# Explosive material

(Redirected from Explosive)
This article is concerned solely with chemical explosives. There are many other varieties of more exotic explosive material, and theoretical methods of causing explosions such as nuclear explosives and antimatter, and other methods of producing explosions, such as abrupt heating with a high-intensity laser or electric arc.

Any explosive material has the following characteristics:

• It is chemically or otherwise energetically unstable.
• The initiation produces a sudden expansion of the material accompanied by the production of heat and large changes in pressure (and typically also a flash or loud noise) which is called the explosion.

## Chemical explosives

Explosives are classified as low or high explosives according to their rates of decomposition. Low explosives burn rapidly (or deflagrate). High explosives undergo detonation. There is no sharp line of demarcation between low and high explosives, due to the difficulties inherent in precisely observing and measuring rapid decomposition. The chemical decomposition of an explosive may take years, days, hours, or a fraction of a second. The slower forms of decomposition take place in storage and are of interest only from a stability standpoint. Of more interest are the two rapid forms of decomposition, burning and detonation. The term "detonation" is used to describe an explosive phenomenon whereby the decomposition is propagated by the explosive shockwave penetrating the explosive material. The shockwave front is capable of passing through the high explosive material at massive speeds. Explosive force is released at 90 degree angles from the surface of an explosive. If the surface is cut or shaped the explosive forces can be focused directionally, and will produce a greater effect. This is known as a shaped charge. In a low explosive, the decomposition is propagated by a flame front which travels much slower through the explosive material. The properties of the explosive indicate the class into which it falls. In some cases explosives may be made to fall into either class by the conditions under which they are initiated. Almost all low explosives can undergo true detonation like high explosives in sufficiently massive quantities. For convenience, low and high explosives may be differentiated by the shipping and storage classes.

### Explosive compatibility groupings

Explosives warning sign

Shipping tags will include a UN or US DOT hazardous material class with compatibility letter as follows.

• 1.1 Mass Explosion Hazard
• 1.2 Nonmass explosion, fragment-producing
• 1.3 Mass fire, minor blast or fragment hazard
• 1.4 Moderate fire, no blast or fragment: consumer fireworks are 1.4G or 1.4S
• 1.5 Explosive substance, very insensitive (with a mass explosion hazard)
• 1.6 Explosive article, extremely insensitive

A Primary explosive substance (1.1A, 1.2A)

B An article containing a primary explosive substance and not containing two or more effective protective features. Some articles, such as detonator assemblies for blasting and primers, cap-type, are included. (1.1B, 1.2B, 1.4B)

C Propellant explosive substance or other deflagrating explosive substance or article containing such explosive substance (1.1C, 1.2C, 1.3C, 1.4C)

D Secondary detonating explosive substance or black powder or article containing a secondary detonating explosive substance, in each case without means of initiation and without a propelling charge, or article containing a primary explosive substance and containing two or more effective protective features. (1.1D, 1.2D, 1.4D, 1.5D)

E Article containing a secondary detonating explosive substance without means of initiation, with a propelling charge (other than one containing flammable liquid, gel or hypergolic liquid) (1.1E, 1.2E, 1.4E)

F Article containing a secondary detonating explosive substance with its means of initiation, with a propelling charge (other than one containing flammable liquid, gel or hypergolic liquid) or without a propelling charge (1.1F, 1.2F, 1.3F, 1.4F)

G Pyrotechnic substance or article containing a pyrotechnic substance, or article containing both an explosive substance and an illuminating, incendiary, tear-producing or smoke-producing substance (other than a water-activated article or one containing white phosphorus, phosphide or flammable liquid or gel or hypergolic liquid) (1.1G, 1.2G, 1.3G, 1.4G)

H Article containing both an explosive substance and white phosphorus (1.2H, 1.3H)

J Article containing both an explosive substance and flammable liquid or gel (1.1J, 1.2J, 1.3J)

K Article containing both an explosive substance and a toxic chemical agent (1.2K, 1.3K)

