Avogador's Number

The number of molecules in a mole is called Avogadro's number (N_A)—defined as 6.02x 10²³ mol^-1.

Learning Objective

Explain relationship between Avogadro's number and mole.

Key Points

Avogadro hypothesized that equal volumes of gas, at the same pressure and temperature, contain equal numbers of molecules, regardless of the type of gas.
Avogadro's constant is a scaling factor between macroscopic and microscopic (atomic scale) observations of nature. It provides the relation between other physical constants and properties.
Albert Einstein proposed that Avogadro's number could be determined based on the quantities observable in Brownian motion. NA was measured for the first time by Jean Baptiste Perrin in 1908.

Terms

gas constant
A universal constant, R, that appears in the ideal gas law, (PV = nRT), derived from two fundamental constants, the Boltzman constant and Avogadro's number, (R = NAk).
Faraday constant
The magnitude of electric charge per mole of electrons.
Brownian motion
Random motion of particles suspended in a fluid, arising from those particles being struck by individual molecules of the fluid.

Full Text

When measuring the amount of substance, it is sometimes easier to work with a unit other than the number of molecules. A mole (abbreviated mol) is a base unit in the International System of Units (SI). It is defined as any substance containing as many atoms or molecules as there are in exactly 12 grams (0.012 kg) of carbon-12. The actual number of atoms or molecules in one mole is called Avogadro's constant (N_A), in recognition of Italian scientist Amedeo Avogadro .

Amadeo Avogadro

Amedeo Avogadro (1776–1856). He established the relationship between the masses of the same volume of different gases (at the same temperature and pressure) corresponds to the relationship between their respective molecular weights.

Avogadro's number (N) refers to the number of molecules in one gram-molecule of oxygen. This indicates an amount of substance as opposed to an independent dimension of measurement. In 1811 Amedeo Avogadro first proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules, regardless of the nature of the gas (i.e., this number is universal and independent of the type of gas). In 1926, Jean Perrin won the Nobel Prize in Physics, largely for his work in determining the Avogadro constant (by several different methods). The value of Avogadro's constant, N_A, has been found to equal 6.02×10²³mol⁻¹.

Role in Science

Avogadro's constant is a scaling factor between macroscopic and microscopic (atomic scale) observations of nature. As such, it provides the relation between other physical constants and properties. For example, it establishes a relationship between the gas constant R and the Boltzmann constant k,

$R = k N_{\rm A} = 8.314\,472(15)\ {\rm J\,mol^{-1}\,K^{-1}}\,$ ;

and the Faraday constant F and the elementary charge e,

$F = N_{\rm A} e = 96\,485.3383(83)\ {\rm C\,mol^{-1}}$ .

Measuring N_A

The determination of N_Ais crucial to the calculation of an atom's mass, since the latter is obtained by dividing the mass of a mole of the gas by Avogadro's constant. In his study on Brownian motion in 1905, Albert Einstein proposed that this constant could be determined based on the quantities observable in Brownian motion. Subsequently, Einstein's idea was verified, leading to the first determination of N_A in 1908 through the experimental work of Jean Baptiste Perrin.

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