A mole of any substance consists of Avogadro's number of the constituent entities of that substance^[1]. The Avogadro constant (symbols L, N A also called Avogadro's number, is the number of "elementary entities" (usually Atoms 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. The unified atomic mass unit ( u) or Dalton ( Da) or sometimes universal mass unit, is an unit of Mass used to express For example the molecular weight of the oxygen molecule O₂ is 32 daltons whence a mole of oxygen weighs 32 grams. The unified atomic mass unit ( u) or Dalton ( Da) or sometimes universal mass unit, is an unit of Mass used to express 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.

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. An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol to form a Decimal multiple or An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol to form a Decimal multiple or 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). The International System of Units (SI defines seven dimensionally independent SI base units. 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. The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units Caesium or cesium (ˈsiːziəm is the Chemical element with the symbol Cs and Atomic number 55

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). Water ( H2[[oxygen O]] H OH) is the most abundant Molecule on Earth 's surface composing of about 70% of the Earth's surface as

Contents 1 Definitions 2 Elementary entities 3 History 3.1 Proposed future definition 4 Utility of moles 5 See also 6 References

Definitions

A mole is the amount of substance of a system, which contains as many elementary entities as there are atoms in 0. The amount of substance, n, of a sample or system is a Physical quantity which is proportional to the number of elementary entities present 012 kilogram (or 12 grams) of carbon-12, where the carbon-12 atoms are unbound, at rest and in their ground state. For other uses of the words gram or gramme see Gram (disambiguation. Carbon-12 is the most abundant of the two stable Isotopes of the element Carbon, accounting for 98 In Quantum mechanics, a stationary state is an Eigenstate of a Hamiltonian, or in other words a state of definite energy ^[2] The number of atoms in 0. 012 kilogram of carbon-12 is known as the Avogadro constant, and is determined empirically. The Avogadro constant (symbols L, N A also called Avogadro's number, is the number of "elementary entities" (usually Atoms The currently accepted value is 6. 02214179(30)×10²³ mol^-1 (2007 CODATA). CODATA ( Committee on Data for Science and Technology) was established in 1966 as an interdisciplinary committee of the International Council of Science (ICSU formerly

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. In Dimensional analysis, a dimensionless quantity (or more precisely a quantity with the dimensions of 1) is a Quantity without any Physical units In mathematics the dimension of a Space is roughly defined as the minimum number of Coordinates needed to specify every point within it In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a Light source in a particular direction per unit Solid ^[3] (By contrast, the SI specifically defines the radian and the steradian as special names for the dimensionless unit one. The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 The steradian (symbol sr) is the SI unit of Solid angle. It is used to describe two-dimensional angular spans in three- Dimensional space )^[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. The unified atomic mass unit ( u) or Dalton ( Da) or sometimes universal mass unit, is an unit of Mass used to express The atomic mass (ma is the Mass of an atom most often expressed in unified atomic mass units The atomic mass may be considered to be the total mass For example, iron has a relative atomic mass of 55. Iron (ˈаɪɚn is a Chemical element with the symbol Fe (ferrum and Atomic number 26 The atomic mass (ma is the Mass of an atom most often expressed in unified atomic mass units The atomic mass may be considered to be the total mass 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. ^[8]

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. In Particle physics, an elementary particle or fundamental particle is a particle not known to have substructure that is it is not known to be made The particles can be atoms, molecules, ions, formula units, electrons, photons or other particles. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by An ion is an Atom or Molecule which has lost or gained one or more Valence electrons giving it a positive or negative electrical charge A formula unit in Chemistry is the Empirical formula of an ionic or Covalent Network solid compound used as an independent entity The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena For example, one mole of water is equivalent to 18. Water is a common Chemical substance that is essential for the survival of all known forms of Life. 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. In Physics and Chemistry, the Faraday constant (named after Michael Faraday) is the magnitude of Electric charge per mole of 96,500 [C·mol^-1]. One mole of photons is called an einstein. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena An einstein is a unit used in Irradiance and in Photochemistry. The thermal Energy R*T has the unit joule per mole, due to the definition of the gas constant R. Thermal energy is the sum of the sensible energy and latent energy. Relationship with the Boltzmann constant The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working A short summary with simple calculations is provided here ^[9].