L Explosive substance or article containing an explosive substance and presenting a special risk (e.g., due to water-activation or presence of hypergolic liquids, phosphides or pyrophoric substances) needing isolation of each type (1.1L, 1.2L, 1.3L)

N Articles containing only extremely insensitive detonating substances (1.6N)

S Substance or article so packed or designed that any hazardous effects arising from accidental functioning are limited to the extent that they do not significantly hinder or prohibit fire fighting or other emergency response efforts in the immediate vicinity of the package (1.4S)

### Low Explosives

Low explosives are normally employed as propellants. Most low explosives are mixtures; most high explosives are compounds, but to both there are notable exceptions. They undergo deflagration at rates that vary from a few centimeters per second to approximately 400 meters per second. Included in this group are smokeless powders, and pyrotechnics such as flares and illumination devices.

### High Explosives

High explosives are normally employed in mining, demolitions and military warheads. They undergo detonation at rates of 1,000 to 8,500 meters per second. High explosives are conventionally subdivided into two classes and differentiated by sensitivity:

• Primary explosives are extremely sensitive to shock, friction, and heat. They will burn rapidly or detonate if ignited.
• Secondary or Base explosives are relatively insensitive to shock, friction, and heat. They may burn when ignited in small, unconfined quantities, but detonation can occur. These are sometimes added in small amount to blasting caps to boost their power. Dynamite, RDX, PETN, HMX, and others are secondary explosives.

Some definitions add a third category:

• Tertiary, also called blasting agents. These are so insensitive to shock that they cannot be detonated by practical quantities of primary explosive, and instead require an intermediate explosive booster of secondary explosive. Some examples would be TNT (trinitrotoluene), ammonium nitrate, and slurry explosives.

Note that many if not most explosive chemical compounds may usefully deflagrate as well as detonate, and are used in high as well as low explosive compositions. This also means that under extreme conditions, propellant can detonate. For example, nitrocellulose deflagrates if ignited, but detonates if initiated by a detonator.

#### Detonation of an Explosive Charge

Also called an initiation sequence or a firing train, this is the sequence of events which cascade from relatively low levels of energy to cause a chain reaction to initiate the final explosive material or main charge. They can be either low or high explosive trains. Low explosive trains are something like a bullet - Primer and a propellant charge. High explosives trains can be more complex, either Two-Step (e.g. Detonator and Dynamite) or Three-Step (e.g. Detonator, Booster and ANFO). Detonators are often made from tetryl and Fulminates.

### Composition of the material

Mixtures of an oxidizer and a fuel

Chemically pure compounds

## Chemical explosive reaction

A chemical explosive is a compound or mixture which, upon the application of heat or shock, decomposes or rearranges with extreme rapidity, yielding much gas and heat. Many substances not ordinarily classed as explosives may do one, or even two, of these things. For example, a mixture of nitrogen and oxygen can be made to react with great rapidity and yield the gaseous product nitric oxide; yet the mixture is not an explosive since it does not evolve heat, but rather absorbs heat.

N2 + O2 → 2NO - 43,200 calories (or 180 kJ) per mole of N2

For a chemical to be an explosive, it must exhibit all of the following:

• Exhibit Rapid Expansion (eg. rapid production of gasses or rapid heating of surroundings)
• Evolution of heat
• Rapidity of reaction
• Initiation of reaction

### Formation of gases

Gases may be evolved from substances in a variety of ways. When wood or coal is burned in the atmosphere, the carbon and hydrogen in the fuel combine with the oxygen in the atmosphere to form carbon dioxide and steam, together with flame and smoke. When the wood or coal is pulverized, so that the total surface in contact with the oxygen is increased, and burned in a furnace or forge where more air can be supplied, the burning can be made more rapid and the combustion more complete. When the wood or coal is immersed in liquid oxygen or suspended in air in the form of dust, the burning takes place with explosive violence. In each case, the same action occurs: a burning combustible forms a gas.

