calculate the mass of butane needed to produce 79.7g of carbon dioxide. express your answer to three significant figures and include the apprppriate units
To calculate the mass of butane needed to produce 79.7g of carbon dioxide, we need to use the balanced chemical equation for the combustion of butane.
The combustion equation for butane (C4H10) is:
2 C4H10 + 13 O2 -> 8 CO2 + 10 H2O
From the equation, we can see that 2 moles of butane produce 8 moles of carbon dioxide.
1 mole of carbon dioxide has a molar mass of 44.01 g/mol. Therefore, 8 moles of carbon dioxide would have a mass of:
8 moles x 44.01 g/mol = 352.08 g
Now, we can set up a proportion to find the mass of butane needed:
(79.7 g CO2) / (352.08 g CO2) = (x g butane) / (1 mole butane)
Simplifying the equation, we find:
x = (79.7 g CO2) / (352.08 g CO2) * (1 mole butane)
Calculating the value, we have:
x ≈ 0.226 g
Therefore, approximately 0.226 grams of butane is needed to produce 79.7 grams of carbon dioxide.
To calculate the mass of butane needed to produce carbon dioxide, you need to understand the balanced chemical equation for the reaction. The balanced equation for the combustion of butane (C4H10) is:
2 C4H10 + 13 O2 -> 8 CO2 + 10 H2O
From this equation, we can see that for every 2 moles of butane (C4H10) burned, 8 moles of carbon dioxide (CO2) are produced.
To solve the problem, follow these steps:
Step 1: Calculate the number of moles of CO2 produced using the given mass. To do this, divide the given mass (79.7g) by the molar mass of CO2, which is 44.01 g/mol.
Moles of CO2 = Mass of CO2 / Molar mass of CO2
Moles of CO2 = 79.7g / 44.01 g/mol
Moles of CO2 ≈ 1.809 mol (rounded to four decimal places)
Step 2: Now that we know the number of moles of CO2 produced, we can use the mole ratio from the balanced equation to find the number of moles of butane required. According to the equation, 2 moles of butane produce 8 moles of CO2.
Moles of butane = (Moles of CO2 / 8) * 2
Moles of butane = (1.809 mol / 8) * 2
Moles of butane ≈ 0.4523 mol (rounded to four decimal places)
Step 3: Finally, calculate the mass of butane using the number of moles and the molar mass of butane (C4H10) which is 58.12 g/mol.
Mass of butane = Moles of butane * Molar mass of butane
Mass of butane = 0.4523 mol * 58.12 g/mol
Mass of butane ≈ 26.30 g (rounded to three significant figures)
Therefore, the mass of butane needed to produce 79.7g of carbon dioxide is approximately 26.30 g.