Relative atomic mass

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Relative atomic mass (symbol: Ar; sometimes abbreviated RAM or r.a.m.), also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to the atomic mass constant. The atomic mass constant (symbol: mu) is defined as being ⁠1/12⁠ of the mass of a carbon-12 atom. [1] [2] Since both quantities in the ratio are masses, the resulting value is dimensionless. These definitions remain valid [3] : 134  even after the 2019 revision of the SI. [lower-alpha 1] [lower-alpha 2]

Contents

For a single given sample, the relative atomic mass of a given element is the weighted arithmetic mean of the masses of the individual atoms (including all its isotopes) that are present in the sample. This quantity can vary significantly between samples because the sample's origin (and therefore its radioactive history or diffusion history) may have produced combinations of isotopic abundances in varying ratios. For example, due to a different mixture of stable carbon-12 and carbon-13 isotopes, a sample of elemental carbon from volcanic methane will have a different relative atomic mass than one collected from plant or animal tissues.

The more common, and more specific quantity known as standard atomic weight (Ar,standard) is an application of the relative atomic mass values obtained from many different samples. It is sometimes interpreted as the expected range of the relative atomic mass values for the atoms of a given element from all terrestrial sources, with the various sources being taken from Earth. [8] "Atomic weight" is often loosely and incorrectly used as a synonym for standard atomic weight (incorrectly because standard atomic weights are not from a single sample). Standard atomic weight is nevertheless the most widely published variant of relative atomic mass.

Additionally, the continued use of the term "atomic weight" (for any element) as opposed to "relative atomic mass" has attracted considerable controversy since at least the 1960s, mainly due to the technical difference between weight and mass in physics. [9] Still, both terms are officially sanctioned by the IUPAC. The term "relative atomic mass" now seems to be replacing "atomic weight" as the preferred term, although the term "standard atomic weight" (as opposed to the more correct "standard relative atomic mass") continues to be used.

Definition

Relative atomic mass is determined by the average atomic mass, or the weighted mean of the atomic masses of all the atoms of a particular chemical element found in a particular sample, which is then compared to the atomic mass of carbon-12. [10] This comparison is the quotient of the two weights, which makes the value dimensionless (having no unit). This quotient also explains the word relative: the sample mass value is considered relative to that of carbon-12.

It is a synonym for atomic weight, though it is not to be confused with relative isotopic mass. Relative atomic mass is also frequently used as a synonym for standard atomic weight and these quantities may have overlapping values if the relative atomic mass used is that for an element from Earth under defined conditions. However, relative atomic mass (atomic weight) is still technically distinct from standard atomic weight because of its application only to the atoms obtained from a single sample; it is also not restricted to terrestrial samples, whereas standard atomic weight averages multiple samples but only from terrestrial sources. Relative atomic mass is therefore a more general term that can more broadly refer to samples taken from non-terrestrial environments or highly specific terrestrial environments which may differ substantially from Earth-average or reflect different degrees of certainty (e.g., in number of significant figures) than those reflected in standard atomic weights.

Current definition

The prevailing IUPAC definitions (as taken from the "Gold Book") are:

atomic weight – See: relative atomic mass [11]

and

relative atomic mass (atomic weight) – The ratio of the average mass of the atom to the unified atomic mass unit. [12]

Here the "unified atomic mass unit" refers to 1/12 of the mass of an atom of 12C in its ground state. [13]

The IUPAC definition [1] of relative atomic mass is:

An atomic weight (relative atomic mass) of an element from a specified source is the ratio of the average mass per atom of the element to 1/12 of the mass of an atom of 12C.

The definition deliberately specifies "An atomic weight ...", as an element will have different relative atomic masses depending on the source. For example, boron from Turkey has a lower relative atomic mass than boron from California, because of its different isotopic composition. [14] [15] Nevertheless, given the cost and difficulty of isotope analysis, it is common practice to instead substitute the tabulated values of standard atomic weights, which are ubiquitous in chemical laboratories and which are revised biennially by the IUPAC's Commission on Isotopic Abundances and Atomic Weights (CIAAW). [16]

Historical usage

Older (pre-1961) historical relative scales based on the atomic mass unit (symbol: a.m.u. or amu) used either the oxygen-16 relative isotopic mass or else the oxygen relative atomic mass (i.e., atomic weight) for reference. See the article on the history of the modern unified atomic mass unit for the resolution of these problems.

