Re: Why do Hydrogen bonds give off heat when they form?

Your intuition is correct when you say it requires energy to break a bond.  But confusion can arise - as it does in your case - as to what is taking up energy and what is giving up energy.  What I will say here applies to all kinds of bond-forming and bond-breaking.  The hydrogen bond is no different in this regard.

When thinking about a problem like this, we distinguish between the part of the universe we are studying - which we call the system - and the rest of the universe - called the surroundings.  In the case of making or breaking bonds, the system is the molecule(s) undergoing the change, and the surroundings is everything around it.

To break a bond, it requires that energy go from the surroundings to the molecule undergoing the reaction.  The surroundings will get cooler because they have lost energy.

When a bond is formed, heat is released from the molecule to the surroundings.  The surroundings get warmer because they have gained energy.

Note that as the surroundings get cooler or warmer, the system, that is, the reacting molecules, do not change temperature.  The energy taken in or given out changes the energy of the system, not its temperature.

To summarize, when we say that bond-breaking requires energy, we mean the molecule undergoing reaction must gain energy.
When we say bond-formation releases energy, we mean the molecule undergoing reaction loses energy.

Take the specific case of forming a hydrogen bond between two isolated molecules.  When we say that forming this bond releases energy, this is exactly what we mean: we mean that the energy of the bonded molecules is lower than the energy of the separate molecules.  Where has the energy gone?  It has gone into the surroundings in the form of heat.

Now, we also have to bear in mind that a bond is never broken in isolation.  Generally, in a chemical rection some bonds are broken and some are formed. The net flow of energy for a reaction equals the net of bond-breaking energy and bond-forming energy.  In some cases, the reacting system gains energy (the surroundings get cooler), in other cases the reacting system loses energy (the surroundings get warmer).

I hope this helps. Please feel free to email me if you still need clarification.

David Reibstein, Outreach Director, Princeton Materials Institute