# Question 8da8d

May 22, 2016

${\text{C"_4"H"_8"O}}_{2}$

#### Explanation:

A compound's empirical formula tells you the smallest whole number ratio that exists between the elements that make up a compound.

In your case, the unknown compound has an empirical formula of $\text{C"_2"H"_4"O}$, which means that it contains carbon, $\text{C}$, hydrogen, $\text{H}$, and oxygen, $\text{O}$, in a $2 : 4 : 1$ ratio.

In other words, one mole of this compound will contain carbon, hydrogen, and oxygen in a $2 : 4 : 1$ mole ratio.

All you have to do now is determine the mass of the empirical formula and compare it with the molar mass of the compound. You will have

$2 \times {\text{12.011 g mol"^(-1) + 4 xx "1.00794 g mol"^(-1) + 1 xx "15.9994 g mol"^(-1) = "44.053 g mol}}^{- 1}$

The molar mass of the compound essentially tells you the mass of one mole of the compound. This means that you will have

$44.053 \textcolor{red}{\cancel{\textcolor{b l a c k}{{\text{g mol"^(-1)))) xx color(blue)(n) = 88color(red)(cancel(color(black)("g mol}}^{- 1}}}}$

Rearrange to get

$\textcolor{b l u e}{n} = \frac{88}{44.053} = 1.9976 \approx 2$

Therefore, the molecular formula of the compound, which tells you the exact number of atoms of each element present in one molecule of the compound, will be

("C"_2"H"_4"O")_color(blue)(2) = color(green)(|bar(ul(color(white)(a/a)"C"_4"H"_8"O"_2color(white)(a/a)|)))#