I don't agree with most of the responses here. Kinetic Energy is the energy involved in motion and vibration is not simply motion (since with it, velocity varies periodically with time). Vibration is both kinetic and potential energy and usually the SUM of the two is the (constant) vibrational energy. Just as a planet's orbital energy has both potential and kinetic terms. Or just as two opposite charges have both P.E. and (probably) K.E. (depending on the system). Heat is a very difficult term, generally its definition is either formal or vague/murky. Mostly, from a practical perspective, heat is the flow of energy. Or even more practical, heat is what a thermometer measures changes of. Perhaps you can see by this that both heat and P.E. are not specific types of energy? So using them to explain only works as long as you're willing to keep the explanation quite superficial. I also have a serious problem understanding the original post: 1) if two molecules have bonded then there is one molecule, right? If the product molecule required the addition of more energy, (and that energy wasn't returned as kinetic, electronic, or vibrational (rotational, etc.) energy) then the product is less stable than the reactants. Some chemical reactions (eg simple acid-base reactions) nearly instantaneously form product, but many reactions (especially the more "interesting" ones) require some more energy to form a transition state (which means a state of higher energy, bond energy to be specific (bond energy being the electromagnetic interactions between all atoms, which involves quantum mechanical interactions)) which then rearranges to form product(s). The over-all reaction may cause cooling or heating and may be slow or fast (but generally chemical reaction steps are very very fast compared to what we can perceive with our natural senses). Energy may come from bond energy or kinetic (thermal) energy (as well as rotational, vibrational, and conformational energy) and be "used" to change atoms' positions or to change the electron clouds surrounding atoms or groups of atoms (usually both). Do bonds break "because of" P.E.? Well, sure - in fact one way we determine whether two atoms are bonded is by measuring their distance apart. While it varies depending on the atoms and electronic states involved, most if not all (I can't think of an example where this is not true) bond breaks require the atoms to separate (distance wise) which therefore requires motion, hence k.e. and that has to come from somewhere. It can come from k.e. (collisions) but as soon as the energy is transferred from velocity (deceleration) it goes somewhere (and we call that P.E. unless some other object rebounds with more k.e.) or it can come from one or more of the many types of P.E. (which include electrostatic, conformation, vibration, and rotation (and by the way, there are several kinds of rotation)). The OP seems to assume that the product molecule is in its lowest (P.E.) energy state, and that is NOT given in the original problem. A molecule may spontaneously decay (if it isn't the lowest energy for the system), so saying added P.E. "causes" a bond to break is only true in certain situations. But bond energy is P.E. by definition, so any change in bonds is a change in P.E. (even if the total P.E. remains constant for the entire system). BTW, the OP also has a problem in the wording: Two molecules form one molecule which then breaks up into (two?) other molecules (or ions). Both the bond (Van der Waals "bonds" are generally not considered "bonds" or "chemical bonds" even though they are bonds between chemicals..but that depends on the context.) making and bond breaking involves changes in P.E. but what the TOTAL P.E. of the 3 states is, is not stated and could be anything A>B>C or A<B<C or A>B<C or A=B<C ..I think that makes for 9 possibilities...
