Jet Contrails

As an automotive instructor, I often explain to my students that "perfect" combustion produces only CO2 and H2O. To illustrate the point, I describe jet contrails as nothing more than ice crystals coming from the combusted jet fuel.

My good friend, a physicist, recently corrected me and said that contrails are actually moisture (already in the atmosphere) that indeed forms ice crystals, but only after being attracted to carbon molecules (soot) from the jet exhaust.

I am trying to get a clarification on this point, but I can find little more than UFO theories and allegations of the Air Force "crop dusting" at 10,000 meters!

The temperature at that altitude would seem to be more than adequate to freeze the expelled H2O (with or without a soot nucleus). Could someone give me a (factual) explanation? Thanks!