What is the empirical formula of a hydrocarbon containing 0.160 moles of carbon and 0.640 moles of hydrogen

Analyze the question: We are given the moles of carbon and hydrogen in a hydrocarbon and asked for the empirical formula, which is the simplest whole-number ratio of atoms in the compound.

Concept: To find the empirical formula from moles:

1. Write down the moles of each element.
2. Divide each by the smallest number of moles.
3. If needed, round to or scale up to whole numbers.

Solution:

| Element | Moles | Divide by smallest (0.160) | Ratio | |---|---|---|---| | C | 0.160 | 0.160 ÷ 0.160 | 1 | | H | 0.640 | 0.640 ÷ 0.160 | 4 |

The ratio of C : H = 1 : 4, so the empirical formula is CH₄.

Check the other options:

• A. CH₂ has a ratio of 1 : 2, which is wrong.
• B. CH₃ has a ratio of 1 : 3, which is wrong.
• D. C₂H₄ has a ratio of 1 : 2, so it is not in the simplest form and does not match anyway.

Exam tip: When the question gives you moles directly, skip the step of dividing mass by atomic mass. Just divide by the smallest value and read off the ratio. If you see a decimal like 1.5, multiply everything by 2. If you see 1.33, multiply by 3.