Factor Analysis of Numeric Isotope Patterns of Compounds Containing Small Numbers of Chlorine and Bromine Atoms

The mass spectra of aromatic compounds containing m bromine and n chlorine atoms display m + n + 1 characteristic molecular-ion peaks at intervals of two amu. For a given compound, the relative intensity of these peaks may be represented by a numeric isotope pattern predicated on a 3:1 ratio of chlorine isotopes and 1:1 ratio of bromine isotopes. For example, the theoretical numeric pattern for any bromodichlorobenzene is 9:15:7:1. It is shown that numeric patterns may be factored, leading to the discovery that the pattern’s lead number identifies the chlorine pattern within the overall pattern and hence n; when the lead number is 9, the chlorine pattern is 9:6:1 and n equals 2. The value of m follows from the number of terms in the pattern. Real patterns follow those predicted closely enough for both n and m to be found for an unknown directly from a normalized numeric isotope pattern (i.e., one in which all terms in the pattern are relative to that of the highest-mass term taken as one). The method exemplified for analyzing patterns should prove useful in courses where numeric isotope patterns are studied.