By Richard Bleil
Let’s have some fun today, shall we? My regular readers just let go of an exasperated sigh, because they know…fun for me means calculations!
But, I love doing things to demonstrate just how minuscule molecules are. So, today, I want to calculate how many aspirin molecules in a regular dose of aspirin per cell in the average human body we take.
Aspirin has an interesting history. Back when settlers were still getting along with the native people, the native population showed these illegal immigrants a trick for getting rid of headaches by chewing on a particular type of bark. As it turns out, this bark is a natural source of the active ingredient in aspirin, namely acetylsalicylic acid. Its formula is C9H8O4 with a molecular mass of 180 g/mol (we’ll need that later). Eventually, analytical chemists analyzed this bark and isolated the active ingredient, and organic chemists learned how to synthesize it cheaply and safely.
A standard aspirin pill has 325 mg of aspirin in it. As a standard dosage is two pills, this means regular strength aspirin is typically 750 mg. There are 1000 mg in 1 g, so this amounts to 0.750 g of acetylsalicylic aspirin.
Doesn’t seem like much. This may be a disappointing post. But…forge ahead!!!
So, we now know we take 0.750 g of aspirin, and that it takes 180 grams to make a mole. This means one standard dose is (0.750/180=)0.0041667 moles of aspirin. Very small number.
A mole is a number. Just like a dozen. It doesn’t matter of what, a dozen is 12. We have 12 eggs, that’s one dozen. We have 4 slices of bacon, that’s 1/3 of a dozen. Look at my bank account, and you’ll see I’m flush with two dozen dollars.
Avogadro realized that different elements had different relative masses. Oxygen is 16 times heavier than hydrogen, and carbon is 12 times heavier. So, if we had 16 grams of oxygen, we have the same number of oxygen atoms as 12 grams of carbon. He didn’t know what this number was exactly, but it greatly simplified the discussions of chemistry because we could discuss number of atoms, rather than masses. As it turns out, one mole is 602,000,000,000,000,000,000,000. Always. Regardless of what we are discussing. So, 0.0041667 moles of aspirin actually contains (0.0041667×602000000000000000000000=)2,510,000,000,000,000,000,000 acetylsalicylic acid molecules.
Maybe it’s not so small after all. It’s certainly a bit larger than the dividing line between scalding emergency room hot and ice hypothermia inducing cold on my shower nob, which, science has proven, is the smallest distance known today. Seriously. There have been papers.
Apparently, if you search online, there are an estimated 37.2 trillion cells in the human body, or 37,200,000,000,000 cells. That’s a lot. And we’re almost at the end of this particular eye popping “HOLY COW!” calculations. All we need to do is divide. So we have (2,510,000,000,000,000,000,000/37,200,000,000,000=)66,900,000.
Think about this for a moment. One dosage of regular aspirin puts about 67 million acetylsalicilic acid molecules in our body per cell! Every time I take a baby aspirin because of my heart attack (75 mg per pill), that’s still over six and a half million aspirin molecules per cell.
I’ve been criticized for this calculation. “But the aspirin doesn’t distribute evenly throughout the body”.
Yes, we realize that the aspirin molecules will accumulate, for example, in the liver in far higher concentrations than that cell on your little toe. That’s not the point. I’m not addressing how and where aspirin goes. I’m pointing out the size difference between molecules and cells. I weigh about 120 lbs and have about 37 trillion cells. But one tiny little baby aspiring has over six million more molecules than cells.
Cells are so small we cannot even see them. We think, “oh, that’s small!” Well, those acetylsalicilic acid molecules are smaller still. The technical term for how small molecules are is, in scientific jargon, “itty bitty”.
It really isn’t a surprise. Each cell is made up of millions upon millions of molecules, so of course molecules are smaller than cells. The National Science Foundation one did a quick true/false survey making the statement, “electrons are larger than atoms”. More than half of the respondents thought this statement was true. I explained this to my class one day, and some smart alec student tried to argue that according to quantum mechanics, the electron can be any size. Well, yes, I get that (I am a quantum mechanist after all), but the electron is part of the atom, and just a part of it. If you put big axles and tires on a truck, they become part of the truck, so you cannot have an axle bigger than the truck.
But I diverge.
Wow, look at that. Over sixty-five million!