Atomic mass

The atomic mass (m_a) is the mass of an atom at rest, most often expressed in unified atomic mass units. The atomic mass is sometimes incorrectly used as a synonym of relative atomic mass, average atomic mass and atomic weight; however, these differ subtly from the atomic mass. The atomic mass is defined as the mass of an atom, which can only be one isotope at a time and is not an abundance-weighted average. The actual numerical difference is usually very small such that it does not effect most bulk calculations but such an error can be critical when considering individual atoms.

The relative atomic mass (A_r) (also known as atomic weight and average atomic mass) is the average of the atomic masses of all the chemical element's isotopes as found in a particular environment, weighted by isotopic abundance. This is frequently used as a synonym for the standard atomic weight and is not incorrect to do so since the standard atomic weights are relative atomic masses, although it is less specific to do so. Relative atomic mass also refers to non-terrestrial environments and highly specific terrestrial environments that deviate from the average or have different certainties (number of significant figures) than the standard atomic weights.

The standard atomic weight refers to the mean relative atomic mass of an element in the local environment of the Earth's crust and atmosphere as determined by the IUPAC Commission on Atomic Weights and Isotopic Abundances. These are what are included in a standard Periodic table and is what is used in most bulk calculations. An uncertainty in brackets is included which often reflects natural variability in isotopic distribution rather than uncertainty in measurement. For artificial elements the isotope formed depends on the means of synthesis, so the concept of natural isotope abundance has no meaning. Therefore for artificial elements the total nucleon count of the most stable isotope (ie, the isotope with the longest half-life) is listed in brackets in place of the standard atomic weight. Lithium represents a unique case where the natural abundances of the isotopes have been perturbed by human activities to the point of affecting the uncertainty in its standard atomic weight, even in samples obtained from natural sources such as rivers.

The relative isotopic mass is the relative mass of the isotope, scaled with carbon-12 as exactly 12. No other isotopes have whole number masses due to the different mass of neutrons and protons, as well as loss/gain of mass to binding energy. However, since mass defect due to binding energy is minimal compared to the mass of a nucleon, rounding the atomic mass of an isotope tells you the total nucleon count. Neutron count can then be derived by subtracting the atomic number.

Mass Defects in atomic masses

The pattern in the amounts the atomic masses deviate from their mass numbers is as follows: the deviation starts positive at hydrogen-1, becomes negative until a minimum is reached at iron-56, iron-58 and nickel-62, then increases to positive values in the heavy isotopes, with increasing atomic number. This corresponds to the following: nuclear fission in an element heavier than iron produces energy, and fission in any element lighter than iron requires energy. The opposite is true of nuclear fusion reactions: fusion in elements lighter than iron produces energy, and fusion in elements heavier than iron requires energy.

Measurement of atomic masses

Direct comparison and measurement of the masses of atoms is achieved with mass spectrometry.

Conversion factor between atomic mass units and grams

The standard scientific unit for dealing with atoms in macroscopic quantities is the mole (mol), which is defined arbitrarily as the amount of a substance with as many atoms or other units as there are in 12 grams of the carbon isotope C-12. The number of atoms in a mole is called Avogadro's number, the value of which is approximately 6.02 × 10²³. One mole of a substance always contains almost exactly the relative atomic or molar mass of that substance (which is the concept of molar mass), expressed in grams. For example, the relative atomic mass of iron is 55.847, and therefore one mole of iron has a mass of 55.847 grams. The formulaic conversion between atomic mass and SI mass in grams for a single atom is

$m_{\rm {grams}}={m_{\rm {u}} \over N_{A}}$

where ${\rm {u}}$ is the atomic mass unit and $N_{A}$ is Avogadro's number.

The relationship between atomic and molecular masses

Similar definitions apply to molecules. One can compute the molecular mass of a compound by adding the atomic masses of its constituent atoms (nuclides). One can compute the molar mass of a compound by adding the relative atomic masses of the elements given in the chemical formula. In both cases the multiplicity of the atoms (the number of times it occurs) must be taken into account, usually by multiplication of each unique mass by its multiplicity.

