A unit (symbolized mol) used to measure the amount of material in a chemical sample. Gram-molecular weight is an older name for the mole and is seldom used. The mole is defined by international agreement as the amount of substance (chemical amount) of a chemical system that contains as many molecules or entities as there are atoms in 12 g of carbon-12 (¹²C). When the mole is used, the elementary entities need not be molecules, but they must always be specified. They may be atoms, molecules, ions, electrons, or specified groups of such particles.

Quantitative measurements in chemistry are concerned with the amount of material in a given sample. Three obvious ways of measuring the amount are to measure the mass m of the sample (using a balance), to measure the volume V (using a measuring cylinder), or to count the number of molecules in the sample, N. Although it is more difficult to devise an experiment to count molecules, this third way of measuring amount is of special interest to chemists because molecules react in simple rational proportions (for example, one molecule of A may react with one, or two, or three molecules of B, and so forth). For example, in calculating how much air should be provided to completely burn a given amount of octane petroleum fuel to carbon dioxide and water, it is necessary to determine from the molecular formulas and the equation for the reaction how many molecules of oxygen (O₂) react with each molecule of octane, and to count the number of molecules of oxygen in a sample of air and the number of molecules of octane in a sample of the fuel.

However, to count molecules is difficult experimentally and inconvenient in practice because the numbers are so large. For any chemical, a mass of 1 kilogram of the sample contains a large number of molecules, of the order 10²³–10²⁴. The mole is defined so that 1 mole of any substance always contains the same number of molecules. This number is large, approximately 6.02 × 10²³, and is known as Avogadro's number. The mole is a more convenient unit in which to measure the amount of a chemical than counting the number of molecules, and it has the same advantages. See also: Avogadro's number

The International System of Units (SI) is the internationally accepted system of quantities and units. The mole is the SI unit of the amount of substance (chemical amount), just as the kilogram is the SI unit of mass, and the meter is the SI unit of length. Although amount of substance is the approved name for this quantity, in practice it is not widely used; the name commonly used is number of moles.

The amount of substance (chemical amount) of a sample, n, may be determined in practice by one of three methods.

The value of n (the amount of substance) may be determined from the mass m by dividing by the molar mass M of the sample, as in Eq. (1).

(1)

If m is expressed in g and M in g/mol, then the value of n will be obtained in mol.

For a gas, the value of n may be determined from the volume V, pressure p, and absolute temperature T by using the ideal gas equation (2),

(2)

where R is the gas constant (R = 8.3145 J K⁻¹ mol⁻¹). If pV is expressed in (N m⁻²) × (m³) = J, and RT in J mol⁻¹, then pV/RT gives the value of n in mol. From the ideal gas equation it is determined that at a pressure of 1 atm (= 101,325 pascals) and a temperature of 0°C (= 273.15 K) the volume occupied by 1 mol of an ideal gas, V = nRT/p, is 22.414 liters (= 22.414 × 10⁻³ m³); and at a pressure of 1 bar (= 10⁵ Pa) the volume is 22.711 liters (1 liter = 10⁻³ m³). See also: Avogadro's law; Gas

For a solution, the amount of solute (or the amount concentration of solution) is frequently determined by titration: if ν_A molecules of A react with ν_B molecules of B in the titration, then at the end point the amount of A used (n_A) is related to the amount of B (n_B) by Eq. (3),

(3)

so that if one is known the other may be determined. See also: Titration

The best experimental value for the number of atoms in 12 g of ¹²C is 6.0221377 (36) × 10²³, where the number in parentheses is the uncertainty in the least significant digits. It follows that one mole of any substance contains this number of molecules (or other entities). This leads to the best estimate of the value of the Avogadro constant, N_A, which is N_A = 6.0221377 (36) × 10²³ mol⁻¹.

The concentration of a solution may be recorded as (mass of solute)/(volume of solution), in units gram/liter; or as (chemical amount of solute)/(volume of solution) in units mol/liter. Because of the proportionality of chemical amount to number of molecules, the latter is the more useful measure of concentration and is generally used in chemistry and biochemistry. The word concentration without a qualifying adjective is generally taken to mean amount concentration, that is, amount-of-substance concentration. See also: Concentration scales

Ian. M. Mills