Mole Concept | What is mole

A mole concept or mole refers to the amount of a substance that has the same number of particles, atoms or molecules as the number of atoms present in 12 grams of C-12 atom, which is an isotope of carbon. So, the mole concept generally tells the number of atoms or such particles which are equal in number to the atoms present in the 12 grams of C-12.

We can say that C-12 atom is taken as a standard to compare the number of atoms or molecules or particles present in the given amount of a substance.

The number of particles present in one mole of any substance = 6.023×10²³. This is because the number of atoms present in C12 with mass 12 grams is equal to the 6.023×10²³. This number is known as an Avogadro's number. So, 1 mole of a substance will contain Avogadro's no. of particles or 6.0222 x 10²³ particles of that substance. It can be atoms, molecules or any other particles. For example, 1 mole of iron will contain 6.0222 x 10²³ atoms of iron, similarly, 1 mole of water will contain 6.0222 x 10²³ molecules of water. So, we can say that as per the definition of mole, the number of atoms present in 1 mole of iron is equal to the number of atoms of C-12 present in 12 grams of C-12.

So, the mole concept was introduced as a convenient method to expressing the number of particles in the given amount of a substance at an atomic or molecular level such as one gram of a pure element which contains a large number of atoms.

We can say that mole is just like a measurement that comprises two main parts that include the numerical magnitude and the units to express the magnitude. For example, if the mass of a ball is 2 kg, the magnitude is 2 and the unit is kilogram. Similarly, a mole is used as a unit of measurement for measuring the number of elementary entities like atoms, molecules, etc., just like kg is used for measuring weight, and meter is used for measuring length.

Furthermore, the mass of one mole of a substance is called the molar mass of that substance. 1 mole of all elements do not have the same mass, however, they have the same number of atoms. For example, the molar mass of a gold is different from the molar mass of carbon.

The mole concept was introduced by a scientist named Lorenzo Romano Amedeo Carlo Avogadro. So, the 1 mole of particles 6.0222 x 10²³ is known as Avogadro's number which represents 6.0222 x 10²³ number of particles just like a pair represents 2 and a dozen represents 12. For example, a boy goes to a shop and ask for Avogadro's number of chocolates then he wants 6.0222 x 10²³ chocolates. However, it has no practical use in daily life. So, it is introduced to represent quantities related to atoms, molecules, electrons, etc.

The number 6.0222 x 10²³ is also known as the Avogadro constant and is denoted by the symbol NA or N0. The number of moles of a given substance in a pure sample can be represented by the below formula;

n = N/N_A

n= number of moles of the substance

N= total number of particles in the given sample

N_A is the Avogadro constant or number.

The term 'mole' was introduced by the German chemist Wilhelm Ostwald. He derived this term from the Latin word 'moles' whose meaning is heap or pile.

Furthermore, the number of moles of a molecule may not be equal to the number of moles of its constituting elements. For example, one mole of carbon dioxide contains N_A number of CO₂ molecules. But, each molecule of carbon dioxide contains 2 oxygen atoms and one carbon atom. So, one mole of CO₂ contains 2 moles of oxygen and 1 mole of carbon.

Number of atoms or molecules = number of moles x 6.022 x 10²³

Furthermore, the atomic mass unit and mole both are based on the same reference substance C 12, so, the molar mass of a substance in gram is numerically equal to its atomic mass in amu.

Let us solve some numerical to understand the mole concept

Calculate the number of moles in the following cases;

i) In 52 gram of Helium (He)

Solution:

1 mole of He = 66.0222 x 10²³ He atoms

The atomic mass of 1 He atom = 4 u

The mass of 6.0222 x 10²³ atoms of He = 4g, which is equal to gram atomic mass of He

1 mole of He = 4 gram or gram atomic mass of He

Now, 4 gram of He = 1 mole

So, 52 gram of He will contain = � x 52 = 13 moles

ii) To find out number of moles in 12.044 x 10²³ atoms of He

Solution:

6.022 x 10²³ atom of He is equal to 1 mole of He

So, 12.044 x 10²³ atom will be equal to 1/6.022 x 10²³ x 12.044 x 10²³ moles = 2 moles

iii) Calculate the mass of 0.5 mole of N₂ gas

Solution:

One molecule of N₂ gas consists of two N atoms.

mass of one N atoms = 14 u

So, atomic mass of 2 N atoms (one molecule of nitrogen) = 14 u + 14 u = 28 u

Now, one mole of Nitrogen gas will contain 6.0222 x 10²³ molecules = 28 g, which is gram molecular mass of Nitrogen gas

So, 1 mole of N₂ contains 28 grams of N2 gas

So, 0.5 mole of N gas will contain = 0.5 x 28 g = 14 g of N₂ gas

iv) Calculate the mass 0.5 mole of N atoms

Solution:

Mass of one mole of N atoms or 6.022 x 10²³ atoms of N = 14 g

So, mass of 0.5 mole of N atoms will be = ½ x 14 g = 7 g

v) Calculate the mass of 2 moles of Oxygen atoms

Solution:

Mass of one mole of O atoms or 6.022 x 10²³ atoms or O = 16 g

So, mass of 2 mole of O atoms will be = 2 x 16 = 32 g

vi) Calculate mass of 3.011 x 10²³ number of N atoms

Solution:

The mass of 6.022 x 10²³ atoms of Nitrogen = 14 g (gram atomic mass of N)

So, mass of 3.011 x 10²³ atoms of Nitrogen = (14 / 6.022 x 10²³) x 3.011 x 10²³ = 7 g

vii) Calculate mass of 6.022 x 10²³ number of N₂ molecules

Sol:

Mass of one molecule of Nitrogen is 28 u as there are two N atoms.

