## What are the most energetic combustible materials?

Most people have seen several examples of combustion reactions that produce different flame temperatures. The temperature of a campfire can be somewhat over 800 deg C, while the flame of an oxyacetylene torch in welding can reach a temperature of over 3000 deg C. The energeticity of combustion reactions can be quantified in several ways:

1. Maximum temperature of the flame that is produced
2. Amount of heat released in combustion (per unit mass or volume of fuel)
3. In the cases of gaseous fuels, aerosols or vapors, the magnitude of sudden pressure increase in the explosion of fuel-oxygen mixture

Note that the amount of heat released per mole of fuel is not a good measure of the energeticity, as you can make the molar heat of combustion of an organic compound practically as large as you want by building longer and longer hydrocarbon chains.

The heat release of combustion reactions, more formally called enthalpy of combustion $\Delta H_c$, is rather easy to measure in the laboratory using a calorimeter. A typical example of a combustion reaction is the burning of methane, described by the reaction equation below: $CH_4 + 2O_2 \rightarrow CO_2 + 2H_2 O$ .

The enthalpy change in this reaction can be calculated from the enthalpies of formation ( $\Delta H_f$) of the reactants and products, which can be found from tables of thermodynamic quantities (in books or online). The enthalpy change in the combustion of a mole of methane is $\Delta_c (CH_4) = \Delta H_f(CO_2 ) + 2\Delta H_f(H_2 O) - \Delta H_f (CH_4 )$,

where the enthalpy of formation of elemental oxygen has not been included as it is zero (as is the $\Delta H_f$ of any element in its most stable form).

The thermodynamic quantities in this are $\Delta H_f(CO_2 ) = -393 kJ/mol$ $\Delta H_f(H_2 O) = -242 kJ/mol$ $\Delta H_f(CH_4 ) = -74.9 kJ/mol$

which give a value of about -802 kJ/mol or -50 kJ/g for the quantity $\Delta H_c (CH_4 )$. An enthalpy change that is negative means that heat is released to the surroundings by the reaction. The formal definition of enthalpy is $H=E+PV$, or internal energy plus pressure times volume, and in constant-pressure processes of simple systems its change is $\Delta H = \Delta E + P\Delta V$. A system that is “simple” in the sense meant here can do work on the surroundings only by expanding: $W = -P\Delta V$. Some systems can do other kinds of work, too, like elastic deformation (which can require an application of force over some distance even without involving a change of volume) or electrical work (charging a battery).

As the heat of combustion increases linearly with increasing $\Delta H_f$:s of the products and decreases linearly with increasing $\Delta H_f$:s of the reactants, the most energetic fuels are those that have a positive heat of formation, which means that energy is consumed when they are formed from their elemental constituents. Straight-chain alkane hydrocarbons like ethane, propane and butane all have negative heats of formation. To make a hydrocarbon that has a positive $\Delta H_f$, we need to have triple bonds between carbon atoms, or highly strained carbon-carbon bonds (such as in small alicyclic rings). An example of the former case is acetylene C2H2, for which $\Delta H_f = 227.4 kJ/mol = 8.7 kJ/g$ and an example of the latter is cyclopropane $(C_3 H_6)$, for which $\Delta H_f = 53.2 kJ/mol = 1.26 kJ/g$. Cyclopropane was used in the past as an anesthetic gas in surgical operations, but this use was discontinued because of the fire/explosion hazard related to it. In addition to molecules with small ring structures, there are also other molecules with large “steric hindrance” like tetra-tert-butylmethane or cubane that have or are predicted to have a positive heat of formation.

Inorganic combustible substances with positive $\Delta H_f$ include hydrazine ( $N_2 H_4$) and cyanogen ( $C_2 N_2$). Both are nasty toxic compounds, and hydrazine can also explode when heated, even with no oxygen present, as it decomposes violently to elemental hydrogen and nitrogen if it’s given enough activation energy (this can happen with acetylene, too). Cyanogen is a gaseous compound that is formed from two cyano groups (-CN). The cyano group is called a pseudohalogen, as it is often found in organic molecules in positions where there could also be a halogen (fluorine, chlorine, bromine or iodine) atom (see chlorobenzene and cyanobenzene). A stoichiometric mixture of cyanogen and oxygen can reach a flame temperature of about 4500 degrees Celsius.  Figure 1. Molecular structures of cyanobenzene (left) and chlorobenzene (right).

