International System of Units – The Physics Hypertextbook Discussion introduction The creation of the metric system following the complete destruction of the traditional-imperial French unit system marks the beginning of a series of events that eventually lead to the currently accepted International System of Units. The great German mathematician Carl Friedrich Gauss (1777–1855) was the first to promote the idea of combining metric units with the second to form a complete and consistent unit system for mechanics. With the help of the German physicist Wilhelm Weber (1804–1891), he was able to extend this concept to include the units for electricity and magnetism. What came to be known as the Gaussian System of Units arose from this proposal. Its organization served as a model for the International System. The International System of Units (called Le Système international d’unités in French and abbreviated as SI by international convention) arose during the Eleventh General Conference of Weights and Measures (Conférence générale des poids et mesures or CGPM) conducted by the International Bureau of Weights and Measures (Bureau international des poids et mesures or BIPM) in Paris in 1960. The SI model has three major components.

Seven well-defined, dimensionally independent, fundamental units (or base units) that are assumed irreducible by convention (meter, kilogram, second, ampère, kelvin, mole, and candela). A large number of derived units formed by combining fundamental units according to the algebraic relations of the corresponding quantities (some of which are assigned special names and symbols and which themselves can be further combined to form even more derived units). The derived units are coherent in the sense that they are all mutually related only by the rules of multiplication and division with no numerical factor other than 1 needed. The derived units are also complete in the sense that one and only one unit exists for every defined physical quantity. Although it is possible to express many units in more than one way, they are all equivalent. (The converse statement is not necessarily true, however. Some units are used for more than one physical quantity.) Twenty currently agreed upon prefixes that can be attached to any of the fundamental units or derived units with special names creating multiples and division as needed. (The exception to this rule is the kilogram, which is already itself a multiple of the gram.

In this case, prefixes should be added to the word gram.) The first three named multiples are the first three powers of ten (101, 102, 103). Subsequent named multiples are larger than the previous named multiple by three orders of magnitude (106, 109, 1012,… ). The first three named divisions are the first three negative powers of ten (10−1, 10−2, 10−3). Subsequent named divisions are smaller than the previous named division by three orders of magnitude (10−6, 10−9, 10−12,… ). Each of the three components are described in greater detail below. fundamental units While it is possible for many units to serve as the fundamental building blocks of a system, the following seven were chosen for historical and practical reasons to serve as the fundamental units of the International System of Units. The meter is the fundamental unit of length in the International System of Units.

It was originally defined in 1799 as one ten millionth of the distance from the equator to the north pole as measured on a line of longitude passing through Paris (so that the circumference of the Earth would be 40 million meters). This would then fix the circumference of the Earth at the reasonably convenient value of 40 million meters. There are two problems with this statement, however. First, although nearly spherical to the eye, the Earth is slightly flattened and deviates from the geometric ideal by about one part in three hundred. A trip around the equator would be 134 km longer that a trip around the poles. Second, a small mistake was made when measuring the equator to pole distance through Paris. The length of the actual meter thus differs from its expected length by about one part in four thousand. In 1889, the BIPM in Paris constructed a precisely machined, platinum-iridium bar with two lines etched at opposite ends. The meter was then defined as the distance between these two lines when stored under specified conditions.

Regionally authorized metrologists (measurement technicians) would then travel to BIPM headquarters in France and copy the etched lines of the international prototype on to their own platinum-iridium bars and create regional prototypes. These would then be used to create local prototypes, which would then be used to create individual prototypes, which would then be used to calibrate measuring devices. Access to the international prototype was strictly controlled so as to keep the wear and tear on it to a minimum and to lessen the possibility of a catastrophic handling error. Given the inaccessibility of the prototype and the possibility of its accidental or intentional destruction a new kind of standard was called for. The definition of the meter based on the international prototype was replaced by a series of definitions based on experiment. The meter is now effectively indestructible as it is possible to reproduced these experiments anywhere in the universe at any time.

The original international prototype meter is still kept at the BIPM under conditions specified in 1889, but it is unlikely that it will ever have any official duties again in the future From 1960 to 1983, the meter was defined as the length equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton 86 atom. After 1983, the definition was changed so that the meter [m] became the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second. The change made in 1983 meant that lengths could now be measured as accurately as times are measured — time being the most accurately measured of all physical quantities. The current definition had the additional effect of fixing the speed of light in a vacuum at exactly 299,792,458 m/s.

