# The mole concept(explanation with examples)

The mole concept(explanation with examples)

“A mole is the amount of substance that contains as many elementary entities (atoms, molecules, ions, or other particles ) as there are atoms in exactly 0.012 kg or 12 kg of the carbon-12 isotope.”

We know that for an atom or molecule, mass is an important property. But for an atom, their numbers are also more important. Molecules are formed by combining of atoms in a definite number ratio.

But when we talk about a chemical reaction, we come to know about the fact that the number of reacting molecules is more notable rather than their masses.

 For expressing numbers, we use many number units.

In our daily life, we use dozen as the most commonly used number unit.

for example, we purchase many things with commonly number unit (dozen), which represent the collection of 12. Other commonly used number units are score (20) and gross (144 or 12 dozens).

For small numbers, these units are suitable. But the main concern is the number of atoms and molecules is huge even the sample of matter is very small. Because of this, we need such a number unit that represents equally large numbers.

 For dealing with elementary entities such as atoms, molecules, ions, and formula units, Mole is determined as a number unit.

It is a SI unit, which is used for measuring the amount of substance. It is defined as follows:

“A mole is the amount of substance that contains as many elementary entities (atoms, molecules, ions, or other particles) as there are atoms in exactly o.o12 kg or 12 g of the carbon-12 isotope.”

The number of carbon atoms in carbon -12 having the mass 12 gram (0.012 kg) is 6.02214076 × 10²³. For all practical purposes, this number is rounded off (upto four significant figures) to  6.022 × 10²³.
Therefore, a mole of any substance would contain its 6.022 × 10²³ elementary entities. Which type of elementary entities it is, depends upon the nature of substance, which we take in under consideration.

### VSEPR THEORY( shapes of molecules)

The elementary entities of different types of substances are listed in table below-

 S.No. Nature of substance Elementary Entity 1 Elements like He, Na,Cu, Ca etc. which exist in atomic form.Also, other elements exist in atomic state. Atom 2 Elements like H,N,O and Cl, which exist in molecular form (H2, N2, O2, Cl2). Molecule 3 Molecular compounds like H2O, NH3,CH4,C2H2 etc. Molecule 4 Ions like Na+,NH4+  H₃O⁺,‎Cl−, SO42− etc Ion 5 Ionic compounds like NaCl, KNO3, NH4Cl etc. Formula unit

FORMULA UNIT means total atoms or ions present in chemical formula of compound of different types. These are the following examples:

CompoundFormula unit
H2OMolecule of H2O containing two H atoms and one O atom.
HClMolecule of HCl containing one H atom and one Cl atom.
NaClOne Na+ and one chloride ion (negative ion).
Na2SO4
 Collection of two Na+ and one SO42− ions.

NOTE:Atoms and molecules are extremely small particles. Their masses are compared on a relative scale with 12-C isotope chosen as standard. (The mole concept(explanation with examples)

The number of elementary entities in one mole of any substance is 6.022×1023. The idea of such a number was first conceived by Italian scientist Amedo Avogadro. Although he never determined this number, in his honour, this number, along with its unit (per mole) is called Avogadro’s Constant. It can be represented by the symbol NA. (The mole concept(explanation with examples)

Molar mass:-

The mass of one mole of any substance is known as its molar mass. This term is applicable to all type of substances whether elements ( atomic or molecular) or compound (moleular or ionic). It is expressed in (kg per mol) kg mol-1 or (gram per mole) g mol-1. The unit g mol-1 is frequently used. It is very important to know that the numerical value of molar mass becomes same as that of atomic or molecular mass and relative atomic or relative molecular mass.

Molar mass = Mass of one mole of the substance = Mass of 6.022×1023elementary entities of the substancs.

Molar Volume:- (Avogadro’s Law and Molar Volume)

Avogadro correlated the volume of a gas and the number of molecules present in it. The relationship given by him is known as the Avogadro’s Law.

This law states thatequal volume of all the gases under similar condition of pressure and temperature contain equal number of molecules.”

Because number of molecules are directly proportional to the number of moles (or amount) of a substance, so we can say the Avogadro’s law as  equal volumes of all the gases under similar conditions of pressure and temperature contain equal number of moles”. So we concluded that equal number of moles of different gases would occupy equal volumes under similar conditions of temperature and pressure.

