A 0.500 g sample of a hydrocarbon is completely burned, producing 1.8 g of carbon dioxide and 0.738 g of water. Determine the empirical formula of the hydrocarbon.
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To determine the empirical formula of the hydrocarbon, we need to find the ratio of carbon to hydrogen atoms in the compound.
Step 1: Determine the moles of carbon and hydrogen in the products.
First, we calculate the moles of carbon dioxide:
1.8 g CO2 x (1 mole CO2 / 44.01 g CO2) = 0.0409 mol CO2
Next, we calculate the moles of water:
0.738 g H2O x (1 mole H2O / 18.02 g H2O) = 0.041 mol H2O
Step 2: Calculate the moles of carbon and hydrogen in the original hydrocarbon.
Since there is no other information given, we assume the hydrocarbon contains only carbon and hydrogen atoms. Therefore, all the carbon and hydrogen present in the products came from the hydrocarbon.
From the balanced chemical equation for the combustion of hydrocarbons, we know that for every 1 mole of carbon in the hydrocarbon, we produce 1 mole of CO2. Similarly, for every 2 moles of hydrogen in the hydrocarbon, we produce 2 moles of H2O.
So, we have:
0.0409 mol CO2 = 0.0409 mol C
0.041 mol H2O = 0.082 mol H
Step 3: Calculate the molar ratio of carbon to hydrogen.
The molar ratio of carbon to hydrogen can be calculated by dividing the number of moles of carbon by the number of moles of hydrogen:
0.0409 mol C / 0.082 mol H ≈ 0.5
This indicates that the molar ratio of carbon to hydrogen is 1:2.
Step 4: Write the empirical formula.
The empirical formula of the hydrocarbon can be determined from the molar ratio of carbon to hydrogen. In this case, the empirical formula is CH2.
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