Question

Combustion of adipic acid yields percentage abundances of `C:49.3%`, `H:6.9%`, and `O:43.8%`. What are the empirical and molecular formulae of adipic acid?

Answer 1

Adipic acid has a molecular formula of `C_6H_10O_4`.

Explanation:

As with all problems of this type, we assume a quantity of `100*g` of stuff, divide thru by the atomic weight of the component elements, and work out the elemental composition with respect to moles:

`"Moles of C"` `=` `(49.3*g)/(12.01*g*mol^-1)` `=` `4.10*mol`.

`"Moles of H"` `=` `(6.9*g)/(1.01*g*mol^-1)` `=` `6.83*mol`.

`"Moles of O"` `=` `(43.8*g)/(15.99*g*mol^-1)` `=` `2.74*mol`.

We divide thru by the smallest molar quantity, that of oxygen, to get the empirical formula of `C_1.5H_2.5O`, which we of course double to give `C_3H_5O_2` because, by definition, whole numbers are required.

Now, the molecular formula is some whole number ratio of the empirical formula:

i.e. `"Molecular formula"` `=` `"(Empirical formula)"xxn`.

So we have to simply solve for `n`.

`146*g*mol^-1=(3xx12.011+5xx1.00794+2xx16.00)xxn*g*mol^-1`

Thus `n=2`, and the molecular formula is `C_6H_10O_4`.