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.
Classification by type of explosion
Explosives are distinguished between high explosives, which detonate, and low explosives, which deflagrate:
- Low Explosives burn through deflagration rather than a detonation wave, are usually a mixture, are initiated by heat and require confinement to create an explosion; and
- High Explosives explode in supersonic reactions and without confinement, are compounds, are initiated by shock or heat and have high brisance (the shattering effect of an explosion).
Note that some explosive materials can fall into either category, according to how they are initiated. For example, nitrocellulose deflagrates if ignited, but detonates if initiated by a strong detonator.
Classification by composition of the material
Mixtures of an oxidizer and a fuel
- gunpowder: potassium nitrate, charcoal and sulphur
- ammonal: ammonium nitrate and aluminium powder.
- ANFO: ammonium nitrate and fuel oil.
- cheddites: chlorates or perchlorates and oil
- Sprengel explosives: a very general class incorporating any strong oxidiser and highly reactive fuel, although in practice the name most commonly was applied to mixtures of chlorates and nitroaromatics
Chemically pure compounds, often mixed with stabilizers
- dynamite: nitroglycerin mixed into a paste with powdered silica, which acts as a stabilizer.
- RDX, PETN: very strong explosives which can be used pure.
- C-4: plastic explosive. Adhesive properties.
- acetone peroxide Simple to make using household items.
Classification by sensitivity of the material
Explosives are classified by their sensitivity, which is the amount of energy to initiate the reaction. This energy can be anything, from a shock, an impact, a friction, an electrical discharge, or the detonation of another explosive. There are two basic divisions on sensitivity:
They are extremely sensitive and require a small quantity of energy to be initiated. They are mainly used in detonators to initiate secondary explosives (Examples: tetryl, Lead azide, Mercury fulminate, lead styphnate, tetrazene, hexanitromannitol).
They are relatively insensitive and need a great amount of energy to initiate decomposition. They have much more power than primary explosives and are used in demolition. The require a detonator to explode. (Examples: Dynamite, TNT, RDX, PETN, HMX, ammonium nitrate, tetryl, picric acid, nitrocellulose, gelignite). Some secondary explosives are insensitive enough that they can be lit with a match -- or a torch -- and will simply burn like wood; a detonation wave is never formed.
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.
Characteristics of Explosions
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.
The following extensive text is adapted from a U.S. Navy public domain document, namely
- Fundamentals of Naval Weapons Systems, Chapter 12, by the Weapons and Systems Engineering Department of the United States Naval Academy
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:
- Formation of gases
- 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.
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.
Categories Of Chemical Explosives
Explosives are classified as low or high explosives according to their rates of decomposition. Low explosives burn rapidly (or deflagrate). High explosives ordinarily detonate. There is no sharp line of demarcation between low and high explosives. 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 of almost instantaneous decomposition. 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. For convenience, low and high explosives may be differentiated in the following manner.
These are normally employed as propellants. They undergo autocombustion at rates that vary from a few centimeters per second to approximately 400 meters per second. Included in this group are smokeless powders, which will be discussed in a later chapter, and pyrotechnics such as flares and illumination devices.
These are normally employed in 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:
- Original. These are extremely sensitive to shock, friction, and heat. They will burn rapidly or detonate if ignited.
- Secondary. These are relatively insensitive to shock, friction, and heat. They may burn when ignited in small, unconfined quantities; detonation occurs otherwise.
Characteristics Of 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.
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 is 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 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 becomes 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.
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 test 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.
- Infinite 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 interpolated 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
RBE = Ks
where K = bubble expansion period for experimental (x) or standard (s) charge.
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.
Density of loading refers to the unit weight of an explosive per unit volume. Several methods of loading are available, and the one used is determined by the characteristics of the explosive. The methods available include pellet loading, cast loading, or press loading. Dependent upon the method employed, an average density of the loaded charge can be obtained that is within 80_95% of the theoretical maximum density of the explosive. High load density can reduce sensitivity by making the mass more resistant to internal friction. If density is increased to the extent that individual crystals are crushed, the explosive will become more sensitive. Increased load density also permits the use of more explosive, thereby increasing the strength of the warhead.
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.
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.
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 gram atoms of oxygen that are excess or deficient for 100 grams of a compound.
OB% = (_1600 / Mol. wt. of compound) * (2X + (Y/2) + M _ Z)
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)
OB% = (_1600 / 227.1) * (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.
Table 12-2. Order of Priorities
|Priority ||Composition of Explosive Products of Decomposition |
|1 ||A metal and chlorine Metallic chloride(solid) |
|2 ||Hydrogen and chlorine HCl (gaseous) |
|3 ||A metal and oxygen Metallic oxide (solid) |
|4 ||Carbon and oxygen CO (gaseous) |
|5 ||Hydrogen and oxygen H2O (gaseous) |
|6 ||CO and oxygen CO2 (gaseous) |
|7 ||Nitrogen N2 (elemental) |
|8 ||Excess oxygen O2 (elemental) |
|9 ||Excess hydrogen H2 (elemental) |
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. Since reactions may occur either under conditions of constant pressure or constant volume, the heat of reaciton can be expressed at constant pressure or at 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.
- 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 molecular volume of one gas is equal to the molecular volume of any other gas. The molecular 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 + .25O2
the explosion of one gram molecule of nitroglycerin produces in the gaseous state: 3 gram molecules of CO2; 2.5 gram molecules of O2. Since a molecular volume is the volume of one gram molecule of gas, one gram molecule of nitroglycerin produces 3 + 2.5 + 1.5 + .25 = 7.25 molecular volumes of gas; and these molecular volumes at 0 °C and atmospheric pressure form an actual volume of 7.25 X 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 of its volume at 0 °C, for each degree of rise in temperature.
Therefore, at 15 °C the molecular volume of any gas is,
- V15 = 22.4 (1 + 15/273) = 23.63 liters per mol
Thus, at 15 °C the volume of gas produced by the explosive decomposition of one gram molecule of nitroglycerin becomes
- V = 23.63 l (7.25 mol) = 171.3 liters/mol
Potential and Relative Strength of the Explosive
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.
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.
Qmp = viQfi - vkQfk
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.
- C6H2(NO2)3CH3 → 6CO + 2.5H2 + 1.5N2 + C
for 10 mol
- 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)
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
- MW = 316.15 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 molecular volumes of gas per gram molecule. Since the molecular volume of one gas is equal to the molecular volume of any other gas, and since all the products of the PETN reaction are gaseous, the re-sulting number of molecular volumes of gas (Nm) is:
- Nm = 2 + 4 + 3 + 2 = 11 mol-volume/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(26.43) + 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 = 0.572(Nm) = 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
This product may then be used to find the relative strength of PETN, which is
- e. RS = Pot (PETN = 6.01 × 106 = 2.21 Pot (TNT) 2.72 × 106
Army Research Office. Elements of Armament Engineering (Part One). Washington, D.C.: U.S. Army Material Command, 1964.
Commander, Naval Ordnance Systems Command. Safety and Performance Tests for Qualification of Explosives. NAVORD OD 44811. Washington, D.C.: GPO, 1972.
Commander, Naval Ordnance Systems Command. Weapons Systems Fundamentals. NAVORD OP 3000, vol. 2, 1st Rev. Washington, D.C.: GPO, 1971.
Departments of the Army and Air Force. Military Explosives. Washington, D.C.: 1967.