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The
mole (symbol: mol) is the International System of Units base unit that measures an
amount of substance. One mole contains Avogadro constant (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
molecule 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 is 18.016 grams. The entity counted is usually an atom (as in C) or a molecule (as in
H20, 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. Official SI Unit definitions 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 is not 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 is the ratio of a dimensionless quantity and a quantity with the unit mole. 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.http://www.iop.org/EJ/article/0026-1394/42/2/001/met5_2_001.pdf
The relationship of the
atomic mass unit (uThe symbol AMU for atomic mass unit was replaced by the symbol u (unified atomic mass unit) in 1961. Before 1961 the symbol amu stood for different masses in chemistry and physics.)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 atomic 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 is each particle of gas is a single atom. All gases have the same molar volume of 22.4
litres per mole at
standard temperature and pressure (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
atomic mass unit, 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 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:
The kilogram is the mass of exactly (6.0221415/0.012)
unbound carbon-12 atoms at rest and in their ground state. http://www.iop.org/EJ/abstract/0026-1394/42/2/001/
This would have the effect of defining Avogadro's number to be precisely
NA = 6.0221415 elementary entities per mole, and, consequently, the mole would become merely a unit of counting, like the
dozen.
Another proposed definition of
NA is:
NA = 602214141070409084099072 = 844468883
This has the nice properties of being a perfect cube, and of being near the current experimental bounds of measurement.http://www.americanscientist.org/template/AssetDetail/assetid/54773
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:
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, just one
millilitre 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 m3http://www.ingentaconnect.com/content/ap/ec/1999/00000048/00000005/art00470, and given that the area of the United States is about 1013 m2http://www.daml.org/2001/12/factbook/us.html, 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 1000000000000 (number) Cell (biology) A. S. Naidu, W. R. Bidlack, R. A. Clemens, "Probiotic Spectra of Lactic Acid Bacteria (LAB)", Critical Reviews in Food Science and Nutrition, Volume 39, Number 1 / January 1999; there are roughly six 1000000000 (number) 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 kmhttp://scienceworld.wolfram.com/astronomy/EarthRadius.html, its volume is approximately 1021 m3. Since about 500 large grapefruit will fit in one cubic meterhttp://www.ams.usda.gov/standards/grpfrtfl.pdf, it therefore follows that a mole of grapefruit would have approximately the same volume as the Earth.
- If you had 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 had a mole of penny, you could give out enough money to everyone in the world so that they could spend a million dollar 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.
See also
References
The
mole (symbol: mol) is the International System of Units base unit that measures an amount of substance. One mole contains Avogadro constant (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
molecule 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 is 18.016 grams. The entity counted is usually an atom (as in C) or a molecule (as in H20, 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. Official SI Unit definitions 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 is not
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 is the ratio of a dimensionless quantity and a quantity with the unit mole. 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.http://www.iop.org/EJ/article/0026-1394/42/2/001/met5_2_001.pdf
The relationship of the
atomic mass unit (uThe symbol AMU for atomic mass unit was replaced by the symbol u (unified atomic mass unit) in 1961. Before 1961 the symbol amu stood for different masses in chemistry and physics.)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 atomic 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 is each particle of gas is a single atom. All gases have the same molar volume of 22.4 litres per mole at
standard temperature and pressure (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 atomic mass unit, 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 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:
The kilogram is the mass of exactly (6.0221415/0.012)
unbound carbon-12 atoms at rest and in their ground state. http://www.iop.org/EJ/abstract/0026-1394/42/2/001/
This would have the effect of defining Avogadro's number to be precisely
NA = 6.0221415 elementary entities per mole, and, consequently, the mole would become merely a unit of counting, like the dozen.
Another proposed definition of
NA is:
NA = 602214141070409084099072 = 844468883
This has the nice properties of being a perfect cube, and of being near the current experimental bounds of measurement.http://www.americanscientist.org/template/AssetDetail/assetid/54773
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:
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, just one
millilitre 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 m3http://www.ingentaconnect.com/content/ap/ec/1999/00000048/00000005/art00470, and given that the area of the United States is about 1013 m2http://www.daml.org/2001/12/factbook/us.html, 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 1000000000000 (number) Cell (biology) A. S. Naidu, W. R. Bidlack, R. A. Clemens, "Probiotic Spectra of Lactic Acid Bacteria (LAB)", Critical Reviews in Food Science and Nutrition, Volume 39, Number 1 / January 1999; there are roughly six 1000000000 (number) 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 kmhttp://scienceworld.wolfram.com/astronomy/EarthRadius.html, its volume is approximately 1021 m3. Since about 500 large grapefruit will fit in one cubic meterhttp://www.ams.usda.gov/standards/grpfrtfl.pdf, it therefore follows that a mole of grapefruit would have approximately the same volume as the Earth.
- If you had 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 had a mole of penny, you could give out enough money to everyone in the world so that they could spend a million dollar 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.
See also
References
