When I was in school, I learned about the mole. No, it is not the mole that we find on our skin or the animal that looks like a rat. This is the unit of measure in chemistry and equates to 6.022 x 10²³ — Just a large number with no units.

They taught it to me this way in my 9th standard I remember: A large number called the Avogadro number denotes the number of atoms in 12 grams of Carbon-12. And this number is equal to 6.022 x 10²³. All my 11th and 12th standard chemistry, I used this mole mechanically.

Recently, that is long after my high school, I came across something interesting regarding this mole concept. First, I found out that the definition of the mole itself has changed. That is my 9th standard definition isn’t valid anymore. And also that we have now included it in SI units as the 7th unit.

The new definition of a mole is simply 6.02214076 × 10²³ particles. The particles may be atoms, electrons, ions, photons, even complex molecules. The mole has gotten rid of its association with Carbon-12 and becomes just another measure like a *dozen* used for bananas or a *pint* used for a beer.

Learning about this new definition, the concept of mole became a little clearer to me after so many years. It was just a measure all along for atomic sized particles. But I had forgotten about why they chose it to be 6.022 x 10²³ and what was this Avogadro number. So I went about reading on that.

In 1811, the Italian scientist Amedeo Avogadro figured something out: The volume of *any* gas at normal pressure and temperature is proportional to the number of molecules. On the surface a very preposterous proposition. At the time, even the molecular concept for elements didn’t exist, so scientists ridiculed it.

How did Avogadro come to this proposition? He had studied both Gay Lussac’s gas laws and John Dalton’s model of atom with his theory that fundamental particles called atoms made everything. Avogadro could reconcile both theories to propose a molecular theory.

And thus, the molecular concept of elements became mainstream in chemistry. That an element can exist as molecules with its atoms together like H2 or O2. And during reactions, the atoms separate to combine in other ways to form compound molecules like H2O.

He then figured out and hypothesized, what is now famously Avogadro’s law: “Equal volumes of all gases, at the same temperature and pressure, have the same number of molecules.” Repeated experiments by other scientists then verified this to be true for all ideal gases.

Now, imagine gases like H2 and O2. Hydrogen has 1 proton in its nucleus and oxygen has 8 protons and 8 neutrons, both weighing almost the same. Since electrons contribute little to atomic mass (they are over 1800 times lighter), if we consider the weight of H2 to be 2 units (2 protons), then weight of O2 will be 32 units.

This means if you measure 2 grams of hydrogen and 32 grams of oxygen in two containers, both will have an equal number of molecules of H2 and O2, correct? But according to Avogadro’s law, if the number of molecules are the same, the volume occupied by the gases will be the same.

Hence 2 grams of hydrogen and 32 grams of oxygen will both occupy a same amount of volume under similar, normal conditions. And by 1890s, scientists like Karoly Than determined this gram-molecular volume to be 22,330 cm³. This was further refined to be 22,414 cm³.

Almost a century after Avogadro, Friedrich Ostwald, a German chemist, introduced the term Mole to define the Molecular weight of ideal gases when their volume is 22.414 liters. This would mean 1 mole of H2 will weigh 2 grams, and 1 mole of O2 will weigh 32 grams. Combined with Avogadro’s law, the mole concept made elementary chemistry much easier and standardized.

Let’s say someone asked you to prepare 18 grams of water from hydrogen and oxygen. You know 18 grams of H2O (water) will need 1 mole of H2 and half a mole of O2. So you will simply measure 22.4 liters of hydrogen, and 11.2 liters of oxygen to burn into your 18 grams of water. Imagine trying to measure the same oxygen and hydrogen in grams!

This ease in chemistry came about only because of Avogadro’s useful insights into molecular theory and his law relating volumes and number of molecules. So in 1909, when French physicist Jean Perrin estimated the number of molecules that 22.414 liters of ideal gases to be close to 6 x 10²³, he named it as Avogadro’s number in his honor.

Later in the 1980s, an international union (IUPAC) defined the mole to mean the amount of substance in exactly 12 grams of pure Carbon-12 isotope. As previously used number based on Jean Perrin’s work on oxygen were both not so accurate and we ran into problems, as there were isotopes of oxygen with slightly different molecular masses.

This last definition is what I learned in my school days. But again recently in 2017, the definition of the mole has changed to represent just the Avogadro’s number of 6.022 x 10²³. Because the mole is just a human defined unit to make chemistry easier. The random Avogadro’s number was the number of molecules in 1 mole of oxygen or almost any gas, and the number stuck.

But unfortunately in schools today, I don’t think any chemistry teacher goes this far to make students understand how the concept of mole or Avogadro’s number came about. Thus making this fundamental and important concept in chemistry dry and mechanical.

Some students may not worry too much about such definitions. They thrive under arbitrary rules and definitions set by others and go about mechanically finishing their studies, doing their work, and living their lives. But for students like me, such arbitrary definitions like the mole make little sense.

Hence I think it is very important, in both science and mathematics, we teach concepts with some history on how a scientist or mathematician discovered a certain principle or method. We should also discuss and make students understand the need the scientists faced to discover, invent, or define something.

This I believe will not only improve learning and application of concepts by students but also help themselves delve into the scientific process. After all, even the greatest scientists were students who were learning as they figured out things and defined the scientific world around us.