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| 9 August 1776, – 9 July 1856 |
For years, people knew various chemicals fairly well; pure chemicals had been isolated already by the 18th century, and by the middle of the 19th century, most of the elements of smallest atomic number had been identified, and chemical formulas and compound names were being standardized.
For instance, potash was a substance that became well-known in medieval times, and was being used to make a precursor of soap as early as AD 500, according to Wikipedia. It was made in two ways: first by refining wood ashes (dissolve the pure mineral from ash, filter, then evaporate the solution to produce crystals), or by mining (e.g. in Ethiopia).
Subsequently, it was discovered that the substance potash was a compound of a metal (as yet nameless), and Hydrogen, and Oxygen. Oxygen had been identified as an element (not divisible into further elements itself), and the metal with which Hydrogen and Oxygen produced potash was called, understandably, Potassium. (The metal was called Kalium in some languages, for which reason it is represented by the symbol K.)
The next, truly major, step in understanding Chemistry was the discovery of the Law of Constant Proportions. People started looking into ways in which Potash and, say, vinegar (subsequently identified as pure acid) combined to completely use up both. Don't take my word for this, but I suspect that almost exactly 60* grams of Distilled Vinegar and 100* grams of limestone would exactly combine to make a certain salt. While the reaction was going on, as the acid was added, bubbles of CO2 would be given off. At the precise moment when an extra drop of acid provokes no bubbling, you know that all the limestone is exactly used up.
If you doubled the amount of one reagent, say the acid, you would have to double the amount of the other reagent. On the other hand, if you wanted to use Vinegar and Lye, for instance, you would have to use 60 grams of Vinegar, and 40* grams of Lye.
If you used 40 grams of Lye, you could exactly combine it with 36* grams of hydrochloric acid instead. And if you wanted to use hydrochloric acid and limestone, surprise! You have to use them in the proportion of 100 to 36.
A gentleman called Proust formulated a chemical law called the Law of Definite Proportions, which stated that a compound always consisted of the same proportion of elements. I have used this principle by implication above. Another law was also observed, namely that the proportions were always simple integer proportions. This must have been astounding at the time, and not easy to spot. Nowadays, with our more accurate scales, we might not have spotted the simple integer proportions, because of the presence of isotopes (see below). But in the good old days, the fact that vinegar and lye always combined in the proportion of 3:2 would have been hard to ignore.
Next came the Law of Multiple Proportions. This said that if two elements combined together in more than one way (e.g. Carbon Dioxide, and Carbon Monoxide), then the different weights of the second chemical that combined with the first chemical would be in simple integer proportion to each other. This was put forward by John Dalton. Dalton is recognized today as the discoverer of the atom. Living in the present time, where the existence of atoms is no longer in doubt, it is almost impossible to put ourselves in the mindset of someone who had no idea what an atom was, and was stumbling towards the concept. Initially, shortly after Dalton's Law was stated, it was thought that all matter consisted of Hydrogen, combined in different ways. Nowadays we would state this principle as: All matter consists of Protons and Neutrons (and electrons, which weigh hardly anything, so who cares, anyway), which would be certainly true. A Hydrogen atom, by weight, consists of almost 100% the Proton it contains, the electron, which it also contains, weighing practically nothing in comparison. So, thinking of Hydrogen as just a big old Proton isn't too far wrong (at least, in terms of weight. The charge lobby would not be amused).
These were the facts that pushed thinking towards the conclusion that there were the same number of molecules in 40 grams of Lye as there were in 100 grams of Limestone, and in 60 grams of Vinegar. (You have to make allowance for the presence of water in the acids; the weight of the water must be adjusted for.) It all boiled down to the following conclusion:
(Molecules, by the way, are the smallest pieces of a compound, such as hydrochloric acid. You can split it up into Hydrogen and Chlorine, but then it would not be hydrochloric acid anymore. Even the element Oxygen is usually found in pairs of atoms, O2, and an Oxygen atom all by itself is pretty unhappy, and soon gets into trouble. So an Oxygen molecule can be divided up into atoms without its losing its identity, but compound molecules, once divided into their separate parts, stop being a compound, and become the constituent elements.)There are exactly the same number of molecules in 100 grams of limestone, as there are in 60 grams of Vinegar.