Standard atomic weight

The IUPAC commission CIAAW maintains an expectation-interval value for relative atomic mass (or atomic weight) on Earth named standard atomic weight. Standard atomic weight requires the sources be terrestrial, natural, and stable with regard to radioactivity. Also, there are requirements for the research process. For 84 stable elements, CIAAW has determined this standard atomic weight. These values are widely published and referred to loosely as 'the' atomic weight of elements for real-life substances like pharmaceuticals and commercial trade.

Also, CIAAW has published abridged (rounded) values and simplified values (for when the Earthly sources vary systematically).

Other measures of the mass of atoms

Atomic mass (ma) is the mass of a single atom. It defines the mass of a specific isotope, which is an input value for the determination of the relative atomic mass. An example for three silicon isotopes is given below. A convenient unit of mass for atomic mass is the dalton (Da), which is also called the unified atomic mass unit (u).

The relative isotopic mass is the ratio of the mass of a single atom to the atomic mass constant (mu = 1 Da). This ratio is dimensionless.

Determination of relative atomic mass

Modern relative atomic masses (a term specific to a given element sample) are calculated from measured values of atomic mass (for each nuclide) and isotopic composition of a sample. Highly accurate atomic masses are available [17] [18] for virtually all non-radioactive nuclides, but isotopic compositions are both harder to measure to high precision and more subject to variation between samples. [19] [20] For this reason, the relative atomic masses of the 22 mononuclidic elements (which are the same as the isotopic masses for each of the single naturally occurring nuclides of these elements) are known to especially high accuracy. For example, there is an uncertainty of only one part in 38 million for the relative atomic mass of fluorine, a precision which is greater than the current best value for the Avogadro constant (one part in 20 million).

IsotopeAtomic mass [18] Abundance [19]
StandardRange
28Si27.97692653246(194)92.2297(7)%92.21–92.25%
29Si28.976494700(22)4.6832(5)%4.67–4.69%
30Si29.973770171(32)3.0872(5)%3.08–3.10%

The calculation is exemplified for silicon, whose relative atomic mass is especially important in metrology. Silicon exists in nature as a mixture of three isotopes: 28Si, 29Si and 30Si. The atomic masses of these nuclides are known to a precision of one part in 14 billion for 28Si and about one part in one billion for the others. However, the range of natural abundance for the isotopes is such that the standard abundance can only be given to about ±0.001% (see table).

The calculation is as follows:

Ar(Si) = (27.97693 × 0.922297) + (28.97649 × 0.046832) + (29.97377 × 0.030872) = 28.0854

The estimation of the uncertainty is complicated, [21] especially as the sample distribution is not necessarily symmetrical: the IUPAC standard relative atomic masses are quoted with estimated symmetrical uncertainties, [22] and the value for silicon is 28.0855(3). The relative standard uncertainty in this value is 10−5 or 10 ppm.

Apart from this uncertainty by measurement, some elements have variation over sources. That is, different sources (ocean water, rocks) have a different radioactive history and so different isotopic composition. To reflect this natural variability, the IUPAC made the decision in 2010 to list the standard relative atomic masses of 10 elements as an interval rather than a fixed number. [23]

