Divide the given mass of CO₂ (88.5 g) by its molar mass (44.01 g/mol):
88.5 g CO₂ / 44.01 g/mol = 2.01 moles CO₂
3. Since the mole ratio between butane and carbon dioxide is 1:4 (1 mole of C₄H₁₀ produces 4 moles of CO₂), we multiply the number of moles of CO₂ by the mole ratio to find the number of moles of butane required:
2.01 moles CO₂ x (1 mole C₄H₁₀ / 4 moles CO₂) = 0.503 moles C₄H₁₀
4. Finally, calculate the mass of butane required by multiplying the number of moles of butane by its molar mass:
0.503 moles C₄H₁₀ x 58.12 g/mol = 29.2 g of butane
Therefore, to produce 88.5 g of carbon dioxide, you would need approximately 29.2 g of butane.