### Evolution of heat

The generation of heat in large quantities accompanies every explosive chemical reaction. It is this rapid liberation of heat that causes the gaseous products of reaction to expand and generate high pressures. This rapid generation of high pressures of the released gas constitutes the explosion. It should be noted that the liberation of heat with insufficient rapidity will not cause an explosion. For example, although a pound of coal yields five times as much heat as a pound of nitroglycerin, the coal cannot be used as an explosive because the rate at which it yields this heat is quite slow.

### Rapidity of reaction

Rapidity of reaction distinguishes the explosive reaction from an ordinary combustion reaction by the great speed with which it takes place. Unless the reaction occurs rapidly, the thermally expanded gases will be dissipated in the medium, and there will be no explosion. Again, consider a wood or coal fire. As the fire burns, there is the evolution of heat and the formation of gases, but neither is liberated rapidly enough to cause an explosion. For those who know something about electronics, this can be likened to the energy discharge of a battery, which is slow; to a flash capacitor, like that in a camera flash and releases its energy all at once.

### Initiation of reaction

A reaction must be capable of being initiated by the application of shock or heat to a small portion of the mass of the explosive material. A material in which the first three factors exist cannot be accepted as an explosive unless the reaction can be made to occur when desired.

## Military explosives

To determine the suitability of an explosive substance for military use, its physical properties must first be investigated. The usefulness of a military explosive can only be appreciated when these properties and the factors affecting them are fully understood. Many explosives have been studied in past years to determine their suitability for military use and most have been found wanting. Several of those found acceptable have displayed certain characteristics that are considered undesirable and, therefore, limit their usefulness in military applications. The requirements of a military explosive are stringent, and very few explosives display all of the characteristics necessary to make them acceptable for military standardization. Some of the more important characteristics are discussed below:

### Availability and cost

In view of the enormous quantity demands of modern warfare, explosives must be produced from cheap raw materials that are nonstrategic and available in great quantity. In addition, manufacturing operations must be reasonably simple, cheap, and safe.

### Sensitivity

Regarding an explosive, this refers to the ease with which it can be ignited or detonated—i.e., the amount and intensity of shock, friction, or heat that is required. When the term sensitivity is used, care must be taken to clarify what kind of sensitivity is under discussion. The relative sensitivity of a given explosive to impact may vary greatly from its sensitivity to friction or heat. Some of the test methods used to determine sensitivity are as follows:

• Impact. Sensitivity is expressed in terms of the distance through which a standard weight must be dropped to cause the material to explode.
• Friction. Sensitivity is expressed in terms of what occurs when a weighted pendulum scrapes across the material (snaps, crackles, ignites, and/or explodes).
• Heat. Sensitivity is expressed in terms of the temperature at which flashing or explosion of the material occurs.

Sensitivity is an important consideration in selecting an explosive for a particular purpose. The explosive in an armor-piercing projectile must be relatively insensitive, or the shock of impact would cause it to detonate before it penetrated to the point desired.

### Stability

Stability is the ability of an explosive to be stored without deterioration. The following factors affect the stability of an explosive:

• Chemical constitution. The very fact that some common chemical compounds can undergo explosion when heated indicates that there is something unstable in their structures. While no precise explanation has been developed for this, it is generally recognized that certain groups, nitro dioxide (NO2), nitrate (NO3), and azide (N3), are intrinsically in a condition of internal strain. Increased strain through heating can cause a sudden disruption of the molecule and consequent explosion. In some cases, this condition of molecular instability is so great that decomposition takes place at ordinary temperatures.
• Temperature of storage. The rate of decomposition of explosives increases at higher temperatures. All of the standard military explosives may be considered to be of a high order of stability at temperatures of -10 to +35 °C, but each has a high temperature at which the rate of decomposition becomes rapidly accelerated and stability is reduced. As a rule of thumb, most explosives become dangerously unstable at temperatures exceeding 70 °C.
• Exposure to sun. If exposed to the ultraviolet rays of the sun, many explosive compounds that contain nitrogen groups will rapidly decompose, affecting their stability.
• Electrical discharge. Electrostatic or spark sensitivity to initiation is common to a number of explosives. Static or other electrical discharge may be sufficient to inspire detonation under some circumstances. As a result, the safe handling of explosives and pyrotechnics almost always requires electrical grounding of the operator.

