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3.4: Masses of Atoms and Molecules

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    Learning Objective
    • Express the masses of atoms and molecules.

    Because matter is defined as anything that has mass and takes up space, it should not be surprising to learn that atoms and molecules have mass.

    Individual atoms and molecules, however, are very small, and the masses of individual atoms and molecules are also very small. For macroscopic objects, we use units such as grams and kilograms to state their masses, but these units are much too big to comfortably describe the masses of individual atoms and molecules. Another scale is needed.

    Atomic Mass Unit

    The atomic mass unit (u; some texts use amu, but this older style is no longer accepted) is defined as one-twelfth of the mass of a carbon-12 atom, an isotope of carbon that has six protons and six neutrons in its nucleus. By this scale, the mass of a proton is 1.00728 u, the mass of a neutron is 1.00866 u, and the mass of an electron is 0.000549 u. There will not be much error if you estimate the mass of an atom by simply counting the total number of protons and neutrons in the nucleus (i.e., identify its mass number) and ignore the electrons. Thus, the mass of carbon-12 is about 12 u, the mass of oxygen-16 is about 16 u, and the mass of uranium-238 is about 238 u. More exact masses are found in scientific references—for example, the exact mass of uranium-238 is 238.050788 u, so you can see that we are not far off by using the whole-number value as the mass of the atom.

    What is the mass of an element? This is somewhat more complicated because most elements exist as a mixture of isotopes, each of which has its own mass. Thus, although it is easy to speak of the mass of an atom, when talking about the mass of an element, we must take the isotopic mixture into account.

    Atomic Mass

    The atomic mass of an element is a weighted average of the masses of the isotopes that compose an element. What do we mean by a weighted average? Well, consider an element that consists of two isotopes, 50% with mass 10 u and 50% with mass 11 u. A weighted average is found by multiplying each mass by its fractional occurrence (in decimal form) and then adding all the products. The sum is the weighted average and serves as the formal atomic mass of the element. In this example, we have the following:

    0.50 × 10 u = 5.0 u
    0.50 × 11 u = 5.5 u
    Sum = 10.5 u = the atomic mass of our element

    Note that no atom in our hypothetical element has a mass of 10.5 u; rather, that is the average mass of the atoms, weighted by their percent occurrence.

    This example is similar to a real element. Boron exists as about 20% boron-10 (five protons and five neutrons in the nuclei) and about 80% boron-11 (five protons and six neutrons in the nuclei). The atomic mass of boron is calculated similarly to what we did for our hypothetical example, but the percentages are different:

    0.20 × 10 u = 2.0 u
    0.80 × 11 u = 8.8 u
    Sum = 10.8 u = the atomic mass of boron

    Thus, we use 10.8 u for the atomic mass of boron.

    Virtually all elements exist as mixtures of isotopes, so atomic masses may vary significantly from whole numbers. Table \(\PageIndex{1}\) lists the atomic masses of some elements. The atomic masses in Table \(\PageIndex{1}\) are listed to three decimal places where possible, but in most cases, only one or two decimal places are needed. Note that many of the atomic masses, especially the larger ones, are not very close to whole numbers. This is, in part, the effect of an increasing number of isotopes as the atoms increase in size. (The record number is 10 isotopes for tin.)

    Table \(\PageIndex{1}\): Selected Atomic Masses of Some Elements
    Element Name Atomic Mass (u) Element Name Atomic Mass (u)
    Aluminum 26.981 Molybdenum 95.94
    Argon 39.948 Neon 20.180
    Arsenic 74.922 Nickel 58.693
    Barium 137.327 Nitrogen 14.007
    Beryllium 9.012 Oxygen 15.999
    Bismuth 208.980 Palladium 106.42
    Boron 10.811 Phosphorus 30.974
    Bromine 79.904 Platinum 195.084
    Calcium 40.078 Potassium 39.098
    Carbon 12.011 Radium n/a
    Chlorine 35.453 Radon n/a
    Cobalt 58.933 Rubidium 85.468
    Copper 63.546 Scandium 44.956
    Fluorine 18.998 Selenium 78.96
    Gallium 69.723 Silicon 28.086
    Germanium 72.64 Silver 107.868
    Gold 196.967 Sodium 22.990
    Helium 4.003 Strontium 87.62
    Hydrogen 1.008 Sulfur 32.065
    Iodine 126.904 Tantalum 180.948
    Iridium 192.217 Tin 118.710
    Iron 55.845 Titanium 47.867
    Krypton 83.798 Tungsten 183.84
    Lead 207.2 Uranium 238.029
    Lithium 6.941 Xenon 131.293
    Magnesium 24.305 Zinc 65.409
    Manganese 54.938 Zirconium 91.224
    Mercury 200.59 Molybdenum 95.94
    Note: Atomic mass is given to three decimal places, if known.

