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 NA. 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?