Mole (unit)

Mole (unit)

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The mole is a unit of measurement
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...

 used in chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

 to express amounts
Amount of substance
Amount of substance is a standards-defined quantity that measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons, and other particles. It is sometimes referred to as chemical amount. The International System of Units defines the amount of substance to be...

 of a chemical substance
Chemical substance
In chemistry, a chemical substance is a form of matter that has constant chemical composition and characteristic properties. It cannot be separated into components by physical separation methods, i.e. without breaking chemical bonds. They can be solids, liquids or gases.Chemical substances are...

, defined as an amount of a substance that contains as many elementary entities (e.g., atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s, molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

s, ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

s, electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s) as there are atoms in 12 gram
Gram
The gram is a metric system unit of mass....

s of pure carbon-12
Carbon-12
Carbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....

 (12C), the isotope
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

 of carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

 with atomic weight
Atomic weight
Atomic weight is a dimensionless physical quantity, the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12...

 12. This corresponds to a value of elementary entities of that substance. It is one of the base units
SI base unit
The International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length...

 in the International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

, and has the unit symbol mol.

The mole is widely used in chemistry, instead of units of mass or volume, as a convenient way to express the amounts of reagents and products of chemical reactions. For example, the chemical equation 2 H2 + O2 → 2 H2O implies that 2 mol of dihydrogen and 1 mol of dioxygen react to form 2 mol of water. The mole may also be used to express the number of atoms, ions, or other elementary entities in some sample. The concentration
Concentration
In chemistry, concentration is defined as the abundance of a constituent divided by the total volume of a mixture. Four types can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration...

 of a solution is commonly expressed by its molarity, the number of moles of the dissolved substance per liter
Litér
- External links :*...

 of solution.

The number of molecules in a mole (known as Avogadro's number
Avogadro's number
In chemistry and physics, the Avogadro constant is defined as the ratio of the number of constituent particles N in a sample to the amount of substance n through the relationship NA = N/n. Thus, it is the proportionality factor that relates the molar mass of an entity, i.e...

) is defined so that the mass of one mole of a substance, expressed in grams, is exactly equal to the substance's mean molecular weight. For example, the mean molecular weight of natural water is about 18.015, so one mole of water is about 18.015 grams. This property considerably simplifies many chemical and physical computations.

The name gram-molecule was formerly used for essentially the same concept. The name gram-atom (abbreviated gat.) has been used for related but distinct concept, namely a quantity of a substance that contains Avogadro's number of atoms, whether isolated or combined in molecules. Thus, for example, 1 mole of MgB2 is 1 gram-molecule of MgB2 but 3 gram-atoms of MgB2.

Definition and related concepts


, the mole is defined by BIPM to be an amount of a substance that contains as many elementary entities (e.g. atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s, molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

s, ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

s, electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s) as there are atoms in 12 gram
Gram
The gram is a metric system unit of mass....

s of pure carbon-12
Carbon-12
Carbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....

 (12C), the isotope
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

 of carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

 with atomic weight
Atomic weight
Atomic weight is a dimensionless physical quantity, the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12...

 12. Thus, by definition, one mole of pure 12C has a mass of exactly 12 g. It also follows from the definition that X moles of any substance will contain the same number of molecules as X moles of any other substance.

The mass per mole of a substance is called its molar mass
Molar mass
Molar mass, symbol M, is a physical property of a given substance , namely its mass per amount of substance. The base SI unit for mass is the kilogram and that for amount of substance is the mole. Thus, the derived unit for molar mass is kg/mol...

. Since the standard unit for expressing the mass of molecules or atoms (the dalton
Dalton
Dalton may refer to:-In Canada:* Dalton, Algoma District, Ontario* Dalton Armoury, a Canadian Forces facility primarily used by the Queen's Own Rifles of Canada- In the United Kingdom :* Dalton, Cumbria, England* Dalton, Dumfries and Galloway, Scotland...

 or atomic mass unit
Atomic mass unit
The unified atomic mass unit or dalton is a unit that is used for indicating mass on an atomic or molecular scale. It is defined as one twelfth of the rest mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state, and has a value of...

) is defined as 1/12 of the mass of a 12C atom, it follows that the molar mass of a substance, measured in grams per mole, is exactly equal to its mean molecular
Molecular mass
The molecular mass of a substance is the mass of one molecule of that substance, in unified atomic mass unit u...

 or atomic mass
Atomic mass
The atomic mass is the mass of a specific isotope, most often expressed in unified atomic mass units. The atomic mass is the total mass of protons, neutrons and electrons in a single atom....

