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Relative atomic mass
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.[a][b]

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

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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

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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 atomic mass constant.[12]

Here the atomic mass constant refers to 1/12 of the mass of an atom of 12C in its ground state, and is equal to one dalton.[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

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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 dalton for the resolution of these problems.

Standard atomic weight

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Main article: 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

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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

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Main article: Isotope geochemistry

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).

Isotope Atomic mass[18] Abundance[19]
Standard Range
28Si 27.97692653246(194) 92.2297(7)% 92.21–92.25%
29Si 28.976494700(22) 4.6832(5)% 4.67–4.69%
30Si 29.973770171(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

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Notes

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References

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Further reading

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Relative atomic mass

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from Grokipedia
Relative atomic mass, denoted as ArA_r, is a dimensionless quantity defined as the ratio of the average mass of the atoms of a (taken from a specific sample) to the mass of one unified atomic mass unit, where the unified atomic mass unit is one-twelfth the mass of a in its ground state. This measure, also known as atomic weight, provides a standardized way to express the mass of elements relative to carbon-12, facilitating comparisons across the periodic table. For elements consisting of a single stable isotope, the relative atomic mass is the relative isotopic mass of that isotope (which approximates but is not exactly equal to the mass number), defined as exactly 12 for carbon-12. However, most elements have multiple stable isotopes with varying natural abundances, so the relative atomic mass Ar(E)A_r(E) for an element EE is calculated as the abundance-weighted average of the relative isotopic masses of its isotopes. This average is determined using the formula Ar(E)=∑(xi⋅Ar(iE))A_r(E) = \sum (x_i \cdot A_r(iE)), where xix_i is the of isotope iEiE and Ar(iE)A_r(iE) is its relative atomic mass. Standard atomic weights, which are recommended values of relative atomic mass for normal terrestrial materials, are periodically evaluated and published by the IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW). These values account for isotopic variability in and are expressed either as single numbers (e.g., 12.011 for carbon) or intervals (e.g., [12.0096, 12.0116]) to reflect measured ranges in different samples. Recent updates, such as those in 2024, have refined values for elements like , , and based on improved isotopic composition data. The is fundamental in chemistry for calculating molar masses, in reactions, and isotopic distributions in analytical techniques like . Variations in isotopic abundances due to geological or anthropogenic processes can lead to slight deviations from standard values, emphasizing the importance of specifying the material source when precision is required.

Definition and Fundamentals

Current Definition

The relative atomic mass ArA_r of an element is defined as the ratio of the average of the atoms of the element (taken from a specified source material) to one-twelfth the of an atom of the 12C^{12}\mathrm{C}, resulting in a . This scale ensures consistency in comparing atomic es across elements and is equivalent to dividing the average atomic by the unified atomic mass unit (u), where 1 u=112m(12C)1 \, \mathrm{u} = \frac{1}{12} m(^{12}\mathrm{C}). The adoption of the standard in 1961 by the International Union of Pure and Applied Chemistry (IUPAC) and the International Union of Pure and Applied Physics (IUPAP) unified previously divergent oxygen-based scales used in chemistry and physics. For elements with multiple stable isotopes, the relative atomic mass is calculated as the abundance-weighted average of the relative isotopic masses: Ar(E)=∑ixiAr,i(E)A_r(\mathrm{E}) = \sum_i x_i A_{r,i}(\mathrm{E}) where xix_i is the amount fraction (isotopic abundance) of isotope ii of element E in the specified material, and Ar,i(E)A_{r,i}(\mathrm{E}) is the relative isotopic mass of that isotope, defined analogously as the ratio of its mass to 112m(12C)\frac{1}{12} m(^{12}\mathrm{C}). This averaging reflects the natural isotopic composition of the element on , making ArA_r representative of typical samples rather than a single isotope. As a relative quantity, ArA_r differs from absolute atomic mass by lacking physical units, emphasizing proportionality to the carbon-12 reference rather than providing an exact mass value in kilograms or similar. In chemical applications, ArA_r values are essential for stoichiometric calculations, as they enable the determination of molar masses (M=Ar×1 g⋅mol−1M = A_r \times 1 \, \mathrm{g \cdot mol^{-1}}) used to relate the masses of reactants and products in balanced equations. This facilitates precise predictions of reaction yields and compositions without needing absolute masses.

