# A certain sugar has a chemical composition of 40 % carbon, 6.6 % hydrogen, and 53.3 percent oxygen. The molar mass is 180 g/mol. What is the molecular formula?

Dec 4, 2015

${C}_{6} {H}_{12} {O}_{6}$

#### Explanation:

We assume 100 g of unknown. In such quantity there are:

$\left(\frac{40 \cdot g}{12.01 \cdot g \cdot m o {l}^{-} 1}\right) C$; $\left(\frac{6.6 \cdot g}{1.00794 \cdot g \cdot m o {l}^{-} 1}\right) H$; and $\left(\frac{53.3 \cdot g}{15.99 \cdot g \cdot m o {l}^{-} 1}\right) O$.

Note that I divide thru by the ATOMIC masses of each component.

I gets the ratio: $3.33 : 6.55 : 3.33$. Now I divide thru by the lowest quotient to give ${C}_{n} {H}_{m} {O}_{o}$ $=$ $C {H}_{2} O$.

$C {H}_{2} O$ is the simplest whole number ratio defining constituent atoms in a species; that is, the empirical formula, the formula found by experiment.

Now it is a fact that while the empirical formula may NOT be the same as the molecular formula, the molecular formula is ALWAYS a multiple of the empirical formula.

So, $M F$ $=$ ${\left(E F\right)}_{n}$. But we have been given a molecular mass!

And $180 \cdot g \cdot m o {l}^{-} 1$ $=$ ${\left(C {H}_{2} O\right)}_{n}$ $=$ ${\left(30 \cdot g \cdot m o {l}^{-} 1\right)}_{n}$.

Clearly, $n$ $=$ $6$. And molecular formula $=$ ${C}_{6} {H}_{12} {O}_{6}$, which is probably the stuff you sprinkle on your cornflakes.

Normally, you would not be given the percentage composition of oxygen (because oxygen content can rarely be measured!). A more advanced question would have given percentage compositions of $H$ and $C$, and left you to figure out the percentage balance was oxygen content.