The gram was the fundamental unit of mass in the metric system, but it is the kilogram (one thousand grams) that plays this role in the International System. (A gram was deemed too small to be of much practical use, I suspect.) The kilogram was originally defined in 1799 as the mass of one liter (one thousand cubic centimeters) of pure liquid water at 0 ℃. … In 1889, the BIPM in Paris constructed a precisely machined, platinum-iridium cylinder from the 1799 definition to serve as the international prototype of the kilogram [kg]. Like the international prototype meter (which was constructed at the same time) access to the international prototype kilogram is strictly controlled to reduce wear and tear on it from normal use and to prevent its accidental or intentional destruction. Unlike the meter, however, no reproducible experiment has yet been designed to define the kilogram. If this prototype should somehow become damaged, the definition of the kilogram would itself become damaged. A number of secondary prototypes exist, scattered around the world in regional standards offices.

They differ from the international prototype by no more than one part in 109 and could be pressed into service should something happen to the original. Still, it should be evident that a better standard is needed. Despite all the best efforts of the BIPM, the mass of the international prototype increases by approximately 1 part in 109 per year due to the inevitable accumulation of contaminants on its surface. This error is just at the limit of uncertainty in the measurement used to calibrate the secondary prototypes and is therefore of some significance. For this reason, the international prototype has a mass of one kilogram only after it has been cleaned and washed by a specified method. It's natural to think of the sun as the timekeeper of our lives, but when compared to contemporary wristwatches and wall clocks, the sun is a pretty terrible clock. Variations in the speed of the Earth as it orbits the sun are great enough that a sundial can disagree with a more conventional clock by as much as 16 minutes and would only be considered accurate four times a year.

To correct for this deviation from the ideal, astronomers imagine a fictitious sun that moves across the sky at a constant rate, makes the same number of transits across the sky as the real sun, and is in the same place as the real sun once a year. The time it takes this fictitious sun to make one circuit around the Earth is called a mean solar day. Since there are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a mean solar day, the original definition of the second was 1/86,400 of a mean solar day (24 x 60 x 60 = 86,400). Natural irregularities in the rotation of the Earth limited the accuracy achievable through this definition, however. The rotation of the Earth varies by about 1 part in 108 between May (when it is slowest) and September (when it is fastest). Furthermore, the rate of the Earth's rotation decreases by about 1 part in 109 per year as energy is drained away by the tidal interactions of the Earth and moon.

Greater accuracies could be achieved from the motion of the Earth around the sun, which is less susceptible to change over the years. The time it takes the sun to make one complete circuit across the sky (from summer solstice to summer solstice, for example) is known as a tropical year. In 1960, the CGPM on advice from the International Astronomical Union declared the second to be 1/31,556,925.9747 of the tropical year. This meant that a day, which formerly defined the second, was now defined by it. A unit day is now 86,400 seconds long by definition. The current standard, adopted in 1967, utilizes the incredible regularity at which certain atomic transitions take place. A second [s] is now defined as 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. Every elementary particle can be thought of as a tiny bar magnet with a north and south pole.

The hyperfine transition of the ground state occurs when the outermost electron of an atom changes its magnetic orientation relative to the nucleus from parallel (pointing in the same direction) to antiparallel (pointing in the opposite direction). A cesium oscillator, commonly referred to as an atomic clock, is a device that counts the hyperfine transitions made by a collection of cesium atoms. Accuracy of 1 part in 1014 are routinely achieved. … The SI unit of electric current is the ampère [A] The SI unit of thermodynamic temperature is the kelvin [K]. The SI unit of amount of substance is the mole [mol]. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles or specified groups of such particles. The SI unit of luminous intensity is the candela [cd]. Fundamental units of the International System quantity candela cd The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

(1979) derived units A large number of derived units formed by combining base units according to the algebraic relations of the corresponding quantities (some of which are assigned special names and symbols and which themselves can be further combined to form even more derived units). The derived units are coherent in the sense that they are all mutually related only by the rules of multiplication and division with no numerical factor other than 1 needed. The derived units are also complete in the sense that one and only one unit exists for every defined physical quantity. Although it is possible to express many units in more than one way, they are all equivalent. The converse statement is not necessarily true, however. Some units are used for more than one physical quantity. N m is used for energy (where it is called a joule) and torque s−1 is used for frequency (hertz), angular frequency (radian per second), becquerel (decays per second) J/kg is used in radiology for absorbed dose (gray) and equivalent dose (sievert) Derived units of the International System with special names quantity s−1 mol prefixes Twenty currently agreed upon prefixes that can be attached to any of the fundamental units or derived units with special names creating multiples and division as needed.

