# The analysis of an organic compound showed that it contains 0.175 mol C, 0.140 mol H, and 0.035 mol N. Its molecular is about 160 g/mol. What is the subscript on in the chemical formula?

Sep 2, 2016

$\text{molecular formula} = {C}_{10} {H}_{8} {N}_{2}$

#### Explanation:

We divide thru the molar quantities by the SMALLEST such molar quantity, that of nitrogen:

$C : \frac{0.175 \cdot m o l}{0.035 \cdot m o l}$ $=$ $5$

$H : \frac{0.140 \cdot m o l}{0.035 \cdot m o l}$ $=$ $4$

$N : \frac{0.035 \cdot m o l}{0.035 \cdot m o l}$ $=$ $1$.

And thus we get an empirical formula of ${C}_{5} {H}_{4} N$.

But the molecular formula is always a whole number mulitple of the empirical formula:

$\text{(molecular formula)"="n"xx"(empirical formula)}$

And then solve for $\text{n} .$

$160 \cdot g \cdot m o {l}^{-} 1$ $=$ $n \times \left(5 \times 12.011 + 4 \times 1.0076 + 14.01\right) \cdot g \cdot m o {l}^{-} 1$.
By this calculation, the empirical mass is $78 \cdot g \cdot m o {l}^{-} 1$. This is tolerably close to half the measured molecular mass. Thus $n \cong 2$. This often occurs if the molecular mass has to be estimated by more traditional means than mass spectroscopy, i.e. boiling point elevation, or by the isopiestic method.

Thus $\text{molecular formula} = {C}_{10} {H}_{8} {N}_{2}$