Avogadro's number, also known as Avogadro's constant or number, is a fundamental constant in chemistry, denoted by NA, 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 NA.
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 NA 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 = NAkA
where
NA represents the Avogadro number
R represents the gas constant
kA represents the Boltzmann constant
Faraday constant and the electron charge:
F = eNA
where
e represents the electron charge
F represents the Faraday constant
Atomic Mass Constant and Molar Mass Constant:
Mu = NA(1u)
where
Mu 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
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