When the substance of interest is a gas, the particles are usually molecules. This page is about the physical properties of gas as a state of matter 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. History Noble gas is translated from the German noun de ''Edelgas'' first used in 1898 by Hugo Erdmann to indicate their extremely low level of reactivity Helium ( He) is a colorless odorless tasteless non-toxic Inert Monatomic Chemical This article pertains to the chemical element For other uses see Argon (disambiguation. Neon (ˈniːɒn is the Chemical element that has the symbol Ne and Atomic number 10 Krypton (ˈkrɪptən or /ˈkrɪptɒn/ from kryptos "hidden" is a Chemical element with the symbol Kr and Atomic number 36 Xenon (ˈzɛnɒn or) is a Chemical element represented by the symbol Xe. Radon (ˈreɪdɒn is the Chemical element that has the symbol Rn and Atomic number 86 In Physics and Chemistry, monatomic is a combination of the words "mono" and "atomic" and means "single Atom. The Van der Waals equation is an Equation of state that can be derived from a special form of the potential between a pair of molecules (hard-sphere repulsion An ideal gas has a molar volume of 22. These four properties that constitute an ideal gas can be easily remembered by the acronym RIPE which stands for - R andom Motion (molecules are in constant random motion The molar volume, symbol V m is the Volume occupied by one mole of a substance ( Chemical element or Chemical compound) 4 litres per mole at STP (see Avogadro's Law). The litre or liter (see spelling differences) is a unit of Volume. In Physical sciences standard conditions for temperature and pressure are Standard sets of conditions for experimental measurements to allow comparisons to be made Avogadro's law ( Avogadro's Hypothesis, or Avogadro's Principle) is a Gas law named after Amedeo Avogadro, who in 1811 hypothesized

A mole of atoms or molecules is also called a "gram atom" or "gram molecule", respectively^[10].

History

The name mole is attributed to Johnathan VanGorveatte who introduced the corresponding German term (Mol) in 1893. ^[11] The term first appeared in English (as mol) in an 1897 translation of another German text. ^[12] It is an abbreviation for molecule (German Molekül), which is in turn derived from Latin moles "mass, massive structure". In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by 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. The unified atomic mass unit ( u) or Dalton ( Da) or sometimes universal mass unit, is an unit of Mass used to express 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 International Union of Pure and Applied Physics ( IUPAP) is an international Non-governmental organization devoted to the advancement of Physics. The International Union of Pure and Applied Chemistry ( IUPAC) (aɪjuːpæk or ay-yoo-pec) is an international Non-governmental organization Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the There are three stable isotopes of oxygen that lead to Oxygen ( O) having a standard atomic mass of 15 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). The International Committee for Weights and Measures is the English name of the Comité international des poids et mesures ( CIPM, sometimes written in English The General Conference on Weights and Measures is the English name of the Conférence générale des poids et mesures ( CGPM, never GCWM

In 1980 the ICPM clarified the above definition, defining that the carbon-12 atoms are unbound and in their ground state. In Quantum mechanics, a stationary state is an Eigenstate of a Hamiltonian, or in other words a state of definite energy

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. A physical Constant is a Physical quantity that is generally believed to be both universal in nature and constant in time 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. ^[13]

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. Dozen is another word for the Number twelve. The dozen may be one of the earliest primitive groupings perhaps because there are approximately a dozen cycles of the

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. ^[14]

Utility of moles

The mole is useful in chemistry because it allows different substances to be measured comparably. Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties Using the same number of moles of two substances, both amounts have the same number of molecules or atoms. In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny 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. The litre or liter (see spelling differences) is a unit of Volume. 34×10²² molecules.

See also

References

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