Reactive metals like magnesium or aluminum often have large heats of combustion, for example the $\Delta H_c (Al)$ is about -838 kJ/mol or -31 kJ/g which is less per gram than the typical values of hydrocarbons, but more per unit volume because Al metal has a significantly higher density than liquefied hydrocarbons. Aluminum is not something that a layman would think of as a combustible fuel, but it is actually very flammable when it’s in the form of very fine powder, and it is used in thermite mixtures and flash powders (pyrotechnic mixtures of Al powder with oxidizers such as potassium perchlorate, which produce a very loud bang and a temperature of over 3000 deg C when ignited in a confined space). Figure 2. Magnesium metal burns with a really high-temperature flame, which makes it useful in firestarters (source: https://en.wikipedia.org/wiki/Magnesium#/media/File:Magnesium_Sparks.jpg ) Figure 3. The thermite mixture, made from finely powdered aluminum and iron oxide, burns with a high temperature flame and has been used in the welding of railroad tracks. (source: https://commons.wikimedia.org/wiki/File:ThermiteReaction.jpg )

When estimating the maximum temperature that can be reached in the combustion of some substance, there is a need to consider not only the enthalpy changes of the reactions, but also the heat capacities of the products that are formed. A quantity denoted $T_f$, and called adiabatic flame temperature, is the temperature that would theoretically be reached when the fuel reacts with oxygen in a system that is thermally insulated (to prevent heat loss to the surroundings) but isobaric (can do work on surroundings by expanding). A basic estimate of $T_f$ is where $\Delta H_c$ is the heat produced in the combustion of 1 mole of the fuel and $C_p$ is the constant-pressure heat capacity of the product mixture at a temperature of about 1000 deg C (partial derivative of enthalpy with respect to temperature at constant pressure). This formula is not accurate for the most energetic combustions, as most combustion reactions don’t proceed all the way to the stoichiometric end products in high temperatures. This is because at high temperatures, the molar entropy change $\Delta S$ of the reaction starts to be a significant factor in determining the molar Gibbs energy change (and equilibrium constant) of the process, and smaller molecules (like $H_2$ and $O_2$ instead of $H_2 O$) usually have a larger molar entropy than large ones. At high temperatures the heat capacity also increases dramatically, because the Boltzmann factor $k_B T$, which gives the energy scale corresponding to absolute temperature T, starts to approach the energy scale of molecular vibrational (and later also electronic) transitions, and energy is therefore distributed to the vibrational and electronic degrees of freedom of the reaction products. At really high temperatures, like inside the Sun, matter is in the form of ionized plasma, but that kind of extreme conditions can’t be produced chemically.

When considering the combustion of reactive metals, another thing that limits the maximum reaction temperature is the boiling point of the reaction products such as $MgO$ or $Al_2 O_3$. The flame temperature in metal combustion can’t usually exceed the boiling point of the most volatile product, as the heat of combustion is not as large as the heat of vaporization of the reaction products. The combustion of zirconium metal in pure oxygen can raise the temperature up to 4000 degrees Celsius, because of the very high boiling point of zirconium oxide.

The factors mentioned above limit the maximum temperature attainable in a chemical combustion reaction to about 5000 degrees Celsius, which is approximately the adiabatic flame temperature of dicyanoacetylene, a derivative of cyanogen. The amount of pressure rise in the combustion reaction, which was mentioned as one measure of the energeticity of the reaction, depends on both the flame temperature and the difference in the number of moles of gas is the reactants and products. Nuclear reactions such as the fission of uranium-235 are able to produce much higher temperatures, up to millions of degrees Celsius, due to the very large energy release in a relatively small volume.