### Power

The term power (or more properly, performance) as it is applied to an explosive refers to its ability to do work. In practice it is defined as its ability to accomplish what is intended in the way of energy delivery (i.e., fragments, air blast, high-velocity jets, underwater bubble energy, etc.). Explosive power or performance is evaluated by a tailored series of tests to assess the material for its intended use. Of the tests listed below, cylinder expansion and air-blast tests are common to most testing programs, and the others support specific uses.

• Cylinder expansion test. A standard amount of explosive is loaded in a cylinder usually manufactured of copper. Data is collected concerning the rate of radial expansion of the cylinder and maximum cylinder wall velocity. This also establishes the Gurney constant or 2E.
• Cylinder fragmentation test. A standard steel cylinder is charged with explosive and fired in a sawdust pit. The fragments are collected and the size distribution analyzed.
• Detonation pressure (Chapman-Jouget). Detonation pressure data derived from measurements of shock waves transmitted into water by the detonation of cylindrical explosive charges of a standard size.
• Determination of critical diameter. This test establishes the minimum physical size a charge of a specific explosive must be to sustain its own detonation wave. The procedure involves the detonation of a series of charges of different diameters until difficulty in detonation wave propagation is observed.
• Infinity diameter detonation velocity. Detonation velocity is dependent on landing density (c), charge diameter, and grain size. The hydrodynamic theory of detonation used in predicting explosive phenomena does not include diameter of the charge, and therefore a detonation velocity, for an imaginary charge of infinite diameter. This procedure requires a series of charges of the same density and physical structure, but different diameters, to be fired and the resulting detonation velocities extrapolated to predict the detonation velocity of a charge of infinite diameter.
• Pressure versus scaled distance. A charge of specific size is detonated and its pressure effects measured at a standard distance. The values obtained are compared with that for TNT.
• Impulse versus scaled distance. A charge of specific size is detonated and its impulse (the area under the pressure-time curve) measured versus distance. The results are tabulated and expressed in TNT equivalent.
• Relative bubble energy (RBE). A 5 to 50 kg charge is detonated in water and piezoelectric gauges are used to measure peak pressure, time constant, impulse, and energy.
The RBE may be defined as Kx 3
RBE = Ks
where K = bubble expansion period for experimental (x) or standard (s) charge.

### Brisance

Main article: Brisance

In addition to strength, explosives display a second characteristic, which is their shattering effect or brisance (from the French meaning to "break"), which is distinguished from their total work capacity. This characteristic is of practical importance in determining the effectiveness of an explosion in fragmenting shells, bomb casings, grenades, and the like. The rapidity with which an explosive reaches its peak pressure is a measure of its brisance. Brisance values are primarily employed in France and Russia.

The sand crush test is commonly employed to determine the relative brisance in comparison to TNT. No single test is capable of directly comparing the explosive properties of two or more compounds; it is important to examine the data from several such tests (sand crush, trauzl, and so forth) in order to gauge relative brisance. True values for comparison will require field experiments.

### Volatility

Volatility, or the readiness with which a substance vaporizes, is an undesirable characteristic in military explosives. Explosives must be no more than slightly volatile at the temperature at which they are loaded or at their highest storage temperature. Excessive volatility often results in the development of pressure within rounds of ammunition and separation of mixtures into their constituents. Stability, as mentioned before, is the ability of an explosive to stand up under storage conditions without deteriorating. Volatility affects the chemical composition of the explosive such that a marked reduction in stability may occur, which results in an increase in the danger of handling. Maximum allowable volatility is 2 ml of gas evolved in 48 hours.

