Avogadro's number

also Avogadro number
The number of molecules in a mole of a substance, approximately 6.0225 × 1023.


Number of units in one mole of any substance (defined as its molecular weight in grams), equal to 6.02214179 1023. The units may be electrons, atoms, ions, or molecules, depending on the nature of the substance and the character of the reaction (if any). Avogadro's law; law of mass action; stoichiometry.

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The number of elementary entities in one mole of a substance. A mole is defined as an amount of a substance that contains as many elementary entities as there are atoms in exactly 12 g of 12C; the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. Experiments give 6.0221367 × 1023 as the value of the Avogadro number. In most calculations the coefficient is rounded off to 6.02. Thus, a mole of 12C atoms has 6.02 × 1023 carbon atoms, a mole of water molecules contains 6.02 × 1023 H2O molecules, a mole of electrons contains 6.02 × 1023 electrons, and so forth. See also Mole (chemistry).

The atomic weight (relative atomic mass) of 12C is exactly 12, by definition. Consider 12 g of 12C (which is one mole and contains the Avogadro number of atoms) compared with 4 g of He, whose atomic weight is 4. The 12 g to 4 g ratio of the masses of the two samples is the same as the 12 to 4 ratio of the masses of the atoms of 12C and He. Therefore the two samples must contain the same number of atoms, and 4 g of He contains the Avogadro number of atoms. The same argument holds for any element. Thus, for an element with atomic weight x, a sample with mass x grams contains the Avogadro number of atoms. Similarly, for a substance with molecular weight y, a sample whose mass is y grams must contain the Avogadro number of molecules. For example, 18 g of water contains 6.02 × 1023 H2O molecules. See also Relative atomic mass.

The Avogadro number is a dimensionless number. The Avogadro constant is defined as the Avogadro number divided by the unit “mole.” The Avogadro constant is usually symbolized by NA, N0, or L. Since NA gives the number of molecules per mole, NA = N/n, where N is the number of molecules present in n moles of a substance.

The Avogadro number relates the mass of a mole of a substance to the mass of a single molecule. For example, for H2O (whose molecular weight is 18) the mass of one mole is 18 g and the mass of one molecule is (18 g)/(6.02 × 1023) ≈ 3 × 10−23 g. The mass m of one molecule of a substance with molar mass M is m = M/NA.

The Avogadro constant NA is related to other fundamental physical constants. The Faraday constant F is the absolute value of the charge on one mole of electrons. Therefore F = NAe, where e is the absolute value of the charge on one electron. Also, R = NAk, where R is the gas constant and k is the Boltzmann constant. See also Gas constant.

Widespread use of the mole concept began only around 1900. The nineteenth-century concept most closely related to the Avogadro number is the number of molecules per unit volume in a gas at 0°C and 1 atm. [The ideal-gas law PV = nRT = (N/NA)RT gives N/V = NAP/RT, so N/V, the number of gas molecules per unit volume, is proportional to the Avogadro constant NA at fixed pressure P and temperature T.] Avogadro hypothesized in 1811 that at a fixed temperature and pressure the number of molecules per unit volume is the same for different gases, but he had no way of estimating this number.

The number of molecules contained in one mole of any substance, = 6.022~ × 1023, but see Avogadro constant. See also Loschmidt's number.

Who is Avogadro and why does he get his own number?

Amedeo Avogadro was a 19th-century Italian physicist. He hypothesized that equal volumes of gases under identical conditions of pressure and temperature contain the same number of molecules. This hypothesis, which became one of the basic concepts of the atomic theory of matter, is known as Avogadro's law. Later, other physicists determined that the number of molecules in the gram molecular volume, or the "mole," is the same for all gases. That number — known as Avogadro's number — is 6.02x10²³. Each year in America, from 6:02 AM to 6:02 PM on 10/23, the mole is celebrated by chemists, mathematicians and physicists. It is part of National Chemistry Week, observed annually from the Sunday through Saturday in October in which the 23rd falls. Happy National Mole Day!

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From our Archives: Today's Highlights, October 23, 2009

Avogadro's number (ävōgä'drō) [for Amedeo Avogadro], number of particles contained in one mole of any substance; it is equal to 602,252,000,000,000,000,000,000, or in scientific notation, 6.02252×1023. For example, 12.011 grams of carbon (one mole of carbon) contains 6.02252×1023 carbon atoms, and 180.16 grams of glucose, C6H12O6, contains 6.02252×1023 molecules of glucose. Avogadro's number is determined by calculating the spacing of the atoms in a crystalline solid through X-ray methods and combining this data with the measured volume of one mole of the solid to obtain the number of molecules per molar volume.

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