The Chemical Origins of Reaction Enthalpy

The Energy consumed as heat during the execution of a chemical transformation at constant pressure is defined as the Reaction Enthalpy (or Heat of Reaction). We can measure the Heat of Reaction calorimetrically, or we can calculate it from the difference between the heat of formation of the products and the reactants. But how the understand or interpret the heat of reaction for a particular transformation requires a detailed understanding of how Chemical Energy is 'stored'.

Molecules form because the electrons in single atoms can become more stable in combination with other atoms. Most of the time, the energy stabilization is associated with particular pairs of atoms in the molecule, and will call the interactions of these pairs a chemical bond. Different pairs of elements have a different ability to form chemical bonds and have different stabilization energies associated with them. The properties of a molecule and the chemical enegy it possesses is clearly determined by the connectivity of the bonding, i.e. which pairs of atoms in the molecule share electrons.

Consider the molecular formula C₂H₆O. As it turns out, two famous molecules share this molecular formula; they are structural isomers. (Links on the Chemical names require the RASMOL , CHIME, or equivalnet molecular (*.pdb) viewer)

The first is Ethanol, CH₃CH₂OH
The second is Dimethyl Ether, CH₃OCH₃

The connectivity of the molecules are different, which gives these two substances different properties. The normal boiling point of ether is only 248 K (-25 ^oC), but the normal boiling point of ethanol is 352 K (79 ^oC).
The Energy content of these molecules is also different: Consider the Heats of Combustion (gas phase)

DH_comb^o(CH₃OCH_3(gas)) = -1328.3 +/- 0.5 kJ/mol

DH_comb^o(CH₃CH₂OH_(gas)) = -1277.1 +/- 0.3 kJ/mol

This means that ethanol is about 50 kJ/mol more stable than dimethyl ether, but with the same molecular formula. We can understand this difference because there are different chemical bonds in the two molecules!

---

The hypothetical state of a molecule after all its bonds are broken can be used as a 'reference', just like we used the standard states of the elements as a reference for the Enthalpies of Formation of molecules. Thus the energetics of a chemical transformation can be estimated from the bonds broken and formed in the reaction

A specific example can be made from our old familiar combustion of methane reaction. We calculated the enthalpy change during this transformation before from traditional thermochemcial methods. We can do this again by using the average bond enthalpies of C-H, C=O, {O=O}, and O-H bonds

So, the Heat of Formation of new molecule, or the Heat of Reactions of a given transformation can be estimated by using average bond energies and the above thermochemical analysis. This is not as accurate as using directly measured heats of formation (which is not an approximation!) but is sometimes very useful as a starting guess.

Lets see how the concept of Bond Dissociation Enthalpies helps us understand the ethanol and ether molecules:

In the Ether molecule there are 6 C-H bonds and two C-O bonds. Therefore the ether molecule is
6*(413) + 2*(358) = 3194 kJ/mol more stable than 2C + 6H + 2O.

Similarly, the Ethanol molecule has 5 C-H bonds, 1 C-C bond, 1 C-O bond, and 1 O-H bond, so ethanol is
5*(413) + (348) + (358) + (463) = 3234 kJ/mol more stable than 2C + 6H + 2O.

Bond enthalpy arguments place the relative Heat of Formation of Ethanol at about 40 kJ/mol more stable (more negative) than that of dimethyl Ether, not a terribly accurate estimate when compared to the experimental value of 51.2 kJ/mol, but sometimes a 20% error is acceptable. At least Bond Enthalpies predict why Ethanol is more stable than Ether (better bonding pairs).

Bond enthalpy sums can be used to estimate the heat of combustion Ethanol. The balanced chemical reaction for the combustion is:

The Heat of this reaction can be calculated from the atomization energies of the products and reactants as follows:

Bonds on the right hand side of reaction (Product Bonds)

4 C=O

6 O-H

Bonds on the left hand side of the reaction (Reactant Bonds)

5 C-H

1 C-C

1 C-O

1 O-H

3 O=O

Note that more than one kind of bond is possible between the same pair of atoms depending on haw many electrons are shared between the elements. If two electrons are shared, we call this a single bond and it is given the symbol ( - ), four electrons shared is a double bond ( = ), etc. We must keep track of the type and neumber of each of the bonds if we wish to estimate thermochemical properties of reactions.

The Enthalpy of reaction is simply the sum of the bond dissociation enthalpies of the reactants minus the sum of the bond dissociation enthalpies of the products or even more simply, the sum of the bond dissociation enthalpies of the bonds broken minus the bonds formed
So, we estimate the heat of combustion of ethanol as:

DH_comb^o(CH₃CH₂OH_(gas))

= {5*(413) + 1*(348) + 1*(358) + 3*(495)} - {4*(799) + 5*(463)}

= -1255 kJ/mol

Clearly are estimate is inexact compared to the experimental value of -1277.1 kJ/mol, but the estimate is within 2% of the heat of combustion, which is pretty good for this type of theory...

Here is another comparison of molecular isomers which demonstrates some limitation in the average bond dissociation enthalpy method, but perhaps teaches us some more subtle points of chemical energetics.

---