(The exception to this rule is the kilogram, which is already itself a multiple of the gram. In this case, prefixes should be added to the word gram.) The first three named mutiples are the first three powers of ten (101, 102, 103). Subsequent named multiples are larger than the previous named multiple by three orders of magnitude (106, 109, 1012,… ). The first three named divisions are the first three negative powers of ten (10−1, 10−2, 10−3). Subsequent named divisions are smaller than the previous named division by three orders of magnitude (10−6, 10−9, 10−12,… ). Whether one pronounces giga with hard or soft g depends on what one thinks the proper pronunciation is. A shift occurred in The US sometime in the mid 1990s (at about the time the Internet took off in popular culture) when "gig" replaced "jig" as the preferred pronunciation. BIPM guidelines don't care how any SI terms are pronounced as long as they're always represented with the proper symbol.

Divisions of the International System † unofficial* also norwegian Mole (unit) Mole (unit) This article is about the chemistry unit "mole" (amount of substance). For other uses, see Mole (disambiguation) . "Nmol" redirects here. For the mathematical technique, see Method of lines . Mole Symbol mol The mole is the unit of measurement in the International System of Units (SI) for amount of substance . It is defined as the amount of a chemical substance that contains as many elementary entities , e.g., atoms , molecules , ions , electrons , or photons , as there are atoms in 12 grams of carbon-12 (12C), the isotope of carbon with relative atomic mass 12 by definition. This number is expressed by the Avogadro constant , which has a value of 7023602214085700000♠6.022140857(74)×1023 mol−1. The mole is one of the base units of the SI, and has the unit symbol mol.

The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. For example, the chemical equation 2 H2 + O2 → 2 H2O implies that 2 mol of dihydrogen (H2) and 1 mol of dioxygen (O2) react to form 2 mol of water (H2O). The mole may also be used to express the number of atoms, ions, or other elementary entities in a given sample of any substance. The concentration of a solution is commonly expressed by its molarity , defined as the number of moles of the dissolved substance per litre of solution. The number of molecules per mole is known as Avogadro's constant , and is defined such that the mass of one mole of a substance, expressed in grams, is equal to the mean relative molecular mass of the substance. For example, the mean relative molecular mass of natural water is about 18.015, therefore, one mole of water has a mass of about 18.015 grams. The term gram-molecule was formerly used for essentially the same concept.

[1] The term gram-atom has been used for a 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 MgBr2 is 1 gram-molecule of MgBr2 but 3 gram-atoms of MgBr2. [2] [3] In honor of the unit, some chemists celebrate October 23, which is a reference to the 1023 scale of the Avogadro constant, as " Mole Day ". Some also do the same for February 6 and June 2. Contents 10 External links Definition and related concepts[ edit ] As of 2011 [update] , the mole is defined by International Bureau of Weights and Measures to be the amount of substance of a system which contains the same number of elementary entities (e.g. atoms , molecules , ions , electrons , photons ) as atoms in 0.012 kilograms of carbon-12 (12C), the isotope of carbon with relative atomic mass 12.

[1] 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 . Since the atomic mass unit (amu) is defined as 1/12 of the mass of the 12C atom, it follows that the molar mass of a substance, measured in grams per mole, is numerically equal to its mean atomic or molecular mass measured in amu. The number of elementary entities in a sample of a substance is technically called its (chemical) amount . 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. [4] Other methods include the use of the molar volume or the measurement of electric charge . [4] 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 7001399625909800000♠39.96259098 ± 6993220000000000000♠0.00000022 grams, whereas one mole of calcium-42 is 7001419586180100000♠41.95861801 ± 6993270000000000000♠0.00000027 grams, and one mole of calcium with the normal isotopic mix is 40.078 ± 0.004 grams. Since the definition of the gram is not (as of 2011 [update] ) mathematically tied to that of the atomic mass unit, the number NA of molecules in a mole (Avogadro's number) must be determined experimentally.