The volume of one mole of a substance is called its molar volume. Its depends upon temperature and pressure conditions. It is related to the density of the substance by the relation-

Molar volume = Molar mass/Density

This relation used for all substances and in any physical state, i.e.,whether a substance is a solid, liquid or gas.

The temperature and pressure dependence of volume is small in case of solids and liquid, but very large in case of gases. For gases, we generally consider their volume under a specified set of temperature and pressure conditions called standard temperature and pressure (STP). The temperature of 0°C (zero degree centigrade or 273K is taken as the standard temperature and 1 bar pressure is taken as the standard pressure.

At STP, one mole of any ideal gas occupies 22.7 L volume. Thus the molar volume (Vm) of any ideal gas at STP is 22.7 L.

MOLES, MASS AND NUMBER RELATIONSHIPS:

We know that mole is a number unit for particles like atoms and molecules. One mole of any substance contains 6.022×1023 particles (elementary entities) and the mass of one mole of a substance is called its molar mass. These facts can be used to correlate the number of moles, mass and the number of particles present in a given sample of a substance. (The mole concept(explanation with examples)

1- Mass and Number of Moles:

Let M be the molar mass of a substance, m be the mass and n be the number of moles in a given sample of substance.we may write-

The mass of 1 mol of the substance = Molar mass = M

∴ The mass of n mol of the substance= m=n×M

or Mass =No. of moles × Molar mass

From the above relation, we may write

No. of moles = Mass/Molar mass

or       n = m/M

2-Number of Particles and Number of Moles:

We know that the number of particles in one mole of any substance is equal to 6.022×1023 or NA.

No. of particles in n moles = N = n × NA

since  n = m/M

No. of particles in a moles = m × NA/M

Also, the number of moles, n = N/NA

3- Mass and Number of Particles:

We know that one mole of substance contains 6.022×1023 particles and its weight is equal to its molar mass, M. Thus,

The mass of NA particles = M

∴ Mass of one particle = M/NA

⇒ We can use these relations to make different calculations.

Some examples, based on above relations:

Question 1How many moles of Iron would weigh 100 gram? ( Atomic mass = 55.8 u)

SolutionSince atomic mass of Iron is 55.8 u. its molar mass is 55.8 g mol-1

No. of moles of Iron = Mass of Iron/Molar mass of Iron

=100 g/55.8 g mol-1

= 1.79 mol

Thus, 1.79 moles if Iron would weigh 100 g.

Question 2 How many copper atoms are present in 21.167 g of Cu ? Molar mass of Cu = 63.5 g mol-1  ?

solutionSince the molar mass of copper is 63.5 g.  63.5 g mol-1 copper contains 6.022×1023 atoms of copper. Therefore, 21.167 g copper would contain

= 6.022×1023×21.167 = 2.007 × 1023 atoms of copper.

Question 3– Calculate the mass of one oxygen atom.

Solution – Molar mass of oxygen, O=16 g mol-1

The number of O atoms in 16 g or 1 mol of O = 6.022×1023 atoms of O.

Thus 6.022×1023 atoms of O weigh = 16.0 g

∴ Mass of 1 atom of O = 16 g/6.022×1023

Thus, mass of 1 atom of O  =

Question – Calculate the following:

a- The number of molecules in 14 g of nitrogen gas.

Solution The molar mass of nitrogen gas, N2 = 2× 14= 28 g mol-1

28 g of nitrogen gas contain 6.022×1023 molecules.

∴ 14 g of nitrogen gas would contain = 14 g/28 g × avagadro no.= 3.011 × 1023    molecules. b- The total number of atoms in 36 g of water.

SolutionMolar mass of water, H2O = 2+16 = 18 g mol-1

∴ the number of molecules in 18 g of water =6.022×1023

One molecule of water H2O contains 3 atoms (2 hydrogen + 1 oxygen)

Thus, the number of atoms in 18 g of water = 3× 6.022×1023 atom = 1.8066 ×1023 atom

∴ Total number of atoms in 36 g of water = 36 g /18 g × 1.8066 ×1023 = 36.132 × 1023 atoms.

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