See also

Notes

  1. ↑ There are only two consequences of the revision that are relevant to the present article. First, the molar mass of carbon-12, M(12C), is no longer defined as exactly equal to 12 g/mol, but instead has to be determined experimentally and thus has an uncertainty. Its current best value [4] [5] : 49  is 12.0000000126(37) g/mol. Here the "(37)" is a measure of the uncertainty; basically, the "26" (the last two digits in 12.0000000126) should be understood as "26 ± 37", as explained at Uncertainty § In measurements . However, this is so close to the old value of 12 g/mol (the relative difference is 1.05×10−9) that, in a vast majority of applications, M(12C) may still be taken to be exactly 12 g/mol; this is of course so by design. Second, the Avogadro constant NA is now exactly equal to 6.02214076×1023  reciprocal moles by definition, whereas previously it had to be determined experimentally and thus had an uncertainty. [3] : 134 
  2. ↑ Immediately following the 2019 revision, M(12C) was equal to 12.0000000000(54) g/mol, corresponding to a relative standard uncertainty [6] of 4.5×10−10. This uncertainty was "inherited" from the relative standard uncertainty that the product hNA had immediately prior to the revision: also 4.5×10−10. (Here h is the Planck constant. Following the revisition, the product hNA has an exact value by definition.) [7] : 143  Conversely, immediately prior to the revision, the Avogadro constant NA had a measured value of 6.022140758(62)×1023 reciprocal moles, corresponding to a relative standard uncertainty of 1.0×10−8. Note that immediately prior to the revision, the product hNA was known far more precisely than either h or NA individually [7] : 139 .

Related Research Articles

A chemical element is a chemical substance that: cannot be broken down into other substances by chemical reactions, consists of one or more atoms, is identified by the number of protons in its nuclei. For example, oxygen has an atomic number of 8, meaning each oxygen atom has 8 protons in its nucleus. Atoms of the same element can have different numbers of neutrons in their nuclei, known as isotopes of the element. Two or more atoms of the same element can combine to form homonuclear molecules. Chemical compounds are molecules made of atoms of different elements, while mixtures contain atoms of different elements not necessarily combined as molecules. Atoms can be transformed into different elements in nuclear reactions, which change an atom's atomic number.

The molecular mass is the mass of a given molecule. Units of daltons (Da) are often used. Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The derived quantity relative molecular mass is the unitless ratio of the mass of a molecule to the atomic mass constant.

<span class="mw-page-title-main">Mole (unit)</span> SI unit of amount of substance

The mole (symbol mol) is a unit of measurement, the base unit in the International System of Units (SI) for amount of substance, a quantity proportional to the number of elementary entities of a substance. One mole contains exactly 6.02214076×1023 elementary entities (approximately 602 sextillion or 602 billion times a trillion), which can be atoms, molecules, ions, ion pairs, or other particles. The number of particles in a mole is the Avogadro number (symbol N0) and the numerical value of the Avogadro constant (symbol NA) expressed in mol-1. The value was chosen on the basis of the historical definition of the mole as the amount of substance that corresponds to the number of atoms in 12 grams of 12C, which made the mass of a mole of a compound expressed in grams, numerically equal to the average molecular mass or formula mass of the compound expressed in daltons. With the 2019 revision of the SI, the numerical equivalence is now only approximate but may be assumed for all practical purposes.

<span class="mw-page-title-main">Avogadro constant</span> Fundamental metric system constant defined as the number of particles per mole

The Avogadro constant, commonly denoted NA or L, is an SI defining constant with an exact value of 6.02214076×1023 mol−1 (reciprocal moles). It is defined as the number of constituent particles (usually molecules, atoms, ions, or ion pairs) per mole (SI unit) and used as a normalization factor in the amount of substance in a sample. In the SI dimensional analysis of measurement units, the dimension of the Avogadro constant is the reciprocal of amount of substance, denoted N−1. The Avogadro number, sometimes denoted N0, is the numeric value of the Avogadro constant (i.e., without a unit), namely the dimensionless number 6.02214076×1023; the value chosen based on the number of atoms in 12 grams of carbon-12 in alignment with the historical definition of a mole. The constant is named after the Italian physicist and chemist Amedeo Avogadro (1776–1856).

The dalton or unified atomic mass unit is a unit of mass defined as ⁠1/12⁠ of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest. It is a non-SI unit accepted for use with SI. The atomic mass constant, denoted mu, is defined identically, giving mu = ⁠1/12⁠m(12C) = 1 Da.