The value adopted by CODATA in 2010 is NA = 7023602214129000000♠6.02214129×1023 ± 7016270000000000000♠0.00000027×1023. [5] In 2011 the measurement was refined to 7023602214078000000♠6.02214078×1023 ± 7016179999999999999♠0.00000018×1023. [6] The number of moles of a sample is the sample mass divided by the molar mass of the material. The history of the mole is intertwined with that of molecular mass , atomic mass unit , Avogadro's number and related concepts.

The first table of relative atomic mass (atomic weight) was published by John Dalton (1766–1844) in 1805, based on a system in which the relative atomic mass of hydrogen was defined as 1. These relative atomic masses were based on the stoichiometric proportions of chemical reaction and compounds, a fact that greatly aided their acceptance: It was not necessary for a chemist to subscribe to atomic theory (an unproven hypothesis at the time) to make practical use of the tables. This would lead to some confusion between atomic masses (promoted by proponents of atomic theory) and equivalent weights (promoted by its opponents and which sometimes differed from relative atomic masses by an integer factor), which would last throughout much of the nineteenth century. Jöns Jacob Berzelius (1779–1848) was instrumental in the determination of relative atomic masses to ever-increasing accuracy. He was also the first chemist to use oxygen as the standard to which other masses 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 mass of oxygen as 100, an innovation that did not catch on. Charles Frédéric Gerhardt (1816–56), Henri Victor Regnault (1810–78) and Stanislao Cannizzaro (1826–1910) expanded on Berzelius' works, resolving many of the problems of unknown stoichiometry of compounds, and the use of atomic masses attracted a large consensus by the time of the Karlsruhe Congress (1860). The convention had reverted to defining the atomic mass 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 mass standard became ever more evident with advances in analytical chemistry and the need for ever more accurate atomic mass determinations.

Developments in mass spectrometry led to the adoption of oxygen-16 as the standard substance, in lieu of natural oxygen.[ citation needed ] The current definition of the mole, based on carbon-12, was approved during the 1960s. [1] [7] The four different definitions were equivalent to within 1%. Scale basis Relative atomic mass of 16O = 16 15.9949146221(15) +0.0318% The name mole is an 1897 translation of the German unit Mol, coined by the chemist Wilhelm Ostwald in 1894 from the German word Molekül ( molecule ). [8] [9] [10] However, the related concept of equivalent mass had been in use at least a century earlier. [11] The mole was made the seventh SI base unit in 1971 by the 14th CGPM.

[12] Unit[ edit ] Since its adoption into the International System of Units in 1971, there have been a number of criticisms of the concept of the mole as a unit like the metre or the second : 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; [7] the SI thermodynamic mole is irrelevant to analytical chemistry and could cause avoidable costs to advanced economies; [13] 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; [14] the SI defines numbers of entities as quantities of dimension one, and thus ignores the ontological distinction between entities and units of continuous quantities. [15] In chemistry, it has been known since Proust's law of definite proportions (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 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 (where the relationship was first demonstrated in 1857). The term "mole" was first used in a textbook describing these colligative properties .[ citation needed ] Other units called "mole"[ edit ] Chemical engineers use the concept extensively, but the unit is rather small for industrial use. [16] For convenience in avoiding conversions in the Imperial (or American customary units ), some engineers adopted the pound-mole (notation lb-mol or lbmol), which is defined as the number of entities in 12 lb of 12C. One lb-mol is equal to 7002453592370000000♠453.59237 mol.

[17] In the metric system, chemical engineers once used the kilogram-mole (notation 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 (notation g-mol), when dealing with laboratory data. [17] Late 20th century chemical engineering practice came to use the kilomole (kmol), which is numerically identical to the kilogram-mole, but whose name and symbol adopt the SI convention for standard multiples of metric units - thus kmol means 1000 moles. This is analogous to the use of kg instead of g. The use of kmol is not only for "magnitude convenience" but also makes the equations used for modelling chemical engineering systems coherent . For example, the conversion of a flowrate of kg/s to kmol/s only requires the molecular mass not the factor 1000 unless the basic SI unit of mol/s were to be used. Indeed, the appearance of any conversion factors in a model can cause confusion and is to be avoided; possibly a definition of coherence is the absence of conversion factors in sets of equations developed for modelling.

