# 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 answer to this question requires only three simple facts from high school chemistry:

• The mass of a fluid ounce of water
• The mass of a water molecule

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.

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 is about 18 amu (two hydrogen atoms and one oxygen atom).

According to Avogadro’s Number, 18 grams of water contain about 6 x 1023 molecules.

We can now calculate the number of molecules as follows.

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.

• Water at room temperature (68 F) is .99821 grams per cc (source)
• One fluid ounce is 29.57353 cubic centimeters (source) (see footnote)
• Avogadro’s Number is 6.02214199 x 1023 molecules per mole (source)
• Hydrogen is 1.00794 amu (source)
• Oxygen is 15.9994 amu (source)
• Thus, water (H2O) is 18.01528 grams per mole

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 = 0 . 9868 x 1024 molecules per fluid ounce

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

Footnote:   Since ounces of liquid volume are not the same as ounces of weight, we want to be careful not to use the conversion factor of one ounce equals 28.349 grams. Nor do we want to use the conversion for troy ounces.
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