What is the empirical formula of a substance that is 53.5% C, 15.5% H, and 31.19% N by weight?

Feb 25, 2016

${C}_{2} {H}_{7} N$ is the simplest whole number ratio defining constituent atoms in a species, and is thus the empirical formula.

Explanation:

As always with these problems, we assume that there are $100$ $g$ of substance, and calculate the elemental composition (we divide thru by the atomic masses of each component):

%C $=$ $\frac{53.5 \cdot g}{12.011 \cdot g \cdot m o {l}^{-} 1}$ $=$ $4.45$ $m o l$ $C$.

%H $=$ $\frac{15.5 \cdot g}{1.00794 \cdot g \cdot m o {l}^{-} 1}$ $=$ $15.38$ $m o l$ $H$.

%N $=$ $\frac{31.19 \cdot g}{14.01 \cdot g \cdot m o {l}^{-} 1}$ $=$ $2.23$ $m o l$ $N$.

We divide thru by the smallest quotient, that of $N$ to give an EMPIRICAL formula of ${C}_{2} {H}_{7} N$ (i.e. we divide each molar quantity by $2.23$!). Without details of molecular weight, this is as far as we can go.