Final answer:
By calculating the moles of carbon and hydrogen from the given masses of CO₂ and H₂O and then converting these moles to grams, we deduced that the total mass of hydrocarbon burned was 6.509 g.
Step-by-step explanation:
To determine how much mass of hydrocarbon was burned, we can use the given masses of CO₂ and H₂O to find the masses of carbon and hydrogen in the original hydrocarbon sample.
The moles of carbon can be determined from the mass of CO₂ by using the molar mass of CO₂ (44.01 g/mol), and the moles of hydrogen can be determined from the mass of H₂O (18.02 g/mol), keeping in mind that each mole of H₂O has two moles of hydrogen atoms.
First, calculate moles of carbon:
Moles of CO₂ = Mass of CO₂ / Molar mass of CO₂
= 22 g / 44.01 g/mol
= 0.5 mol
Next, calculate moles of hydrogen:
Moles of H₂O = Mass of H₂O / Molar mass of H₂O
= 4.5 g / 18.02 g/mol
= 0.25 mol
Note that for every mole of H₂O, there are two moles of hydrogen atoms, therefore:
Moles of hydrogen = 0.25 mol × 2
= 0.5 mol
To find the total mass of the hydrocarbon, we add together the masses of carbon and hydrogen, keeping in mind that carbon has a molar mass of 12.01 g/mol and hydrogen has a molar mass of 1.008 g/mol.
Mass of carbon in the hydrocarbon = Moles of carbon × Molar mass of carbon
= 0.5 mol × 12.01 g/mol
= 6.005 g
Mass of hydrogen in the hydrocarbon = Moles of hydrogen × Molar mass of hydrogen
= 0.5 mol × 1.008 g/mol
= 0.504 g
Total mass of hydrocarbon = Mass of carbon + Mass of hydrogen
= 6.005 g + 0.504 g
= 6.509 g
Therefore, the mass of hydrocarbon burned is 6.509 g.