# What is the molecular formula of the C_3H_5O_2, if the gram molecular mass is 146 g/mol?

Aug 29, 2017

We gots an empirical formula.......and we use this to determine a molecular formula of ${C}_{6} {H}_{10} {O}_{4}$.

#### Explanation:

We gots an empirical formula of ${C}_{3} {H}_{5} {O}_{2}$ OF WHICH THE MOLECULAR FORMULA IS A SIMPLE WHOLE NUMBER MULTIPLE.

Why the shouting? Because I want to emphasize that the molecular formula may be represented as ${\left\{{C}_{3} {H}_{5} {O}_{2}\right\}}_{n}$.

And thus .............................

$146 \cdot g \cdot m o {l}^{-} 1 \equiv n \times \left\{3 \times 12.011 + 5 \times 1.00794 + 2 \times 16.00\right\} \cdot g \cdot m o {l}^{-} 1$

And so $n = \frac{146 \cdot g \cdot m o {l}^{-} 1}{73.0 \cdot g \cdot m o {l}^{-} 1}$

And clearly $n = 2$............

And thus our $\text{molecular formula} = 2 \times {C}_{3} {H}_{5} {O}_{2} = {C}_{6} {H}_{10} {O}_{4}$.