Concentrations expressed as kmol/m3 are numerically the same as those in mol/dm3 i.e. the molarity conventionally used by chemists for bench measurements; this equality can be convenient for scale-up. Greenhouse and growth chamber lighting for plants is sometimes expressed in micromoles per square meter per second, where 1 mole of photons = 6.02 x 1023 photons. [18] Proposed future definition[ edit ] Main article: New SI definitions In 2011, the 24th meeting of the General Conference on Weights and Measures (CGPM) agreed a plan for a possible revision of the SI base unit definitions on an as yet undetermined date. This plan, set forward in the meeting's first resolution, included a proposal to redefine the mole in a way that will fix "the Avogadro constant to be equal to exactly 6.022 14X ×1023 when it is expressed in the SI unit mol−1.... [19] .... the symbol X in this Draft Resolution represents one or more additional digits to be added to the numerical values .... using values based on the most recent CODATA adjustment".

Related units[ edit ] The SI units for molar concentration are mol/ m 3. However, most chemical literature traditionally uses mol/ dm 3, or mol dm −3, which is the same as mol/ L . These traditional units are often denoted by a capital letter M (pronounced "molar"), sometimes preceded by an SI prefix , for example, millimoles per litre (mmol/L) or millimolar (mM), micromoles/litre (µmol/L) or micromolar (µM), or nanomoles/L (nmol/L) or nanomolar (nM). The demal (D) is an obsolete unit for expressing the concentration of a solution . It is equal to molar concentration at 0 °C, i.e., 1 D represents one mole of the solute present in one cubic decimeter of the solution at 0 °C. [20] It was first proposed in 1924 as a unit of concentration based on the decimeter rather than the liter; at the time there was a factor of 1.000028 difference between the liter and the cubic decimeter.

[21] The demal was used as a unit of concentration in electrolytic conductivity primary standards. [22] These standards were later redefined in terms of molar concentration. [23] The unit's holiday[ edit ] October 23, denoted 10/23 in the US, is recognized by some as Mole Day . [24] It is an informal holiday in honor of the unit among chemists. The date is derived from Avogadro's constant, which is approximately 6.022×1023. It starts at 6:02 a.m. and ends at 6:02 p.m. Alternatively, some chemists celebrate June 2 or February 6, a reference to the 6.02 part of the constant. [25] [26] [27] Convert Amount of substance - Advertisement 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 (SI) defines the amount of substance to be proportional to the number of elementary entities present.

The SI unit for amount of substance is the mole. It has the unit symbol mol. The mole is defined as the amount of substance that contains an equal number of elementary entities as there are atoms in 0.012kg of the isotope carbon-12. This number is called Avogadro's number and has the value 6.02214179(30)×1023. It is the numerical value of the Avogadro constant which has the unit 1/mol, and relates the molar mass of an amount of substance to its mass. Read more Mole_(unit) Mole_(unit) Mole (unit) The mole (symbol: mol) is the SI base unit that measures an amount of substance . The mole is a counting unit. One mole contains Avogadro's number (approximately 6.02214×1023 ) entities (atoms or molecules). A mole is much like "a dozen" in that both are absolute numbers (having no units) and can describe any type of elementary object (object made up of atoms).

The mole's use, however, is usually limited to measurement of subatomic , atomic , and molecular structures; tradition and its magnitude 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-12 is 12 grams, while for water it is 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). Contents 6 References Definitions A mole is the amount of substance of a system, which contains as many elementary entities as there are atoms in 0.012 kilogram (or 12 grams ) of carbon-12 , where the carbon-12 atoms are unbound, at rest and in their ground state. [1] 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 6.02214279(30)×1023 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. [2] (By contrast, the SI specifically defines the radian and the steradian as special names for the dimensionless unit one.) [3] 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. [3] 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. [4] The relationship of the atomic mass unit (u [5] ) 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. 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. 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. 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: 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: The kilogram is the mass of exactly (6.0221415×1023/0.012) unbound carbon-12 atoms at rest and in their ground state. [6] This would have the effect of defining Avogadro's number to be precisely NA = 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 NA is: NA = 602214141070409084099072 = 844468883 This has the convenient properties of being a perfect cube, and of being near the current experimental bounds of measurement. [7] 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 mL of water contains over 6.02×1022 molecules. See also ^ Official SI Unit definitions ^ (2006) "Introduction", The International System of Units (SI), 8 (in English), International Bureau of Weights and Measures, 13-14. Retrieved on 2007-02-09.

