Stoichiometry: Or, How Napoleon Blew His Enemies Away

1/28/2016

Napoleon Bonaparte, Emperor of the French, first-rate military tactician, as well as a gunner by training. And, not known by many, a mathematical wizard - which may explain his success.

But what does this have to do with chemistry? Everything.

"In every combustion there is disengagement of the matter of fire or of light. A body can burn only in pure air [oxygen]. There is no destruction or decomposition of pure air and the increase in weight of the body burnt is exactly equal to the weight of air destroyed or decomposed. The body burnt changes into an acid by addition of the substance that increases its weight. Pure air is a compound of the matter of fire or of light with a base. In combustion the burning body removes the base, which it attracts more strongly than does the matter of heat, which appears as flame, heat and light." - Antoine-Laurent Lavoisier, 'Memoire sur la combustion en général' (1777)

In an earlier article, me mentioned one of the great names in chemistry, Antoine Lavoisier. We didn’t go into the details of his career as the progenitor of all modern chemists, partly because we’d like you to look it up yourselves (and partly because the story will stretch beyond our 1000 word limit). But there is one instance of his story that is quite profound, and it has to do with our subject matter.

In 1772, Lavoisier discovered that metals, such as magnesium, actually gained weight when reacted with oxygen. The prevailing theory at the time (and by that we mean scientific theory, not a ‘guess’) was that when materials are burned, they change and emit an ethereal fire-ish elements called ‘phlogiston’, rather than absorb oxygen from the air. This is the birth of the scientific branch of stoichiometry, the study of measuring elements, by themselves and in reactions.

Back in the day, chemistry was rather crude as it inherited the methods used in alchemy, estimates and approximation (much like how your grandma cooks by ‘agak-agak’ the proportions of ingredients). By the time Lavoisier was involved, it was known that and under or over approximation produces either waste or shortage in results. This became very relevant not long after that as the nations of Europe need to economize in the production of gunpowder for the French Revolutionary and Napoleonic wars.

After peace broke out, chemistry, and specifically Lavoisier’s law of the conservation of mass, became essential during the Industrial Revolution. The chemical industry boomed particularly in the production of sulfuric, nitric acid and soda ash in the first half of the 19th century and synthetic dyes as well as pharmaceuticals in the second. But for all this mass production to be possible, chemists must be sure that they have the right proportions of things, any miscalculations may lead to disaster.

A Practical Example of Application: The Gunpowder

The original method before stoichiometry depends on trial and error and are based on proportions. For instance, when making gunpowder certain ratios of sulfur, charcoal powder and saltpeter (potassium nitrate) are recommended, but none of them would produce consistent and optimal results.

In 1780, these proportions are 15 parts saltpeter, 3 parts charcoal and 2 parts sulfur. With the later understanding of their respective elemental composition and the adherence to Lavoisier’s law on the conservation of mass, this translates to:

How equation balancing can go wrong, and to lose points in exams....

But at close inspection, this equation doesn’t seem to balance, and likely to create wastes that may damage the average musket in the long run.

Optimization

This is where the concept of stoichiometric ratio comes in. A stoichiometric ratio, is the ratio of a reagent that follows three principles: (1) all of the reagent is consumed in the reaction, (2) there is no deficiency of the reagent, and (3) there is no excess of reagents. Meaning everything that comes in, will react into the desired output, leaving nothing behind.

To do this, firstly we must consider the input. Is everything chemically pure, with no contaminants, and do we really understand the composition of the reagents? Back in the day, sulfur can be found in its elemental form easily, as they’re mined from volcanic vents that accumulates the stuff. Saltpeter as well can be produced in its pure form through a rather disgusting method involving urine and manure. Charcoal however, is the devil in the detail. It’s not purely carbon, as they are produced through the anaerobic heating of wood, leaving much of the original cellulose unconverted, making the earlier equation incomplete.

