This post was originally published on Randi.org

As much as it riles up proponents of science-based medicine like myself, homeopathy can be a great teaching tool. But most of the time this opportunity is squandered. Articles, lectures, papers, and talks critical of homeopathy quickly skip over the chemistry and the math that makes the philosophy so implausible. “The molar limit,” is casually thrown out as the smoking gun, but guessing that most people haven’t had a chemistry class after high school, this is potentially as bad as simply stating, “Water has memory.” What is more important is the why, the how, and of course the math.

I believe that you won’t get at an entrenched audience simply sounding the bulls**t claxon; you have to build upon the scaffolding most people already have, and work your way up to the skeptical position. In communication research, this is called schema theory, and it predicts that new information is best understood when you have some prior framework to understand it with.

As Phil Plait said, “If you teach a man to reason, he will think for a lifetime.” Likewise, I believe that if you teach someone the reason why homeopathy can’t work, it is much more powerful. To that end, and just in time to dovetail with Steven Novella’s homeopathy debate, I aim to provide a neutral explainer below focusing on chemistry of homeopathy’s main claim—high dilution equals high potency.

So what is the molar limit? What is Avogadro’s number? We have to start with the basics.

In the early 19th century Italian scientist Amedeo Avogadro proposed the idea that the volume of a gas is proportional to the number of molecules or atoms in that gas, regardless of its state (temperature, pressure, etc.). Fill a balloon with a liter of helium, as the theory goes, and you would be able to figure out how many helium atoms are inside.

This formed the basis for the mole; a unit describing how many elementary particles (molecules, atoms, or ions) are in some standard amount of stuff. That standard was made to be exactly 12 grams of carbon-12 (a form of carbon with 6 protons and 6 neutrons). So, one mole of carbon-12 equals 12 grams.

When you look at a periodic table, you’ll see numbers in the corners of the various boxes. One (typically bolded) is the atomic number—the amount of protons bound up in the atom. You’ll also see another number, the atomic weight—more or less the number of protons added to the number of neutrons in the atom. For carbon, the atomic number is 6 and the atomic weight is 12.011.

Life on Earth owes everything to carbon, and chemists honor it by basing many of their measurements on it. They define the mass of other molecules or atoms in relation to carbon as a standard. So, it follows that the atomic weight of other atoms or molecules in grams is also equivalent to one mole. One mole of hydrogen, with an atomic mass of 1, weighs 1 gram, and contains the same amount of molecules as one mole of carbon. If this seems like a convenient way to do things, that’s because it is! This standardization has made the life of many a student that much easier.

For example, water has two hydrogen atoms and one oxygen atom. A mole of water would then equal the atomic weight of all the atoms in the substance in grams. Looking to a periodic table, one mole of water is 18 grams, and again those 18 grams contain the same number of molecules as there are atoms in 12 grams of carbon.

A hundred years after Avogadro, American physicist Robert Millikan was able to measure the charge of a single electron. And because Michael Faraday had discovered in 1834 that a mole of electrons has a certain charge, dividing the two values resulted in an accurate description of how many atoms or molecules or ions are in one mole of a substance. As any recent chemistry student could recite by heart, it turned out to be 6.02*1023.

So now we know what skeptics talk about when they mention Avogadro, but what does that have to do with homeopathy? Well, homeopaths bring the science down upon themselves, and it isn’t too kind.

One Molecule in Many Universes

Now that we know about moles, we can evaluate the claims of homeopathy directly. Homeopathy states that the more you dilute a substance, the more potent is gets. But without making things too simple, in modern medicine “the dose makes the poison.” The smaller the dose, the smaller the effect. This isn’t really up for debate—it is the foundation of all pharmacology.

If the chemistry of homeopathy cannot pass this very low bar of potency, there is no need to try to overturn other established science with “water memory” claims.

Homeopathic remedies are typically prepared by diluting some original substance down, down, down. Let’s say that we want to make a remedy out of something with a molar mass of 100 grams (all the atomic weights of the molecule summed up). On the “X scale” developed by homeopaths, our remedy would supposedly get stronger every time we diluted it by a factor of 10. So, if I put 100 grams of the substance I want to dilute in one liter of water, I will have a solution with a concentration of 1 mol/L. At this point, 6.02*1023 molecules of my substance are floating around in the water. Then we start diluting.

Going by factors of ten (according to what we have to do for the X-scale), by the time we reach 24 dilutions (24X), something troubling happens. If you divide 6.02*1023 by 1024 you get a concentration of 0.6 molecules per liter. That’s right, you have a whole jug of remedy with most likely not one molecule of your original substance.

For perspective, you could drink a solution of arsenic and survive at a dilution of 8X.

But it gets worse. At 60X, it would require giving two billion doses of our remedy per second to six billion people for 4 billion years to deliver a single molecule of the original material to any patient.

And it still gets worse. At 400X, you would need to search the volume of 10320 universes to find just one molecule of our original remedy. But search in your local pharmacy and you will find homeopathic flu remedies at this dilution.

Before we get into debates of “well it worked for me!” and water with “memory,” we have to start with what we know, and we know that the human body needs something to react to. Based on everything we know, a bottle of homeopathic remedy should produce the same reaction as a bottle of water. That’s precisely what the studies say.

Building scientific literacy means building from the ground up. We don’t have to get tangled up in the buzzword-filled gumbo of alternative medicine to learn about homeopathy. Chemistry tells us pretty much all we need to know, and teaches us a bit in the process.

For more about the homeopathy debate, check out Steve Novella’s recent posts.