    Molecular Mass

    Now that we understand that atoms have mass, it is easy to extend the concept to the mass of molecules. The molecular mass is the sum of the masses of the atoms in a molecule. This may seem like a trivial extension of the concept, but it is important to count the number of each type of atom in the molecular formula. Also, although each atom in a molecule is a particular isotope, we use the weighted average, or atomic mass, for each atom in the molecule.

    For example, if we were to determine the molecular mass of dinitrogen trioxide, N2O3, we would need to add the atomic mass of nitrogen two times with the atomic mass of oxygen three times:

    2 N masses = 2 × 14.007 u = 28.014 u
    3 O masses = 3 × 15.999 u = 47.997 u
    Total = 76.011 u = the molecular mass of N2O3

    We would not be far off if we limited our numbers to one or even two decimal places.

    Example \(\PageIndex{1}\)

    What is the molecular mass of each substance?

    1. \(\ce{NBr3}\)
    2. \(\ce{C2H6}\)

    Add one atomic mass of nitrogen and three atomic masses of bromine:

    Solutions to Example 3.4.1
    1 N mass = 14.007 u
    3 Br masses = 3 × 79.904 u = 239.712 u
    Total = 253.719 u = the molecular mass of NBr3

    Add two atomic masses of carbon and six atomic masses of hydrogen:

    Solutions to Example 3.4.1
    2 C masses = 2 × 12.011 u = 24.022 u
    6 H masses = 6 × 1.008 u = 6.048 u
    Total = 30.070 u = the molecular mass of C2H6

    The compound \(\ce{C2H6}\) also has a common name—ethane.

    Exercise \(\PageIndex{1}\)

    What is the molecular mass of each substance?

    1. \(\ce{SO2}\)
    2. \(\ce(PF3}\)
    Answer a

    64.063 u

    Answer b

    87.968 u

    Chemistry is Everywhere: Sulfur Hexafluoride

    On March 20, 1995, the Japanese terrorist group Aum Shinrikyo (Sanskrit for "Supreme Truth") released some sarin gas in the Tokyo subway system; twelve people were killed, and thousands were injured (Figure \(\PageIndex{2a}\)). Sarin (molecular formula \(\ce{C4H10FPO2}\)) is a nerve toxin that was first synthesized in 1938. It is regarded as one of the most deadly toxins known, estimated to be about 500 times more potent than cyanide. Scientists and engineers who study the spread of chemical weapons such as sarin (yes, there are such scientists) would like to have a similar less dangerous chemical to study, indeed one that is nontoxic, so they are not at risk themselves.

    Sulfur hexafluoride is used as a model compound for sarin. \(\ce{SF6}\) (a molecular model of which is shown Figure \(\PageIndex{2b}\)) has a similar molecular mass (about 146 u) as sarin (about 140 u), so it has similar physical properties in the vapor phase. Sulfur hexafluoride is also very easy to accurately detect, even at low levels, and it is not a normal part of the atmosphere, so there is little potential for contamination from natural sources. Consequently, \(\ce{SF6}\) is also used as an aerial tracer for ventilation systems in buildings. It is nontoxic and very chemically inert, so workers do not have to take special precautions other than watching for asphyxiation.

    Figure \(\PageIndex{2}\): Sarin and Sulfur Hexafluoride © Thinkstock. (a) Properly protected workers clear out the Tokyo subway after the nerve toxin sarin was released. (b) A molecular model of \(\ce{SF6}\). (c) A high-voltage electrical switchgear assembly that would be filled with \(\ce{SF6}\) as a spark suppressant.

    Sulfur hexafluoride also has another interesting use: a spark suppressant in high-voltage electrical equipment. High-pressure \(\ce{SF6}\) gas is used in place of older oils that may have contaminants that are not environmentally friendly (Figure \(\PageIndex{2c}\)).

    Key Takeaways

    • The atomic mass unit (u) is a unit that describes the masses of individual atoms and molecules.
    • The atomic mass is the weighted average of the masses of all isotopes of an element.
    • The molecular mass is the sum of the masses of the atoms in a molecule.

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