(2006) "SI Units", The International System of Units (SI), 8 (in English), International Bureau of Weights and Measures, 28. Retrieved on 2007-02-09. ^ ^ The 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. ^ Base unit definitions: Mole Unit of amount of substance (mole) Abbreviations : CGPM, CIPM, BIPM Following the discovery of the fundamental laws of chemistry, units called, for example, "gram-atom" and "gram-molecule," were used to specify amounts of chemical elements or compounds. These units had a direct connection with "atomic weights" and "molecular weights," which were in fact relative masses. "Atomic weights" were originally referred to the atomic weight of oxygen, by general agreement taken as 16.

But whereas physicists separated isotopes in the mass spectrograph and attributed the value 16 to one of the isotopes of oxygen, chemists attributed that same value to the (slightly variable) mixture of isotopes 16, 17, and 18, which was for them the naturally occurring element oxygen. Finally, an agreement between the International Union of Pure and Applied Physics (IUPAP) and the International Union of Pure and Applied Chemistry (IUPAC) brought this duality to an end in 1959/60. Physicists and chemists have ever since agreed to assign the value 12, exactly, to the "atomic weight," correctly the relative atomic mass, of the isotope of carbon with mass number 12 (carbon 12, 12C). The unified scale thus obtained gives values of relative atomic mass. It remained to define the unit of amount of substance by fixing the corresponding mass of carbon 12; by international agreement, this mass has been fixed at 0.012 kg, and the unit of the quantity "amount of substance" was given the name mole (symbol mol).

Following proposals of IUPAP, IUPAC, and the International Organization for Standardization (ISO), the CIPM gave in 1967, and confirmed in 1969, a definition of the mole, eventually adopted by the 14th CGPM (1971): 1. 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." 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. At its 1980 meeting, the CIPM approved the 1980 proposal by the Consultive Committee on Units of the CIPM specifying that in this definition, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to. Metric System Units Metric System Units Go to Metric Prefixes Brief Historical Intro The first standardized system of measurement, based on the decimal was proposed in France about 1670.

However, it was not until 1791 that such a system was developed. It was called the "metric" system, based on the French word for measure. The driving force was the growing importance of weights in the sciences, especially chemistry. At that time, every country had their own system of weights and measures. England had three different systems just within its own borders!! On May 20, 1875, delegates of 17 countries signed the Meter Convention. It was amended in 1921 and today 48 countries are signatories. The modern metric system has been renamed Systeme International d'Unites (International System of Units) and is denoted by the letters SI. SI was established in 1960, at the 11th General Conference on Weights and Measures. It was then that units, definitions, and symbols were revised and simplified. There are three major parts to the metric system: the seven base units, the prefixes and units built up from the base units.

Here is a list of the base units which make up the metric system: Physical Quantity candela cd Prefixes were also agreed on in 1791 The set from kilo- down to milli- was developed then. For the multipliers (prefixes greater than 1), Greek was used and for the fractions (prefixes less than 1), Latin was used. In 1958, the International Committee on Weights and Measures added Mega-, Giga-, and Tera- to the multipliers and micro-, nano-, and pico- to the fractions. In 1960, at the 11th General Conference on Weights and Measures, everything was officially adopted. Since that time, additional prefixes have been added as the need arose. Typically, as scientific instruments get better and better, smaller and smaller quantities can be detected. So, new fractional prefixes need to be added. When they are, new multipliers are added also, to keep the system symmetrical. A brief mention about when the adoptions took place can be found here. Non-SI Units Commonly Used 1) Liter: symbol = L. The SI unit for volume is m3 (cubic meter).

One dm3 (cubic decimeter) equals one L. A cubic decimeter is a cube 0.1 m on a side. 2) cubic centimeter: symbol = cm3. Often used for measuring the volume of solids, one cm3 equals one milliliter (mL). 3) Ångström: symbol = Å. One Å equals 10¯8 cm. This unit, named for Anders Jonas Ångström, is often used for the wavelengths of electromagnetic radiation as well as the length of chemical bonds. Its use is being replaced by nm and pm, respectively. Definitions of Selected Units The Meter The meter has a most interesting history. The original definition was one ten-millionth of the distance from the North Pole to the Equator. From that, French scientists made a bar of 90% platinum and 10% iridium and put two marks on it to signify the meter distance. This particular alloy was used because it resisted expansions due to temperature very well and it could take a high polish, resulting in the ability to take a very fine line. This reduced the error due to the width of the lines.

