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STOICHIOMETRY AND THERMOCHEMISTRY OF EXPLOSIVES:

A Group Challenge Problem

Ref.: Consult the Learning Objectives for the topic of “Explosives” on the Plebe Chemistry Webpage:

http://www.usna.edu/ChemDept/plebeChem/

By this time in the General Chemistry course, you have developed skills in handling

stoichiometry, in calculating energy changes during reactions, and in using the gas laws to describe

physical parameters where appropriate. These skills permit examination of some of the phenomena

associated with the performance of explosives. Clearly, this is an application of chemistry which is of

significant interest in military operations, and which is important in the civilian sector as well.

Introduction: An explosive is a material, either a compound or a mixture, that contains oxygen and

fuel in a proportion that supports rapid combustion in an enclosed, airless space. An explosion generates

gases that expand several thousand times over that of the original sample; this occurs in a fraction of a

second, and usually at a high temperature. Because of this expansion, an explosion exerts a mechanical

force sufficient to burst a sealed container or force a projectile out of a gun.

There are two classifications of explosives, categorized according to the speed with which the reaction

moves through the system. A low explosive deflagrates, meaning that it burns and causes heaving, but

does not produce a shock wave. This is the explosive of choice for purposes such as the quarrying of

large blocks of stone for building, and for use as a propellant in guns. Such materials are often mixtures

of separate oxidizer and fuel compounds. A high explosive detonates, meaning the chemical reaction

moves through the explosive at a speed greater than the speed of sound. To shatter rock into gravel, or

in other applications (such as artillery blasts) where maximum destructive effect is desired, a high

explosive would be chosen. Typically, high explosives are very reactive compounds that, in effect,

contain their own oxygen and fuel within an individual molecule of the explosive. The different effects

depend on how fast heat and gas are produced by the reaction; this, in turn, depends on how fast the

reaction moves through the material. Three thousand feet per second is the speed that has been chosen

to mark the division between a low explosive and a high explosive.

Black powder, a mixture of potassium nitrate, charcoal, and sulfur, is a low explosive, used in guns and

in quarrying rock for building stone. TNT (trinitrotoluene), and RDX (cyclotrimethylene trinitramine)

are examples of high explosives. RDX is a military explosive with a detonation velocity as high as

27,000 fps. Interestingly, stoichiometry and energy considerations do not really distinguish the two

types of explosives; both release large volumes of gas, and significant amounts of heat during the

combustion. Basic principles of chemistry can be used to calculate such energy and volume changes

that accompany the reaction of an explosive.

Stoichiometry: Nearly all explosives in this exercise contain some combination of carbon,

oxygen, hydrogen, and nitrogen. Since the explosion is a combustion, we should expect that typical

combustion products will be formed. The actual products of any chemical reaction must be determined

experimentally, but some generalizations can be used to predict the products of related reactions, such as

those of explosives.

Follow these guidelines in order:

All the nitrogen in the explosive is converted to nitrogen gas (N2).

All the hydrogen in the explosive is converted to water vapor (steam).

The carbon is usually converted to carbon dioxide. If not enough oxygen is

present to convert all of the carbon to carbon dioxide, then some carbon monoxide

forms. If there is not enough oxygen to accomplish that, then only carbon

monoxide and soot (solid carbon), or soot alone, forms.

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Oxygen Balance

Zero Oxygen Balance: Explosive has just enough oxygen to convert all of its hydrogen

to water and all of its carbon to carbon dioxide.

Positive Oxygen Balance: Extra oxygen atoms remain after all of the hydrogen has been

converted to water and all of the carbon to carbon dioxide. O2 is a product.

Negative Oxygen Balance: There is insufficient oxygen in the explosive compound to

convert all of the hydrogen and carbon to H2O and CO2, respectively.

Thermochemistry: Enthalpy is the amount of heat absorbed or released at constant pressure. The

heat is evidence that a change in the energy of the system has occurred. Even though an explosion

does not occur at constant pressure, the enthalpy of formation for an explosive can be used (along with

H values for other reactants and products) in a calculation of the energy change for the explosive

reaction, as a first approximation. Bond dissociation energies can also be used. However, these are

average values, based on bond strengths in many stable compounds. Because explosives are such

reactive molecules, however, the use of standard bond dissociation energies may not give very accurate

results. Still, they do provide an ‘order of magnitude’ estimate of the energy released during the

reaction.

In an explosion, much of the potential energy stored in the chemical bonds of the explosive material is

converted into kinetic energy of the gaseous products formed. (Other ambient gases, such as N2 in air,

would also absorb that heat.) To estimate the temperature that the gases could reach, we need a value of

the heat capacity for these materials. For this exercise, a molar heat capacity of (7/2)R can be used for

reactants or products that are gases, as a first approximation. This value is a general one; the actual heat

capacity will vary with temperature and the nature of the gas.

