Avogadro’s Number

Avogadro’s number, also known as Avogadro’s constant or number, is a fundamental constant in chemistry, denoted by N_A, which honors the great pioneer Amedeo Avogadro. It refers to the number of units of atoms, molecules, or ions in one mole of a substance, and has been empirically established as 6.0221367 × 10²³. This constant is always expressed in chemistry using the unit “per mole”. Therefore, regardless of the substance in question, one mole of it is always equal to N_A.

What is Avogadro’s Number?

Avogadro’s number which is also known as the Avogadro constant is defined as the number of atoms, molecules, and ions in one gram of atom of any element, one gram of molecule of a compound one gram of ion of a substance respectively. Further, it can be illustrated as the number of atoms that are known to exist in 12 grams of C-12 atom. Avogadro’s number is represented as Na which is known as Avogadro’s constant whose number value is 6.022×10²³ particles per mole.

The image added below shows Avogadro’s Number

Importance of Avogadro’s Constant

Chemical substances are typically evaluated at the atomic level using atomic mass units, which are defined as one-twelfth of the mass of a carbon atom. For instance, the atomic mass unit of hydrogen is 1.00794 amu. However, it is difficult to determine a particle’s (such as an atom, electron, or molecule) reaction capacity using atomic mass units. To address this, chemists established a relationship between atomic mass units and grams by setting 1 amu equal to 1.66 x 10^-24 grams. Through this conversion factor, we can easily convert between gram measurements and the invisible unit of measurement used by atomic mass units. This is where the significance of Avogadro’s number lies.

How was Avogadro’s Number Determined?

Accurately determining Avogadro’s number requires measuring a single quantity on both the atomic and macroscopic scales using the same unit of measurement. It is possible by American physicist Robert Millikan’s measurement of the charge on an electron. The charge on a mole of electrons had already been established and is known as the Faraday constant, with a best estimate value of 96,485.3383 coulombs per mole of electrons according to the National Institute of Standards and Technology (NIST). Modern experiments have determined the charge on a single electron to be 1.60217653 x 10^-19 coulombs per electron. Dividing the Faraday constant by the charge on a single electron yields a value for Avogadro’s number of 6.02214154 x 10²³ particles per mole.

Formula of Avogadro’s Number

The formula for measuring Avogadro’s Number is as follows,

• Avogadro’s Number =  6.022×10²³ Particles.
• One Mole of Substance = 6.022×10²³ Particles.

Various examples explaining Avogadro’s Number are,

• 1.008 gram of hydrogen atoms = 1 mole of hydrogen = 6.022×10²³ atoms of hydrogen.
• 23 gram of sodium atoms = 1 mole of sodium = 6.022×10²³ atoms of sodium.
• 18 gram of water = 1 mole of water = 6.022×10²³ atoms of water.

We can say that the number of particles 6.022×10²³ is equal to 1 mole of the substance.

Derivation of The Formula of Avogadro’s Number

1 mole of a substance is also defined as a mass of substance containing N_A molecules.

1 a.m.u (atomic mass unit) = 1.66 × 10^-24

One mole is also defined as the amount of a substance that contains as many entities as there are atoms in exactly 12 g of the 12C isotope.

Mass of one atom of carbon-12 element = 12 × 1.66×10^-24 = 1.992×10^-23 g

Since one mole of Carbon-12 atom weighs 12 g.

Therefore, 

The number of atoms =12 g mol^-1 / 1.992648 × 1023 g atom^-1 = 6.0221367 × 1023 atoms mol^-1. 

