Mole (unit) Totally Explained

The mole (symbol: mol) is the SI base unit that measures an amount of substance. One mole contains Avogadro's number (approximately 6.022) entities. A mole is much like "a dozen" in that both are absolute numbers (having no units) and can describe any type of elementary object. The mole's use, however, is usually limited to measurement of subatomic, atomic, and molecular structures; tradition and its hugeness compared to more common units make it impractical for other uses.
In practice, one often measures an amount of the substance in a gram-mole, which is the quantity of a substance whose mass in grams is equal to its formula weight. Thus a gram-mole for Carbon is 12.01 grams, while for water it's 18.016 grams. The entity counted is usually an atom (as in C) or a molecule (as in H₂O, molecular formula weight = 2 H atoms + 1 O atom ≈18).

Definitions

A mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram (or 12 grams) of carbon-12, where the carbon-12 atoms are unbound, at rest and in their ground state. The number of atoms in 0.012 kilogram of carbon-12 is known as the Avogadro constant, and is determined empirically. The currently accepted value is 6.02214179(30) mol^-1 (2007 CODATA).
   According to the SI, the mole isn't dimensionless, but has its very own dimension, namely "amount of substance", comparable to other dimensions such as mass and luminous intensity. (By contrast, the SI specifically defines the radian and the steradian as special names for the dimensionless unit one.) The SI additionally defines the Avogadro constant as having the unit reciprocal mole, as it's the ratio of a dimensionless quantity and a quantity with the unit mole.
   The relationship of the atomic mass unit (u) to Avogadro's number means that a mole can also be defined as: That quantity of a substance whose mass in grams is the same as its formula weight. For example, iron has an relative atomic mass of 55.845 u, so a mole of iron has a mass of 55.845 grams. This notation is very commonly used by chemists and physicists.
   Scientists and engineers (chemical engineers in particular) sometimes measure amount of substance in units of gram-moles, kilogram-moles, pound-moles, or ounce-moles; these measure the quantity of a substance whose mass in grams, kilograms, pounds, or ounces (respectively) is equal to its formula weight. The SI mole is identical to the gram-mole.

Elementary entities

When the mole is used to specify the amount of a substance, the kind of elementary entities (particles) in the substance must be identified. The particles can be atoms, molecules, ions, formula units, electrons, photons or other particles. For example, one mole of water is equivalent to 18.016 grams of water and contains one mole of H₂O molecules, but three moles of atoms (two moles H and one mole O).
When the substance of interest is a gas, the particles are usually molecules. However, the noble gases (He, Ar, Ne, Kr, Xe, Rn) are all monoatomic, that's each particle of gas is a single atom. All gases have the same molar volume of 22.4 litres per mole at STP (see Avogadro's Law).
A mole of atoms or molecules is also called a "gram atom" or "gram molecule", respectively.

History

The name mole (German Mol) is attributed to Wilhelm Ostwald who introduced the concept in the year 1902. It is an abbreviation for molecule (German Molekül), which is in turn derived from Latin moles "mass, massive structure". He used it to express the gram molecular weight of a substance. So, for example, 1 mole of hydrochloric acid (HCl) has a mass of 36.5 grams (atomic masses Cl: 35.5 u, H: 1.0 u).
Prior to 1959 both the IUPAP and IUPAC used oxygen to define the mole, the chemists defining the mole as the number of atoms of oxygen which had mass 16 g, the physicists using a similar definition but with the oxygen-16 isotope only. The two organizations agreed in 1959/1960 to define the mole as such:
ť The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12; its symbol is "mol."

This was adopted by the ICPM (International Committee for Weights and Measures) in 1967, and in 1971 it was adopted by the 14th GCPM (General Conference on Weights and Measures).
In 1980 the ICPM clarified the above definition, defining that the carbon-12 atoms are unbound and in their ground state.

Proposed future definition

As with other SI base units, there have been proposals to redefine the kilogram in such a way as to define some presently measured physical constants to fixed values. One proposed definition of the kilogram is: ť The kilogram is the mass of exactly (6.0221415/0.012) unbound carbon-12 atoms at rest and in their ground state.

This would have the effect of defining Avogadro's number to be precisely N_A = 6.0221415 elementary entities per mole, and, consequently, the mole would become merely a unit of counting, like the dozen.
Another proposed definition of N_A is: ť N_A = 602214141070409084099072 = 84446888³

This has the nice properties of being a perfect cube, and of being near the current experimental bounds of measurement.

Utility of moles

The mole is useful in chemistry because it allows different substances to be measured in a comparable way. Using the same number of moles of two substances, both amounts have the same number of molecules or atoms. The mole makes it easier to interpret chemical equations in practical terms. Thus the equation:
ť 2H₂ + O₂ → 2H₂O

can be understood as "two moles of hydrogen plus one mole of oxygen yields two moles of water."
Moles are useful in chemical calculations, because they enable the calculation of yields and other values when dealing with particles of different mass.
Number of particles is a more useful unit in chemistry than mass or weight, because reactions take place between atoms (for example, two hydrogen atoms and one oxygen atom make one molecule of water) that have very different weights (one oxygen atom weighs almost 16 times as much as a hydrogen atom). However, the raw numbers of atoms in a reaction are not convenient, because they're very large; for example, just one mL of water contains over 3 (or 30,000,000,000,000,000,000,000) molecules.

Moles of everyday entities

Note: all of the following are accurate to approximately one significant figure.

Given that the volume of a grain of sand is approximately 10^-12 m³, and given that the area of the United States is about 10¹³ m², it therefore follows that a mole of sand grains would cover the United States in approximately one centimeter of sand.
A human body contains very roughly one hundred trillion cells; there are roughly six billion people on Earth; so the total number of human cells on the planet is approximately 100*6=6, which is very close to one mole.
Since the Earth has a radius of about 6400 km, its volume is approximately 10²¹ m³. Since about 500 large grapefruit will fit in one cubic meter, it therefore follows that a mole of grapefruit would have approximately the same volume as the Earth.
If you'd exactly one mole of sheets of paper, you could make one million equal stacks from sea level on the earth that would pass the sun.
If you'd a mole of pennies, you could give out enough money to everyone in the world so that they could spend a million dollars every hour, day and night, for the rest of their lives.
If you wanted to use trial and error to find the combination to an e-mail password that contained exactly six alphanumeric characters, it would take you up to 6^36 different tries, which is approximately 10^28, which is over 17,000 moles.

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