So, mass of 6.022 x 10²³ molecules of Nitrogen (one mole of molecules molecule) or gram molecular mass of nitrogen molecules = 28 g

viii) Calculate number of particles in 46 g of Na atoms

Sol:

One mole of Na has 6.022 x 10²³ atoms

Mass of one Na atom is 23 u.

Mass of 6.022 x 10²³ atoms or 1 mole atoms of Na = 23 g (gram atomic mass)

Now, 23 g contains 6.022 x 10²³ atoms or particles

Then, 46 g of Na will contain = (6.022 x 10²³ / 23) x 46 = 12.044 x 10²³ atoms

ix) Calculate number of molecules in 8 g of O₂ molecules

Sol:

Atomic mass of one Oxygen atom = 16 u

In O₂, the mass of two O atoms = 32 u

If we take mass in grams, then mass of 1 mole or 6.022 x 10²³ molecules of Oxygen = 32 g

Now, in 32 g we have 6.022 x 10²³ molecules

So, in 8 g of O₂, we will have (6.022 x 10²³ / 32) x 8 = 1.5 x 10²³ molecules

x) Calculate number of particles in 0.1 mole of carbon atoms

Sol:

1 mole of carbon contains 6.022 x 10²³ atoms

So, 0.1 mole of carbon will contain = (6.022 x 10²³ /1) x 0.1 = 0.6022 x 10²³ atoms or particles

xi) Calculate the mass of 0.5 mole of silver

Sol:

Mass of 1 mole of silver (Ag) = gram atomic mass of Ag = 108 g

So, mass of 0.5 mole of silver (Ag) = (108/1) x 0.5 = 54 g

xii) Calculate the mass of 0.5 mole of sugar ( C₁₂ H₂₂ O₁₁)

Sol:

Mass of one molecule of sugar = 12 x12 + 1 x 22 +16 x 11

= 144 + 22 + 176 = 342 u

One mole of sugar contains 6.022 x 10²³ molecules

Mass of 6.022 x 10²³ molecules or 1 mole of sugar = 342 g

So, mass of 0.5 mole of sugar is = 342 x 0.5 = 171 g

Mole concept formulas

There are lots of formulas in mole concept that can be used to solve numerical involving mole concept, such as;

i) To convert mass in grams into moles

Number of moles = given mass in grams/ molar mass in g/mol

n = m / M, where m is mass given in grams and M is molar mass

ii) To convert given number of moles into grams

Mass in grams = number of moles x molar mass g/mol

m = n x M, where n is number of moles and M is molar mass

iii) To convert given number of moles of atom into number of atoms

Number of atoms or molecules = number of moles x Avogadro's number

N = n x N₀, where n is number moles and N0 is Avogadro's number, which can also be represented by N_A

iv) To convert given number of atoms or molecules into moles

Number of moles = given number of atoms or molecules / Avogadro's number

n = N/ N₀, where n is number of moles, N is given number of atoms or molecules and N₀ is Avogadro's number

Let us see some solved examples to understand how to use the above formulas;

i) Calculate the number of moles in 52 g or Helium (He)

Atomic mass of He = 4u

Molar mass of He = 4g

So, the number of moles = given mass / molar mass

n = m / M, where m is given mass in grams and M is molar mass

So, n = 52 / 4 = 13 moles

ii) Find number of moles in 12.044 x 10²³ number of He atoms

The number of moles = given number of particles / Avogadro's number

n = N/ N_A = 12.044 x 10²³ / 6.022 x 10²³ = 2 moles

iii) Calculate the mass 0.5 mole of N₂ gas

Sol. n = m / M (number of moles = mass in grams / molar mass)

Gram molecular mass of N₂ gas is 28 g.

m = n x M (M is molar mass = gram molecular mass)

= 0.5 x 28 g = 14 g

iv) Calculate mass of 0.5 mole of N atoms

m = n x M

Here, M is gram atomic mass of N, which is 14 g

m = 0.5 x 14 g = 7 g

v) Calculate mass of 3.011 x 10²³ number of N atoms

Number of particles or atoms = number of moles x Avogadro's number

N = n x N₀

No. of moles, n = N / N₀ = 3.011 x 10²³ / 6.022 x 10²³ = 0.5 mole

Now, 3.011 x 10²³ number of N atoms = 0.5 mole

Now apply formula, m = n x M (mass = number of moles x molar mass)

Here, M is gram atomic mass of N = 14 g

m = 0.5 x 14 = 7 g

vi) Calculate mass of 6.022 x 10²³ number of N2 molecules

m = n x M or (mass = number of moles x molar mass)

N = n x N₀ (given number of particles = number of moles x Avogadro's no.)

6.002 x 10²³ = no of moles x 6.002 x 10²³

So, no of moles (n) = 1.

Mass, m = n x M = 1 x 48 g = 48 g. Here, Molar mass = gram molecular mass of Nitrogen, which is 48 g.