Chapter 15. al-Razi (Stoichiometry)


Take one mann of white Al-Qilī and an equal quantity of Lime and pour over it [the mixture] 7 times its amount of water, and boil it until it is reduced to one half. Purify it [by filtration and decantation] 10 times. Then place it in thin evaporating cups [kīzān], and hang it then in [heated] beakers [jāmāt]. Return what separates out [to the cup], and raise it [the cup] gradually, and protect from dust whatever drops from the cups into the beakers, and coagulate it into salt.

 — al-Rāzī, The Book of Secrets, ca. 920 AD [1]


Imagine that you are so pleased with your mead-making experience that you resolve to brew up your entire 100 gallon/year entitlement at once. You'll have an entire year's worth of birthday presents, Christmas presents, anniversary and wedding gifts that you won't have to fret over. Who wouldn't enjoy a refreshing bottle of Samson's Special Reserve? You fit out two 55 gallon drums with fermentation locks to let the gas out without letting air in. You buy 100 pounds of honey, 100 pounds of lemons and 100 pounds of tea at wholesale prices and get a local bar to save 100 empty beer bottles for you. Not only don't they charge you, they even wash them in their industrial-size dishwasher. You realize that you can save on yeast since one yeast makes two and two make four and four make eight and so on, so you only need one packet of yeast. You're prepared for the yeast to take a little longer than usual to get going, but you're not expecting months to go by with precious little in the way of gas. Eventually you get tired of waiting and prepare to bottle the stuff anyway, but there's a problem.

Belatedly you realize that you don't have anywhere near the right number of bottles; you implicitly and erroneously assumed that each bottle would hold a gallon when in fact they are 12-ounce bottles. Hurriedly you use your old friend, UFA from Chapter 3 to calculate the number of bottles needed:

Before bottling, you give your Bee-jolet a little taste; it's terrible. More like industrial-strength lemon-tea furniture polish from Hell than anything you would even remotely consider drinking. That's when you realize that you made the same error with your ingredients that you made with the bottles. The poor yeasts never had a fighting chance! You spend the rest of the day flushing your experiment down the toilet and hoping that it doesn't set off a pollution alarm at the water-treatment plant.

You've probably already spotted your mistake, but let's walk through it anyway before you waste enough groceries that FoodWatch distributes "Wanted" posters with your smiling face on them. The honey calculation is easy:

Your original mead had less than half the honey called for by the recipe; no wonder it fizzled out.

The lemons are a little more difficult. You could use:

But your wholesaler sells lemons by the pound. A 10 pound bag of lemons contains an average of 40 lemons, so:

With almost twice the lemons called for by the recipe, it's no wonder your mead had more pucker than a goldfish in a pickle jar.

The tea holds complications of its own. You used tea in bags for your smaller batch, but your wholesaler sells bulk tea by the pound. A box of 25 tea-bags weighs 50 grams, so:

Your original mead had 100 times the required amount of tea! It should have pleased any tea-totaler, since it was almost totally tea.

At this point in the narrative structure I'll bet you're wondering what your mead recipe can possibly have in common with lime and al-qilī. The Author wanted an example that would make absolutely clear the folly of confusing weight with number. You learned to balance metathesis reactions in Chapter 7 and redox reactions in Chapter 11. Balanced reactions give you the relative number of moles of each reactant and product but atoms and molecules are too small to count out individually. As in our mead example it is often more convenient to weigh things out than it is to count them out. The question of how much of one thing in a reaction goes with a given amount of another is called a stoichiometric question.



Reference [26], p. 391.