Answer :
Final Answer
The hydrocarbon's empirical formula is CH₂, determined from the ratio of carbon and hydrogen atoms based on the given product masses of CO₂ and water.
Explanation
To determine the empirical formula of the hydrocarbon, we need to find the ratio of carbon atoms to hydrogen atoms in the compound based on the given mass of products formed.
First, we calculate the moles of CO₂ and water produced:
Moles of CO₂ = 47.0 mg / molar mass of CO₂
Moles of water = 38.4 mg / molar mass of water
Then, we find the moles of carbon and hydrogen in the hydrocarbon:
Moles of carbon = Moles of CO₂
Moles of hydrogen = Moles of water * 2 (since water has 2 hydrogen atoms)
Finally, we convert the moles of carbon and hydrogen back to mass:
Mass of carbon = Moles of carbon * molar mass of carbon
Mass of hydrogen = Moles of hydrogen * molar mass of hydrogen
The ratio of carbon to hydrogen atoms in the hydrocarbon is given by:
Ratio = Mass of carbon / Mass of hydrogen
Based on this ratio, we can deduce the empirical formula. In this case, the calculated ratio leads to a 1:2 ratio of carbon to hydrogen atoms, resulting in the empirical formula CH₂.
This empirical formula represents the simplest whole-number ratio of atoms in the hydrocarbon, providing valuable information about its composition.
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