Avogadro constant

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The Avogadro constant (symbols: L, N_A), also called the Avogadro number and, in German scientific literature, sometimes also known as the Loschmidt constant/number, is formally defined to be the number of "entities" in one mole,^[1]^[2] that is the number of carbon-12 atoms in 12 grams (0.012 kg) of unbound carbon-12 in its rest-energy electronic state. The current best estimate of this number is ^[3]:

$N_A = (6.022 \, 1415 \pm 0.000 \, 0010)10^{23} \mbox{mole}^{-1} \,$

1 History and terminology
2 Application
3 Additional physical relations
4 Measurement of the Avogadro constant
5 See also
6 References and notes
7 External links

[edit] History and terminology

The Avogadro constant is named after the early nineteenth century Italian scientist Amedeo Avogadro, who is credited with being the first to realize that the volume of a gas (strictly, of an ideal gas) is proportional to the number of atoms or molecules. The French chemist Jean Baptiste Perrin in 1909 proposed naming the constant in honor of Avogadro. American chemistry textbooks picked it up in the 1930's followed by highschool textbooks starting in the 1950s ^[4].

Avogadro never attempted to measure the constant: the numerical value was first estimated by the Austrian physicist Johann Josef Loschmidt in 1865 using the kinetic theory of gases.^[5] In German-speaking countries, the constant may still be referred to as the Loschmidt constant or Loschmidt's number: however this name is more correctly reserved for the number of particles in a given volume of an ideal gas (symbol:n₀):^[6]

$n_\circ = \frac{RT}{p} \,$

equal to (2.686 7773 ± 0.000 0047)×10²⁵ m⁻³ at 273.15 K and 101.325 kPa with R the gas constant, T the temperature and p the pressure.

This constant is related to the Avogadro constant by the relation:

$R = N_Ak_B \,$

with k_B the Boltzmann constant hence

$N_A = \frac{n_\circ p}{k_B T} \,$

The connection with Loschmidt is the explanation for the symbol L, often used instead of N_A to refer to the Avogadro constant.

Before 1960, there were conflicting definitions of the mole, and hence of the Avogadro number (as it was known at the time), based on 16 grams of oxygen: physicists generally used oxygen-16 while chemists generally used the "naturally occurring" isotope ratio. Switching to 12 grams of carbon-12 as the basis ended this dispute and had other advantages.^[7]

At this time, the Avogadro number was defined as the number of atoms in 12 grams of carbon-12, that is as a dimensionless quantity, while a mole was defined as one Avogadro number of atoms, molecules or other entities. When the mole entered the International System of Units (SI) in 1971 as the base unit of amount of substance, the definitions were interchanged: what had previously been a number became a physical constant with the unit of reciprocal moles (mol⁻¹).

The genitive form "Avogadro's constant (number)" is often used but not recommended, particularly as Avogadro never attempted to measure the constant himself.^[8]

[edit] Application

The Avogadro constant can be applied to any substance. It corresponds to the number of atoms or molecules needed to make up a mass equal to the substance's atomic or molecular mass, in grams. For example, the atomic mass of iron is 55.847 g/mol, so N_A iron atoms (i.e. one mole of iron atoms) have a mass of 55.847 g. Conversely, 55.847 g of iron contains N_A iron atoms. The Avogadro constant also enters into the definition of the unified atomic mass unit, u:

$1 \ u = \frac{1}{N_A} \ g = (1.660 \, 538\, 86 \pm 0.000\, 000\, 28) 10^{-24} \ g$

[edit] Additional physical relations

Because of its role as a scaling factor, the Avogadro number provides the link between a number of useful physical constants when moving between the atomic scale and the macroscopic scale. For example, it provides the relationship between:

the gas constant R and the Boltzmann constant k_B:

$R = k_BN_A = 8.314 \, 472 \, \pm \, 0.000 \, 015 \, Jmole^{-1}K^{-1}\,$

in J mol⁻¹ K⁻¹

the Faraday constant F and the elementary charge e:

$F = N_Ae = 96 \, 485.3383 \, \pm \,0.0083 \,\, Cmole^{-1} \,$

in C mol⁻¹

[edit] Measurement of the Avogadro constant

A number of methods can be used to measure the Avogadro constant. One modern method is to calculate the Avogadro constant from the density (ρ) of a crystal, the relative atomic mass (M), and the unit cell length (a) determined from x-ray crystallography. Very accurate values of these quantities for silicon have been measured at the National Institute of Standards and Technology (NIST) and used to obtain the value of the Avogadro constant:

$N_A = \frac{4M}{a^3\rho} \,$