## 1. From how much to how many

We deem rice, water, and sand as uncountable (money too, but not for me unfortunately). When we scoop rice for others, it would be very odd to ask “how many rice you want” and to proceed with giving the exact number of rice grains.

But Chemistry is odd, very odd. It is a precise, mathematical science. It deals not with how much, but how many. In this topic, we will learn how to calculate the exact number of particles, be it water molecules in your water bottle or silicon atoms in sand.

## 2. Astronomically large numbers of infinitesimally small atoms

Since atoms are so very small, it takes a huge number of atoms to make up the things around us. Let’s take your graphite pencil lead as an example. Even one thin, feather-light piece has around 2×1021 carbon atoms! This is an astronomical number, with 21 zeroes behind the 2.

## 3. No more mumbo jumbo, when you have Avogadro

Thankfully, when we count the number of particles, we do not need to fumble with all the zeroes. This is because chemists count in moles. We can express 6×1023 particles as one mole (unit symbol = mol). This special number of 6×1023 has a special name: the Avogadro number.

A mole (1 mol) is the Avogadro number of particles, which is 6×1023.

When we are given a large number of particles, we can convert it to the number of moles by dividing it with the Avogadro number.

number of moles = number of particles ÷ Avogadro number

So back to the piece of graphite pencil lead with 2×1021 carbon atoms. To find the number of moles, we shall divide it by the Avogadro number, 6×1023 to get 0.00333 mol.

## 4. No mess with the molar mass of atoms

The molar mass of the atoms of an element, which is the mass of 1 mol of atoms, is numerically equal to the relative atomic mass.

Being numerically equal means that they have the same number, like 12 for the case of carbon. However, they are not actually the same. Unlike mass, relative atomic mass is a ratio with no unit. It is the ratio of the mass of an atom relative to one-twelfth (1/12) of the mass of carbon-12. The actual mass of a single atom is in fact a very small number when expressed in grams.

## 5. The molar mass of molecules

In the same vein, the mass of 1 mol of molecules is numerically equal to the relative molecular mass. You can find the relative molecular mass of a molecule by adding the relative atomic mass of each of the constituent atom.

Confused? Let’s demonstrate by finding the molar mass of water.

H2O

• ### STEP 2: Add the relative atomic mass, Ar of all the atoms in a molecule to get the relative molecular mass, Mr

Mr of H2O
= 2 × Ar of H + Ar of O
= 2 × 1 + 16
= 18

• ### STEP 3: Sneakily add the unit for grams behind and voila, you get the molar mass

Molar mass of H2O = 18 g/mol

## 6. Tell me more, tell me mole

Armed with the knowledge of molar mass, you can find out the number of moles of anything from its mass.

Say you have 200 g of water in your mug. To find the number of moles, simply divide the mass by molar mass: 200 ÷ 18 = 11.1 mol.

number of moles = mass ÷ molar mass