How Many Molecules Are 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. Lets 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. 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 Avogrados Number Finally, use  Avogadros number to determine the number of molecules in a drop of water. Avogadros 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 molesmolecules 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 moleculesatoms 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. Ill 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 Earths Water. Earths Water Distribution. U.S. Geological Survey, 28  August  2006.