### Hygroscopicity

The introduction of moisture into an explosive is highly undesirable since it reduces the sensitivity, strength, and velocity of detonation of the explosive. Hygroscopicity is used as a measure of a material's moisture-absorbing tendencies. Moisture affects explosives adversely by acting as an inert material that absorbs heat when vaporized, and by acting as a solvent medium that can cause undesired chemical reactions. Sensitivity, strength, and velocity of detonation are reduced by inert materials that reduce the continuity of the explosive mass. When the moisture content evaporates during detonation, cooling occurs, which reduces the temperature of reaction. Stability is also affected by the presence of moisture since moisture promotes decomposition of the explosive and, in addition, causes corrosion of the explosive's metal container. For all of these reasons, hygroscopicity must be negligible in military explosives.

### Toxicity

Due to their chemical structure, most explosives are toxic to some extent. Since the effect of toxicity may vary from a mild headache to serious damage of internal organs, care must be taken to limit toxicity in military explosives to a minimum. Any explosive of high toxicity is unacceptable for military use.

## Measurement of chemical explosive reaction

The development of new and improved types of ammunition requires a continuous program of research and development. Adoption of an explosive for a particular use is based upon both proving ground and service tests. Before these tests, however, preliminary estimates of the characteristics of the explosive are made. The principles of thermochemistry are applied for this process.

Thermochemistry is concerned with the changes in internal energy, principally as heat, in chemical reactions. An explosion consists of a series of reactions, highly exothermic, involving decomposition of the ingredients and recombination to form the products of explosion. Energy changes in explosive reactions are calculated either from known chemical laws or by analysis of the products.

For most common reactions, tables based on previous investigations permit rapid calculation of energy changes. Products of an explosive remaining in a closed calorimetric bomb (a constant-volume explosion) after cooling the bomb back to room temperature and pressure are rarely those present at the instant of maximum temperature and pressure. Since only the final products may be analyzed conveniently, indirect or theoretical methods are often used to determine the maximum temperature and pressure values.

Some of the important characteristics of an explosive that can be determined by such theoretical computations are:

• Oxygen balance
• Heat of explosion or reaction
• Volume of products of explosion
• Potential of the explosive

### Oxygen balance (OB%)

Oxygen balance is an expression that is used to indicate the degree to which an explosive can be oxidized. If an explosive molecule contains just enough oxygen to convert all of its carbon to carbon dioxide, all of its hydrogen to water, and all of its metal to metal oxide with no excess, the molecule is said to have a zero oxygen balance. The molecule is said to have a positive oxygen balance if it contains more oxygen than is needed and a negative oxygen balance if it contains less oxygen than is needed. The sensitivity, strength, and brisance of an explosive are all somewhat dependent upon oxygen balance and tend to approach their maximums as oxygen balance approaches zero.

The oxygen balance (OB) is calculated from the empirical formula of a compound in percentage of oxygen required for complete conversion of carbon to carbon dioxide, hydrogen to water, and metal to metal oxide.

The procedure for calculating oxygen balance in terms of 100 grams of the explosive material is to determine the number of moles of oxygen that are excess or deficient for 100 grams of a compound.

$OB% = \frac{-1600}{Mol. wt. of compound} \times (2X + (Y/2) + M - Z)$

where

X = number of atoms of carbon, Y = number of atoms of hydrogen, Z = number of atoms of oxygen, and M = number of atoms of metal (metallic oxide produced).

In the case of TNT (C6H2(NO2)3CH3),

Molecular weight = 227.1

X = 7 (number of carbon atoms)

Y = 5 (number of hydrogen atoms)

Z = 6 (number of oxygen atoms)

Therefore

$OB% = \frac{-1600}{227.1} \times (14 + 2.5 - 6)$
OB% = -74% for TNT

Because sensitivity, brisance, and strength are properties resulting from a complex explosive chemical reaction, a simple relationship such as oxygen balance cannot be depended upon to yield universally consistent results. When using oxygen balance to predict properties of one explosive relative to another, it is to be expected that one with an oxygen balance closer to zero will be the more brisant, powerful, and sensitive; however, many exceptions to this rule do exist. More complicated predictive calculations, such as those discussed in the next section, result in more accurate predictions.

