# A hydrocarbon is composed of 85.57% carbon and 14.43% hydrogen and a molar mass of 28.06 mol. What is the molecular formula?

Dec 16, 2016

The stuff is $\text{ethylene}$, ${H}_{2} C = C {H}_{2}$.

#### Explanation:

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

And thus...........

$\text{Moles of carbon} = \frac{85.57 \cdot g}{12.011 \cdot g \cdot m o {l}^{-} 1} = 7.12 \cdot m o l$

$\text{Moles of hydrogen} = \frac{14.43 \cdot g}{1.00794 \cdot g \cdot m o {l}^{-} 1} = 14.32 \cdot m o l$

We divide thru by the smallest molar quantity (that of carbon) to get an $\text{empirical formula}$ of $C {H}_{2}$.

Now it is a fact that the molecular formula is a whole number multiple of the empirical formula:

i.e. $28.06 \cdot g \cdot m o {l}^{-} 1 = n \times \left(12.011 + 2 \times 1.00794\right) \cdot g \cdot m o {l}^{-} 1$.

Clearly, $n = 2$, and the $\text{molecular formula}$ is ${C}_{2} {H}_{4}$.