Gas Laws: In determination of pressures and volumes of gases, we will use the ideal gas law as a

first approximation, even though the system is far from the ideal condition of one atmosphere pressure

and room temperature. More exact equations can (and must) be applied if greater accuracy is required.

DATA

Explosive Hf° (kJ/mol) Density (g/mL)

nitrogylcerine (C3H5O9N3) 380.1 1.591

HMX (C4H8O8N8) -75.0 1.90

PETN (C5H8O12N4) 506.7 1.77

TNT (C7H5O6N3) 74.6 1.65

Methane (CH4) -75

Ethylene oxide (C2H4O) -53

ANFO C10H22 -177 1.75 (mixture)

NH4NO3 -365.6 stoichiometric

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C

CC

C

CC

CH3

NN

N

H HO

O

O

O

OO

TNT

C

C

O

H

H

C

OH

OH

H

N

N

N

O

O

O

O

O

O

Trinitroglycerine

N CN

CNC

N

C

H

H

HH

H

H

N O

O

H

H

N

N

O

O

N O

O

OO

HMX

C

C

CC O

H

H

HC

O

H

H

O

HH

O

H

N

N

N

N

O

O

O

O

O

O

OOPETN

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Explosives Project Report Submission

Purpose: Perform the calculations needed to estimate (a) the pressure that would be generated upon

detonation of 1.00 cm3 of an explosive if it were confined to its original volume and (b) the volume to

which the product gases of the explosive will expand in returning to room temperature and pressure (1

atm, 25C.

Report Submission:

Memorandum (one-page should be sufficient, but it may be longer if needed)

Completed Worksheet (see attached)

One submission per group with all members the team providing a signature on the memo to

indicate that they have equally contributed to the project.

Memo Guidance:

Paragraph 1: Introduction: State the purpose of the project and report the key findings (i.e., results,

actual values).

Paragraph 2: Approach: A narrative description of the strategy used to obtain the results. Provide a

description of the process that leads from the initial assumptions to the final results explaining what

intermediate results needed to be calculated along the way. Don’t provide values!! Describe the process.

Paragraph 3: Conclusions: This is a critical evaluation of the results. Several simplifying assumptions

have been employed in these calculations. State the approximations. Comment on the validity of each of

these when applied to the problem of explosives (i.e., consider our discussions in class about these

approximations and the conditions under which they are valid and the conditions under which they are

likely to yield poor results).

Peer Evaluation:

Within a Team: Email to urban@usna.edu with a brief statement of what each member of the team did

and a ranking of the effort from 1 – 4. 1 = most significant effort on the team. 4 = least significant effort

on the team. All four numbers must be used (no ties!).

Between Teams. Each team is charged with assigning a grade to one other team’s memo.

Team Bonus: A quiz on the topic of explosives will be given. Team bonuses on that quiz may be

awarded if all members of a given team demonstrate high performance on the quiz.

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SC111 – Explosives Module Worksheet Names _____________________________________

1. a. Write the balanced chemical reaction for the decomposition of your explosive, using the

assumptions presented in the Stoichiometry section (page 1) and the information above. Include

the physical states (s, l, g).

b. What type of oxygen balance does your explosive have? Zero, Positive, or Negative?

2. a. Using information from this document and your textbook, calculate Hrxn per mole of your

explosive. Report your final answer with units of kJ/mol.

b. Calculate the heat evolved, q, when 1.00 cm3 of the explosive reacted. Report with units

of kJ.

Hrxn =

q =

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3. Calculate the change in temperature (in Kelvin) of the gases formed by the explosion (using 1.00

cm3 of explosive), assuming that all the energy produced by the reaction appears as an increase

in the temperature of the gases before they expand from their original volume. Note that the

molar heat capacity of the gases is assumed to be 29.10 J/mol K.

4. What is the pressure of the gases confined to the original 1.00 cm3 volume after the temperature

increases from room temperature, 25.0C (= Ti), but before the container bursts? Report your

answer in units of atm. Hint: find Tf first.

5. Calculate the volume of the hot gases (at Tf in #5) after the container has burst. The pressure is

then atmospheric pressure (1.00 atm). Report your answer in units of L.

Comment: It is clear that the assumptions used in this exercise greatly over-simplify the problem. However, they do

illustrate the large energy release, and convey an idea about the high temperatures and pressures that are achieved as a result

of an explosion. Concepts required for a more sophisticated treatment, such as chemical reaction rates or the response of

materials to various forces, will be examined next semester, and in future physics and engineering courses.

T =

P =

V =