Uses of Avogadro’s Number

Various uses of Avogadro’s Number are,

• Avogadro’s number not only represents the number of units in a mole of a substance, but it is also closely linked to Gay-Lussac’s law. In 1811, Avogadro resolved the issues with Gay-Lussac’s law by proposing that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules.
• The Avogadro number plays a crucial role in establishing the relationship between the mass and volume of gases. According to this concept, equal volumes of gases at the same temperature and pressure contain an equal number of molecules, irrespective of the gas’s chemical identity. In other words, if we consider the temperature and pressure of the gas constant, the volume and moles of an ideal gas are directly proportional to each other for a given mass of the gas.
• The Avogadro number also aids in determining the atomicity of gases. Atomicity refers to the ratio of the molecular mass to the atomic mass of a substance. Avogadro’s law can be used to identify atomicity, as it provides the number of atoms present in a molecule of a substance. For instance, the atomicity of a molecule of oxygen (O₂) is 2 since it contains two oxygen atoms. Similarly, the atomicity of a molecule of sulfur (S₈) is 8, as it consists of eight sulfur atoms.
• In addition to its other applications, the Avogadro number can be used to establish a relationship between the molecular mass and the vapour density of a gas. This relationship is based on the definition of vapour density, which is the ratio of the mass of a gas to the volume it occupies at a specific temperature and pressure. By substituting the value of the relative molecular mass into this definition, we can obtain the vapour density. Specifically, the vapour density of a gas is equal to half the relative molecular mass of the gas. Therefore, we can express this relationship as Vapor Density (V.D) = Relative molecular mass / 2, or Relative molecular mass = 2 x Vapor Density.

Significance of Avogadro’s Number

Avogadro’s number is related to the quantity and number of particles in a substance, which describes the link between the macroscopic and microscopic worlds.

Additionally, it provides the relationship between several physical constants and their characteristics, including

Gas constant and Boltzmann constant:

R = N_Ak_A

where 
N_A represents the Avogadro number
R represents the gas constant
k_A represents the Boltzmann constant

Faraday constant and the electron charge:

F = eN_A

where 
e represents the electron charge
F represents the Faraday constant

Atomic Mass Constant and Molar Mass Constant:

M_u = N_A(1u)

where 
M_u represents the molar mass constant
1u represents the atomic mass constant

Solved Examples on Avogadro’s Number

Example 1: Calculate the mass of (i) an atom of silver (ii) a molecule of carbon dioxide.

Solution:

(i) Atomic mass of silver = 108 u

1 mole of Ag atom = 108 g = 6.022×10²³ atoms

Mass of one atom of silver = 108 / 6.022×10²³ = 1.793×10^-22 g

(ii) Molecular mass of CO₂ = 1×12+2×16 = 44 u

1 mole of CO₂ = 44 g = 6.022×10²³ atoms

Mass of one molecule of CO₂ = 44 / 6.022×10²³ = 7.307×10^-23 g

Example 2: How many atoms and molecules of Sulphur are present in 64.0 g of Sulphur (S₈)?

Solution:

Molecular mass of S₈ = 32 × 8 = 256 u

1 mole of Sulphur molecules = 256 g = 6.022 × 10²³ molecules of Sulphur

1 gram of Sulphur molecules = 6.022 × 10²³ / 256 = 0.023523 × 10²³ molecules

64 gram of Sulphur molecules = 64 × 0.023523 × 10²³ = 1.505 × 10²³ molecules

1 molecules of Sulphur S₈ contains 8 atom of Sulphur

1.505 × 10²³ molecules of Sulphur contains 8 Sulphur atom = 8 × 1.505 × 10²³ = 1.204 × 10²⁴ atoms

FAQs on Avogadro’s Number

Q1: What is Avogadro’s number?

Answer:

Avogadro’s number represents the number of particles, including atoms, molecules, ions, and other particles, that are present in one mole of a substance. The value of Avogadro’s number is approximately 6.022 x 10²³ particles per mole.

Q2: Who discovered Avogadro’s number?

Answer:

Avogadro’s number is named in honor of Amedeo Avogadro, an Italian scientist who in 1811 proposed the hypothesis that equal volumes of gases at the same temperature and pressure contain the same number of molecules. The value of Avogadro’s number, however, was not determined by Avogadro himself but through a combination of experimental measurements and theoretical calculations by various scientists over many years.

Q3: What is the significance of Avogadro’s number?

Answer:

Avogadro’s number is important as it provides a link between macroscopic properties of matter like mass and volume to microscopic properties like the number of atoms or molecules present. Additionally, it is utilized to determine the molar mass of a substance, which is necessary for several chemical calculations, such as determining solution concentration or predicting the amount of a reactant needed in a chemical reaction.

Q4: Can Avogadro’s number be used for any substance?

Answer:

Certainly! Avogadro’s number is a constant that represents the number of particles in one mole of any substance, regardless of its chemical composition. It is not specific to any particular element, compound, or mixture, but rather represents a fundamental constant of nature applicable to all types of particles.