Avogadro's Number: Value, Calculation & Significance

Avogadro’s number is the number of units in one mole of any substance which is defined as its molecular weight in grams. The value of Avogadro Number is 6.02214076 x 10²³.

The units can be electrons, atoms, ions, or molecules, depending on the character of the reaction and the nature of the substance. Avogadro's constant has the dimension of one divided by the amount of substance (in SI Unit Dimension). Thus, the number in front of the unit will change as the unit changes. Example: 30 minutes is the same as 0.5 hours even though 30 is not the same as 0.5.

Avogadro’s number helps to form a bridge between the macroscopic world and the microscopic world by giving a relationship of the amount of substance to the number of particles. It also helps to give a relationship between other physical constants as well, including:

• It gives the relationship between the gas constant R and the Boltzmann constant. Thus, k_B: R=k_BN_A
• It gives the relationship between the Faraday constant F and the elementary charge. Thus, e: F=N_Ae
• It gives the relationship between atomic mass unit u and molar mass constant. Thus, M_u: 1u=M_u/N_A

Key Terms: Avogadro's Constant, Molecular mass, Atomic Mass, Electron, Atom, Boltzmann Constant, Faraday's Constant, Proton, Coulomb’s Per Electron

What is Avogadro’s Number?

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The number of particles, ions, or atoms present in one mole (1 mol) of a given substance is known as Avogadro’s number.

• Simply, it is a proportionality constant that relates the molar mass of a substance to the mass of a sample.
• A mole is a chemist unit of counting particles like atoms, molecules, ions, electrons, protons which are represented by a value of 6.022 x 10²³.

Avogadro’s Number

• A mole of the hydrogen atom is to say 6.022 x 10²³ atoms of hydrogen, while a mole of the hydrogen molecule means 6.022 x 10²³ molecules of hydrogen or 2 x 6.022 x 10²³ atoms of hydrogen.
• Similarly, a mole of oxygen molecule means 6.022 x 10²³ molecules of oxygen or 2 x 6.022 x 10²³ atoms of oxygen.
• Avogadro's number can be indicated using the symbol L or N_A.
• Avogadro's number, on its own, is known to be a dimensionless quantity.
• For example, in case the number of particles in 3 moles of a substance was to be determined, the value would be:
  = 3 x 6.023 x 10²³ = 1.81 x 10²⁴ particles

Avogadro’s Number Derivation

It can be said that:

• The estimate of the value of Faraday is 96,485.3383 coulombs per mole of electrons.
• The charge of an electron based on modern experiments is 1.60217653 x 10^-19 coulombs per electron.
• If the division of the charge on one mole of an electron occurs by the charge on a single electron, it can result in the value of Avogadro’s number of 6.02214154 x 10²³ particles per mole.
• Another method to determine Avogadro’s number, on the macroscopic scale, is with detailed measurements of the density of an ultrapure sample of a material.
• As per the atomic scale, the measurement of the material density occurs by employing x-ray diffraction techniques.
• It helps to determine the number of atoms per unit cell present in the crystal.
• This also helps to evaluate the distance between the equivalent points that define the unit cell.

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Facts about Avogadro’s Number

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The number of units/ constituent particles/ ions/ atoms present in one mole of a substance is called Avogadro's constant or Avogadro’s number.

• It is represented by NA or L.
• Avogadro Constant is equal to 6.022140587 x 10²³ mol^-1 in the SI Unit System.
• The number of particles in one mole of any substance is equal to 6.023 x 10²³. For example, one mole of hydrogen implies 6.023 x 10²³. Similarly, one mole of water molecule implies 6.023x10²³ molecules, etc. 
• The units can be electrons, ions, or molecules and depend on the nature of the substance and the character of the reaction.
• Example: The number of constituent particles in 5 moles of substance will be equal to: = 5 x 6.023 x 10²³ = 30.01 x 10²³ particles.

Avogadro’s Number History

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How was Avogadro’s Number Measured?

