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
• Avogadro’s Number

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.

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.