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The chemistry of fireworks

Dear Reader,

It is this time of year again and we need to think about chemistry for the first years again. Now before I get going I need to give you all a newsflash…..

Chemistry is fun !

One topic which I know that you have been doing is stoichiometry, a bit of a long word ! It is associated with the ratio of different things, a favourite of mine is the stochiometry of explosives, fuels and fireworks. Now what with the disgusting deeds in Norway this year I do not want to discuss explosives with you and frankly I think you might find a discussion of the chemistry of a candle a little dull so I have chosen to do fireworks.

My trusty copy of Michael. S. Russell’s book (The Chemistry of Fireworks) reveals that a range of mixtures of potassium nitrate, sulphur and charcoal (porous carbon) are used to make gun powders. A typical firework uses gunpowder in it for a range of purposes.

The book explains how the typical gunpowder operates by the following reaction

4KNO3 + 7C + S → 3CO2 + 3CO + 2N2 + K2CO3 + K2S

What we need to move forwards is a little thermodynamic data, I hold the view that thermodynamics is a misnomer it should be thermostatics as thermodynamics deals mostly with things which have reached a stationary (equilibrium) state.

Using the heats of formation of the reagents and the products we can estimate the heat of the reaction.

KNO3         DHf = – 494 kJ mol-1

C               DHf = 0.0 kJ mol-1

S                DHf = 0.0 kJ mol-1

CO2            DHf = – 393.8 kJ mol-1

CO              DHf = – 110.6 kJ mol-1

N2               DHf =   0.0 kJ mol-1

K2CO3        DHf = -1151 kJ mol-1

K2S             DHf = -1000 kJ mol-1

We can use these values to estimate the amount of heat released with gunpowder burns

For the reaction

4KNO3 + 7C + S → 3CO2 + 3CO + 2N2 + K2CO3 + K2S

The amount of heat given out is -1688.2 kJ mol-1, as the mass of the bits on the left hand side is 520.077 grams per mole we can make an estimate of how much energy is released when a kilo of gunpowder burns. Which is 3246 kJ. This compares with 4476 kJ for a kilo of TNT.

For those of you who are interested TNT detonates by the equation

2 C7H5N3O6 → 3N2 + 12 CO + 2 C + 5H2

As one kilo of gunpowder will release 15.38 moles of gas while a kilo of TNT will release 44 moles of gas. As the power of an explosive is given by the product of the energy released in the detonation and the volume of gas. Then it is clear that gun powder is about four times weaker an explosive than TNT.

Back to stoichiometry, if we change the mixture used to make gunpowder then the energy yield will change. Before we get going we need to work out some rules.

  1. The reagents are converted into atoms firstly
  2. The first compound to form is potassium sulphide
  3. The second compound to form is potassium carbonate
  4. Then carbon atoms are combined with oxygen atoms to form carbon monoxide
  5. The last oxygen atoms are used to convert carbon monoxide to carbon dioxide

Using these simple rules and the heats of formation I have been able to create a graph of the heat given out per kilo of gunpowder for a range of different amounts of potassium nitrate, I have fixed the number of moles of carbon and sulphur at seven and one respectively. You should be able to see that the heat given out per kilo is highest when 5.21 equivilents of potassium nitrate is used. This peak in the energy per kilo is close to the classic mixture of gunpowder.

Energy per kilo of gunpowder

For an explosive we normally need both heat and gas production, in the following graph I have shown the volume of gas generated per kilo of the powder. We can see that this decreases as more and more of the mixture is made of potassium nitrate.

Volume of gas per kilo of gunpowder

The explosive power of an explosive is given by the product of the gas volume and the heat of reaction, we can see here in this graph that the peak is at 2.92 equiv of potassium nitrate. I think that this calculation is a little misleading as the heat of reaction is so low for a mixture with so little potassium nitrate.

Explosive power of gunpowder

I suspect that the lack of potassium nitrate will slow down the reaction or maybe make it snuff out, so the normal ratio of four moles of potassium nitrate to seven of charcoal and one of sulphur is a good compromise.

It is interesting that a 85 % (w/w) potassium nitrate and 15 % charcoal mixture has been used as a fire extinguishing mixture. Lets do the maths for this mixture and consider the ratios.

If one kilo contains 850 grams of potassium nitrate (KNO3), then this kilo will contain 8.416 moles of potassium nitrate. If all the oxygen atoms in this potassium nitrate are liberated then we will have 25.25 moles of oxygen atoms.

150 grams of carbon is 12.489 moles of carbon.

If we assume that all the potassium atoms are converted into potassium carbonate then we will form 4.208 moles of potassium carbonate.

We will have 8.28 moles of carbon atoms left and 12.624 moles of oxygen atoms left.

If the oxygen atoms react with the carbon atoms to form carbon monoxide then we will form 8.28 moles of carbon monoxide which leaves behind 4.34 moles of oxygen atoms. The oxygen atoms react further to form 4.34 moles of carbon dioxide leaving behind 3.94 moles of carbon monoxide.

The final tally of what we have formed is

4.21 moles of potassium carbonate (K2CO3)

4.34 moles of carbon dioxide (CO2)

3.94 moles of carbon monoxide (CO)

These products have a combined heat of formation of – 6989 kJ while the reactants had a combined heat of formation of -4157 kJ. This means the fire fighting gunpowder generates about 2931 kJ per kilo of gunpowder which is similar to a conventional gunpowder.

The firefighting gunpowder makes only 8.57 litres of gas per kilo of gunpowder which causes it to have an explosive power of 563 x 103 L kJ kg-2 which compares with 839 x 103 L kJ kg-2 for normal gunpowder. I suspect that the lack of sulphur in the fire control gunpowder will slow down the reaction which will reduce further the explosive effect of this special gunpowder.

From my consideration of the firefighting gunpowder the change in the ingredients has caused the volume of gas generated to become lower. I hope that this example of stochiometry has been interesting.

Finally I need to give you all some advice,

The maximum penalty for making and experimenting with homemade explosives and fireworks is death ! I can accept no responsibility for any stupid experiment you choose to try at home. Some friends of mine once had a student who thought he would make an explosive, the student demolished a student flat and was killed in the explosion ! Learn from this man’s stupidity and do not repeat his error ! My advice is never to fool about with fireworks or to try to make your own.

On the subject of fireworks, here is some good advice for the next time you let some off. It is based on the British firework code.

  1. Only buy legal fireworks.
  2. Don’t drink alcohol if setting off fireworks.
  3. Keep fireworks in a closed box.
  4. Follow the instructions on each firework.
  5. Light them at arm’s length, using a taper.
  6. Stand well back.
  7. Never go near a firework that has been lit. Even if it hasn’t gone off, it could still explode.
  8. Never put fireworks in your pocket or throw them.
  9. Always supervise children around fireworks.
  10. Light sparklers one at a time and wear gloves.
  11. Never give sparklers to children under five.
  12. Never use petrol, E85, diesel fuel, paint thinner or other liquid fuels on a bonfire.
  13. Keep pets indoors.
  14. Look after your eyes. Fireworks are for a moment, eye injuries are for life !
  15. Don’t fool about with fireworks.

If you do want to fool with fireworks then please see this movie.

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