The process can be adiabatic or not adiabatic-I don't think that matters because we can either have E=w or E=q+w (either way, we won't have E=q). It depends on the work. If there's constant volume, no PV work is done, and so E=q. So, internal energy is different from the heat of the reaction when PV WORK IS DONE, because then E=q + w.