Study Notes on Atomic Mass

3.1 Atomic Mass

  • Overview of Atomic Mass

    • Focuses on the study of mass relationships of atoms and molecules.
    • Understanding these relationships aids in the explanation of the composition of compounds and how composition changes.

  • Definition of Atomic Mass

    • The mass of an atom is determined by the number of electrons, protons, and neutrons it contains.
    • Important for laboratory work, since atoms are incredibly small particles.
    • Even a tiny speck of dust can contain up to $1 imes 10^{21}$ atoms, making individual atom measurement impractical.
    • We cannot weigh a single atom directly, but we can determine the mass of one atom relative to another.

  • Establishing Standard Atomic Mass

    • A value must be assigned to the mass of one atom of a specific element to serve as a standard.
    • By international agreement, atomic mass (also referred to as atomic weight) is expressed in atomic mass units (amu).
    • One amu is defined as a mass equal to one-twelfth the mass of one carbon-12 atom, which contains six protons and six neutrons.
    • Therefore, the atomic mass of carbon-12 is set at 12 amu.
    • This sets the standard for measuring atomic mass for other elements.
    • Example: Hydrogen atom's mass is 8.400% that of carbon-12. Thus:
    • If carbon-12 = 12 amu, then hydrogen atomic mass = $0.08400 imes 12 ext{ amu} = 1.008 ext{ amu}$.
    • The atomic mass of oxygen is 16.00 amu, and that of iron is 55.85 amu.
    • Consequently, an average iron atom is about 56 times as massive as a hydrogen atom.

  • Average Atomic Mass

    • Atomic masses listed in tables often differ from whole numbers; for example, carbon is listed as 12.01 amu instead of 12.00 amu.
    • This discrepancy arises because naturally occurring elements usually have multiple isotopes, requiring an average mass calculation based on the mixture of isotopes.
    • For carbon, the natural abundances are:
    • Carbon-12: 98.90%
    • Carbon-13: 1.10%
    • The atomic mass of carbon-13 is measured at 13.00335 amu.
    • Calculation for average atomic mass of natural carbon:
    • Average atomic mass = $(0.9890 imes 12 ext{ amu}) + (0.0110 imes 13.00335 ext{ amu})$
    • Result = $12.01 ext{ amu}$.
    • Note: Percentages should be converted to fractions for calculations. Thus, 98.90% becomes $0.9890$.
    • Since there are significantly more carbon-12 atoms than carbon-13, the average atomic mass is much closer to 12 amu than to 13 amu.
    • It is critical to understand that stating the atomic mass of carbon as 12.01 amu refers to the average value; if examined individually, carbon atoms would have masses of either 12.00 amu or 13.00335 amu, never 12.01 amu.

  • Terminology Note

    • One atomic mass unit is also referred to as one dalton.

  • Isotopic Distribution of Carbon

    • Isotopes of carbon:
    • Carbon-12 (C-12): 98.90% (Atomic mass = 12.00 amu)
    • Carbon-13 (C-13): 1.10% (Atomic mass = 13.00335 amu)