# A compound is composed of 85.64% carbon and 14.36% hydrogen. The compound has a formula mass of 42.08 grams. What is the molecular formula?

Jun 24, 2016

$\text{Molecular formula} = {C}_{3} {H}_{6}$

#### Explanation:

As with all of these problems, we assume $100 \cdot g$ of unknown compound.

And thus, we determine the elemental composition by the given percentages.

$\text{Moles of carbon} = \frac{85.64 \cdot g}{12.011 \cdot g \cdot m o {l}^{-} 1} = 7.13 \cdot m o l$.

$\text{Moles of hydrogen} = \frac{14.36 \cdot g}{1.00794 \cdot g \cdot m o {l}^{-} 1} = 14.25 \cdot m o l$.

Clearly, there are $2$ $\text{moles}$ of hydrogen per mol of carbon. And thus the empirical formula is $C {H}_{2}$.

And $\text{molecular formula}$ $=$ $n \times \left(\text{empirical formula}\right)$

Thus,

$42.08 \cdot g \cdot m o {l}^{-} 1 = n \times \left(12.011 + 2 \times 1.00794\right) \cdot g \cdot m o {l}^{-} 1$

And thus $n = 3$, and $\text{molecular formula}$ $=$ ${C}_{3} {H}_{6}$.