Heats of Formation of High Explosives1
Objectives:
Students will be able to…
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Use WebMO to determine the heat of formation.
Use the NIST Web book to find experimental values for heats of formation.
Compare experimental to computational results and determine which engine is the most accurate.
Use the calculated heats of formation to determine the relative strengths of various explosives.
Determine what features in a molecule contribute toward explosive strength and use that knowledge to
design a new molecule to compare to their other results.
Introduction:
Nitroglycerin was first synthesized in 1847, and was later used by Alfred Nobel in the
production of commercial explosives. Though very powerful, nitroglycerin has drawbacks as an
explosive because it is extremely sensitive to shock. In fact, the transport of liquid nitroglycerin
was banned in California after a crate exploded in San Francisco killing 15 people. Even Nobel’s
own little brother was killed in a nitroglycerin explosion in one of their factories.
Explosions differ from combustion (burning) because they happen at a much faster rate.
Combustions reactions are propagated by the flame front moving through the burning material.
This heats up nearby molecules causing them to burn as well. The reaction can only occur as
fast as the flame front moves. In an explosion, the reaction is propagated by a supersonic blast
wave that passes through the material.2
The speed of the reaction also affects the balanced chemical reaction. Combustion requires
oxygen from the air to react with the burning material to make products such as carbon dioxide
and water. An explosion happens so quickly that atmospheric oxygen has no time to react with
the material. All oxygen must come from the explosive material itself. Nitroglycerin explodes
according to the reaction below:
4C3H5N3O6  12CO2 + O2 + 3N2
In this activity you will examine the heats of formation of various compounds. You will evaluate
how well two different semi-empirical computational models predict heats of formation by
comparing the calculated values to experimental values that can be accessed online. You will
also examine trends in heats of formation for some related molecules and determine the heat
1
Adapted from: Bumpus, John A., Anne Lewis, and Stotts Corey. "Characterization of High Explosives and Other
Energetic Compounds by Computational Chemistry and Molecular Modeling." Journal of Chemical Education 84.2
(2007): 329-32.
2
Rzepa, Henry S. "Nitroglycerin." Web. 05 Apr. 2012.
<http://www.ch.ic.ac.uk/rzepa/mim/environmental/html/nitroglyc_text.htm>.
of formation for various known explosives. You will then use the information you have
collected to design your own explosive and find a computational value for its heat of formation.
This will allow you to predict the effectiveness of your explosive relative to TNT.
Part 1 – Generating Heats of Formation
In Table 1, you will find a list of molecules. Build each molecule in WebMO and run a geometry
optimization using Mopac/PM3. Determine the Hf by running a “molecular energy” job in Mopac using
the AM1 and PM3 models. The data will be given in units of kcal/mol. Record these results in Table 1.
Determine the experimental values for Hf by accessing the NIST Chemistry WebBook at
http://webbook.nist.gov/chemistry/. Use the option that allows you to search by name and input your
molecule name. Click on the link for gas phase thermochemistry data. The Hf listed will have units of
kJ/mol , which you will need to convert to kcal/mol to compare to the WebMO data. Record these
values in Table 1.
Figure 1: Structures of Selected Explosives
O 2N
O 2N
O
NO 2
-
O
N
N
O
O
+
+
N
N
O
-
O
+
+
N
-
N
O
NO 2
O
N
Tetranitromethane
+
O
-
+
N
O
O
RDX
O
O
-
+
O N
O
+
O
O N
+
N
-
O
-
N
O
N
N
O
+
N O
-
+
O
O
nitroglycerin
-
+
N
O
N
N
O
HMX
N
TNT
-
+
N
O
O
O
-
-
O
-
Table 1: Experimental and Computed Heats of Formation
Compound
AM1 (kcal/mol)
PM3 (kcal/mol)
kJ/mol
Methane
Nitromethane
Dinitromethane
Trinitromethane
Tetranitromethane
Ethane
Propane
Butane
Pentane
Hexane
Heptane
Octane
Nonane
Decane
RDX
TNT
Nitroglycerin
HMX
Experimental
kcal/mol
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Part 2 – Comparing Data
In Excel, make a plot of heat of formation for methane, ethane, propane, butane, pentane, hexane,
heptane, octane, nonane, and decane vs. number of carbon atoms. Include all three sets of data (AM1,
PM3 and experimental) on one graph.
Make another plot with the heat of formation vs. number of nitro groups for methane, nitromethane,
dinitromethane, trinitromethane, and tetranitromethane. Include all three sets of data (AM1, PM3, and
experimental) on one graph.
For the data with experimental values, plot the calculated values vs. experimental heats of formation.
You can include data from both computational models on one plot. If the data were in complete
agreement, they would fall on a straight line with a slope of 1 that begins at the origin.
1. Which model (AM1 or PM3) gave results that were the closest to the experimental heats of
formation?
