Bond dissociation energy is the energy required to break a single bond between two atoms. Calculating the average BDEC for all the bonds in a molecule is one way to estimate the melting point of a substance.
Molecules can exist in several forms, depending on the interconnection of its atoms. These forms are known as polymorphs. A common polymorphism is when a molecule has two different crystal structures, each with its own set of interconnecting atoms.
For example, diamond and graphite are both types of carbon, but they have very different structures. One is a solid substance while the other is a thin material. Both have the same number of carbon atoms, but they are arranged differently to form these different structures.
Polymorphism can also occur in liquid form. Liquid oxygen has two separate forms: one form having eight oxygen atoms surrounding each atom of iron and the other having ten oxygen atoms surrounding each atom of iron.
Elimination of hydrogen bonds
In addition to covalent bonds, hydrogen bonds can also be a significant factor in the stability of molecules. Like covalent bonds, hydrogen bonds can be strong or weak depending on the energy spent between atoms to connect them.
Unlike covalent bonds, hydrogen bonds can be easily broken as it is only a partial bond between atoms. Water is a great example of a compound that has strong hydrogen bonds within it, keeping the H2O molecules connected.
To calculate the bond dissociation energy for the breaking of all the hydrogen bonds in methane (CH4), we first have to find out how many individual hydrogen bond pairs there are: 4 × 4 = 16. Then we have to find out how much energy it takes to break one such pair: 2 × 8 = 16.
Elimination of carbon-hydrogen bonds
The next type of bond cleavage is called elimination, or C-H fission. This occurs when a hydrogen atom attached to a carbon atom is removed, taking the carbon atom with it.
This happens in organic compounds when a carbonyl group (-CO-) is present. A carbonyl group can be thought of as a compound containing an oxygen atom attached to a carbon atom, with two hydrogen atoms attached.
An example of this would be glucose, also known as sugar. When glucose is heated, it undergoes oxidation which removes the -OH group from the carbon atom. This leaves just the molecule of glucose, which is simply two oxygen atoms bonded to six carbon atoms.
Like bond cleavage in SN2 reactions, bond cleavage in C-H fission can be considered spontaneous if the energy required to break the bonds is less than the energy obtained from the reaction.
Break all the C-H bonds
In this next section, we will calculate the bond dissociation energy for breaking all the C-H bonds in a molecule of methane, CH4. We will use the same principles as above, only instead of calculating the energy for one C-H bond, we will calculate it for all four!
Methane is a common hydrocarbon gas. It consists of one carbon atom and four hydrogen atoms arranged in the shape of a pyramid with a hydrogen atom at the top. This structure is called a methyl group.
To calculate the dissociation energy of all the C-H bonds in methane, we will use the formula:
\(\Delta_{CE}=\frac{2}{m_{CH}^{2}m_{H}^{+}}}\frac{n}{V}\)
Where n is the number of moles of CH4 being dissolved, V is the volume in liters of solution, and mCH2 and mH+ are the molecular weights of methane in grams per mole and hydrogen in grams per mole, respectively.
We will solve this problem two different ways. The first way will be to solve for n, then plug that into the rest of equation to get ΔCE. The second way will be to solve for ΔCE directly.
Add up the dissociation energies
So, now you have all of your bond dissociation energies for all of the bonds in methane. How do you calculate the total bond energy change when one methane molecule dissociates?
Again, remember that energy can’t be created or destroyed, only transferred. As the bonds in methane break, the bond energy is transferred to the new molecules. The total bond energy of the new molecules is what you’re looking for here.
You add up all of the individual bond dissociation energies to get this total bond energy change. For example, one carbon atom has a single bond with a hydrogen atom with a bond energy of 84 kJ/mol. When one methane molecule dissociates, one carbon atom loses one hydrogen atom. The total bond energy change is therefore 84 kJ/mol*. One mol of CH4 = 4*12*22 = 96 g = 86400 mg = 864000 å mol−1, so n=86400Å4=0.00864Å4.
Now that you have calculated this very small unit of length, you can use it to calculate the van der Waals radius! Rvdrw>(86400 Å4)²/(12 Å). This gives us a van der Waals radius of 5.1 Å.
So there we have it! A very quick and (hopefully) easy look at how to calculate the Bond Dissociation Energy and how to use it to find the van der Waals radius.
Continued…
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Convert to joules
Once you have your kcal/mol value, you can convert it to joules by multiplying by Avogadro’s number (6.022×1023). One mole of any chemical compound contains Avogadro’s number of molecules, so this conversion is very useful!
For example, one mole of methane has a bond dissociation energy of 27 kcal/mol, so its bond dissociation energy in joules is:
(6.022×1023)x(27kcal/mol) = 1.91×10−19J
This is the amount of energy needed to break all the bonds in a mole of methane. Now imagine how much that is per one molecule! One molecule of methane has that much potential energy embedded within it.
Compare to heat of combustion
The heat of formation is also related to the chemical reaction of a material, specifically the formation of a compound from its constituent elements.
The difference is that the heat of formation considers the energy required to bring together the atoms or molecules to form the compound, not just the breaking of bonds within the compound.
This requires studying some pretty complex physics, including kinetic molecular theory and equilibrium theories.
The heat of formation is typically calculated for a certain temperature, like room temperature (around 20°C or 68°F). This is because at this temperature, the molecules are in equilibrium; moving faster or slower will not change the number of molecules present.
For more information on how to calculate the heat of formation, read more about electron transfer reactions.
Why is this useful?
Knowing the bond dissociation energy of methane is useful in determining the relative stability of compounds. If a compound is formed by the substitution of hydrogen in methane, then the compound will be more stable if it requires more energy to break the C-H bonds.
For example, if you had two compounds A and B, where A is stable and B is unstable, then if you add enough energy to convert A into hydrogen atoms and B into hydrogen atoms, then more of the A molecules will convert into hydrogen than B molecules will.
This is because A has stronger C-H bonds than B does, so it takes more energy to break all of the C-H bonds in A. This property is called lattice stability, and it applies to many different compounds.
What factors influence bond dissociation energy?
In general, the stronger the chemical bond, the more energy is required to break that bond. For example, it takes more energy to break a carbon-carbon bond than a carbon-hydrogen bond.
The difference in bond strength between types of bonds is what determines the relative dissociation energies of different molecules. For instance, it takes more energy to break a methyl group (-CH3) from methane than it does to break a hydrogen atom (-H) from methane because the carbon-methyl bond is stronger.
Bond dissociation energy can be influenced by temperature as well. As temperature increases, atoms and molecules vibrate more and gain kinetic energy. This can make it easier to break chemical bonds, such as weaker chemical bonds in a compound.
Dissociation energies can also depend on whether or not the molecule is in its lowest possible energy state, also known as its ground state.
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