Molecules of Lactose - the Teeny Tiny Truth

Let's take a nostalgic stroll back to high school chemistry. Yeah, I'm getting all misty eyed too. But if you ever learned the concept of gram molecular weight and Avogadro's Number, that's where it first came up. (If not, you're special and you don't need to read this but you already know the answer.)

Avogadro's number is 6.022∙10²³. That's a really really really huge number. Written out in full it reads: 602,200,000,000,000,000,000,000. The number is important because that's how many molecules exist in a mole of any substance. A "mole" is short for gram molecular weight.

The molecular weight of a molecule is the weight of N₀ such molecules. The molecular weight of a molecule is equal to the sum of the atomic weights of its constituting atoms.

So what's the molecular weight of lactose? (Aha. This suddenly gets relevant.) Lactose's chemical formula is C₁₂H₂₂O₁₁. I'll do the math for you. A mole of lactose molecules weights about 342 grams.

Now one gram is a tiny amount. There are 454 grams in a pound, 28.375 grams in an ounce. An eight ounce glass of milk has 12 grams of lactose. If you held an ounce of lactose in your hand, you couldn't even feel that it was there. Yet that one gram still contains 1,760,233,918,128,654,970,766 molecules of lactose. Rounded, that's 1.76•10²¹ molecules. (6.022∙10²³ / 342)

That's why I tell people with lactose intolerance not to get worried about a few molecules of lactose. Or even a few billion. A few molecules can't hurt you. Your system wouldn't even recognize them.

Those with dairy protein allergies need to be a bit more careful, but similar math applies. Proteins are far heavier than lactose. They can weight a million times more. And even nanograms of protein can set off a reaction. A nanogram is one billionth of a gram. Even a million billion is small next to Avogardo's number, though. If you divide 1.76•10²¹ by a million billion, you're still left with 1.76•10⁶ or 1,760,000. Almost two million protein molecules are needed at the very least to set out a reaction in the most sensitive person. The real minimum is probably larger than this.

Caution is definitely the byword for those who are anaphylactic to milk. For the rest of us, just remember a few molecules are the same as none at all.