## What is a Mole Concept?

Mole concept is a method to determine the amount of any substance that consists of some elemental particles using a grouping unit called ‘mole’. The mole concept enables one to handle the large amount of small elementary particles. The mole concept can be used in many calculations related to mole calculation, molar amount, mole ratio, and so on, which are significant in chemistry.

## Calculation of Minute Particles

The size of elementary particles like atoms, molecules, ions and electrons are really small such that determining their number in a particular amount is very difficult. For example, if we count the same type of coins worth twenty lakhs, it will take a lot of time and effort. However, if the total mass of the bag is 10000 g and the mass of one coin is 5 g, then the number of coins can be easily calculated by dividing the total mass by mass of one coin. Thus, the number of coins will be equal to 2000.

Like this we can find the number of minute particles using their relation with mass. If the particles are of same mass and size, then we could count even very huge numbers of them based on the mass concept. The mass of minute particles can be found out using many modern methods. For example, the mass of atomic hydrogen is found to be 1.67 ×10^{-24} g. This is very accurate value. However, for practical usage we are using relative atomic mass.

Relative atomic mass is obtained using a reference mass of an atom. The mass of an atom is compared with the mass of this reference atom, and the mass is expressed as how many times it is heavier than the reference atom. Usually, the relative mass of elements has been calculated using 1/12 mass of a carbon-12 atom as one unit.

The atoms were arranged on the basis of their atomic number and relative atomic mass in the periodic table.

## Avogadro’s Number, GAM and GMM

When an element is taken in an amount which is equal to its relative atomic mass, it will contain ${\text{N}}_{\text{A}}$ number of those atoms in it. ${\text{N}}_{\text{A}}$is called as Avogadro number and it is equal to $\text{6}{\text{.022\xd710}}^{\text{23}}$. Taking the example of carbon, the relative atomic mass of carbon is 12. Thus, 12 g of carbon will contain $\text{6}{\text{.022\xd710}}^{\text{23}}$carbon atoms. Another example; the relative atomic mass of oxygen is 16, thus 16 g of oxygen will contain 6.022×1023 oxygen atoms. This amount of an element which is equal to its relative atomic mass is taken as Gram atomic mass (GAM). One GAM is equal to $\text{6}{\text{.022\xd710}}^{\text{23}}$atoms.

Taking this to next level we could find the number of atoms in a given amount of substance. One GAM of carbon is equal to 12 g and 2 GAM of carbon is equal to 24 g. Thus, 24 g of carbon contains 2 × $\text{6}{\text{.022\xd710}}^{\text{23}}$atoms.

Same concept can be applied for molecules also. In that case, instead of Gram atomic mass (GAM) gram molecular mass (GMM) is taken. GMM is the sum of relative atomic masses of all the elements present in a molecule calculated from the molecular formula. For example, GMM of ${\text{CO}}_{\text{2}}$ is 44 g, this can be calculated as the following;

Relative atomic mass of carbon = 12

Relative atomic mass of oxygen = 16 and there are two oxygen atoms

Then the molecular mass of carbon dioxide = $\text{12+}\left(\text{2\xd716}\right)\text{=44}$and that of is 18 g.

Relative atomic mass of hydrogen = 1 and there are two hydrogens.

Relative atomic mass of oxygen =16

Then the molecular mass of water = (2×1) +16 = 18

One GMM is equal to $\text{6}{\text{.022\xd710}}^{\text{23}}$molecules. Thus, Formula mass is different from molecular mass; it is calculated from empirical formula which is known as the simplest formula.

## What is a ‘Mole’?

Mole can be simply considered as a grouping unit like pair and dozen, which is used to represent the number of elementary particles, especially atoms and molecules. The word ‘mole’ in Latin means ‘bulky heap’ of some material. One pair contains 2 entities, one dozen contains 12 entities and similarly one mole contains $\text{6}{\text{.022\xd710}}^{\text{23}}$entities.

One mole of atom denotes $\text{6}{\text{.022\xd710}}^{\text{23}}$atoms in it. One mole of molecule denotes $\text{6}{\text{.022\xd710}}^{\text{23}}$molecules in it. If we are taking one mole of chocolates, it will contain $\text{6}{\text{.022\xd710}}^{\text{23}}$chocolates!!!

The number $\text{6}{\text{.022\xd710}}^{\text{23}}$is equal to one GAM/GMM, thus we can sum up this like the following;

Knowing the number of moles can lead to the amount of substance and if the amount of a given substance is provided then the number of particles (atoms or molecules) can be calculated. Also, the molecular mass of an unknown substance can be calculated if the number of moles and amount is known. This can be used to identify compounds.

The mass in grams of one mole of a substance is known as molar mass and the unit is g/mol. It can be stated like the mass of particles present in one mole of a substance.

The atomic mass of one mole of an element in grams is measured in atomic mass unit (amu). For example, the atomic mass of carbon is 12 amu which means one mole of carbon will weigh 12 grams and 2 moles will weigh 24 grams and thus, the we can find how many moles are present in given mass.

## Common Mistakes

- Do not confuse between ‘mole’ and ‘molecule’.
- Differentiate between atom and molecule. For example, when it is referred as chlorine atom take GAM in to consideration and when it says chlorine gas remember that the chlorine gas is diatomic. Thus, GMM should be taken.
- Do not consider mole as unit of mass. Mole is a unit which denotes the number of particles.
- Do not confuse between molar mass, molecule mass and formula mass.

## Formulas

- $\begin{array}{l}\text{GAM=Gramatomicmass}\hfill \\ \text{Givenmass=amountofthegivensubstanceingrams}\hfill \end{array}$

- $\begin{array}{l}\text{GAM=Gramatomicmass}\hfill \\ \text{6}{\text{.022\xd710}}^{\text{23}}\text{istheAvogadronumber}\hfill \end{array}$

- $\begin{array}{l}\text{GMM=Grammolecularmass}\hfill \\ \text{Givenmass=amountofthegivensubstanceingrams}\hfill \end{array}$

- $\begin{array}{l}\text{GMM=Grammolecularmass}\hfill \\ \text{6}{\text{.022\xd710}}^{\text{23}}\text{istheAvogadronumber}\hfill \\ \text{}\hfill \end{array}$

- $\begin{array}{l}\text{GAM=Gramatomicmass}\hfill \\ \text{GMM=Grammolecularmass}\hfill \end{array}$

- $\begin{array}{l}\text{GAM=Gramatomicmass}\hfill \\ \text{GMM=Grammolecularmass}\hfill \\ \text{Givenmass=amountofthegivensubstanceingrams}\hfill \\ \text{}\hfill \end{array}$

## Practice Problem

Q. What is the number of particles (atoms/molecules) present in 42 g of nitrogen?

(Atomic mass of nitrogen=14, atomic mass of Oxygen=16, atomic mass of hydrogen=1, atomic mass of chlorine=35.5)

Ans. 9.033 × 10^{23}

## Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for Bachelors and Masters in Chemistry.

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