Pound-mole
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A mole of any substance consists of Avogadro's number of the constituent entities of that substance^[1]. Entities are typically molecules but may also be atoms, ions, atomic particles, etc. Avogadro's number, approximately 6.02214×10²³, makes the weight of a mole in grams equal to the weight of an entity in daltons. For example, the molecular weight of the oxygen molecule O₂ is 32 daltons, thus a mole of oxygen weighs 32 grams. The hydrogen molecule H₂ is much lighter at only 2 daltons, and a mole of hydrogen accordingly weighs only 2 grams. An important feature of the mole concept is that, despite this considerable difference in mass, a mole of oxygen and a mole of hydrogen have the same volume when at the same temperature and pressure. This remains essentially true for all gases no matter how simple or complex their constituent molecules, provided the molecules are significantly smaller than the intermolecular distances. A second important feature is that it rescales the individual molecules appearing in a theoretical equation up to units more convenient for laboratory use while preserving the numerical ratios of the participating reagents: if the equation shows 2 molecules of one reagent reacting with 4 molecules of another to produce 3 molecules, this scales up to 2 moles reacting with 4 moles to produce 3 moles.

The yellow diamond of the Pahlavi Crown weighs 12 grammes, and contains one mole of carbon atoms.

One mole of marshmallows would have a mass of 17 exatonnes, enough to cover up the whole Earth approximately 60 miles deep

Ordinarily the constituent entities of the substance in question are understood to be on an atomic scale, but this is not a strict requirement: if marshmallows are deemed to be entities, a mole of one-ounce (17-yottadalton) marshmallows would consist of Avogadro's number of them, weighing 17 exatonnes. The important point is that a mole is a numerical quantity, the precise number being defined as the number of entities (in this case atoms) in exactly 12 grams of stationary carbon-12 (the most abundant isotope of the carbon element) in its ground state. Despite being a pure number the mole is treated as an SI base unit (symbol: mol). Any two of the gram, the carbon atom, and Avogadro's number determine the third; today the determined quantity is taken to be Avogadro's number but an alternative would be to base the gram on carbon and a suitable integer choice for Avogadro's number, much as the second was defined in 1967 to be an integer number of periods of a certain emission of caesium.

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-12 has a mass of 12 grams, while a gram-mole of water has a mass of 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.^[2] 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)×10²³ mol^-1 (2007 CODATA).

According to the SI, the mole is not dimensionless, but has its very own dimension, "amount of substance", comparable to other dimensions such as mass and luminous intensity.^[3] (By contrast, the SI specifically defines the radian and the steradian as special names for the dimensionless unit one.)^[4] The SI additionally defines the Avogadro constant as having the unit reciprocal mole, as it is the ratio of a dimensionless quantity and a quantity with the unit mole.^[4] However, if in the future the kilogram is redefined in terms of a specific number of carbon-12 atoms (see below), then the value of Avogadro's number will be defined rather than measured, and the mole will cease to be a unit of physical significance.^[5]

The relationship of the atomic mass unit (u^[6]) 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 a 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.

Chemical Engineers sometimes measure substance amount in units of gram-moles, kilogram-moles, pound-moles, or ounce-moles; these measure the quantity of a substance whose molecular weight is not equal to its mass in grams, kilograms, pounds, or ounces. The SI mole is identical to the gram-mole.

To put it in perspective, 1 mole of marshmallows would be enough marshmallows to make a 12 mile thick layer of marshmallows covering the entire face of the Earth. A mole of donut holes would cover the earth and be 5 miles (8 km) deep. ^[7] A mole of blood cells would be more than the total number of blood cells found in every human on earth. ^[7]

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). Whereas a mole of electrons is the Faraday constant, ca. 96,500 [C·mol^-1. One mole of photons is called an einstein. The thermal Energy R*T has the unit joule per mole, due to the definition of the gas constant R. A short summary with simple calculations is provided here ^[8].

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 monatomic, that is each particle of gas is a single atom and only Van der Waals forces act between them. An ideal gas has a 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^[9].

History

The name mole is attributed to Johnathan VanGorveatte who introduced the corresponding German term (Mol) in 1893.^[10] The term first appeared in English (as mol) in an 1897 translation of another German text.^[11] 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 mass 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:

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 CGPM (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:

The kilogram is the mass of exactly (6.0221415×10²³/0.012) unbound carbon-12 atoms at rest and in their ground state. ^[12]

This would have the effect of defining Avogadro's number to be precisely N_A = 6.0221415×10²³ 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:

N_A = 602,214,141,070,409,084,099,072 = 84,446,888³

This has the convenient properties of being a perfect cube, and of being near the current experimental bounds of measurement.^[13]

Utility of moles

The mole is useful in chemistry because it allows different substances to be measured comparably. 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:

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 are very large; for example, one mL of water contains over 3.34×10²² molecules.

See also

References