Relation to Atomic Mass Unit

The unified atomic mass unit (u), also known as the dalton (Da), is a non-SI unit of mass defined as exactly one twelfth of the mass of an unbound neutral atom of the nuclide 12^{12}C in its nuclear and electronic ground state. This definition establishes u as the atomic mass constant, with a fixed value of 1.66053906892(52)×10−271.66053906892(52) \times 10^{-27} kg according to the 2022 CODATA recommended values. Relative atomic masses, being dimensionless ratios, are numerically equivalent to the corresponding atomic or molecular masses when expressed in u; for example, the relative atomic mass of Ar(\ceH)≈1.008A_\mathrm{r}(\ce{H}) \approx 1.008 corresponds to a mass of approximately 1.008 u per atom. This equivalence provides a practical scale for quantifying atomic masses on an absolute basis, bridging the abstract relative scale to measurable physical quantities in kilograms. The unified atomic mass unit connects relative atomic masses to the molar mass constant MuM_\mathrm{u}, defined such that the molar mass MM of a substance is given by M=Ar×MuM = A_\mathrm{r} \times M_\mathrm{u}, where Mu≈1M_\mathrm{u} \approx 1 g mol−1^{-1}. This relation enables the conversion of relative atomic masses to molar masses in grams per mole, facilitating applications in chemistry such as stoichiometry and quantitative analysis. The 2019 redefinition of the SI base units fixed the values of the Avogadro constant NA=6.02214076×1023N_\mathrm{A} = 6.02214076 \times 10^{23} mol−1^{-1} and the kilogram via the Planck constant, thereby establishing an exact value for u in kilograms independent of physical artifacts or experimental measurements of the carbon-12 mass. As a result, MuM_\mathrm{u} is no longer exactly 1 g mol−1^{-1} but is precisely Mu=1.000 000 001 05(31)×10−3M_\mathrm{u} = 1.000\,000\,001\,05(31) \times 10^{-3} kg mol−1^{-1}, though the difference is negligible for most practical purposes and maintains the approximate equivalence.

Historical Development

Early Concepts of Atomic Weight

The concept of atomic weight originated with , who in his 1808 work A New System of Chemical Philosophy proposed that atoms of different elements combine in simple whole-number ratios by weight, establishing a system of relative atomic weights with assigned a value of 1 as the lightest element. Dalton's table included approximate values for about 20 known elements, derived from analyses of compounds like and oxides, assuming atoms were indivisible and each element had atoms of uniform mass. Jöns Jacob Berzelius significantly refined these ideas during the 1810s and 1820s through meticulous gravimetric analyses of thousands of compounds, publishing his first comprehensive table in 1818. Initially using oxygen as the standard with a value of 100 for convenience in calculations, Berzelius later adopted in his 1826 table to align with emerging conventions, yielding relative masses like ≈ 1 and carbon ≈ 12.3, which improved accuracy over Dalton's estimates by incorporating laws of definite and multiple proportions. Early atomic weight tables by Dalton and Berzelius presupposed that elements consisted of a single type of atom with identical masses, resulting in or near- approximations such as and ≈ 14, based on stoichiometric ratios in compounds without knowledge of isotopes. This assumption facilitated the organization of chemical data but faced challenges from observations of non- values, exemplified by William Prout's hypothesis that all atomic weights were exact multiples of 's weight, implying elements were aggregates of hydrogen "protyle" atoms. Prout's idea, though ultimately disproven by precise measurements revealing fractional masses, stimulated further experimental scrutiny of atomic weights throughout the .

