P
-4.2
cReference 2.
Silicon
Si
0
Titanium
Ti
0
Organic Compoundsc
RATES OF CHEMICAL REACTIONS
Lactose (hydrate)
C12H22 0 11'H2O
-651
Shellac
C16H24 0 5
-227
The preceding section discussed how the chemist can make a ther-Hexachloroethane
C ' C1'
- 54
modynamic determination of the spontaneity of a chemical reaction.
Starch (polymer)
(C6H1005)n
-227 (per unit)
However, even if these calculations indicate that a reaction should Anthracene
C14H10
+32
be quite spontaneous (the value for oG is a large, negative num-Polyvinyl chloride (PVC)
(-CH 2CHC1-) n
-23 (per unit)b
ber), there is no guarantee that the reaction will proceed rapidly
2 8
Chemistry o f Pyrotechnics Basic Chemical Principles
29
when the reactants are mixed together at 25°C (298 K). For ex-A+ B -- C+D
ample, the reaction
Wood + 0 2 } CO 2 + H O
2
has a large, negative value for AG at 25 0 C. However (fortunately!) wood and oxygen are reasonably stable when mixed together at 25°C (a typical room temperature). The explanation of this thermodynamic mystery lies in another energy concept known as the energy of activation.
This term represents that amount of en-
ergy needed to take the starting materials from their reasonably FREE
stable form at 25°C and convert them to a reactive, higher-energy ENERGY,
excited state. In this excited state, a reaction will occur to form G
the anticipated products, with the liberation of considerable energy - all that was required to reach the excited state, plus more.
Figure 2.1 illustrates this process.
The rate of a chemical reaction is determined by the magnitude C+ D
of this required activation energy, and rate is a temperature-de-
( PRODUCTS)
pendent phenomenon. As the temperature of a system is raised, an exponentially-greater number of molecules will possess the necessary energy of activation. The reaction rate will therefore increase accordingly in an exponential fashion as the temperature rises.
This is illustrated in Figure 2.2.
Much of the pioneering
work in the area of reaction rates was done by the Swedish chem-REACTION PROGRESS
ist Svante Arrhenius, and the equation describing this rate-temperature relationship is known as the Arrhenius Equation FIG. 2.1 The free energy, G, of a chemical system as reactants Ea/RT
A and B convert to products C and D. A and B must first acquire k = Ae
(2.3)
sufficient energy ("activation energy") to be in a reactive state.
As products C and D are formed, energy is released and the where
final energy level is reached.
The net energy change, AG,
k
the rate constant for a particular reaction at temperature corresponds to the difference between the energies of the prod-T. (This is a constant representing the speed of the re-ucts and reactants. The rate at which a reaction proceeds is de-action, and is determined experimentally.)
termined by the energy barrier that must be crossed - the acti-A = a temperature-independent constant for the particular revation energy.
action, termed the "pre-exponential factor."
E a = the activation energy for the reaction.
R = a universal constant known as the "ideal gas constant."
T = temperature, in degrees Kelvin.
i
If the natural logarithm On) of both sides of equation (2.3) be obtained, with slope of -Ea /R .
Activation energies can be
is taken, one obtains
obtained for chemical reactions through such experiments. The Arrhenius Equation, describing the rate-temperature relation-In k = In A - Ea/RT
(2.4)
ship, is of considerable significance in the ignition of pyro-Therefore, if the rate constant, k, is measured at several tem-technics and explosives, and it will be referred to in subse-peratures and in k versus l /T is plotted, a straight line should quent chapters.
3 0
Chemistry of Pyrotechnics
Basic Chemical Principles
31
RATE,
(MOLES/SEC)
Picric acid
FIG. 2. 3 Many "unstable" organic compounds are used as explosives. These molecules contain internal oxygen, usually bonded TEMPERATURE, K
to nitrogen, and undergo intramolecular oxidation-reduction to form stable products - carbon dioxide, nitrogen, and water.
FIG. 2.2 The effect of temperature on reaction rate. As the tem-The "mixing" of oxidizer and fuel is achieved at the molecular perature of a chemical system is increased, the rate at which that level, and fast rates of decomposition can be obtained.
system reacts to form products increases exponentially.
large positive numbers indicate electron deficiency. It is there-ENERGY-RICH BONDS
fore not surprising that structures with such.bonding arrange-ments are particularly reactive as electron acceptors (oxidizers).
Certain covalent chemical bonds (such as N-O and Cl-O) are par-It is for similar reasons that many of the nitrated carbon-contain-ticularly common in the high-energy field. Bonds between two ing ("organic") compounds, such as nitroglycerine and TNT, are highly electronegative atoms tend to be less stable than ones be-so unstable (Figure 2.3). The nitrogen atoms in these molecules tween atoms of differing electronegativity. The intense competi-want to accept electrons to relieve bonding stress, and the car-tion for the electron density in a bond such as Cl-O is believed bon atoms found in the same molecules are excellent electron do-to be responsible for at least some of this instability. A modern nors. Two very stable gaseous (high entropy) chemical species, chemical bonding theory known as the "molecular orbital theory"
N2 and C02 , are produced upon decomposition of most nitrated predicts inherent instability for some common high-energy spe-carbon-containing compounds, helping to insure a large, nega-cies. The azide ion,