Mole (unit)

In chemistry and physics, the mole is an SI base unit of amount of substance. Loosely speaking, the mole may be defined for a pure substance (consisting of one kind of molecules only) as the amount of substance that weighs as much in grams as the molecular weight of the molecule. For instance, a mole of pure water (H₂O, molecular weight 18.02) is the amount of water that weighs 18.02 gram.

This definition is somewhat loose in the sense that "weighs" is better expressed by "has mass". Further the term "molecular weight" is being phased out and replaced by relative molecular mass. And the definition given here is too restricted, it can be extended to different entities, molecules, ions, atoms, electrons, etc.

A more modern definition relies on Avogadro's constant N_A (≈ 6×10²³): a mole consists of N_A entities. Clearly, the total mass of a mole is the sum of the masses of its entities. Consider a pure substance of entities with molecular mass w u (unified atomic mass unit, 1 u = 1/N_A gram ≈ 1.6 10⁻²⁴ gram), then a mole has mass w (N_A u) = w gram. For example, N_A molecules of water have the mass 18.01528 gram. So, a mole is a unit of measurement, which relates the number of entities (atoms, molecules, or ions) to the mass of the material. The word "mole" is shortened from "gram molecular weight", the original term. Industrial chemists also used a "kilogram molecular weight", equal to 1 Kmole.

Chemical reaction formulae are expressed in molecules and atoms, which are impractical to measure or count directly. However, as the atomic weight of any given atom is constant, and generally known, it is possible to quantify the amount of substance by measuring the weight in grams, and dividing by the molecular weight of the molecule (the sum of the atomic weights of the individual atoms in the molecule), which yields the number of moles in the sample weighed.

One can include the definition of Avogadro's constant in the definition of mole and replace gram by the SI unit kilogram. This leads to the following rather technical definition: a mole is defined in the SI as the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of ¹²C (carbon-12).

One mole of an ideal gas occupies 22.414 litres at "standard temperature and pressure" (273.15K and 101.325 kPa).

Another way to phrase this explanation is that a mole is the molecular mass in grams. Using the ¹²C isotope, a mole of ¹²C is 12 grams. For purposes of illustration, in answer to the question How many ¹²C atoms are needed to have a mass of exactly 12 grams? that number, Avogadro's number, is the number of ¹²C atoms in 12 grams of ¹²C. The abbreviation for Avogadro’s number is NA. NA is defined by:

NA x (mass of ¹²C atom) = 12 g

In other words, the number of entities (atoms or molecules) of a substance in one mole is Avogadro's constant. This also applies to all other such entities. The atomic mass of magnesium is 24.305 amu, the average isotopic mass of magnesium as it naturally occurs. The molar mass of magnesium in grams can be derived in the same way. From the equation NA x (mass of atom) = X grams” we get 1 amu = 1g/NA or 1 amu = 1.66054x10^-24g. Using this we calculate for magnesium: NA x 24.305 amu x (1.66054x10^-24 g/amu) = 24.305 g

This means that a mole of magnesium atoms has a mass of 24.305 grams. This example shows that the atomic mass of any element can be interpreted in two ways: (1) the average mass of a single atom in atomic mass units (amu) or (2) the average mass of a mole of atoms in grams. For magnesium, (1) the average mass of a single magnesium atom is 24.305 amu or (2) the average mass of a mole of magnesium atoms is 24.305 g;

Correspondingly: a mole of hydrogen, molecular mass 1.0079 is 1.0079 grams, a mole of lithium, molecular mass 6.94, is 6.94 grams. Molecules also have the same measure. A molecule of water, H₂O is two hydrogen (at 2 times 1.0079) and one oxygen (15.9994) for a combined molecular mass of 18.0152. So a mole of water would contain 18.0152 grams.

Notes

Sources

• mole. Sizes.com (2006-11-07). Retrieved on 2007-05-11.