A. If molecules really exist, what size are they?
Take something made of one single material and divide it in half. Take one of the halves and divide it again into smaller pieces. Now divide one of those pieces. If you can keep dividing the material into smaller and smaller pieces, you'll eventually get to the individual atoms the material is made of. In many materials, groups of atoms stick together to make somewhat larger natural units, known as molecules.
The fact that matter is made of atoms is no longer news. Nowadays, we have microscopes that let us see how atoms are arranged at the surfaces of materials, and physicists routinely isolate individual atoms and molecules and experiment with them one at a time. But 100 years ago, there were no such microscopes and no tools to isolate individual molecules, so the evidence that atoms exist was much less direct. Furthermore, in some experiments, matter behaved very differently from the way people expected atoms to behave-so differently that some people thought the experiments proved atoms weren't real.
Albert Einstein did believe that matter came in smallest-possible units, and as he later said, he wanted "to find facts which would guarantee as much as possible the existence of atoms of definite finite size". He found what he was looking for in a microscopic effect of the energy of heat.
By the early 19th century, physicists had worked out some of the mathematical laws of heat, even though they had an incomplete understanding of what heat actually is. Even before that time, people began to realize that certain facts about heat would make sense if materials were made of small minimum-size units. The basic idea was that an object's thermal energy is simply the energy of its molecules in constant random motion; the greater the energy of the random motion, the hotter the object.
Many real thermal phenomena were exactly what this idea suggested they should be. On the other hand, not all thermal processes seemed to match such expectations. In particular, some materials behaved differently at very low temperatures, more so as the temperature came closer to absolute zero (-273.15°C). Some materials even showed different behavior at room temperature. This indicated that something was wrong with the idea; what exactly was wrong only became clear later. But because of these problems a few scientists doubted entirely that matter existed in basic units. Many others, who did assume molecules were real, often just described the idea as a useful working hypothesis.
Some of the most persuasive evidence that molecules exist came from chemistry. Today it's common knowledge that water is made from atoms of hydrogen and oxygen. It had long been known that, to produce water from hydrogen and oxygen gas without having any of either gas left over, you had to use twice as many liters of hydrogen as oxygen. Similar exact recipes were known for producing other substances. In the early 19th century, the physicist Amedeo Avogadro realized these recipes implied something important: no matter what types of gas you were working with, equal volumes of gas at the same temperature and pressure are made of equal numbers of molecules.
Starting from this idea, plus the recipes for many different chemical reactions, chemists were able to deduce something about the masses of each type of molecule and the atoms that make up each type. They found that hydrogen atoms were the least massive of all the atoms, carbon atoms were about twelve times as massive as hydrogen atoms, oxygen atoms were sixteen times as massive as hydrogen atoms, and so on. Chemists could furthermore work out that molecules of hydrogen and oxygen should be made of two atoms each, water molecules of two hydrogen atoms and one oxygen atom each, and so on.
The one thing chemists and physicists could not work out from this was the actual mass of any one kind of molecule. It was one thing to know that a water molecule is about 18 times as massive as a hydrogen atom; it was another entirely to know that a water molecule's mass is about 30 yoctograms (30 x 10-24 grams).
What they could do, though, was work with standard quantities of any given substance that were proportional to the molecular masses. Since hydrogen molecules were supposed to be made of two hydrogen atoms each, the standard quantity of hydrogen was taken as two grams. And since water molecules were supposed to be 18 times as massive as hydrogen atoms, the standard quantity of water was 18 grams. The standard quantity of a substance was called a "gram-molecule", or "mole" for short. Defining a mole this way meant that one mole of any substance would have the same number of molecules as one mole of any other substance-whatever that number actually was. If you knew that number-how many molecules of something made one mole of it-you could figure out the mass of just one of the molecules. People tried various experiments to determine that number, but the early results were not very precise.
This was the situation when Einstein began searching for facts to establish the size of atoms. He found a way that, if the earlier estimates were at least in the right neighborhood, would let us determine molecular masses more precisely than ever before. As we mentioned earlier, this clue was in a microscopic effect of the energy of heat. Einstein found that, if molecules really existed, then small particles dispersed among the molecules of a fluid should also have a random motion, very much like the thermal motion of gas molecules. (.....continued)