Calculating the Number of Atoms and Molecules in a Drop of Water

Have you ever wondered how many atoms are in a drop of water or how many molecules are in a single droplet? The answer depends on your definition of the volume of a droplet of water. Water drops vary dramatically in size, so this starting number defines the calculation. The rest of it is a simple chemistry calculation.

Let's use the volume of a water drop that is used by the medical and scientific community. The accepted average volume of a drop of water is exactly 0.05 mL (20 drops per milliliter). It turns out there are over 1.5 sextillion molecules in a drop of water and more than 5 sextillion atoms per droplet.

Chemical Formula of Water

To calculate the number of molecules and atoms in a water drop, you need to know the chemical formula of water. There are two atoms of hydrogen and one atom of oxygen in each water molecule, making the formula H₂O. So, each molecule of water contains 3 atoms.

Molar Mass of Water

Determine the molar mass of water. Do this by adding up the mass of hydrogen atoms and oxygen atoms in a mole of water by looking up the atomic mass of hydrogen and oxygen on the periodic table. The mass of hydrogen is 1.008 g/mol and the mass of oxygen is 16.00 g/mol, so the mass of a mole of water can be calculated as follows:

mass water = 2 x mass hydrogen + mass oxygen

mass water = 2 x 1.008 + 16

mass water = 18.016 g/mol

In other words, one mole of water has a mass of 18.016 grams.

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Density of Water

Use the density of water to determine the mass of water per unit volume. The density of water actually varies depending on conditions (cold water is denser; warm water is less dense), but the value typically used in calculations is 1.00 gram per milliliter (1 g/mL). In other words, 1 milliliter of water has a mass of 1 gram. A drop of water is 0.05 mL of water, so its mass would be 0.05 grams.

One mole of water is 18.016 grams, so in 0.05 grams, in one drop, the number of moles is:

• moles of water in one drop = 0.05 grams x (1 mole/18.016 grams)
• moles of water in one drop = 0.002775 moles

Using Avogrado's Number

Finally, use Avogadro's number to determine the number of molecules in a drop of water. Avogadro's number tells us there are 6.022 x 10²³ molecules of water per mole of water. So, next we calculate how many molecules there are in a drop of water, which we determined contains 0.002775 moles:

• molecules in a drop of water = (6.022 x 10²³ molecules/mole) x 0.002275 moles
• molecules in a drop of water = 1.67 x 10²¹ water molecules

Put another way, there are 1.67 sextillion water molecules in a water drop.

Now, the number of atoms in a droplet of water is 3x the number of molecules:

• atoms in a drop of water = 3 atoms/molecule x 1.67 x 10²¹ molecules
• atoms in a drop of water = 5.01 x 10²¹ atoms

Or, there are about 5 sextillion atoms in a drop of water.

Atoms in a Drop of Water vs. Drops in the Ocean

One interesting question is whether there are more atoms in a drop of water than there are drops of water in the ocean. To determine the answer, we need the volume of water in the oceans. Sources estimate this to be between 1.3 billion km³ and 1.5 km³. I'll use the USGS (United States Geologic Survey) value of 1.338 billion km³ for the sample calculation, but you can use whichever number you would like.

1.338 km³ = 1.338 x 10²¹ liters of seawater

Now, your answer depends on the size of your drop, so you divide this volume by your drop volume (0.05 ml or 0.00005 L or 5.0 x 10^-5 L is the average) to get the number of drops of water in the ocean.

number of drops of water in the ocean = 1.338 x 10²¹ liters total volume / 5.0 x 10^-5 liters per drop

number of drops of water in the ocean = 2.676 x 10²⁶ drops

So, there are more drops of water in the ocean than there are atoms in a drop of water. How many more drops depends mainly on the size of your drops, but there are between 1,000 and 100,000 more drops of water in the ocean than atoms in a drop of water.

Source

Gleick, P.H. "Where is Earth's Water." Earth's Water Distribution. U.S. Geological Survey, 28 August 2006.