Mole Concept Explained

Daniel Iyamuremye -

October 23, 2021, on a socio-platform of Chemistry, we were reminded by a friend who forwarded us a Happy Mole Day wish. October 23(6.02 am-6.02 pm), each year, is Mole Day.

This reminded me of a conversation I had with a secondary school teacher some years back who said that the concept of mole was difficult to understand for secondary school students. That was confirmed through different questions asked in other international chemistry platforms I participate in and pushed me to revisit this concept and write this post.

The Mole Day pops up at an appropriate moment when we are talking about chemical equation, interpretation of a chemical equation and stoichiometry.

The mole concept is very fundamental in chemistry. It is used in many operations and activities such as; establishment of chemical equations, stoichiometric calculations, preparations of mixtures and solutions, quantitative analysis, calculations of amounts of reactants involved in industrial operations, etc.

A Mole is simply a measuring unit in which quantities of  chemical species are expressed. In the same way as when I say a class of students, you may understand 20 students, a full stadium it may mean 20,000 spectators, 1 ton of rice to mean 1000 Kg of rice, 1 century to mean 100 years, etc.

A Mole is defined as the amount of a chemical species that contains as many elementary entities (atoms, molecules, ions, electrons) as there are atoms of Carbon in 12 g of Carbon-12. This number is equal to 6.02 x 1023, or Avogadro Number (NA). This number has been named after an Italian Chemist and Physicist, Amedeo Avogadr. It is represented by the symbol NA.

Avogadro is particularly known for his hypothesis, in 1811, known as Avogadro’s Law that states, Equal volumes of all gases contain the same number of molecules (or atoms if the gas is monatomic) at the same pressure and temperature. Later on it was proved that this hypothesis was true only for ideal gases.

As mentioned above, a Mole is a unit to measure a quantity of chemical species that can be expressed in terms of the number of elementary particles, as seen in the previous paragraph, or in terms of mass.

Molar Mass (Mm)

The Molar mass, Mm, is the mass of 1 Mole of a chemical species, and is equivalent to the relative mass of the chemical species expressed in grams.

Examples of molar masses (Mm): H2O(18g), NH3(17g), CO(28g), OH-(17g)

Let’s start by examples to illustrate the relationship between the Mole Concept and Avogadro Number, using hydrogen (H2), oxygen (O2) and carbon (C)

1. How many molecules of hydrogen are in 2.016 g of hydrogen, corresponding to the Molar mass of hydrogen?

The number of hydrogen molecules is calculated by dividing the molar mass by the mass of one molecule of hydrogen expressed in grams.

Mass of H2 molecule in grams: 2 x 1.008 amu x 1.6603x10-24 g/amu = 3.3471x10-24g

Number of molecules in 2,016g = 2.016g / 3.3471x10-24g = 6.02x1023

2. How many molecules of oxygen are in 32 g of oxygen, the molar mass of oxygen?

The mass of O2 molecule in grams: 2x16 amu x 1.6603x10-24 g/amu= 5.3130x10-23g

Number of O2 molecules in 32 g: 32g/5.3130x10-23g = 6.02x1023

3. How many carbon atoms are in 12 g of carbon, the molar mass of carbon (carbon is considered as a monoatomic molecule, C)?

The mass of C atom in grams: 12 amu x 1.6603x10-24 g/amu = 1.9924x10-23g

Number of C atoms in 12 g: 12 g/1.9924x10-23g = 6.02x1023

As you can notice, when the molar mass expressed in grams of any substance is divided by the molecular mass expressed in grams, you get the same number for any chemical species: 6.02x1023

To help understanding more the Mole Concept, let’s take the following example:

A shop or supermarket sells biscuits by packet.

Each packet contains 100 biscuits and each biscuit weighs 2.5g.

When you buy a packet of biscuits, you know that you are buying 100 biscuits weighing a total of  250g, or 100 biscuits of 2.5 g each.

If you tell someone what you have bought, you can say; a packet of biscuits, or 100 biscuits, or 250 g of biscuits. The quantity of biscuits you have bought is the same, but expressed in different ways.

In the same way, the term Mole represents a quantity of chemical species that can be expressed in number, 6.02 x 1023 (Avogadro Number) or in mass of those species expressed in grams. The mass of 1 Mole is called Molar Mass (Mm) of the chemical species.

Examples:

  1. 1 Mole of hydrogen gas, H2, is equivalent to 2.016 g of hydrogen gas, or 6.02x1023 molecules of H2.
  2. 0.5 Mole of hydrogen gas, H2, is equivalent to 2.016g/2 = 1.008 g of hydrogen gas, H2, or ½ x 6.02x1023 = 3.01x1023 molecules, H2.
  3. 1 Mole of hydrogen atoms, H, is equivalent to 1.008 g of H atoms or 6.02x1023 of H atoms.

Therefore we can briefly say that 1 Mole is equal to an Avogadro Number (6.02 x1023) of a chemical species; that number of a chemical species can be translated into mass of chemical species:

  • 1 Mole of water = 6.02x1023 molecules of H2O = 18 g of Water
  • 1 Mole of carbon = 6.02x1023 atoms of C = 12 g of carbon
  • 1 Mole of electrons = 6.02x1023 electrons (e) = 6.02x1023 x 1.60 x10-19 C = 96,500 C = 1 Faraday (i.e. 1 mole of electrons bears a total electrical charge of 1 Faraday).

To convert any amount of substance in moles, you divide the amount of the substance, expressed in grams, by its molar mass expressed also in grams:
Moles = Weight(g)/Mm(g)

Examples:
Calculate the number of moles in: (i) 10g of water, (ii) 18 g of Calcium Hydroxide, (iii) 1kg of Sulphuric Acid:

  1. Moles of water (H2O): 10 g/18.0154 g = 0.555
  2. Moles of Calcium Hydroxide (Ca(OH)2): 18 g/74.0928 g = 0.243
  3. Moles of Sulphuric Acid (H2SO4): 1,000 g/98.0796 g = 19.196

The number of molecules present in each amount of those substances is found by multiplying the number of moles of each substance by the Avogadro Number.

Final note:

The source of difficulty experienced by many in understanding the Mole Concept may result from the fact that it expresses the same reality but in two different ways.

  1. The Mole expresses a number 6.02 x1023: therefore, 1 mole of H2 molecules has the same number of molecules as 1 mole of H2O molecules, 1 mole of OH- ions. Just as the number of 100 babies equal the number of 100 adult people.
  2. The mole also expresses a mass called the Molar mass: the molar mass of each substance or chemical species differs: 1 mole of H2 = 2 g, 1 mole of H2O = 18 g, 1 mole of OH- ions = 17 g. Just as the weight of 100 babies is ≈ 500 Kg (5 Kg x 100), whereas that of 100 adult people ≈ 6500 Kg (65 Kg x 100).
  3. 1m3 of cotton occupies the same volume as 1m3 of water, but the quantity of matter in 1m3 of cotton is very little compared to the quantity of matter in 1m3 of water. In the same way, the quantity of matter in 1 mole of H2 is different from the quantity of matter present in 1 mole of H2O.