Complete Beginner’s Guide to Mole Concept

In this post we will discuss about mole concept in detail.

Have you seen a ₹ 10 note? Probably yes. How about ₹ 100? Probably yes. Most of us have seen the common denominations of Indian currency ranging from ₹ 10 to ₹ 2000. All of these denominations help in the transaction of money.

Similarly, while dealing with chemical reactions, one has to take the help of numerical denominations to specify quantities of matter getting consumed or produced. Atoms being such a small unit, it’s much harder to deal with a number of atoms as a unit of measurement. In order to overcome this problem, Italian scientist Amedeo Avogadro is credited with coming up with the concept of mole to identify the number of particles present.

Amedeo Avogadro was the first to realize that the volume of a gas (i.e., an ideal gas) is proportional to the number of atoms or molecules.

To put it  into context, what is the value of one mole?

Let me give you some mind-boggling observations! Are you ready?

Here these are:

1. If you had a mole of pennies, you could give out enough money to everyone in the world so that they could spend a million dollars every hour, day and night, for the rest of their lives.

2. If you had exactly one mole of sheets of paper, you could make one million equal stacks from sea level on the earth that would pass the sun.

3. If you wanted to use trial and error to find the combination for an e-mail password, if it contained exactly six alphanumeric characters, it would take you up to 636 different tries, which is approximately 1028, which is over 17,000 moles.

So the genuine question would be, “Why should we study mole?”

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 magnitude’s units. For example, when a ball’s mass 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?

The unit which is used to express the quantity is just a matter of convenience. The mole is a concept of quantity in terms of number and mass. This concept relates the mass of any material to the number of atoms, ions or molecules in it.

The mole, as per definition accepted internationally, is defined as follows:

“The mole is the amount of a substance which contains the same number of chemical units, i.e., atoms, molecules and ions, as there are atoms in exactly 12 gram of pure carbon-12 (C-12)“.

12 g of carbon-12 is found to contain 6.022*10²³ atoms of carbon-12. Thus, a mole represents a collection of 6.022*10²³ chemical units (atoms, molecules or ions).

The number 6.022*10²³ is called Avogadro’s number. Avogadro’s number is commonly denoted by N_A. Thus, a mole is the quantity of any material which contain one Avogadro number of chemical units, i.e., atoms molecules or ions.

Mole concept can be applied to both the molecular and ionic substances. For example,

1 mole of CO₂ = 6.022*10²³ molecules of CO₂ = Mass of 6.022*10²³ molecules of CO₂ = 44 gram of CO₂ 

1 mole of NaCl = Mass of 6.022*10²³ NaCl ion pairs = 58.5 g of NaCl

1 mole of H⁺ ion = Collection of 6.022*10²³ H⁺ ion 

1 mole of H₂ molecules = Collection of 6.022*10²³ H₂ molecules 

1 mole of H atoms = Collection of 6.022*10²³ H atoms 

Symbol of the mole unit

The unit of each physical quantity has been given standard symbol, e.g., gram is denoted by g, kilogram is denoted by kg, meter is denoted by m and Newton is denoted by N. The unit of mole is given by symbol mol, so express 1 mole as 1 mol.

Mathematical form of mole

Mole-Number relation

1 mole = 6.022*10²³ units

Number of moles = ^{Given number of units}/_6.022*10²³

Mole-Weight relation

Number of moles = ^{Weight of substance}/_{Molar mass}

The mass of 6.022*10²³ particles of any substance is  termed the molar mass of the substance.

Mole-Volume relation

Number of moles = ^{Volume of gas}/_{Molar volume} (at same Pressure and Temperature)

At STP (standard temperature and pressure T=273 K and P=1 atm), Number of moles = ^{Volume of gas}/_22.4

Gram Atomic Mass and Gram Molecular Mass

The term gram atomic mass, gram molecular mass and gram ionic mass were used to express the mass of one Avogadro’s number of atoms, molecules or ions respectively. These terms are no longer used. The term which is used for describing one Avogadro’s number of chemical units, nowadays is called a mole. Thus, for any substance

1 gram atomic mass = 1 gram atom = Mass of 6.022*10²³ atoms of any substance

1 gram molecular mass = 1 gram molecule = Mass of 6.022*10²³ molecules of any substance

1 gram ion = Mass of 6.022*10²³ ions

For hydrogen,

1 gram atomic mass = Mass of 6.022*10²³ atoms of hydrogen (H) = 1.008 g, and

1 gram molecular mass = Mass of 6.022*10²³ molecules of hydrogen (H₂) = 2.016 g

What is molar mass?

Mass of 1 mole of any substance is called its molar mass. The molar mass is measured in the units of gram per mole (g/mol). One mole contain 6.022*10²³ chemical units. Therefore,

Molar mass of a substance = Mass of 6.022*10²³ molecules of any substance

e.g.,  Molar mass of hydrogen (H₂) = Mass of 6.022*10²³ molecules of hydrogen (H₂)

But, Mass of 6.022*10²³ molecules of hydrogen (H₂) = 2.016 g

So, Molar mass of hydrogen (H₂) = 2.016 g/mol

What is molar volume?

One mole of any gaseous substances at 273 K and one atmosphere pressure occupies a volume equal to 22.4 litre or 22400 ml. The volume occupied by one mole of any gaseous substances called molar volume. So, 

Molar volume of any gaseous substance at 273 k and 1 atm pressure = 22.4 L/mole = 22400 ml/mol

How many moles are there in a certain mass of a substance?

We can calculate the number of moles in a certain mass of a substance by using the formula provided below:

Where W is mass of substance in grams and M is molar mass of substance in g/mol.

How many molecules are there in a certain mass of a substance?

We can calculate the number of molecules in a certain mass of substance by using the formula provided below:

Where W is mass of substance in grams and M is molar mass of substance in g/mol.

Questions based on mole concept

Problem 1: Neon gas consists of single atoms, what mass of neon contains 6.022*10²³ atoms?

Solution: From mole concept, 6.022*10²³ atoms = 1 mole of substance = Atomic mass

So, mass of neon that contains 6.022*10²³ atoms is numerically equal to its atomic mass.

Atomic mass of neon = 20.1 u

Mass of 6.022*10²³ atoms of neon = 20.1 g

Problem 2: How many moles of Mg atoms are there in 100 g of magnesium? (Atomic mass of magnesium = 24 u)

Solution: Mass of Mg = 100 g

Atomic mass of Mg = 24 u

Molar mass of Mg = 24 g/mol

Number of moles of Mg = ^{Given mass of Mg}/_{Molar mass of Mg} = ^(100g)/_(24g/mol) = 4.17 mol

Problem 3: How many molecules are present in 9 g of water. (Atomic mass of H and O are 1 u and 16 u respectively)

Solution: We know that 1 mole of a compound contains 6.022*10²³ molecules.

Given mass of water = 9 g

Molar mass of water (H₂O) = 18 g/mol

18 g of water contains 6.022*10²³ molecules.

So, 9 g of water contain molecules = 6.022*10²³ * ^{9 g}/_{18 g} = 3.011*10²³ molecules.

Problem 4: Calculate the number of moles in 50 g of H₂O₂. (Atomic mass of H and O are 1 u and 16 u respectively)

Solution: Given mass of H₂O₂ = 50 g

Molar mass of H₂O₂ = 34 g/mol

Number of moles =  ^{Given mass}/_{Molar mass} =   ^{50 g}/_{34 g/mol} = 1.47 mol

Note: Try more number  of question to get a clear concept of solving numerical based on mole concept.

Read More: What is Dalton’s Atomic Theory?

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