# Logic Puzzle #22: The Art of Uncovering the Molecular Formula … Solution

##### by Arvin Moser, Team Manager, Application Scientists, ACD/Labs

As more information is needed to solve an unknown, it becomes useful to understand what information is available, make a hypothesis and then get to the grunt work of eliminating the unlikely candidates.

Below is a summary explaining some of the information that can be extracted from the problem set.

1. Given an unknown compound as organic, the focus is best kept with the elements C, H, N and O.
2. The ESI(neg.)-ToF spectrum indicates a singly-charged ion at m/z 692.137. If we presume this is the [M-H]- ion with a tolerance of 1 mDa, then we can limit the number of possible molecular formula(e) (MF). See the table below.
3. The MS isotope pattern excludes atoms such as Cl, Br and S.
4. The upper range for the C atoms is 57 (≈693/12).
5. The 13C / 12C ratio indicates the C atom count at closer to 36 (≈40/100*100/1.1).
6. The 13C NMR data indicates at least 12 C atoms.
7. The carbons at 70, 167 and 169 ppm indicate at least 3 O atoms.
8. The height difference for the C atoms at 43 and 47 ppm in respect to the other signals indicates a potential dimer or trimer or more. Multiples for the total C atoms are: 10C+2C, 20C+2C, 30C+2C, etc.
9. Multiples for the protonated C/H atoms are: 5 CH: 1 CH2: 1 NH = 6C/8H, 10 CH: 2 CH2: 2 NH = 12C/16H, 15 CH: 3 CH2: 3 NH = 18C/24H. The OH groups are not indicated.

Table of Potential Molecular Formulae

# MF Calc. Mass Mass Diff. RDBE (N(III);N(V))

1 C32H27N3O15 ___692.137 0.000 21.0;24.0

2 C31H21N10O10 __692.137 0.000 26.5;36.5

3 C30H15N17O5 ___692.137 0.000 32.0;49.0

4 C17H23N15O16 __692.138 0.000 14.0;29.0

5 C46H15N9 ______692.138 -0.001 44.0;53.0

6 C47H21N2O5 ___692.138 -0.001 38.5;40.5

7 C32H17N14O6 __692.138 -0.001 31.5;45.5

8 C33H23N7O11 __692.138 -0.001 26.0;33.0

The remaining MF C32H27N3O15 is the best fit for the unknown compound.