Avogadro's number

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

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 N_A, N₀, or L. Since N_A gives the number of molecules per mole, N_A = 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/N_A.

The Avogadro constant N_A 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 = N_Ae, where e is the absolute value of the charge on one electron. Also, R = N_Ak, 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/N_A)RT gives N/V = N_AP/RT, so N/V, the number of gas molecules per unit volume, is proportional to the Avogadro constant N_A 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.

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