One area in which oxygen balance can be applied is in the processing of mixtures of explosives. The family of explosives called amatols are mixtures of ammonium nitrate and TNT. Ammonium nitrate has an oxygen balance of +20% and TNT has an oxygen balance of −74%, so it would appear that the mixture yielding an oxygen balance of zero would also result in the best explosive properties. In actual practice a mixture of 80% ammonium nitrate and 20% TNT by weight yields an oxygen balance of +1%, the best properties of all mixtures, and an increase in strength of 30% over TNT.

### Heat of explosion

When a chemical compound is formed from its constituents, the reaction may either absorb or give off heat. The quantity of heat absorbed or given off during transformation is called the heat of formation. The heats of formations for solids and gases found in explosive reactions have been determined for a temperature of 15 °C and atmospheric pressure, and are normally tabulated in units of kilocalories per gram molecule. (See table 12-1). Where a negative value is given, it indicates that heat is absorbed during the formation of the compound from its elements. Such a reaction is called an endothermic reaction. The convention usually employed in simple thermochemical calculations is arbitrarily to take heat contents of all elements as zero in their standard states at all temperatures (standard state being defined as the state at which the elements are found under natural or ambient conditions). Since the heat of formation of a compound is the net difference between the heat content of the compound and that of its elements, and since the latter are taken as zero by convention, it follows that the heat content of a compound is equal to its heat of formation in such nonrigorous calculations. This leads us to the principle of initial and final state, which may be expressed as follows: "The net quantity of heat liberated or absorbed in any chemical modification of a system depends solely upon the initial and final states of the system, provided the transformation takes place at constant volume or at constant pressure. It is completely independent of the intermediate transformations and of the time required for the reactions."

From this it follows that the heat liberated in any transformation accomplished through successive reactions is the algebraic sum of the heats liberated or absorbed in the different reactions. Consider the formation of the original explosive from its elements as an intermediate reaction in the formation of the products of explosion. The net amount of heat liberated during an explosion is the sum of the heats of formation of the products of explosion, minus the heat of formation of the original explosive.

The net heat difference between heats of formations of the reactants and products in a chemical reaction is termed the heat of reaction. For oxidation this heat of reaction may be termed heat of combustion.

In explosive technology only materials that are exothermic — that is, have a heat of reaction that causes net liberation of heat — are of interest. Hence, in this text, heats of reaction are virtually all positive. Reaction heat is measured under conditions either of constant pressure or constant volume. It is this heat of reaction that may be properly expressed as "heat of the explosion."

### Balancing chemical explosion equations

In order to assist in balancing chemical equations, an order of priorities is presented in table 12-2. Explosives containing C, H, O, and N and/or a metal will form the products of reaction in the priority sequence shown. Some observation you might want to make as you balance an equation:

• The progression is from top to bottom; you may skip steps that are not applicable, but you never back up.
• At each separate step there are never more than two compositions and two products.
• At the conclusion of the balancing, elemental forms, nitrogen, oxygen, and hydrogen, are always found in diatomic form.
Table 12-2. Order of Priorities
Priority Composition of explosive Products of decomposition Phase of products
1 A metal and chlorine Metallic chloride Solid
2 Hydrogen and chlorine HCl Gas
3 A metal and oxygen Metallic oxide Solid
4 Carbon and oxygen CO Gas
5 Hydrogen and oxygen H2O Gas
6 Carbon monoxide and oxygen CO2 Gas
7 Nitrogen N2 Gas
8 Excess oxygen O2 Gas
9 Excess hydrogen H2 Gas

Example, TNT:

C6H2(NO2)3CH3; constituents: 7C + 5H + 3N + 6O

Using the order of priorities in table 12-1, priority 4 gives the first reaction products:

7C + 6O → 6CO with one mol of carbon remaining

Next, since all the oxygen has been combined with the carbon to form CO, priority 7 results in:

3N → 1.5N2

Finally, priority 9 results in: 5H → 2.5H2

The balanced equation, showing the products of reaction resulting from the detonation of TNT is:

C6H2(NO2)3CH3 → 6CO + 2.5H2 + 1.5N2 + C

Notice that partial moles are permitted in these calculations. The number of moles of gas formed is 10. The product, carbon, is a solid.