History

Before the 1960s, this was expressed so that the oxygen-16 isotope received the atomic weight 16, however, the proportions of oxygen-17 and oxygen-18 present in natural oxygen, which were also used to calculate atomic mass led to two different tables of atomic mass.

Formerly chemists and physicists used two different atomic mass scales. The chemists used a scale such that the natural mixture of oxygen isotopes had an atomic mass 16, while the physicists assigned the same number 16 to the atomic mass of the most common oxygen isotope (containing eight protons and eight neutrons). The unified scale based on carbon-12, ¹²C, met the physicists' need to base the scale on a pure isotope, while being numerically close to the old chemists' scale.

The term atomic weight is being phased out slowly and being replaced by relative atomic mass, in most current usage. The history of this shift in nomenclature reaches back to the 1960's and has been the source of much debate in the scientific community. The debate was largely created by the adoption of the unified atomic mass unit and the realization that weight was in some ways an inappropriate term. The argument for keeping the term "atomic weight" was primarily that it was a well understood term to those in the field, that the term "atomic mass" was already in use (as it is currently defined) and that the term "relative atomic mass" was in some ways redundant. In 1979, in a compromise move, the definition was refined and the term "relative atomic mass" was introduced as a secondary synonym. Twenty years later the primacy of these synonyms was reversed and the term "relative atomic mass" is now the preferred term; however the "standard atomic weights" have maintained the same name.

Table of standard atomic weights

For more accurate standard atomic weights, including uncertainties, see Periodic table (detailed).

Not to be confused with atomic mass.

See also: standard atomic weight

Relative atomic mass (symbol: A_r; 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: m_u) is defined as being ⁠1/12⁠ of the mass of a carbon-12 atom. Since both quantities in the ratio are masses, the resulting value is dimensionless. These definitions remain valid even after the 2019 redefinition of the SI base units.

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 (A_r,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. "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. 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. 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

and

relative atomic mass (atomic weight) — The ratio of the average mass of the atom to the unified atomic mass unit.

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

The IUPAC definition 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. 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).

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

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

Atomic mass (m_a) 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 (m_u = 1 Da). This ratio is dimensionless.

Determination of relative atomic mass

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 for virtually all non-radioactive nuclides, but isotopic compositions are both harder to measure to high precision and more subject to variation between samples. 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	Abundance
		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:

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

The estimation of the uncertainty is complicated, especially as the sample distribution is not necessarily symmetrical: the IUPAC standard relative atomic masses are quoted with estimated symmetrical uncertainties, and the value for silicon is 28.0855(3). The relative standard uncertainty in this value is 1×10^–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.

See also

• International Union of Pure and Applied Chemistry (IUPAC)
• Commission on Isotopic Abundances and Atomic Weights (CIAAW)

Further reading

• Possolo, Antonio; van der Veen, Adriaan M.H.; Meija, Juris; Brynn Hibbert, D. (2018-01-04). "Interpreting and propagating the uncertainty of the standard atomic weights (IUPAC Technical Report)". Pure and Applied Chemistry. 90 (2): 395–424. doi:10.1515/pac-2016-0402. S2CID 145931362. Retrieved 2019-02-08.

External links

• IUPAC Commission on Isotopic Abundances and Atomic Weights
• NIST relative atomic masses of all isotopes and the standard atomic weights of the elements
• Standard Atomic Weights

See also

• Atomic mass unit
• Isotope
• Molecular mass
• Jean Stas

External links

• NIST relative atomic masses of all isotopes and the standard atomic weights of the elements

• IUPAC goldbook definition of atomic mass

• IUPAC goldbook definition of relative atomic mass & atomic weight

• Tutorial on the concept and measurement of atomic mass

• Atomic Weights and the International Committee — A Historical Review