To find the empirical formula of the hydrocarbon, we start by determining the moles of carbon (C) and hydrogen (H) produced from the combustion of the hydrocarbon based on the products formed.
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Convert Grams of CO2 to Moles of C:
- The molar mass of CO2 (carbon dioxide) is approximately 44.01 g/mol. \[ \text{Moles of CO2} = \frac{47.1 , \text{g}}{44.01 , \text{g/mol}} \approx 1.07 , \text{mol} \]
- Since each CO2 molecule contains one carbon atom, the moles of carbon is also 1.07 mol.
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Convert Grams of H2O to Moles of H:
- The molar mass of H2O (water) is approximately 18.02 g/mol. \[ \text{Moles of H2O} = \frac{19.35 , \text{g}}{18.02 , \text{g/mol}} \approx 1.07 , \text{mol} \]
- Each H2O molecule contains two hydrogen atoms, so the moles of hydrogen is: \[ \text{Moles of H} = 1.07 , \text{mol H2O} \times 2 = 2.14 , \text{mol H} \]
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Calculate the Ratio of Moles of C and H:
- We have approximately 1.07 mol of C and 2.14 mol of H. We can find the ratio by dividing each value by the smallest number of moles: \[ \text{Ratio of C} = \frac{1.07}{1.07} = 1 \] \[ \text{Ratio of H} = \frac{2.14}{1.07} \approx 2 \]
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Determine the Empirical Formula:
- From the ratio, we find that there is 1 mole of carbon for every 2 moles of hydrogen. Therefore, the empirical formula of the hydrocarbon is: \[ \text{Empirical formula} = \text{CH}_2 \]
Thus, the empirical formula of the hydrocarbon is \( \text{CH}_2 \).