# The percentage composition of acetic acid is found to be 39.9% carbon, 6.7% hydrogen, and 53.4% oxygen, how would you determine the empirical formula of acetic acid?

Oct 26, 2015

We assume $100 \cdot g$ of compound. Therefore the acid contains $39.9 \cdot g \cdot C$; $6.7 \cdot g \cdot H$; and $53.4 \cdot g \cdot O$.

#### Explanation:

We divide the percentage composition by the atomic mass of each constituent element:

$\frac{39.9 \cdot g}{12.011 \cdot g \cdot m o {l}^{-} 1} = 3.32 \cdot m o l$

$\frac{6.7 \cdot g}{1.0794 \cdot g \cdot m o {l}^{-} 1} = 6.65 \cdot m o l$

$\frac{53.4 \cdot g}{16.00 \cdot g \cdot m o {l}^{-} 1} = 3.34 \cdot m o l$

We divide thru by the lowest quotient $\left(3.32\right)$ to get $C : H : O \equiv 1 : 2 : 1$.

So the empirical formula is $C {H}_{2} O$. And the empirical formula is the simplest whole number ratio that defines constituent atoms in a species.

Now it is a fact that the molecular formula of acetic acid is ${H}_{3} C - C \left(= O\right) O H = {C}_{2} {H}_{4} {O}_{2}$. Is this a mulitple of the empirical formula; i.e. what is $n$ for ${\left(C {H}_{2} O\right)}_{n} = {C}_{2} {H}_{4} {O}_{2}$?