Exactly how many molecules are there in 100 grams of limestone? This is Avogadro's famous number: roughly 6.0221415 × 1023 , which is a little more than .6 million million million millions.
Is this a universal constant? No; it tells us more about how big a gram is than about the universe. If the proverbial men from Mars were to talk to us about the subject, their "Avogadro's number" would depend on what units of mass they were using.
More interestingly, the question you should be asking is: why these particular numbers: 60 grams of Vinegar, 100 grams of Limestone, etc, etc?
Let's talk about Lye, which is Sodium Hydroxide: NaOH. Physicists, using techniques that I'd find it difficult to explain, figured out exactly how many protons and neutrons were contained in an atom of Sodium. You can look these up yourself; if you Google Sodium, you get the Wikipedia article on Sodium, which tells you that Sodium is element number 11, so it has 11 Protons in each atom. That's what makes it Sodium; only Sodium has 11 Protons per atom, and all Sodium atoms have exactly 11 Protons. In addition to Protons, each atom has, usually, 12 Neutrons. (Why? I don't know; there are usually an equal number of Protons and Neutrons, but atoms have some freedom in choosing how many neutrons they have.) There are also 11 electrons, but they're so light that we're going to ignore them. So the total number of Protons and Neutrons in a Sodium atom is 23**. (A Periodic Table is a convenient display of all the elements; we're interested mostly in the top three rows.)
Oxygen is element number 8, and it therefore has 8 Protons, and usually 8 Neutrons.
Hydrogen is element number 1, and has one Proton, and no Neutrons, usually.
So if we add up all the Protons and Neutrons in an entire molecule of Lye, or Sodium Hydroxide, we get 23 + 16 + 1, which is 40.
A single molecule of Sodium Hydroxide would react with a single molecule of HCl (Hydrochloric Acid). If each Proton and Neutron were to weigh a gram (which they certainly do not), then that would explain why matters stand as explained above. But whatever they weigh, chemists reasoned that if you took the molecular weight in grams, the same thing would happen. (If you took it in milligrams, the same thing would happen, too.) Basically, you're reacting 6.022... x 1023 molecules of one substance with an equal number of molecules of the other, and so logically, they use each other up almost exactly. A few are sure to be left over, but the principle is the same.
Isotopes
You might have noticed a lot of hedging above: "A Sodium atom usually contains..." and so on. A Sodium atom usually contains 12 neutrons. A few renegade Sodium molecules, however, contain only 11 neutrons, so the overall average atomic weight of Sodium is 22.98976928... (protons or neutrons), which tells you that the vast majority of sodium atoms contain 12 neutrons. (I can just imagine Chemists doing a phone survey of Sodium atoms: "Excuse me, but do you have a minute to answer a few questions? We're from the Chemistry Association, and we would like to know, how many neutrons do you have, sir?" Then, using standard polling techniques, they adjust for sample size ...)
A Hydrogen atom, as I said, usually has no neutrons at all. (They probably get shaken off when the Hydrogen atom travels really fast! Just kidding.) But a few of them do have a proton, and a few even have two protons. All three types of Hydrogen combine with Oxygen to make water in the usual way, and it is very hard to tell that they have extra protons.
Chlorine atoms are the most diverse. According to Wikipedia, the most common occurrences are 35Cl (75.77%), which has 17 protons 18 neutrons, and 37Cl (24.23%) which has 17 protons--of course, because the 17 protons are characteristic of Chlorine, otherwise it would be some other element--and 20 neutrons. If you multiply 35 by 75.77% and 37 by 24.23% and add, you get the average "weight" of a Chlorine atom, namely 36.46 times the weight of a proton (or neutron). The various different kinds of Chlorine atom are called isotopes of Chlorine, which means "in the same place". All these atoms react like a Chlorine atom, but some of them are heavier, or denser, than others. Similarly with Sodium and Hydrogen.
The interesting thing about Avogadro's number is that it tells us the weight of a single Proton (or Neutron). According to Wikipedia, the weight of a Proton is 1.672621777×10−27 kilograms. (A Kilogram is one thousand grams.) If you multiply the weight of one Proton by Avogadro's number, guess what you'll get? One gram.
Arch
[*Actually, 60.1, 100.086, and 36.46 (ouch), respectively
**Actually, 22.98976928.]
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