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Chemistry LibreTexts

4.7.1: Practice Atomic Mass

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  • Exercise \(\PageIndex{1}\)

    The element lithium is found in nature as a mixture of 6Li and 7Li.  Given that the average atomic mass of lithium is 6.94 amu, which isotope is more abundant?


    7Li is more abundant.  Since the average mass is really close to 7 amu, you have a lot more of the isotope with a mass of 7 amu than you do of the isotope with a mass of 6 amu.


    Exercise \(\PageIndex{1}\)

    The element strontium has the following natural abundances.  Calculate the average atomic mass.

    82.58 % is 88Sr with mass of 87.9056 amu

    9.86 % is 86Sr with mass of 85.9093 amu

    7.00 % is 87Sr with mass of 86.9089 amu

    0.56 % is 84Sr with mass of 83.9134 amu


    Add up (uncertain digits are underlined):

    72.59244 amu

      8.47066 amu

      6.08362 amu

      0.46992 amu

    Total is 87.61664 amu which rounds to 87.62 amu


    Exercise \(\PageIndex{1}\)

    If there were chemists on another planet, their periodic table might be different because the elements might have different "natural" abundances.  If on the other planet, the element titanium had the following natural abundances, calculate the average atomic mass that the chemists on that planet would use.

    73.64 % is 49Ti with mass of 48.9479 amu

    18.82 % is 50Ti with mass of 49.9448 amu

    7.54 % is 48Ti with mass of 47.9479 amu


    Add up (uncertain digits are underlined):

    36.04523 amu

      9.39961 amu

      3.61527 amu

    Total is 49.06011 amu which rounds to 49.06 amu

    Calculating the other way:

    I realized that this is not one our our goals for Chem 142.  We do this in Chem 101.  I left the problems here anyway in case you are curious.

    Exercise \(\PageIndex{1}\)

    The element antimony is made up of two isotopes, 121Sb with a mass of 120.9038 amu and 123Sb with a mass of 122.9042 amu.  Given that the average atomic mass is 121.760 amu, what are the percent abundances of the two isotopes?


    The average atomic mass is equal to the sum of the fractional abundance times mass of each isotope.

    average = (fractional abundance of 121Sb)(mass of 121Sb) + (fractional abundance of 123Sb)(mass of 123Sb)

    Set the fractional abundance of 121Sb = x.  Since there are only 2 isotopes, and they must add up to 1 whole, the fractional abundance of 123Sb = 1 – x


    121.760 amu = (x)(120.9038 amu) + (1 – x)(122.9042 amu)

    121.760 amu = (x)(120.9038 amu) + 122.9042 amu – (x)(122.9042 amu)             now subtract 122.9042 amu from both sides

    – 1.1442 amu = (x)(120.9038 amu) – (x)(122.9042 amu)                                     combine terms on right

    – 1.1442 amu = (x)(–2.0004 amu)                                                                     divide both by – 2.0004 amu

    0.571986 = x

    So fractional abundance of 121Sb is 0.5720, and percent abundance is 57.20 %.  

    Fractional abundance of 123Sb is therefore 0.4280, and percent abundance is 42.80 %


    Exercise \(\PageIndex{1}\)

    On our imaginary planet, the element zinc is made up of two isotopes, 66Zn with a mass of 65.9260 amu and 68Zn with a mass of 67.9248 amu.  Given that their average atomic mass for zinc is 66.840 amu, what are the percent abundances of the two isotopes on that planet?


    66.840 amu = (x)(65.9620 amu) + (1 – x)(67.9248 amu)

    66.840 amu = (x)(65.9620 amu) + 67.9248 amu – (x)(67.9248 amu)             now subtract 67.9248 amu from both sides

    – 1.0848 amu = (x)(65.9620 amu) – (x)(67.9248 amu)                                 combine terms on right

    – 1.0848 amu = (x)(–1.9628 amu)                                                              divide both by – 1.9628 amu

    0.5526798 = x

    So fractional abundance of 66Zn is 0.5527, and percent abundance is 55.27 %.  

    Fractional abundance of 68Zn is therefore 0.4473, and percent abundance is 44.73 %


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