Evolution to the Carbon-12 Scale

In the early , atomic weights were primarily determined using chemical methods on the so-called chemical scale, where the average atomic mass of oxygen was set exactly to 16. This scale, rooted in precise gravimetric analyses, facilitated stoichiometric calculations but began to face challenges as physical techniques emerged. Between and the , the discovery of isotopes fundamentally altered this framework; Francis Aston's development of the mass spectrograph in 1919 allowed the identification and measurement of individual isotopes, revealing that natural oxygen consisted of multiple isotopes (¹⁶O, ¹⁷O, and ¹⁸O). Physicists thus advocated for a physical scale where the mass of the ¹⁶O isotope was defined exactly as 16, independent of natural isotopic variations. This shift highlighted discrepancies arising from the ¹⁶O/¹²C , as accurate conversions between scales required precise isotopic abundance data, which early measurements struggled to provide consistently. The divergence between the chemical and physical scales became more pronounced, with atomic weights on the physical scale being approximately 0.027% lower than on the chemical scale due to the slightly higher average mass of natural oxygen relative to pure ¹⁶O. By the mid-20th century, Aston's advancements from the 1920s onward had enabled detailed isotopic studies, but the dual scales caused confusion in cross-disciplinary work, particularly in and chemistry. In April 1957, during an informal discussion in , mass spectrometrist Alfred O. Nier proposed adopting the ¹²C = 12 scale to Josef Mattauch, arguing it would unify the fields with minimal adjustment—only a 42 ppm shift for chemists compared to 275 ppm if retaining an oxygen-based standard. This suggestion gained traction as it leveraged carbon's abundance, stability, and central role in both and , while resolving the oxygen isotopic variability issue. The proposal culminated in formal adoption through international collaboration. In 1960, the International Union of Pure and Applied Physics (IUPAP) endorsed the ¹²C = 12 standard at its Ottawa , followed by the International Union of Pure and Applied Chemistry (IUPAC) approval at its 1961 Montreal . This joint IUPAC/IUPAP recommendation, detailed in the 1961 report by Cameron and Wichers, established the unified scale where the relative atomic mass of ¹²C is exactly 12, eliminating the chemical-physical discrepancy and providing a single, isotope-specific reference for all elements. The transition ensured consistency in determinations, with the first table of standard atomic weights on this scale published shortly thereafter. In 1975, IUPAC confirmed the exact definition of ¹²C in its atomic weights report, solidifying the scale's role by incorporating updated isotopic data and emphasizing its precision for calculations.

Standard Atomic Weights

Calculation from Isotopic Composition

The standard atomic weight, denoted as Ar(\ceE)A_r(\ce{E}), of an element \ceE\ce{E} is determined by the of the relative isotopic masses of its isotopes, using their natural isotopic abundances as weights. This is expressed mathematically as Ar(\ceE)=∑iri⋅Ar,iA_r(\ce{E}) = \sum_i r_i \cdot A_{r,i} where rir_i represents the fractional abundance of ii (such that ∑iri=1\sum_i r_i = 1), and Ar,iA_{r,i} is the relative isotopic mass of that isotope, defined relative to the atomic mass unit based on 12\ceC=12^{12}\ce{C} = 12 u. A representative example is , which has two stable isotopes: 35\ceCl^{35}\ce{Cl} with relative isotopic mass 34.96885268 and abundance 0.7576, and 37\ceCl^{37}\ce{Cl} with relative isotopic mass 36.96590259 and abundance 0.2424. The calculation yields Ar(\ceCl)=(0.7576×34.96885268)+(0.2424×36.96590259)≈35.452A_r(\ce{Cl}) = (0.7576 \times 34.96885268) + (0.2424 \times 36.96590259) \approx 35.452 This value falls within the reported interval for chlorine's . The abundances rir_i used in this calculation are typically derived from terrestrial samples, reflecting the characteristic isotopic composition of normal Earth materials. However, non-terrestrial samples can exhibit slight deviations; for instance, oxygen in lunar rocks shows δ¹⁸O values ranging from 5.64‰ to 6.19‰ relative to terrestrial standards, potentially altering the calculated Ar(\ceO)A_r(\ce{O}) by small amounts outside the terrestrial interval due to minor shifts in heavy isotope enrichment. IUPAC conventions specify that for elements with variable isotopic compositions in nature, Ar(\ceE)A_r(\ce{E}) is reported as an interval [a, b] encompassing the range observed in terrestrial materials, with the conventional value as the midpoint and uncertainty as u(Ar(\ceE))=(b−a)/12u(A_r(\ce{E})) = (b - a)/\sqrt{12}
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