C10H12N2O
First, lookup the atomic weights of C, H, N, and O
Atomic weight of Carbon = 12.0107
Atomic weight of Hydrogen = 1.00794
Atomic weight of Nitrogen = 14.0067
Atomic weight of Oxygen = 15.999
Now determine the ratio of atoms of each element by dividing their mass percentage by their atomic weights.
Carbon = 68.2 / 12.0107 = 5.67827
Hydrogen = 6.86 / 1.00794 = 6.805961
Nitrogen = 15.9 / 14.0067 = 1.135171
Oxygen = 9.08 / 15.999 = 0.567535
Now determine a simple integer ratio of small integers that closely approximates the ratio of relative molar amounts.
5.67827 : 6.805961 : 1.135171 : 0.567535
Going to first divide all values by 0.567535 (picked because it's the smallest in the above ratios) getting
10.005 : 11.992 : 2.000 : 1
These numbers are all extremely close to integers so it looks like the empirical formula for Serotonin is C10H12N2O
Let's compute the molar mass of the empirical formula
10 * 12.0107 + 12 * 1.00794 + 2 * 14.0067 + 15.999 = 176.2 g/mol
Since that calculated molar mass matches the desired target, we're done. If the calculated mass was smaller, or the desired mass was larger (like 352 g/mol) we would have multiplied the number of atoms by the appropriate factor. But that's not needed, so the molecular formula for Serotonin is C10H12N2O
