An Ounce of Water

	How many molecules of water are in one fluid ounce?
	About 1024, which is one septillion or 1,000,000,000,000,000,000,000,000.

The molecular weight of a hydrogen atom is about one amu and an oxygen atom is about 16 amu (atomic mass units). Thus, the molecular weight of a water molecule (two hydrogen atoms and one oxygen atom) is about 18 amu. Using Avogadro's Number, we know that 18 grams of water contain about 6 x 1023 molecules.

Since one fluid ounce of water equals about 30 cubic centimeters (cc), and water at room temperature has a density of about one gram per cc, we can now calculate the number of molecules.

30 * (6 x 1023) / 18 = 1024 molecules per fluid ounce.

That didn't even require a calculator. But if we have one handy, we can do the calculation with more digits of precision using the following numbers. We should also include the units of measurement to verify that they cancel out properly.

Now we can calculate a more precise result.

	0	.	99821	grams per cc
*	29	.	57353	cc per fluid ounce
*	6	.	02214 x 1023	molecules per mole
/	18	.	01528	grams per mole
=	9	.	86813 x 1023	molecules per fluid ounce

After all that work, we find that our initial answer above is off by less than 1.4 percent. Close enough for "government work" or casual conversation about homeopathic dilutions.