DISCLAIMER:

IFSA DOES NOT RECOMMEND ANY ATTEMPT BY STUDENTS OR TEACHERS TO PRODUCE GUNPOWDER IN SCHOOL. AND WE DOUBT YOU WOULD INVOLVE YOURSELVES IN THE MORE DISGUSTING PARTS OF THE PRODUCTION PROCESS. THOUGH IF ANY ARE FOOLISH ENOUGH TO TRY, WE ARE NOT RESPONSIBLE FOR ANY RESULTING DAMAGE.

Now that we know what goes into the reaction, we then need to determine what comes out of it. Before mass spectrometry was developed, chemists went through the labour intensive method of subjecting residues and gasses to tests in order to know what they’re made of. A less exact method would be to break down the formula of the reagents into the likeliest resulting chemicals. This adds art to the science.

So since we have partially carbonized cellulose, potassium nitrate and sulfur, what would come out the other end?

I call it chemical scrabble...

One rule of thumb to follow is that lighter and simpler chemicals are more likely to be produced from a reaction, as they require less energy to synthesize or decompose into. Compounds requiring single or double replacements of atoms require more energy (nature tends to take the path of least resistance). In the process of a chemical reaction, energies are released and absorbed, and following the law of the conservation of energy and the second law of thermodynamics, none of it was created or destroyed – otherwise the world’s energy problems would be solved ages ago.

So now we list down the likeliest suspects, and try balancing the equation:

Voila!

I’m Sick Of Chemistry, Let’s Do Some Physics!

So now we have the definite recipe, how much do we need? Let’s assume Napoleon wants to shoot a 10-kilogram cannonball at his enemies standing 1 kilometer away. This is a question of physics, thus it includes the assumption of firing angle, let’s say 5 degrees from the same level as the enemy infantry formations.

Using the formulas for ballistics (God bless Isaac Newton!), we can deduce that the 10kg cannonball must travel at a velocity of 237.68 meters per second. We also must assume that the gunpowder is completely efficient, and the cannon is free from windage (i.e. zero gap between the diameter of the cannonball and the cannon’s bore), as well as zero friction between itself and the projectile, including between the projectile and the air. And since force equals mass times acceleration (F = ma), we therefore need about 2376.8 Newtons of force.

The key to sending a solid iron ball to some unwitting Austrian infantrymen is pressure and speed. How much gas would a gram of gunpowder produce? At what velocity? Having enough of both and multiplying these two together equals maximum muzzle velocity; not having enough of either would only create a fizzle. The gunpowder must create a lot of gas and as quickly as possible.

So from the perfected gunpowder formula we can use the mole unit (as explained in the video) to calculate how much gasses are produced (carbon dioxide, carbon monoxide, steam and nitrogen), how much they expand due to heat, as well as considering how much space is involved in terms of internal ballistics (clue: iron have a density of 7.874g/cm3, what is the diameter of a 10kg sphere of the stuff?).

Just for fun, I’m going to leave these questions off. Figure it out for yourselves, don’t expect people to spoon-feed you your whole life, if you think school is tough wait till you get a job.

Conclusion

So what we’ve shown you is an example of how stoichiometry is put in application. This allows chemistry to transcend its academic roots into solving real world problems. Without it, whole industries in the 19th century would not be possible, whether it’s to produce pharmaceuticals, artificial fertilizers, steel, semiconductors, or even the food we eat, the exactness of chemistry had become the lynchpin of human civilization.

Ponder this

In more ways than one, stoichiometry allows us to utilise chemistry efficiently and effectively. In what other way can we use stoichiometry to link the separate branches of science?

Why do chemists use the average atomic mass rather than the atomic weight of a specific isotope? It'll be much easier to calculate, and much more exact to boot.

Discuss

Solve the problem at hand: how much gunpowder is needed to fire a 10kg cannonball 1km away? Consider the internal dimensions of the cannon, the volume of gasses generated during combustion.