To determine the empirical formula of the hydrocarbon, follow these steps:
1. Assume a 100-gram Sample:
Since the percentages given are by mass, we can assume a hydrocarbon sample of 100 grams for simplicity.
- Mass of carbon (C) in the sample: [tex]\( 84.6\% \times 100 \text{ g} = 84.6 \text{ g} \)[/tex]
- Mass of hydrogen (H) in the sample: [tex]\( 15.4\% \times 100 \text{ g} = 15.4 \text{ g} \)[/tex]
2. Calculate Moles of Each Element:
Use the atomic masses to convert the masses to moles.
- Moles of carbon (C):
[tex]\[
\text{moles of C} = \frac{84.6 \text{ g}}{12 \text{ g/mol}} = 7.05 \text{ mol}
\][/tex]
- Moles of hydrogen (H):
[tex]\[
\text{moles of H} = \frac{15.4 \text{ g}}{1 \text{ g/mol}} = 15.4 \text{ mol}
\][/tex]
3. Find the Simplest Whole Number Ratio:
Divide the number of moles of each element by the smallest number of moles calculated to determine the simplest ratio.
- Ratio of carbon to the smallest number of moles:
[tex]\[
\frac{7.05 \text{ mol}}{7.05 \text{ mol}} = 1
\][/tex]
- Ratio of hydrogen to the smallest number of moles:
[tex]\[
\frac{15.4 \text{ mol}}{7.05 \text{ mol}} \approx 2
\][/tex]
Hence, the ratio of carbon to hydrogen is approximately [tex]\( 1:2 \)[/tex].
4. Determine the Empirical Formula:
Using the simplest whole number ratio of carbons to hydrogens, we can write the empirical formula.
- The empirical formula is [tex]\( \text{C}_1\text{H}_2 \)[/tex], which simplifies to [tex]\( \text{CH}_2 \)[/tex].
Thus, the empirical formula for the hydrocarbon is [tex]\( \text{CH}_2 \)[/tex].
