It is common to have problems finding out how many molecules are in a drop of water, because you have to handle a series of concepts that can be somewhat confusing if you do not master chemical calculations. The concepts that must be known are conversion units, volume, mass, density, the chemical formula, the calculation of the mole and Avogadro’s number.

The way to calculate the molecules of a drop of water, step by step, could be as follows:

- Know the chemical formula of water to know the mass of a mole of water.
- Know the density of water to know the mass per unit volume.
- Multiply the mass per unit volume, and then by the volume of a drop of water, to find the mass per drop.
- Convert grams to moles , to find the moles of water per drop.
- Use Avogadro’s number to find the number of water molecules per drop.

In the event that you also wanted, there is a way to know the number of atoms that are in a drop of water. It would be developed by multiplying the number of molecules by the number of atoms in a drop of water.

The drop as such is not considered a standard measure, and is only used when you want to refer to very small volumes of liquids. In some fields, such as medicine and pharmacy, drops are required as a means of drug dosing, so depending on the dropper or dropper used, it is necessary to know how many drops have a given volume unit. . Usually, to obtain a milliliter of a certain substance, 15 to 40 drops are needed. Normally the relationship is taken that 20 drops occupy 1 mL.

**volume of a drop of water**

The volume of a drop of water is the first thing to look for to know how many molecules are in it. On average, a drop of water with a volume of 0.05 mL is identified, which is what results from the relationship that 20 drops occupy 1 mL. So to start calculating the number of molecules in a drop of water, you start with this relationship.

**Chemical formula and molar mass of water**

To determine the mass of a water molecule, it is enough to know the mass of water using its chemical formula. The formula for water, H 2 O, indicates that in each of its molecules there are two hydrogen atoms and one oxygen atom.

To know the molar mass of water, one would have to look up the atomic masses of hydrogen and oxygen in the periodic table, and then add the masses of the hydrogens and oxygens.

According to 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 one mole of water is:

Mass of water = 2 x mass of hydrogen + mass of oxygen,

that is to say:

Mass of water = 2 x (1.008 g/mol) + 16.00 g/mol = 18.016 g/mol.

Therefore, the mass of one mole of water is 18.016 grams.

**water density**

The density of water is used to find the mass per unit volume. Keep in mind that the density of water varies with temperature, so that water at lower temperatures is denser than when it is at higher temperatures. The typical value of the value of the density of water is taken to be 1.00 g/m; thus, 1 mL of water has 1 gram, but a drop of water has a volume smaller than the millimeter of which we are speaking, so the mass for that considered volume of a drop of 0.05 mL would have to be calculated.

Mass of a drop of water = 1 g/mL x 0.05 mL = 0.05 grams

Knowing the mass of a drop of water from its density, we can know the moles that are in that mass, knowing that the moles can be calculated from the mass divided by the molecular mass that has already been calculated previously. .

Moles in a drop of water = 0.05 grams x (1 mol/18.016 grams) = 0.02775 moles

Therefore, we can say that in a drop of water there are 0.002775 moles of water.

**Atoms, molecules and Avogadro’s number**

Amadeo Avogadro first proposed that the volume of a gas at a given pressure and temperature is proportional to the number of atoms or molecules in that gas, regardless of its type. Although he did not determine the exact ratio, he is considered the discoverer of this relationship between moles and the number of molecules of a gas.

Avogadro’s number is fundamental to understanding both the composition of molecules and their interactions and combinations. For example, since one oxygen atom will combine with two hydrogen atoms to create a water molecule (H 2 O), one mole of oxygen (6,022.10 23 O atoms) will combine with two moles of hydrogen (2 × 6,022.10 23 H atoms) to form one mole of H 2 O.

Another property of Avogadro’s number is that the mass of one mole of a substance is equal to the molecular weight of that substance. For example, the average molecular weight of water is 18.016 atomic mass units (amu), so a mole weight of water is 18.016 grams.

According to this, in the 16.00 g/mol of oxygen, the number of water molecules would contain 6,022.10 23 oxygen atoms, and the 2.016 g of hydrogen that reacts with it would contain double (12,044.10 23 ) hydrogen atoms.

The very large numbers involved in counting microscopic particles could lead to inconvenience, so it has been chosen to count atoms and molecules using the unit called mole. Thus, a mole contains 6,022.10 23 of the microscopic particles that make up the substance in question.

Avogadro’s number is the number of molecules in a mole. This means that per mole of water there will be 6,022.10 23 water molecules. Since we have 0.002775 moles of water in a drop, we could calculate how many molecules it is as follows:

Molecules in a drop of water = (6,022.10 23 molecules/mol) x 0.002775 moles = 1.67.10 21 molecules of water

There are three atoms per molecule of water. Knowing this, and knowing the number of molecules, we can know the atoms that are in a drop of water.

Atoms in a drop of water = (3 atoms/molecule) x 1.67.10 21 = 5.01.10 21 atoms

**How many drops of water are in the ocean?**

Once the atoms in a drop of water are known, the following question could be posed, which seems like a paradox: are there more atoms in a drop of water than drops of water in the ocean? To do this, it must be known that the approximate estimate of water in the oceans on Earth is approximately 1,338 billion km 3 , which translates as 1,338.10 21 liters of water.

Based on the number of liters, you can find out the number of drops of water in the ocean, dividing both amounts:

Number of drops of water in the ocean = 1,338.10 21 liters of water / 5.0.10 -5 liters per drop = 2,676.10 26 drops

This number of drops is greater than the number of atoms, so it can be concluded that there are more drops of water in the ocean than there are molecules or atoms in a single drop of water.

## References

*Avogadro’s Number and the Mole | Introduction to Chemistry* . (2022). Retrieved February 27, 2022 from https://courses.lumenlearning.com/introchem/chapter/avogadros-number-and-the-mole/

Helmenstine, A. (2020). *How Many Molecules and Atoms in a Drop of Water? *Retrieved on February 27, 2022 from https://sciencenotes.org/how-many-molecules-and-atoms-in-a-drop-of-water/

Number of Atoms in a Drop of Water. (2016). Retrieved February 27, 2022 from https://chem.libretexts.org/Ancillary_Materials/Exemplars_and_Case_Studies/Exemplars/Biology/Number_of_Atoms_in_a_Drop_of_Water