2. What relationships were you able to determine from the first two graphs?
3. Consider the equation for determining relative explosive strength on the last page of the lab.
How is relative strength related to heat of formation? What other factors affect the relative
strength?
Part 3 – Comparing the Explosive Strength3
You can determine the relative effectiveness of an explosive compound if you know its heat of
formation. The relative strengths of some common explosives are listed in Table 2.
Table 2: Strength of Various Common Explosives Relative to TNT
Explosive
Formula
Relative Strength
TNT
C7H5N3O6
100%
HMX
C4H8N8O8
170%
RDX
C3H6N6O6
160%
PETN
C7H8N4O12
166%
EGDN
C2H4N2O6
*183%
Nitroglycerin
C3H5N3O9
150%
*value calculated using the attached method
Oxygen Balance
-10.5
-4
-3
-2
0
0.5
Using what you learned in Parts 1 and 2, design a new explosive. One thing to consider in building your
molecule is the oxygen balance. High explosives do not react extensively with atmospheric oxygen,
which means that all of the oxygen it reacts with comes from the molecule itself. In general, the closer
the oxygen balance is to zero, the more effective the explosive will be. Unreacted carbon atoms will
result in a lot of smoke after the explosion.
Oxygen balance can be calculated using the equation below4:
If the formula is written as CaHbNcOd
Then the oxygen balance = d – 2a – 0.5b
Build your molecule in WebMO, optimize the geometry, and calculate the heat of formation. Use the
information on the next page to find its relative effectiveness.
1. Draw the structure of your new compound, and explain why you chose this molecule. You may
want to consider some of the factors you described in Part 2 question 3.
2. Calculate the oxygen balance.
3. What model did you use to calculate the Hf and why?
4. What is the calculated Hf? Discuss the accuracy of this value.
5. Write the balanced explosive reaction and calculate the heat of explosion (show your work).
6. What is your value for relative strength (show work)?
7. Discuss what features of your molecule contributed to this value.
3
"Chemical Explosives." Federation of American Scientists. Web. 29 Mar. 2012. <http://www.fas.org/man/dod101/navy/docs/es310/chemstry/chemstry.htm>.
4
Ten Hoor, Marten J. "The Relative Explosive Power of Some Explosives." Journal of Chemical Education 80.12
(2003): 1397.
Calculating Relative Explosive Effectiveness
To calculate the explosive strength of a molecule, relative to TNT, we need to determine the explosive
reaction and compare the Hf of the reactants to the Hf of the products. We can use those numbers to
determine a value for the heat of explosion.
Heat of Explosion = Hf,reactants - Hf, products
To determine the products of an explosive reaction, recombine the elements in the reactant according
to the Kistiakowsky–Wilson Rules:
1.
2.
3.
4.
5.
Metal + O  metal oxide
C + O  CO (gas)
2H + O  H2O (gas)
CO + O  CO2 (gas, CO comes from step 2)
Excess O, H, N  O2, H2, N2
For example:
Balance the combustion of TNT: C7H5N3O6
1.
2.
3.
4.
5.
No metals, so we can skip step 1.
6C + 6O  6CO leaving 1C, 5H, and 3N
No oxygen left for this step.
No oxygen left for this step either.
5H  5/2 H2 and 3N  3/2 N2
So, overall…
C7H5N3O6  6CO + 5/2 H2 + 3/2 N2 + C
or
2 C7H5N3O6  12CO + 5H2 + 3N2 +2C
The heat of formation of the reactant can be calculated on WebMO or looked up on NIST. In this
example, the heat of formation of TNT is -54.4 kJ/mol.
The heat of formation of the products will usually only involve the Hf of water, carbon dioxide, or
carbon monoxide. These are listed in table 3. The other values can be ignored because the heat of
formation of an element is zero.
Table 3: Heats of Formation of common explosive products
Product
Hf
H2O
-240.6 kJ/mol
CO2
-393.5 kJ/mol
CO
-111.8 kJ/mol
Using the heats of formation in table 3, the heat of explosion of TNT can be calculated as:
Heat of Explosion = (-54.4) – 6(-111.8) = 616.4kJ/mol
The relative strength of the explosive is then calculated using the following equation wheren is the
number of moles of gas per mole of explosive, E is the heat of explosion calculated above, and MW is
the molecular weight of the explosive in g/mol.
Relative Strength (%) = 840nE/MW2
This calculation gives the strength of an explosive relative to TNT. If you plug in the values for TNT, the
equation should give you a value close to 100%.
Teacher Notes -- Heats of Formation of High Explosives
Standards:
This activity addresses goals in the following Next Gen Practices.
