Traumatic acid contains 63.13% carbon, 8.830% hydrogen, and 28.03% oxygen. its molar mass is 228 g/mol. determine the empirical and the molecular formulas of traumatic acid.

Q1)
firstly we need to determine the empirical formula of the compound. empirical formula is the simplest ratio of components in the compound.
percentages of the elements have been given, so lets assume we are calculating for a compound of 100g 
                                  C                               H                              O
mass                       63.13 g                    8.830 g                       28.03 g
molar mass             12 g/mol                   1 g/mol                      16 g/mol
number of moles     63.13/12                   8.830/1                      28.03/16
                                5.26                           8.830                           1.75
divide by the smallest number of moles 
                                5.26/1.75                   8.830/1.75                   1.75/1.75
                                = 3.01                        = 5.04                           =1
rounded off to the nearest whole numbers 
C - 3
H - 5
O - 1
therefore empirical formula = C₃H₅O

Q2)
we have to next determine the molecular formula of the compound 
molecular formula gives the actual composition of elements in the compound. 
since we know the empirical formula and molecular mass, we can find how many empirical units are in the molecular formula.
mass of empirical unit = Cx3 + Hx5 + Ox1
                                    = 12 g/mol x 3 + 1g/mol x 5 + 16 g/mol x 1
                                    = 36 + 5 + 16 = 57 g/mol
the molecular mass = 228 g/mol
then number of empirical units in the molecular formula = 228 / 57 = 4
therefore there are 4 empirical units 
then the molecular formula = 4 x empirical formula =4 (C₃H₅O)
molecular formula = C₁₂H₂₀O₄