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?

1 Answer
Sep 5, 2016

Answer:

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#.