How Many Atoms Are in a Drop of Water?

Calculate Atoms and Molecules in a Water Droplet

There are approximately 5 sextillion atoms in a drop of water.
There are approximately 5 sextillion atoms in a drop of water. Shawn Knol, Getty Images

How many atoms are in a drop of water? 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 water drop and more than 5 sextillion atoms per droplet.

How To Calculate the Number of Atoms and Molecules in a Water Drop

Here are the steps used to perform the calculation to determine how many molecules  and how many atoms are in a volume of water.

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 a 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:

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.

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 more dense; warm water is less dense), but the value typically used in calculations is 1.00 gram per milliliter (1 g/mL).

Or, 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 the number of moles is:

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

Avogrado's Number To Determine Number of Molecules

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 numbers 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 Compared With Drops in the Oceans

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 value of 1.338 billion km3 for the sample calculation, but you can use whichever number you 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.

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

# 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 1000 and 100,000 more drops of water in the ocean than atoms in a drop of water.

Reference

Gleick, P.H. Earth's Water Distribution. Water Science for Schools. U.S. Geological Survey. 28 August 2006.