Specifically, Gay-Lussac’s law of combining volumes interested Avogadro.

• Thus, the brainchild behind this entire concept was Amedeo Avogadro, who in 1811 had proposed that the volume of gas was proportional to the number of molecules, irrespective of the nature of the gas.

• His ideas were inconclusive and met opposition from Dalton. After his death, a chemist named Stanislao Cannizzaro brought attention to the world about Avogadro’s ideas.
• In 1909, a Nobel Prize winner physicist named Jean Baptiste Perrin named the number after Avogadro in his honor.
• It is also known as the Loschmidt constant in a few of the German works and was defined as the number of molecules in 12 grams of the isotope carbon-12 (12C).

Significance of Avogadro’s Number

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Avogadro’s number defines the relationship between macroscopic and microscopic worlds by relating to the amount and number of particles in a substance. It also gives the relationship between several physical constants and their properties, such as:

• Gas constant (R) and Boltzmann constant (kB): R = N_Ak_B.
• Faraday constant (F) and the elementary charge (e): F = NA_e
• Atomic mass unit (u) and molar mass constant (M): 1u = M_u/N_A

At the microscopic level or more precisely at atomic levels, substances are measured in atomic mass units (amu). The atomic mass unit (amu) is defined as 1/12th weight of the mass of one carbon (C-12) atom.

Thus, 1 amu = 1.66 x 10^-24 grams

Important Terms During Calculations

Some important terms are:

• Atomic mass: Mass of one atom of an element.
• Atomic mass unit (amu): 1/12th the mass of a carbon-12 atom.
• Molar mass: Molar Mass, which is also known as gram atomic mass, it is the numerical value of atomic mass. Units change from u to g.
• Molecular mass- The sum of all atomic masses comprising the molecule.
• The conversion formulae for Avogadro’s number, number of particles, and moles. 

Molecular Mass Calculation

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A simple example to calculate molecular mass is shown below.

Consider a molecule of H₂SO₄. It consists of 2 hydrogen, 1 sulfur, and 4 oxygen atoms.

Solution: Molecular mass = 2(Atomic mass of hydrogen) + 1 (Atomic mass of sulfur) + 4 (Atomic mass of oxygen)

H: 2 x 1= 2g

S: 1 x 32= 32g

O: 4 x 16= 64g

Molecular mass = 2g + 32g + 64g= 100g

Consider a mole of HCl. It consists of 1 hydrogen and 1 chlorine atom.

Solution: Molecular mass= 1(Atomic mass of hydrogen) + 1 (Atomic mass of chlorine)

= 1 + 35.5

Molecular mass= 36.5g

Previous Year Questions

1. With increasing principal quantum number, the energy difference…
2. The following sets of quantum numbers represent four… (AIEEE 2012)
3. Which quantum number is not related to the Schrodinger… (Rajasthan PMT 2002)
4. As the electron in Bohr’s orbit of hydrogen atom passes from state…
5. The correct set of four quantum numbers for the outermost electron… (KCET 2012)
6. The correct set of four quantum numbers for the valence electrons… (JEE Main 2013)
7. Principal, azimuthal and magnetic quantum numbers are… (AIIMS 1999)
8. What is size of gold nuclei...?​
9. How the linear velocity v of an electron in the Bohr orbit is related...?
10. The value of Planck's constant (h) is… (VITEEE 2017)
11. Wave mechanical model of the atom depends upon…
12. Dual behavior of matter was proposed by… (JKCET 2010)
13. Though the quantum theory of light can explain…

Things to Remember

• Avogadro’s number can be defined as the number of units in one mole of a substance that can be expressed as its molecular weight in grams.
• Avogadro Constant formula 6.02214076 x 10²³.
• Avogadro indicated by NA or L.
• It helps to give the relation between gas constant R and the Boltzmann constant, Faraday constant F and the elementary charge, atomic mass unit u and molar mass constant.
• Avogadro's number is known to be a dimensionless quantity, if considered on its own.

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