Relative atomic mass
Relative atomic mass or 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 is defined as being of the mass of a carbon-12 atom. Since both quantities in the ratio are masses, the resulting value is dimensionless; hence the value is said to be relative.
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 that are present in the sample. This quantity can vary substantially between samples because the sample's origin may have produced unique combinations of isotopic abundances. 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 is an application of the relative atomic mass values obtained from multiple 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. Standard atomic weight is nevertheless the most widely published variant of relative atomic mass.
Additionally, the continued use of the term "atomic weight" 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" 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. 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 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 than those reflected in standard atomic weights.
Current definition
The prevailing IUPAC definitions are:and
Here the "unified atomic mass unit" refers to of the mass of an atom of C in its ground state.
The IUPAC definition of relative atomic mass is:
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.
Historical usage
Older historical relative scales based on the atomic mass unit used either the oxygen-16 relative isotopic mass or else the oxygen relative atomic mass 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 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 values and simplified values.
Other measures of the mass of atoms
Atomic mass is the mass of a single atom, with unit Da or u. 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.The relative isotopic mass is specifically the ratio of the mass of a single atom to the mass of a unified atomic mass unit. This value, too, is relative, and therefore dimensionless.
Determination of relative atomic mass
Modern relative atomic masses are calculated from measured values of atomic mass 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 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.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: Si, Si and Si. The atomic masses of these nuclides are known to a precision of one part in 14 billion for Si 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%.
The calculation is as follows:
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. The relative standard uncertainty in this value is 1 or 10 ppm.
Apart from this uncertainty by measurement, some elements have variation over sources. That is, different sources 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.