### Volume of products of explosion

The law of Avogadro states that equal volumes of all gases under the same conditions of temperature and pressure contain the same number of molecules. From this law, it follows that the molar volume of one gas is equal to the molar volume of any other gas. The molar volume of any gas at 0 °C and under normal atmospheric pressure is very nearly 22.4 liters or 22.4 cubic decimeters. Thus, considering the nitroglycerin reaction.

C3H5(NO3)3 → 3CO2 + 2.5H2O + 1.5N2 + 0.25O2

the explosion of one mole of nitroglycerin produces in the gaseous state: 3 moles of CO2; 2.5 moles of O2. Since a molar volume is the volume of one mole of gas, one mole of nitroglycerin produces 3 + 2.5 + 1.5 + 0.25 = 7.25 molar volumes of gas; and these molar volumes at 0 °C and atmospheric pressure form an actual volume of 7.25 × 22.4 = 162.4 liters of gas. (Note that the products H2O and CO2 are in their gaseous form.)

Based upon this simple beginning, it can be seen that the volume of the products of explosion can be predicted for any quantity of the explosive. Further, by employing Charles' Law for perfect gases, the volume of the products of explosion may also be calculated for any given temperature. This law states that at a constant pressure a perfect gas expands 1/273.15 of its volume at 0 °C, for each degree Celsius of rise in temperature.

Therefore, at 15 °C the molar volume of an ideal gas is,

V15 = 22.414 (288.15/273273.15) = 23.64 liters per mole

Thus, at 15 °C the volume of gas produced by the explosive decomposition of one mole of nitroglycerin becomes

V = (23.64 l/mol)(7.25 mol) = 171.4 l

### Explosive strength

The potential of an explosive is the total work that can be performed by the gas resulting from its explosion, when expanded adiabatically from its original volume, until its pressure is reduced to atmospheric pressure and its temperature to 15 °C. The potential is therefore the total quantity of heat given off at constant volume when expressed in equivalent work units and is a measure of the strength of the explosive.

An explosion may occur under two general conditions: the first, unconfined, as in the open air where the pressure (atmospheric) is constant; the second, confined, as in a closed chamber where the volume is constant. The same amount of heat energy is liberated in each case, but in the unconfined explosion, a certain amount is used as work energy in pushing back the surrounding air, and therefore is lost as heat. In a confined explosion, where the explosive volume is small (such as occurs in the powder chamber of a firearm), practically all the heat of explosion is conserved as useful energy. If the quantity of heat liberated at constant volume under adiabatic conditions is calculated and converted from heat units to equivalent work units, the potential or capacity for work results.

Therefore, if

Qmp represents the total quantity of heat given off by a mole of explosive of 15 °C and constant pressure (atmospheric);

Qmv represents the total heat given off by a mole of explosive at 15 °C and constant volume; and

W represents the work energy expended in pushing back the surrounding air in an unconfined explosion and thus is not available as net theoretical heat;

Then, because of the conversion of energy to work in the constant pressure case,

Qmv = Qmp + W

from which the value of Qmv may be determined. Subsequently, the potential of a mole of an explosive may be calculated. Using this value, the potential for any other weight of explosive may be determined by simple proportion.

Using the principle of the initial and final state, and heat of formation table (resulting from experimental data), the heat released at constant pressure may be readily calculated.

m n

Qmp = viQfi - vkQfk

1 1

where:

Qfi = heat of formation of product i at constant pressure

Qfk = heat of formation of reactant k at constant pressure

v = number of moles of each product/reactants (m is the number of products and n the number of reactants)

The work energy expended by the gaseous products of detonation is expressed by:

W = P dv

With pressure constant and negligible initial volume, this expression reduces to:

W = P·V2

Since heats of formation are calculated for standard atmospheric pressure (101 325 Pa, where 1 Pa = 1 N/m²) and 15 °C, V2 is the volume occupied by the product gases under these conditions. At this point

W/mol = (101 325 N/m²)(23.63 L/mol)(1 m³/1000 L) = 2394 N·m/mol = 2394 J/mol

and by applying the appropriate conversion factors, work can be converted to units of kilocalories.