<span class="mw-page-title-main">Molar mass</span> Mass per amount of substance

In chemistry, the molar mass of a chemical compound is defined as the ratio between the mass and the amount of substance of any sample of the compound. The molar mass is a bulk, not molecular, property of a substance. The molar mass is an average of many instances of the compound, which often vary in mass due to the presence of isotopes. Most commonly, the molar mass is computed from the standard atomic weights and is thus a terrestrial average and a function of the relative abundance of the isotopes of the constituent atoms on Earth. The molar mass is appropriate for converting between the mass of a substance and the amount of a substance for bulk quantities.

<span class="mw-page-title-main">Mass number</span> Number of heavy particles in the atomic nucleus

The mass number (symbol A, from the German word: Atomgewicht, "atomic weight"), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approximately equal to the atomic (also known as isotopic) mass of the atom expressed in atomic mass units. Since protons and neutrons are both baryons, the mass number A is identical with the baryon number B of the nucleus (and also of the whole atom or ion). The mass number is different for each isotope of a given chemical element, and the difference between the mass number and the atomic number Z gives the number of neutrons (N) in the nucleus: N = A − Z.

<span class="mw-page-title-main">Amount of substance</span> Ratio of the number of particles in a sample to Avogadros constant

In chemistry, the amount of substance (symbol n) in a given sample of matter is defined as a ratio (n = N/NA) between the number of elementary entities (N) and the Avogadro constant (NA). The entities are usually molecules, atoms, ions, or ion pairs of a specified kind. The particular substance sampled may be specified using a subscript, e.g., the amount of sodium chloride (NaCl) would be denoted as nNaCl. The unit of amount of substance in the International System of Units is the mole (symbol: mol), a base unit. Since 2019, the value of the Avogadro constant NA is defined to be exactly 6.02214076×1023 mol−1. Sometimes, the amount of substance is referred to as the chemical amount or, informally, as the "number of moles" in a given sample of matter.

Naturally occurring erbium (68Er) is composed of six stable isotopes, with 166Er being the most abundant. Thirty-nine radioisotopes have been characterized with between 74 and 112 neutrons, or 142 to 180 nucleons, with the most stable being 169Er with a half-life of 9.4 days, 172Er with a half-life of 49.3 hours, 160Er with a half-life of 28.58 hours, 165Er with a half-life of 10.36 hours, and 171Er with a half-life of 7.516 hours. All of the remaining radioactive isotopes have half-lives that are less than 3.5 hours, and the majority of these have half-lives that are less than 4 minutes. This element also has numerous meta states, with the most stable being 167mEr.

Naturally occurring terbium (65Tb) is composed of one stable isotope, 159Tb. Thirty-seven radioisotopes have been characterized, with the most stable being 158Tb with a half-life of 180 years, 157Tb with a half-life of 71 years, and 160Tb with a half-life of 72.3 days. All of the remaining radioactive isotopes have half-lives that are less than 6.907 days, and the majority of these have half-lives that are less than 24 seconds. This element also has 27 meta states, with the most stable being 156m1Tb, 154m2Tb and 154m1Tb.

Naturally occurring cerium (58Ce) is composed of 4 stable isotopes: 136Ce, 138Ce, 140Ce, and 142Ce, with 140Ce being the most abundant and the only one theoretically stable; 136Ce, 138Ce, and 142Ce are predicted to undergo double beta decay but this process has never been observed. There are 35 radioisotopes that have been characterized, with the most stable being 144Ce, with a half-life of 284.893 days; 139Ce, with a half-life of 137.640 days and 141Ce, with a half-life of 32.501 days. All of the remaining radioactive isotopes have half-lives that are less than 4 days and the majority of these have half-lives that are less than 10 minutes. This element also has 10 meta states.

<span class="mw-page-title-main">Isotopes of lanthanum</span>

Naturally occurring lanthanum (57La) is composed of one stable (139La) and one radioactive (138La) isotope, with the stable isotope, 139La, being the most abundant (99.91% natural abundance). There are 39 radioisotopes that have been characterized, with the most stable being 138La, with a half-life of 1.02×1011 years; 137La, with a half-life of 60,000 years and 140La, with a half-life of 1.6781 days. The remaining radioactive isotopes have half-lives that are less than a day and the majority of these have half-lives that are less than 1 minute. This element also has 12 nuclear isomers, the longest-lived of which is 132mLa, with a half-life of 24.3 minutes. Lighter isotopes mostly decay to isotopes of barium and heavy ones mostly decay to isotopes of cerium. 138La can decay to both.

