Mass

Unified atomic mass unit

• The unified atomic mass unit ($\mathrm{u}$) (or dalton ($\mathrm{Da}$))
  • non-SI unit of mass
  • defined as $\frac{1}{12}$ of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest.
• The atomic mass constant is a constant defined as $m_{\mathrm{u}}=\frac{1}{12}m{(}^{12}\text{C})=1\text{u}=1.66053906892(52)\times 10^{-27}\text{kg}$

Atomic mass

the meaning of the term relative in this context is that the atomic mass is a dimensionless quantity, as it is the ratio of the mass of an atom to the unified atomic mass unit.

of an isotope of an element

• atomic mass ($m_{\mathrm{a}}$ or $m$)
  • “Rest mass of an atom in its ground state. The commonly used unit is the unified atomic mass unit.” (IUPAC)
  • units:
    • $\mathrm{kg}$ (the SI unit)
    • $\mathrm{g}$
    • $\mathrm{u}$
  • examples:
    • $m({}_{}^{}{}_{}^{12}\mathrm{C})=12\mathsf{u}$ (the atomic mass of an carbon-12 atom is $12\mathsf{u}$)
    • $m({}_{}^{}{}_{}^{13}\mathrm{C})=13.0033548378\mathsf{u}$ (the atomic mass of an carbon-13 atom is $13.0033548378\mathsf{u}$)
• The relative isotopic mass (of a particular isotope of an element)
  • dimensionless
  • $\frac{m}{1\mathrm{u}}$, where $m$ is the atomic mass of the isotope (in $\mathrm{u}$)
  • (example: the relative isotopic mass of ${}_{}^{}{}_{}^{13}\mathrm{C}$ is $\frac{13.0033548378\mathrm{u}}{1\mathrm{u}}=13.0033548378$)

of an element

• The average atomic mass (or just atomic mass) of an element
  • $m(E)={\sum }_i\left(m_i\cdot f_i\right)$
    • $m(E)$ is the average atomic mass of the element $E$ (in $\mathrm{u}$)
    • $m_i$ is the atomic mass of the $i$-th isotope of the element (in $\mathrm{u}$)
    • $f_i$ is the natural abundance of the $i$-th isotope of the element (in $\%$)
  • example:
    • The natural abundance of ${}_{}^{}{}_{}^{12}\mathrm{C}$ and ${}_{}^{}{}_{}^{13}\mathrm{C}$ are $98.93\%$ and $1.07\%$ respectively.
    • The average atomic mass of carbon is $m(\mathrm{C})=\left(m({}_{}^{}{}_{}^{12}\mathrm{C})\times \text{NA}({}_{}^{}{}_{}^{12}\mathrm{C})\right)+\left(m({}_{}^{}{}_{}^{13}\mathrm{C})\times \text{NA}({}_{}^{}{}_{}^{13}\mathrm{C})\right)=12.011\mathsf{u}$.
• relative atomic mass (or atomic weight (deprecated)) (of an element)
  • dimensionless
  • $A_r(E)$
  • ”The ratio of the average mass of the atom to the unified atomic mass unit.” (IUPAC)
  • “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.” (Atomic Weights of the Elements 1979)
• standard atomic weight ($A_r^{\circ }(E)$)
  • “the weighted arithmetic mean of the relative isotopic masses of all isotopes of that element weighted by each isotope’s abundance on Earth” (Wikipedia)
  • Fourteen chemical elements are defined as an interval (e.g. $A_r^{\circ }(\mathrm{H})=[1.00784,1.00811]$)
  • abridged atomic weight (the standard atomic weight with numbers reduced to five significant figures)
  • IUPAC Periodic Table of the Isotopes
  • https://ciaaw.org/abridged-atomic-weights.htm
  • https://en.wikipedia.org/wiki/Template:Standard_atomic_weight_of_the_elements

of a compound

• molecular mass (for molecular compound, or formula mass for ionic compound)

from Wikipedia:

“The molecular mass (for molecular compounds) and formula mass (for non-molecular compounds, such as ionic salts) are commonly used as synonyms of molar mass, as the numerical values are identical (for all practical purposes), differing only in units (dalton vs. g/mol or kg/kmol). However, the most authoritative sources define it differently. The difference is that molecular mass is the mass of one specific particle or molecule (a microscopic quantity), while the molar mass is an average over many particles or molecules (a macroscopic quantity).”