## Table of Content

Introduction Formulae Solved Examples

## What is the Mole Concept?

The mole concept is a convenient method of expressing the amount of a substance. Any measurement can be broken down into two parts – the numerical magnitude and the units that the magnitude is expressed in. For example, when the mass of a ball is measured to be 2 kilograms, the magnitude is ‘2’ and the unit is ‘kilogram’.

When dealing with particles at an atomic (or molecular) level, even one gram of a pure element is known to contain a huge number of atoms. This is where the mole concept is widely used. It primarily focuses on the unit known as a ‘mole’, which is a count of a very large number of particles.

### What is a Mole?

A mole is defined as the amount of a substance that contains exactly 6.02214076 * 10^{23}‘elementary entities’ of the given substance.

The number 6.02214076*10^{23} is popularly known as the Avogadro constant and is often denoted by the symbol ‘N_{A}’. The elementary entities that can be represented in moles can be atoms, molecules, monoatomic/polyatomic ions, and other particles (such as electrons).

For example, one mole of a pure carbon-12 (^{12}C) sample will have a mass of exactly 12 grams and will contain 6.02214076*10^{23} (N_{A}) number of ^{12}C atoms. The number of moles of a substance in a given pure sample can be represented by the following formula:

*n = N/N _{A}*

Where n is the number of moles of the substance (or elementary entity), N is the total number of elementary entities in the sample, and N_{A} is the Avogadro constant.

The word “mole” was introduced around the year 1896 by the German chemist Wilhelm Ostwald, who derived the term from the Latin word moles meaning a ‘heap’ or ‘pile.

The number of moles of a molecule may not always be equal to the number of moles of its constituent elements. For example, a mole of water contains N_{A} number of H_{2}O molecules. However, each water molecule contains 2 hydrogen atoms and one oxygen atom. Therefore, one mole of H_{2}O contains 2 moles of hydrogen and one mole of oxygen.

## Related Quantities and their Formulae

### Atomic and Molecular Mass

The **atomic mass** of an element is the mass of one atom of the element expressed in atomic mass units (amu). It accounts for the abundance of the various isotopes of the element and assigns an average value to the mass of one atom of the element.

For example, the atomic mass of carbon is 12.011 atomic mass units since carbon samples generally contain 98.89% of the carbon-12 isotope, 1.11% of carbon-13, and trace amounts of carbon-14. However, the atomic masses of these isotopes are different.

The atomic mass of a carbon-12 atom is 12 atomic mass units, but that of a carbon-13 atom is 13 amu. The atomic mass of an element is roughly equal to the sum of all the protons and neutrons present in its nucleus.

The **molecular mass** of an element is the sum of the atomic masses of all its constituent elements. This quantity is also represented in terms of atomic mass units. Therefore, the molecular mass of water is equal to the sum of the atomic masses of its constituents – hydrogen and oxygen.

The atomic mass of hydrogen is 1.00794 amu and that of oxygen is 15.9994. Since water molecules contain 2 hydrogen atoms and only one oxygen atom, the molecular mass of H_{2}O is 18.0154 amu.

### Molar Mass

The **molar mass** of a substance is defined as the total mass of one mole of the substance. It is often represented in terms of ‘grams per mole’ (g/mol). However, the SI unit of this quantity is kg/mol. Molar mass can be represented by the following formula:

*Molar mass of a Substance = (Mass of the Substance in grams)/(Number of Moles)*

For example, the molar mass of water is approximately 18.015 g/mol, which is the mass of N_{A} number of water molecules.

### Gram Atomic Mass and Gram Molecular Mass

The gram atomic mass of an element is the mass of one mole of that element. Similarly, the gram molecular mass of a compound refers to the mass of a single mole of the compound. Therefore, the gram atomic mass of hydrogen is approximately 1.007g and the gram molecular mass of water is approximately 18.015g.

### Related Formulae

The number of moles in a given sample of an element/compound can be calculated by dividing the total mass of the sample by the molar mass of the element/compound, as described by the following formula.

*Number of Moles = (Mass of the Sample)/(Molar Mass)*

The total number of atoms/molecules in a sample can be calculated by multiplying the number of moles with the Avogadro constant. This formula can be written as:

*Number of Atoms or Molecules = (Number of Moles)*(6.022*10 ^{23})*

The relationship between the atomic mass unit (amu) and the gram is given by:

*1 amu = (1gram)/(6.022*10 ^{23}) = 1.66*10^{-24} grams*

Therefore, the mass of one mole of an element will be equal to its atomic mass in grams.

## Solved Examples on the Mole Concept

Some solved example questions on the mole concept are provided in this subsection.

**Q.1:** How many moles of iron are present in a pure sample weighing 558.45 grams?

**A.1:** The molar mass of iron is 55.845 g/mol. Therefore, the number of moles of iron in the pure sample weighing 558.45 grams is:

= 10 moles.

**Q.2:** How many molecules of water are present in 36 grams of water?

**A.2:** The molar mass of water is 18 (approximately). Therefore, 36 grams of water makes up a total of 2 moles. Each mole has 6.022*10^{23} water molecules. The total number of H_{2}O molecules in 36 grams of water is: 12.044*10^{23}

**Q.3:** How many grams of carbon can be found in 1 mole of carbon dioxide?

**A.3:** 1 mole of CO_{2} contains 1 mole of carbon and 2 moles of oxygen. The molar mass of carbon is 12.0107 g/mol. Therefore, 1 mole of CO_{2} contains 12.01 grams of carbon and 32 grams of oxygen.

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