Naturally occurring niobium (41Nb) is composed of one stable isotope (93Nb). The most stable radioisotope is 92Nb with a half-life of 34.7 million years. The next longest-lived niobium isotopes are 94Nb and 91Nb with a half-life of 680 years. There is also a meta state of 93Nb at 31 keV whose half-life is 16.13 years. Twenty-seven other radioisotopes have been characterized. Most of these have half-lives that are less than two hours, except 95Nb, 96Nb and 90Nb. The primary decay mode before stable 93Nb is electron capture and the primary mode after is beta emission with some neutron emission occurring in 104–110Nb.

Naturally occurring chromium (24Cr) is composed of four stable isotopes; 50Cr, 52Cr, 53Cr, and 54Cr with 52Cr being the most abundant (83.789% natural abundance). 50Cr is suspected of decaying by β+β+ to 50Ti with a half-life of (more than) 1.8×1017 years. Twenty-two radioisotopes, all of which are entirely synthetic, have been characterized, the most stable being 51Cr with a half-life of 27.7 days. All of the remaining radioactive isotopes have half-lives that are less than 24 hours and the majority of these have half-lives that are less than 1 minute. This element also has two meta states, 45mCr, the more stable one, and 59mCr, the least stable isotope or isomer.

Naturally occurring vanadium (23V) is composed of one stable isotope 51V and one radioactive isotope 50V with a half-life of 2.71×1017 years. 24 artificial radioisotopes have been characterized (in the range of mass number between 40 and 65) with the most stable being 49V with a half-life of 330 days, and 48V with a half-life of 15.9735 days. All of the remaining radioactive isotopes have half-lives shorter than an hour, the majority of them below 10 seconds, the least stable being 42V with a half-life shorter than 55 nanoseconds, with all of the isotopes lighter than it, and none of the heavier, have unknown half-lives. In 4 isotopes, metastable excited states were found (including 2 metastable states for 60V), which adds up to 5 meta states.

<span class="mw-page-title-main">Standard atomic weight</span> Relative atomic mass as defined by IUPAC (CIAAW)

The standard atomic weight of a chemical element (symbol Ar°(E) for element "E") is the weighted arithmetic mean of the relative isotopic masses of all isotopes of that element weighted by each isotope's abundance on Earth. For example, isotope 63Cu (Ar = 62.929) constitutes 69% of the copper on Earth, the rest being 65Cu (Ar = 64.927), so

<span class="mw-page-title-main">Mass (mass spectrometry)</span> Physical quantities being measured

The mass recorded by a mass spectrometer can refer to different physical quantities depending on the characteristics of the instrument and the manner in which the mass spectrum is displayed.

The molar mass constant, usually denoted by Mu, is a physical constant defined as one twelfth of the molar mass of carbon-12: Mu = M(12C)/12. The molar mass of an element or compound is its relative atomic mass or relative molecular mass multiplied by the molar mass constant.

<span class="mw-page-title-main">Atomic mass</span> Rest mass of an atom in its ground state

The atomic mass (ma or m) is the mass of an atom. Although the SI unit of mass is the kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (symbol: Da) – equivalently, unified atomic mass unit (u). 1 Da is defined as 1⁄12 of the mass of a free carbon-12 atom at rest in its ground state. The protons and neutrons of the nucleus account for nearly all of the total mass of atoms, with the electrons and nuclear binding energy making minor contributions. Thus, the numeric value of the atomic mass when expressed in daltons has nearly the same value as the mass number. Conversion between mass in kilograms and mass in daltons can be done using the atomic mass constant .

<span class="mw-page-title-main">Commission on Isotopic Abundances and Atomic Weights</span> International scientific committee

The Commission on Isotopic Abundances and Atomic Weights (CIAAW) is an international scientific committee of the International Union of Pure and Applied Chemistry (IUPAC) under its Division of Inorganic Chemistry. Since 1899, it is entrusted with periodic critical evaluation of atomic weights of chemical elements and other cognate data, such as the isotopic composition of elements. The biennial CIAAW Standard Atomic Weights are accepted as the authoritative source in science and appear worldwide on the periodic table wall charts.