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Practice 2 – Develop and use models
Practice 4 – Analyze and interpret data
Practice 5 – Use computational thinking
Notes:
IntroductionThe balanced reaction for nitroglycerin is slightly different from the reaction on the source
website for the sake of consistency. There are several ways to determine the products of an
explosive reaction. The method that I gave is the most simple, but there are better
approximations that are built on these rules. Marten ten Hoor lists the rules for several
methods in the appendix of his article.4
Part 1—
This activity assumes that students have some prior experience building molecules in WebMO.
If you need more direction in how to use the program, step-by-step instructions appear in some
of the other activities.
Because of the long list of molecules the students need to compute values for, I would break the
list up among students or groups of students and then have the class share data. This can be an
opportunity to differentiate the activity as some of the molecules are more difficult to construct
in WebMO than others.
When constructing compounds with nitro groups, make both N-O bonds single bonds and make
sure that no hydrogen atoms are added to the structures before running them. The NIST site
does not have gas phase data available for Trinitromethane or HMX.
The values listed in the NIST WebBook are usually in kJ/mol. They can be converted by the
students or, if you are trying to save time, by a unit conversion applet such as this:
http://www.colby.edu/chemistry/PChem/Hartree.html. There are sometimes multiple values of
heat of formation for a given molecule, so student answers may vary in the last significant
figure.
Table 1.b: Experimental and Computed Heats of Formation (my values)
Compound
Methane
Nitromethane
Dinitromethane
Trinitromethane
Tetranitromethane
Ethane
Propane
Butane
Pentane
Hexane
Heptane
Octane
Nonane
Decane
RDX
TNT
Nitroglycerin
HMX
AM1 (kcal/mol)
-7.68
-7.72
5.54
27.67
56.01
-16.25
-22.92
-29.58
-36.23
-42.88
-49.54
-56.18
-62.84
-69.49
82.70
47.99
-31.5
188
PM3 (kcal/mol)
-13.03
-15.99
-12.04
-4.81
6.26
-18.16
-23.66
-29.11
-34.54
-39.98
-45.41
-50.85
-56.28
-61.72
42.10
5.88
-78.8
69.28
kJ/mol
-74.84
-81
-58.9
-82
-83.8
-103.8
-123.6
-146.4
-167.1
-187.8
-208.7
-228.3
-249.7
192
24.1
-279.1
--
Experimental
Kcal/mol
-17.88
-19.4
-14.08
-19.6
-20.03
-24.81
-30.01
-34.99
-39.94
-44.89
-49.64
-54.56
-59.68
45.89
5.76
-66.71
--
Part 2—
Student data should be graphed with both sets of calculated data and the experimental data
onto one plot. This makes it easy to visually assess which data set best aligns with the
experimental data.
Figure: Heat of formation vs. Number of carbon atoms for methane-decane
Number of Carbons
0
0
2
4
6
8
10
12
-10
Heat of Formation
-20
-30
AM1
PM3
-40
Exp.
-50
-60
-70
-80
Figure: Heat of formation vs. Number of nitro groups for methane – tetranitromethane
60
50
Heat of Formation
40
30
20
AM1
10
PM3
Experimental
0
-10
0
1
2
3
4
5
-20
-30
Number of Nitro Groups
Figure: Calculated Heat of Formation vs. Experimental Heat of Formation
100
Calculated Heat of Formation
80
-80
60
40
20
AM1
0
-60
-40
-20
-20 0
20
40
60
PM3
-40
-60
-80
-100
Experimental Heat of Formation
Part 3—
This section is meant to give students an idea of how these values of Hf are then used to
predict the explosive strength of compounds. I also wanted to give them a chance to make up
potentially explosive compounds and predict their strength.
Heat of Explosion can be determined experimentally in a bomb calorimeter under argon, much
the same way that heat of combustion can be measured in a bomb calorimeter under room air.
The products of an explosion differ from the products of combustion due to the speed at which
the reaction takes place. There is no time for the reactants to mix with atmospheric oxygen, so
they react only with the oxygen in the compound.
For TNT the value for n is 10 because we do not include the moles of carbon.
The values calculated will be relative to TNT (which calculates to 100%). Students may need a
lot of help with this section. It is not part of the standard chemistry curriculum, but I think it is
valuable for them to see how these numbers are used in the “real world.”
Additional Resources:

This link contains an Army paper that gives a good discussion of the meaning of Heat of
Explosion. It goes into detail about why the values are reported as positive numbers
instead of following chemistry conventions.
http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA268584

The semiempirical method for determining heats of formation has limitations. The third
table shows how it is less accurate for more complicated molecules. Density function
theory can be used to determine heat of formation, but the process is much more
complicated and requires additional calculations. A discussion of that method can be
found in this paper:
Tao, Wei, Zhu Weihua, Zhang Xiaowen, Li Yu-Fang, and Xiao Heming. "Molecular Design of
1,2,4,5-Tetrazine-Based High-Energy Density Materials." J. Phys. Chem. 2009.113 (2009):
9404.