Re: Forming chemical bonds releases energy, why?

Rich,

The relationship between individual molecules and thermodynamics is 
sometimes a challenge to explain, particularly since most simple 
descriptions leave out the important point that energy and thermodynamics 
are statistical properties of entire systems.  It's difficult for me to 
think about how properties, such as temperature, are defined if our scale 
is limited to individual atoms or molecules.  The subtlety of 
thermodynamics is that energy can come in many forms.

It's important for us to think about chemical systems or reactions as 
statistical ensembles than individual atoms.  Collisions among a collection 
of atoms and molecules give rise to the bulk properties (extrinsic 
variables) of a system, such as chemical potential, pressure, and 
temperature.  The bulk properties are a function of the individual 
components (intrinsic properties) of the system, such as the number of 
molecules, the volume they occupy, and the internal energy or entropy.

If we express the free energy of the system in it's differential form, we 
see how these variables relate to one another:

	dG = (Vdp) + (-SdT) + (udN)

The point I'd like to stress is that each relationship has units of energy. 
 If you change the pressure, the free energy changes by a certain amount.  
We can keep the free energy fixed and allow the volume to change in 
response to pressure changes.  The bulk properties of the system depend 
first on a corresponding intrinsic property, and secondly on all the other 
properties of the system.

The key to understanding the effects of energy changes at a molecular level 
is to remember how one function affects another.  The relationship between 
entropy and temperature is an easy one to understand in the context of 
internal motions.  Above absolute zero, any system experiences molecular 
motions.  These can be in the form of bond stretching, bond bending, 
intermolecular collisions, diffusion (or tumbling), etc.  The frequency of 
ALL motions, in total, give rise to our observed temperature.  We can turn 
the relationship around and describe the same relationship as a change in 
temperature affects the frequency or energy of these motions.  Bond 
stretching is slow at low temperatures and fast at high temperatures.  As 
we pump more energy into the system in the form of heat, we expect our 
molecules shake around a lot more.

Since (Vdp), (udN) and (-SdT) are all defined as units of energy, you can 
see how each relationship affects the system as a whole.  If we keep the 
volume and free energy fixed, then a change in temperature will increase 
the pressure of a system.  We can require the pressure and free energy to 
stay fixed, and allow the volume to change.

Chemical reactions can affect the energy of the system, resulting in a 
temperature change.  For example, if we have a simple A + B = AB 
association, where we form one bond between molecule A and B, there is a 
net change in the number of molecules in the system.  As a result, there is 
a change in system energy in the form of (udN).  If the free energy of the 
system does not change, then the energy may be observed in the form of a 
temperature or volume change.

The simplest example I can think of is heating water.  The density of water 
in an open beaker is greater just above freezing than it is below the 
boiling point.  In going from 4C to 95C, we pump thermal energy in the 
system.  The result is change in density, or volume.  (We'll assume no 
water has boiled away, so that (uDN) is constant).  If we heat the water in 
a sealed vessel where we can measure pressure (such as a piston), we will 
observe that the (-SdT) energy has caused a change in system pressure.  In 
a steam engine, we pull of the excess energy from heat in the form of 
pressure that forces the piston out giving us mechanical work.

Another example of chemical work is the energy associated with dissolving a 
salt in water.  If you add urea to water, the solution gets cold.  If you 
add NaOH to water, the solution gets hot.  Each of these can be explained 
as an affect on the chemical potential of water; the resulting change in 
(udN) energy causes a change in both (-SdT) and (Vdp) energy.  The 
temperature change is obvious when you touch the side of the beaker.  The 
pressure-volume work is observed as a difference in volume; if we could 
dissolve the salt in water keeping the volume fixed (such as placing our 
system in a piston), we would then observe a change in pressure.

Thanks for asking such a stimulating question.  (Keep up the good work!)

Regards,
Dr. James Kranz