[Calculating rocket fuel performance mathematically] gets worse exponentially as the number of different elements and the number of possible species [of reaction products] increases. With a system containing carbon, hydrogen, oxygen, and nitrogen, you may have to consider fifteen species or more. And if you toss in boron, say, or aluminum, and perhaps a little chlorine and fluorine—the mind boggles.
But you’re stuck with it (remember, I didn’t ask you to do this!) and proceed—or did in the unhappy days before computers. First, you make a guess at the chamber temperature. (Experience helps a lot here!) You then look up the relevant equilibrium constants for your chosen temperature. Devoted and masochistic savants have spent years in determining and compiling these. Your equations are now before you, waiting to be solved. It is rarely possible to do this directly. So you guess at the partial pressures of what you think will be the major constituents of the mixture (again, experience is a great help) and calculate the others from them. You add them all up, and see if they agree with your predetermined chamber pressure. They don’t, of course, so you go back and readjust your first guess, and try again. And again. And eventually all your species are in equilibrium and you have the right ratio of hydrogen to oxygen and so on, and they add up to the right chamber pressure.
Next, you calculate the amount of heat which would have been evolved in the formation of these species from your propellants, and compare that figure with the heat that would be needed to warm the combustion products up to your chosen chamber temperature. (The same devoted savants have included the necessary heats of formation and heat capacities in their compilations.) And, of course, the two figures disagree, so you’re back to square one to guess another chamber temperature. And so on.
Clark, John D. Ignition! An Informal History of Liquid Rocket Propellants. Rutgers University Press Classics, 2017. p. 84 (italics in original)