, measured in daltons; which is to say, to the substance's mean molecular or atomic weight
Atomic weight
Atomic weight is a dimensionless physical quantity, the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12...

.

The number of elementary entities in a sample of a substance is technically called its (chemical) amount
Amount of substance
Amount of substance is a standards-defined quantity that measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons, and other particles. It is sometimes referred to as chemical amount. The International System of Units defines the amount of substance to be...

. Therefore, the mole is a convenient unit for that physical quantity. One can determine the chemical amount of a known substance, in moles, by dividing the sample's mass by the substance's molar mass. Other methods include the use of the molar volume
Molar volume
The molar volume, symbol Vm, is the volume occupied by one mole of a substance at a given temperature and pressure. It is equal to the molar mass divided by the mass density...

 or the measurement of electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

.

It should be noted that the mass of one mole of a substance depends not only on its molecular formula, but also on the proportion of the isotopes of each element present in it. For example, one mole of calcium-40 is ± grams, whereas one mole of calcium-42 is ± grams, and one mole of calcium
Calcium
Calcium is the chemical element with the symbol Ca and atomic number 20. It has an atomic mass of 40.078 amu. Calcium is a soft gray alkaline earth metal, and is the fifth-most-abundant element by mass in the Earth's crust...

 with the normal isotopic mix is 40.078 ± 0.004 grams.

Since the definition of the gram is not mathematically tied to that of the dalton, the number NA of molecules in a mole (Avogadro's number) must be determined experimentally. The value adopted by CODATA
Committee on Data for Science and Technology
The Committee on Data for Science and Technology was established in 1966 as an interdisciplinary committee of the International Council for Science. It seeks to improve the compilation, critical evaluation, storage, and retrieval of data of importance to science and technology.The CODATA Task...

 in 2006 is NA = ± . In 2011 the measurement was refined to ± .

History


The history of the mole is intertwined with that of molecular mass
Molecular mass
The molecular mass of a substance is the mass of one molecule of that substance, in unified atomic mass unit u...

, atomic mass unit
Atomic mass unit
The unified atomic mass unit or dalton is a unit that is used for indicating mass on an atomic or molecular scale. It is defined as one twelfth of the rest mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state, and has a value of...

, Avogadro's number
Avogadro's number
In chemistry and physics, the Avogadro constant is defined as the ratio of the number of constituent particles N in a sample to the amount of substance n through the relationship NA = N/n. Thus, it is the proportionality factor that relates the molar mass of an entity, i.e...

 and related concepts.

The first table of atomic weight
Atomic weight
Atomic weight is a dimensionless physical quantity, the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12...

s was published by John Dalton
John Dalton
John Dalton FRS was an English chemist, meteorologist and physicist. He is best known for his pioneering work in the development of modern atomic theory, and his research into colour blindness .-Early life:John Dalton was born into a Quaker family at Eaglesfield, near Cockermouth, Cumberland,...

 (1766–1844) in 1805, based on a system in which the atomic weight of hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

 was defined as 1. These atomic weights were based on the stoichiometric
Stoichiometry
Stoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. In a balanced chemical reaction, the relations among quantities of reactants and products typically form a ratio of whole numbers...

 proportions of chemical reactions and compounds, a fact that greatly aided their acceptance: It was not necessary for a chemist to subscribe to atomic theory
Atomic theory
In chemistry and physics, atomic theory is a theory of the nature of matter, which states that matter is composed of discrete units called atoms, as opposed to the obsolete notion that matter could be divided into any arbitrarily small quantity...

 (an unproven hypothesis at the time) to make practical use of the tables. This would lead to some confusion between atomic weights (promoted by proponents of atomic theory) and equivalent weight
Equivalent weight
Equivalent weight is a term which has been used in several contexts in chemistry. In its most general usage, it is the mass of one equivalent, that is the mass of a given substance which will:...

s (promoted by its opponents and which sometimes differed from atomic weights by an integer factor), which would last throughout much of the nineteenth century.

Jöns Jacob Berzelius (1779–1848) was instrumental in the determination of atomic weights to ever-increasing accuracy. He was also the first chemist to use oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

 as the standard to which other weights were referred. Oxygen is a useful standard, as, unlike hydrogen, it forms compounds with most other elements, especially metals. However, he chose to fix the atomic weight of oxygen as 100, an innovation that did not catch on.