As science moved into the 1900s, it was becoming apparent that wavelength measurements were among the most accurate ones in all of science. In 1907, the red line of cadmium at 6438 Å was adopted as a new meter standard, however many continued to advocate the green line at 5460 Å in mercury's spectrum. By the way, using a particular wavelength of light as a standard for measurement was made as early as 1829. It took almost 80 years for the technology of measurement to become exact enough for use as an international standard. In 1960, the orange line at 6058 Å of krypton-86 was adopted. The wavelength was specified as : λvac = 6057.802106 Å so that one meter equaled: 1,650,763.73 Hz¯1 If you want to be really technical, this is the 2p10 to 5d5 transition (following the notation of Paschen). It can also be written: 2P10 to 5d5. So there!

The definition was changed once again, in 1983, to the following: The meter is the length of path travelled by light in vacuum during a time interval of 1 / 299,792,458 of a second. By the way, this definition depends on the fact that the speed of light is defined (not measured) as exactly 299,792,458 meters per second. I think the meter's definition journey is over. The Kilogram An interesting fact about the kilogram is that it is the only SI base unit to incorporate a prefix. (By the way, teachers have been known to test that fact.) Why wasn't the gram used? I don't know for sure, but the gram is such a small amount of stuff that it would be easy to make a mistake in creating a standard. So I suspect they decided to deal with a larger amount of material. Here is the definition of the kilogram, adopted in 1901: it is equal to the mass of the international prototype of the kilogram.

What that means is that there is a cylinder of 90% platinum/10% iridium in a vault in Paris, France and that lump of stuff weighs exactly one kilogram, by definition. I have heard, although I have no proof, that it has been removed for use only 4 times during the 1900s. The kilogram is the only unit still based on a single lump of stuff. All the other definitions can be reproduced with a high degree of accuracy in any laboratory with the proper equipment. Interestingly enough, the kilogram is losing weight and scientists are calling for the kilogram to be redefined in a more accurate way. Amount of Substance (The Mole) In 1860, at the first ever international meeting of chemists, it was decided that hydrogen would serve as the standard for all atomic weights. It was defined as weighing exactly one atomic mass unit (amu). (The concept of mole had not yet been introduced into chemistry.) In 1906, oxygen was made the standard. There wasn't anything wrong with hydrogen, it was just that oxygen formed compounds with almost every element known and hydrogen did not. So oxygen was defined to weigh exactly 16 amu.

However, in 1929, the discovery of the O-17 isotope and later the O-18 isotope (both stable) changed matters, even though the two isotopes comprised only 0.24% of all oxygen atoms. Also, it was discovered that oxygen from different sources world-wide had slightly different mixes of the three isotopes. This was a BIG problem. In response, the physics community defined the amu as 1/16 the weight of the lightest oxygen isotope (which was O-16), while chemists do not come up with a new definition so fast. This meant that the atomic weights used by people in physics were different than those used in chemistry. This situation could not be tolerated. During the years 1958-1961 this issue was first debated by the world-wide chemistry and physics community and then voted upon. What emerged from the debate were two possible new standards: fluorine and carbon. The final vote showed carbon as the winner. Although fluorine had the advantage of only one natural isotope, carbon is much the safer element to handle.

Also, while carbon has two natural, stable isotopes, the isotopic mix between carbon-12 and carbon-13 is well known and stable world-wide. These years were at the height of the Cold War between the USA and the Soviet Union. Despite this, the Soviet physics and chemistry communities was well-represented in the debate and the voting. As a personal note, the ChemTeam was in elementary school during those years. I can still hear the air raid siren being tested every Friday at 10AM and I remember the drop-and-cover drills in case of nuclear attack (!). From 1971, the official wording (unchanged to the present day) is as follows: 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. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. By the way, some books will rearrange the definition.

For example: The amount of a substance of specified chemical formula, containing the same number of formula units (molecules, atoms, ions, electrons, etc.) as there are in 0.012 kilograms (exactly) of the pure nuclide carbon-12. This definition came from a reference book published in 1972 and is, of course, saying the same thing as the first definition.

Question: What SI unit (International System of Units) of measurement is defined as "The amount of substance that contains an equal number of elementary entities as there are atoms in 0.012kg of the isotope carbon-12"?
Answer: Mole