  Comets provide a valuable window into the chemical and physical conditions at
the time of their formation in the young solar system. We seek insights into
where and when these objects formed by comparing the range of abundances
observed for nine molecules and their average values across a sample of 29
comets to the predicted midplane ice abundances from models of the protosolar
nebula. Our fiducial model, where ices are inherited from the interstellar
medium, can account for the observed mixing ratio ranges of each molecule
considered, but no single location or time reproduces the abundances of all
molecules simultaneously. This suggests that each comet consists of material
processed under a range of conditions. In contrast, a model where the initial
composition of disk material is `reset', wiping out any previous chemical
history, cannot account for the complete range of abundances observed in
comets.
  Using toy models that combine material processed under different thermal
conditions we find that a combination of warm (CO-poor) and cold (CO-rich)
material is required to account for both the average properties of the
Jupiter-family and Oort cloud comets, and the individual comets we consider.
This could occur by the transport (either radial or vertical) of ice-coated
dust grains in the early solar system.
  Comparison of the models to the average Jupiter-family and Oort cloud comet
compositions suggest the two families formed in overlapping regions of the
disk, in agreement with the findings of A'Hearn et al. (2012) and with the
predictions of the Nice model (Gomes et al. 2005, Tsiganis et al. 2005).
