A hydrocarbon contains 14.2% hydrogen by mass. This compound has a relative molecular mass of 56g/mol. Calculate the empirical formula and the molecular formula.

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The empirical formula of a compound gives the simplest whole number ratio of atoms and the molecular formula gives the actual number of atoms of each element in a molecule. The molecular formula is a whole-number multiple of the empirical formula.

To find the empirical formula one must calculate the number of moles of each element in the compound. We are told that this is a hydrocarbon, meaning it contains hydrogen and carbon, and that it is 14.2% hydrogen by mass. Therefore if we have 100 grams of this compound 14.2 grams will be hydrogen and the remaining 85.8 grams will be carbon.

Using the molar masses of hydrogen and carbon, convert both to moles:

14.2 g H x (1 mol/1.00g) = 14.2 moles H

85.8 g C x (1 mol/12.0 g) = 7.1 moles C

Now divide each number of moles by the smallest (7.1) to get a whole-number mole ratio:

(14.2 moles H)/(7.1) = 2

(7.1 moles C)/(7.1) = 1

The mole ratio of C to H is 2:1, so the empirical formula is `CH_2.`

To find the molecular formula, compare the given molar mass of the compound to the molar mass of the empirical formula:

Molar mass of compound = 56 g/mol

Molar mass of `CH_2` = (12.0) + 2(1.00) = 14.0 g/mol

56/14.0 = 4, so the molecular formula is 4 times the empirical formula:

`4(CH_2)` = `C_4H_8`

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