W/mol = 0.572 kcal/mol

Once the chemical reaction has been balanced, one can calculate the volume of gas produced and the work of expansion. With this completed, the calculations necessary to determine potential may be accomplished.

For TNT:

C6H2(NO2)3CH3 → 6CO + 2.5H2 + 1.5N2 + C

for 10 mol

Then:

Qmp = 6(26.43) - 16.5 = 142.08 kcal/mol

Note: Elements in their natural state (H2, O2, N2, C, etc.) are used as the basis for heat of formation tables and are assigned a value of zero. See table 12-2.

Qmv = 142.08 + 0.572(10) = 147.8 kcal/mol

As previously stated, Qmv converted to equivalent work units is the potential of the explosive. (MW = Molecular Weight of Explosive)

Potential = Qmv kcal/mol × 4185 J/kcal × 103 g/kg × 1 mol/(mol·g)

Potential = Qmv (4.185 × 106) J/(mol·kg)

For TNT,

Potential = 147.8 (4.185 × 106)/227.1 = 2.72 × 106 J/kg

Rather than tabulate such large numbers, in the field of explosives, TNT is taken as the standard explosive, and others are assigned strengths relative to that of TNT. The potential of TNT has been calculated above to be 2.72 × 106 J/kg. Relative strength (RS) may be expressed as

R.S. = Potential of Explosive/(2.72 × 106)

### Example of thermochemical calculations

The PETN reaction will be examined as an example of thermo-chemical calculations.

PETN: C(CH2ONO2)4
Molecular weight = 316.15 g/mol
Heat of formation = 119.4 kcal/mol

(1) Balance the chemical reaction equation. Using table 12-1, priority 4 gives the first reaction products:

5C + 12O → 5CO + 7O

Next, the hydrogen combines with remaining oxygen:

8H + 7O → 4H2O + 3O

Then the remaining oxygen will combine with the CO to form CO and CO2.

5CO + 3O → 2CO + 3CO2

Finally the remaining nitrogen forms in its natural state (N2).

4N → 2N2

The balanced reaction equation is:

C(CH2ONO2)4 → 2CO + 4H2O + 3CO2 + 2N2

(2) Determine the number of molar volumes of gas per mole. Since the molar volume of one gas is equal to the molar volume of any other gas, and since all the products of the PETN reaction are gaseous, the resulting number of molar volumes of gas (Nm) is:

Nm = 2 + 4 + 3 + 2 = 11 Vmolar/mol

(3) Determine the potential (capacity for doing work). If the total heat liberated by an explosive under constant volume conditions (Qm) is converted to the equivalent work units, the result is the potential of that explosive.

The heat liberated at constant volume (Qmv) is equivalent to the liberated at constant pressure (Qmp) plus that heat converted to work in expanding the surrounding medium. Hence, Qmv = Qmp + work (converted).

a. Qmp = Qfi (products) - Qfk (reactants)
where: Qf = heat of formation (see table 12-2)
For the PETN reaction:
Qmp = 2(26.343) + 4(57.81) + 3(94.39) - (119.4) = 447.87 kcal/mol
(If the compound produced a metallic oxide, that heat of formation would be included in Qmp.
b. Work = 0.572Nm = 0.572(11) = 6.292 kcal/mol
As previously stated, Qmv converted to equivalent work units is taken as the potential of the explosive.
c. Potential J = Qmv (4.185 × 106 kg)(MW) = 454.16 (4.185 × 106) 316.15 = 6.01 × 106 J kg
This product may then be used to find the relative strength (RS) of PETN, which is
d. RS = Pot (PETN) = 6.01 × 106 = 2.21 Pot (TNT) 2.72 × 106