References

  1. 1 2 International Union of Pure and Applied Chemistry (1980). "Atomic Weights of the Elements 1979" (PDF). Pure Appl. Chem. 52 (10): 2349–84. doi: 10.1351/pac198052102349 .
  2. ↑ International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry , 2nd edition, Oxford: Blackwell Science. ISBN   0-632-03583-8 . p. 41. Electronic version.
  3. 1 2 International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN   978-92-822-2272-0, archived from the original on 18 October 2021
  4. ↑ "2022 CODATA Value: molar mass of carbon-12". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.
  5. ↑ Tiesinga, Eite; Mohr, Peter J.; Newell, David B.; Taylor, Barry N. (30 June 2021). "CODATA recommended values of the fundamental physical constants: 2018". Reviews of Modern Physics. 93 (2). doi:10.1103/RevModPhys.93.025010. PMC   9890581 .
  6. ↑ "Standard Uncertainty and Relative Standard Uncertainty". CODATA reference. NIST. Archived from the original on 24 July 2023. Retrieved 30 August 2023.
  7. 1 2 Mohr, Peter J; Newell, David B; Taylor, Barry N; Tiesinga, Eite (1 February 2018). "Data and analysis for the CODATA 2017 special fundamental constants adjustment". Metrologia. 55 (1): 125–146. doi: 10.1088/1681-7575/aa99bc .
  8. ↑ Definition of element sample
  9. ↑ de Bièvre, Paul; Peiser, H. Steffen (1992). "'Atomic Weight' — The Name, Its History, Definition, and Units" (PDF). Pure and Applied Chemistry . 64 (10): 1535–43. doi:10.1351/pac199264101535.
  10. ↑ IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " relative atomic mass ". doi : 10.1351/goldbook.R05258
  11. ↑ IUPAC Gold Book – atomic weight
  12. ↑ IUPAC Gold Book – relative atomic mass (atomic weight), A r
  13. ↑ IUPAC Gold Book – unified atomic mass unit
  14. ↑ Greenwood, Norman N.; Earnshaw, Alan (1984). Chemistry of the Elements. Oxford: Pergamon Press. pp. 21, 160. ISBN   978-0-08-022057-4.
  15. ↑ International Union of Pure and Applied Chemistry (2003). "Atomic Weights of the Elements: Review 2000" (PDF). Pure Appl. Chem. 75 (6): 683–800. doi:10.1351/pac200375060683. S2CID   96800435.
  16. ↑ IUPAC Gold Book – standard atomic weights
  17. ↑ National Institute of Standards and Technology. Atomic Weights and Isotopic Compositions for All Elements.
  18. 1 2 Wapstra, A.H.; Audi, G.; Thibault, C. (2003), The AME2003 Atomic Mass Evaluation (Online ed.), National Nuclear Data Center . Based on:
  19. 1 2 Rosman, K. J. R.; Taylor, P. D. P. (1998), "Isotopic Compositions of the Elements 1997" (PDF), Pure and Applied Chemistry , 70 (1): 217–35, doi:10.1351/pac199870010217
  20. ↑ Coplen, T. B.; et al. (2002), "Isotopic Abundance Variations of Selected Elements" (PDF), Pure and Applied Chemistry , 74 (10): 1987–2017, doi:10.1351/pac200274101987
  21. ↑ Meija, Juris; Mester, Zoltán (2008). "Uncertainty propagation of atomic weight measurement results". Metrologia. 45 (1): 53–62. Bibcode:2008Metro..45...53M. doi:10.1088/0026-1394/45/1/008. S2CID   122229901.
  22. ↑ Holden, Norman E. (2004). "Atomic Weights and the International Committee—A Historical Review". Chemistry International. 26 (1): 4–7.
  23. ↑ "Changes to the Periodic Table". Archived from the original on 2019-07-15.

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