Charles Frédéric Gerhardt
Charles Frédéric Gerhardt
Charles Frédéric Gerhardt was a French chemist.-Biography:He was born in Strasbourg, where he attended the gymnasium. He then studied at the Karlsruhe Institute of Technology, where Friedrich Walchner's lectures first attracted his interest to chemistry...

 (1816–56), Henri Victor Regnault
Henri Victor Regnault
Henri Victor Regnault was a French chemist and physicist best known for his careful measurements of the thermal properties of gases. He was an early thermodynamicist and was mentor to William Thomson in the late 1840s....

 (1810–78) and Stanislao Cannizzaro
Stanislao Cannizzaro
Stanislao Cannizzaro, FRS was an Italian chemist. He is remembered today largely for the Cannizzaro reaction and for his influential role in the atomic-weight deliberations of the Karlsruhe Congress in 1860.-Biography:...

 (1826–1910) expanded on Berzelius' works, resolving many of the problems of unknown stoichiometry of compounds, and the use of atomic weights attracted a large consensus by the time of the Karlsruhe Congress
Karlsruhe Congress
The Karlsruhe Congress was an international meeting of chemists held in Karlsruhe, Germany from 3 to 5 September, 1860. It was the first international conference of chemistry worldwide.- The meeting :...

 (1860). The convention had reverted to defining the atomic weight of hydrogen as 1, although at the level of precision of measurements at that time — relative uncertainties of around 1% — this was numerically equivalent to the later standard of oxygen = 16. However the chemical convenience of having oxygen as the primary atomic weight standard became ever more evident with advances in analytical chemistry and the need for ever more accurate atomic weight determinations.

Developments in mass spectrometry
Mass spectrometry
Mass spectrometry is an analytical technique that measures the mass-to-charge ratio of charged particles.It is used for determining masses of particles, for determining the elemental composition of a sample or molecule, and for elucidating the chemical structures of molecules, such as peptides and...

 led to the adoption of oxygen-16 as the standard substance, in lieu of natural oxygen. The current definition of the mole, based on carbon-12, was approved during the 1960s. The four different definitions were equivalent to within 1%.
Scale basis relative to C = 12 from the C = 12 scale
Atomic weight of hydrogen = 1 1.00794(7) −0.788%
Atomic weight of oxygen = 16 15.9994(3) +0.00375%
Relative atomic mass of O = 16 15.9949146221(15) +0.0318%


The name mole is an 1897 translation of the German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....

 unit Mol, coined by the chemist
Chemist
A chemist is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties such as density and acidity. Chemists carefully describe the properties they study in terms of quantities, with detail on the level of molecules and their component atoms...

 Wilhelm Ostwald
Wilhelm Ostwald
Friedrich Wilhelm Ostwald was a Baltic German chemist. He received the Nobel Prize in Chemistry in 1909 for his work on catalysis, chemical equilibria and reaction velocities...

 in 1893 from the German word Molekül (molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

). However, the related concept of equivalent mass had been in use at least a century earlier.

The mole as a unit


Since its adoption into the International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

, there have been a number of criticisms of the concept of the mole as a unit like the meter or the second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

:
  • the number of molecules, etc. in a given lump of material is a fixed dimensionless quantity that can be expressed simply as a number, so does not require its own base unit;
  • the SI thermodynamic mole is irrelevant to analytical chemistry and is causing avoidable costs to advanced economies;
  • the mole is not a true metric (i.e. measuring) unit, rather it is a parametric unit and amount of substance is a parametric base quantity;
  • the concepts of the SI quantity 'amount of substance' and unit 'mole' are confusing and difficult to teach.
  • the SI defines numbers of entities as quantities of dimension one, and thus ignores the ontological distinction between entities and units of continuous quantities.


In chemistry, it has been known since Proust's
Joseph Proust
Joseph Louis Proust was a French chemist.-Life:Joseph L. Proust was born on September 26, 1754 in Angers, France. His father served as an apothecary in Angers. Joseph studied chemistry in his father’s shop and later came to Paris where he gained the appointment of apothecary in chief to the...

 law of definite proportions
Law of definite proportions
In chemistry, the law of definite proportions, sometimes called Proust's Law, states that a chemical compound always contains exactly the same proportion of elements by mass. An equivalent statement is the law of constant composition, which states that all samples of a given chemical compound have...

