Answer :
Final answer:
The empirical formula of the hydrocarbon is determined to be CH₄ by using the mass of CO₂ and H₂O produced from its combustion to calculate the moles of carbon and hydrogen.
Explanation:
Determining the Empirical Formula of a Hydrocarbon
The question involves finding the empirical formula of a hydrocarbon using combustion analysis data. To determine the empirical formula, we must calculate the number of moles of carbon and hydrogen in the hydrocarbon. We will use the mass of CO₂ and H₂O produced from the combustion to find these values.
First, we find the moles of carbon from the mass of CO₂ produced. We know that each mole of CO₂ contains one mole of carbon. Using the molar mass of CO₂ (44.01 g/mol), we have:
47.0 mg CO₂ × (1 mol CO₂ / 44.01 g) = 1.068×10⁻³ mol C
Next, we calculate the moles of hydrogen from the mass of H₂O produced. Each mole of H₂O contains two moles of hydrogen. Using the molar mass of H₂O (18.015 g/mol), we get:
38.4 mg H₂O × (1 mol H₂O / 18.015 g) × (2 mol H / 1 mol H₂O) = 4.260×10⁻³ mol H
Now, we find the mole ratio of carbon to hydrogen by dividing their respective mole numbers:
1.068×10⁻³ mol C / 4.260×10⁻³ mol H = 0.250 mol C / 1 mol H
After dividing by the smallest number of moles, we have approximately 1 mole of C to 4 moles of H. Therefore, the empirical formula of the hydrocarbon is CH₄.
