Molecules of Caffeine
May 9, 2008 – 12:15 am
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I thought about writing today's post on some rough equivalents for the number of water molecules in a liter of water. Then I found out there are roughly...
... water molecules in a liter of water. Double that for the number of hydrogen atoms. That's 33.428 and change septillion molecules. And to give you an idea of how immense that is, it's as many inches as there are in roughly 89.9 million light years. If you counted one molecule per second, it would take you around a million trillion years to count all the molecules in a liter of water.
Now, how do we get that number?
Well, there's a unit of measurement in chemistry known as a mole, which represents 6.02214×1023 entities (atoms, molecules, etc). An atom's atomic mass unit is basically the weight in grams of one mole of it in its elemental state.
So a water molecule's atomic mass unit would be the combined atomic masses of two hydrogens (1.00794 each) and an oxygen (15.9994), giving you a weight of roughly 18.01528 grams per mole of water. As a liter of water weighs one kilogram, you divide 1,000 by 18.01528 to get roughly 55.51. Then you multiply 55.51 by 6.02214×1023 to get your 33.428 septillion (and change) molecules.
But we can still have some fun with these basic numbers, now that we know how to calculate the weight of a molecule and count how many are in a specific amount of a substance.
For example, how many caffeine molecules are in a can of Mountain Dew? If we look at the diagram to the left, we see that caffeine contains 4 nitrogens (14.007 grams per mole), 2 oxygens (15.9994 grams per mole), 3 carbons (12.0107 grams per mole), and 9 hydrogens (1.00794 grams per mole) for an approximate weight of 133.13036 grams per mole of caffeine molecules.
Wikipedia states there are 55.2 milligrams of caffeine per 12 ounce can of Mountain Dew. That's 55.2/1000ths of a gram, so divide 0.0552 by 133.13036 194.19 to find out that a can of Mountain Dew has 0.04146% 0.02843% of one mole of caffeine in one can. Multiply that times 6.02214×1023 and you get...
... molecules of caffeine in one can of Mountain Dew. If you had a penny for every molecule of caffeine in a can of Mountain Dew, you'd have roughly 471.6 trillion tons of pennies worth 1.71 billion billion (a.k.a. a quintillion) dollars. And it's worth noting that Red Bull has roughly 2.1 times as much caffeine per ounce as Mountain Dew while Jolt sports close to 2.6 times as much caffeine per ounce as Mountain Dew.
Now that you know about moles, what fun figures can you come up with? Post them in the comments section below.
3 Responses to “Molecules of Caffeine”
A caffeine molecule actually has 8 carbon atoms, not 3. Your structural diagram is correct, but the unlabeled atoms (e.g., the node at the far left of the "pentagon," between the two nitrogen atoms) of all such diagrams are assumed to be be carbon. Also, individual carbon-hydrogen bonds are not usually shown, so any node with fewer than four bonds (e.g., the same carbon atom as in the previous example) is assumed to have enough hydrogen atoms to make up the difference.
The empirical formula for caffeine is actually C8 H10 N4 O2. (Sorry, I cannot figure out how to enter subscripts in your blog.) So, unless I have made an arithmetic mistake, caffeine weighs 194.1918 g/mol. I leave the rest of the calculation as an exercise for the student.
By Peter Chastain on May 9, 2008
@Peter,
Thanks for the heads up. I've made corrections above.
By Greg Bulmash on May 10, 2008