 (1794) that knowledge of the mass of each of the components in a chemical system is not sufficient to define the system. Amount of substance can be described as mass divided by Proust's "definite proportions", and contains information that is missing from the measurement of mass alone. As demonstrated by Dalton's
John Dalton
John Dalton FRS was an English chemist, meteorologist and physicist. He is best known for his pioneering work in the development of modern atomic theory, and his research into colour blindness .-Early life:John Dalton was born into a Quaker family at Eaglesfield, near Cockermouth, Cumberland,...

 law of partial pressures (1803), a measurement of mass is not even necessary to measure the amount of substance (although in practice it is usual). There are many physical relationships between amount of substance and other physical quantities, the most notable one being the ideal gas law
Ideal gas law
The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...

 (where the relationship was first demonstrated in 1857). The term "mole" was first used in a textbook describing these colligative properties
Colligative properties
Colligative properties are properties of solutions that depend on the number of molecules in a given volume of solvent and not on the properties/identity of the molecules. Colligative properties include: relative lowering of vapor pressure; elevation of boiling point; depression of freezing point...

.

Other units called "mole"


Chemical engineers use the concept extensively, but the unit is rather small for industrial use. For convenience in avoiding conversions, some American engineers adopted the pound-mole (noted lb-mol or lbmol), which is defined as the number of entities in 12 lb
Pound (mass)
The pound or pound-mass is a unit of mass used in the Imperial, United States customary and other systems of measurement...

 of 12C. One lb-mol is equal to .
In the metric system, chemical engineers once used the kilogram-mole (noted kg-mol), which is defined as the number of entities in 12 kg of 12C, and often referred to the mole as the gram-mole (noted g-mol), when dealing with laboratory data. However modern chemical engineering practice is to use the kilomole (kmol), which is identical to the kilogram-mole, but whose name and symbol adopt the SI convention for standard multiples of metric units.

Kilogram


As with other SI base unit
SI base unit
The International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length...

s, there have been proposals to redefine the kilogram
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

 in such a way as to define some currently measured physical constants to fixed values. One proposed definition of the kilogram is:
The kilogram is the mass of exactly unbound carbon-12 atoms at rest and in their ground state.

This would have the effect of defining the Avogadro constant to be precisely elementary entities per mole.

A decision on this proposal
New SI definitions
A committee of the International Committee for Weights and Measures has proposed revised formal definitions of the SI base units, which are being examined by the CIPM and which may be considered by the 25th CGPM, in 2014....

 is expected by the CGPM in October 2011.

Related units


The SI units for molar concentration are mol/m
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

3. However, most chemical literature traditionally uses mol/dm
Decimetre
A decimetre is a unit of length in the metric system, equal to one tenth of a metre, the SI base unit of length. In simple words there are 10 cm in a decimetre....

3, or mol dm
Decimetre
A decimetre is a unit of length in the metric system, equal to one tenth of a metre, the SI base unit of length. In simple words there are 10 cm in a decimetre....

−3, which is the same as mol/L
Litre
pic|200px|right|thumb|One litre is equivalent to this cubeEach side is 10 cm1 litre water = 1 kilogram water The litre is a metric system unit of volume equal to 1 cubic decimetre , to 1,000 cubic centimetres , and to 1/1,000 cubic metre...

. These traditional units are often denoted by a capital letter M , sometimes preceded by an SI prefix
SI prefix
The International System of Units specifies a set of unit prefixes known as SI prefixes or metric prefixes. An SI prefix is a name that precedes a basic unit of measure to indicate a decadic multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol...

, for example, millimoles per litre
Litre
pic|200px|right|thumb|One litre is equivalent to this cubeEach side is 10 cm1 litre water = 1 kilogram water The litre is a metric system unit of volume equal to 1 cubic decimetre , to 1,000 cubic centimetres , and to 1/1,000 cubic metre...

 (mmol/L) or millimolar (mM), micromoles/litre (µmol/L) or micromolar (µM), or nanomoles/L (nmol/L) or nanomolar (nM).

The unit's holiday


October 23 is called Mole Day
Mole Day
Mole Day is an unofficial holiday celebrated among chemists on October 23, between 6:02 AM and 6:02 PM, making the date 6:02 10/23 in the American style of writing dates...

. It is an informal holiday in honor of the unit among chemists in North America. The date is derived from Avogadro's number, which is approximately 6.022×1023. It officially starts at 6:02 A.M. and ends at 6:02 P.M.