{"id":669,"date":"2018-03-20T15:19:09","date_gmt":"2018-03-20T15:19:09","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-orgbiochemistry\/?post_type=chapter&p=669"},"modified":"2018-08-13T01:48:55","modified_gmt":"2018-08-13T01:48:55","slug":"6-2-atomic-and-molar-masses","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-monroecc-orgbiochemistry\/chapter\/6-2-atomic-and-molar-masses\/","title":{"raw":"6.2 Atomic and Molar Masses","rendered":"6.2 Atomic and Molar Masses"},"content":{"raw":"
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Learning Objective<\/h3>\r\n
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  1. Learn how the masses of moles of atoms and molecules are expressed.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
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    Now that we have introduced the mole and practiced using it as a conversion factor, we ask the obvious question: why is the mole that particular<\/em> number of things? Why is it 6.022 \u00d7 1023<\/sup> and not 1 \u00d7 1023<\/sup> or even 1 \u00d7 1020<\/sup>?<\/p>\r\n

    The number in a mole, Avogadro\u2019s number, is related to the relative sizes of the atomic mass unit and gram mass units. Whereas one hydrogen atom has a mass of approximately 1 u, 1 mol of H atoms has a mass of approximately 1 gram<\/em>. And whereas one sodium atom has an approximate mass of 23 u, 1 mol of Na atoms has an approximate mass of 23 grams<\/em>.<\/p>\r\n

    One mole of a substance has the same mass in grams that one atom or molecule has in atomic mass units.<\/em><\/strong> The numbers in the periodic table that we identified as the atomic masses of the atoms not only tell us the mass of one atom in u but also tell us the mass of 1 mol of atoms in grams.<\/p>\r\n\r\n

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    Note<\/h3>\r\n

    One mole of a substance has the same mass in grams that one atom or molecule has in atomic mass units.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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    Example 3<\/h3>\r\n

    What is the mass of each quantity?<\/p>\r\n\r\n

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    1. 1 mol of Al atoms<\/li>\r\n \t
    2. 2 mol of U atoms<\/li>\r\n<\/ol>\r\n

      Solution<\/p>\r\n[reveal-answer q=\"380140\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"380140\"]\r\n\r\n1. One mole of Al atoms has a mass in grams that is numerically equivalent to the atomic mass of aluminum. The periodic table shows that the atomic mass (rounded to two decimal points) of Al is 26.98, so 1 mol of Al atoms has a mass of 26.98 g.\r\n\r\nAccording to the periodic table, 1 mol of U has a mass of 238.03 g, so the mass of 2 mol is twice that, or 476.06 g.[\/hidden-answer]\r\n\r\n<\/div>\r\n

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      Skill-Building Exercise<\/h3>\r\n

      What is the mass of each quantity?<\/p>\r\n\r\n

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        1 mol of Au atoms<\/p>\r\n\r\n<\/div><\/li>\r\n \t

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        5 mol of Br atoms<\/p>\r\n\r\n<\/div><\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n\r\n<\/div>\r\n

        The mole concept can be extended to masses of formula units and molecules as well. The mass of 1 mol of molecules (or formula units) in grams is numerically equivalent to the mass of one molecule (or formula unit) in atomic mass units. For example, a single molecule of O2<\/sub> has a mass of 32.00 u, and 1 mol of O2<\/sub> molecules has a mass of 32.00 g. As with atomic mass unit\u2013based masses, to obtain the mass of 1 mol of a substance, we simply sum the masses of the individual atoms in the formula of that substance. The mass of 1 mol of a substance is referred to as its molar mass<\/strong>, t<\/span>he mass of 1 mol of atoms, molecules, or formula units, depending on\u00a0<\/span><\/span> whether the substance is an element, a covalent compound, or an ionic compound.<\/p>\r\n\r\n

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        Example 4<\/h3>\r\n

        What is the mass of 1 mol of each substance?<\/p>\r\n\r\n

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        1. NaCl<\/li>\r\n \t
        2. bilirubin (C33<\/sub>H36<\/sub>N4<\/sub>O6<\/sub>), the principal pigment present in bile (a liver secretion)<\/li>\r\n<\/ol>\r\n

          Solution<\/p>\r\n[reveal-answer q=\"819891\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"819891\"]\r\n

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            Summing the molar masses of the atoms in the NaCl formula unit gives<\/p>\r\n\r\n

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            1 Na molar mass:<\/td>\r\n23.00 g<\/td>\r\n<\/tr>\r\n
            1 Cl molar mass:<\/td>\r\n35.45 g<\/span><\/td>\r\n<\/tr>\r\n
            Total:<\/td>\r\n58.45 g<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n

            The mass of 1 mol of NaCl is 58.45 g.<\/p>\r\n<\/li>\r\n \t

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            Multiplying the molar mass of each atom by the number of atoms of that type in bilirubin\u2019s formula and adding the results, we get<\/p>\r\n\r\n

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            33 C molar mass:<\/td>\r\n33 \u00d7 12.01 g<\/td>\r\n396.33 g<\/td>\r\n<\/tr>\r\n
            36 H molar mass:<\/td>\r\n36 \u00d7 1.01 =<\/td>\r\n36.36 g<\/td>\r\n<\/tr>\r\n
            4 N molar mass:<\/td>\r\n4 \u00d7 14.00 =<\/td>\r\n56.00 g<\/td>\r\n<\/tr>\r\n
            6 O molar mass:<\/td>\r\n6 \u00d7 16.00 =<\/td>\r\n96.00 g<\/span><\/td>\r\n<\/tr>\r\n
            Total:<\/td>\r\n<\/td>\r\n584.69 g<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n

            The mass of 1 mol of bilirubin is 584.69 g [\/hidden-answer]<\/p>\r\n<\/li>\r\n<\/ol>\r\n<\/div>\r\n

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            Skill-Building Exercise<\/h3>\r\n

            What is the mass of 1 mol of each substance?<\/p>\r\n\r\n

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              barium sulfate (BaSO4<\/sub>), used to take X rays of the gastrointestional tract<\/p>\r\n\r\n<\/div><\/li>\r\n \t

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              adenosine (C10<\/sub>H13<\/sub>N5<\/sub>O4<\/sub>), a component of cell nuclei crucial for cell division<\/p>\r\n\r\n<\/div><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

              Be careful when counting atoms. In formulas with polyatomic ions in parentheses, the subscript outside the parentheses is applied to every atom inside the parentheses. For example, the molar mass of Ba(OH)2<\/sub> requires the sum of 1 mass of Ba, 2 masses of O, and 2 masses of H:<\/p>\r\n\r\n

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              1 Ba molar mass:<\/td>\r\n1 \u00d7 137.33 g =<\/td>\r\n137.33 g<\/td>\r\n<\/tr>\r\n
              2 O molar mass:<\/td>\r\n2 \u00d7 16.00 g =<\/td>\r\n32.00 g<\/td>\r\n<\/tr>\r\n
              2 H molar mass:<\/td>\r\n2 \u00d7 1.01 g =<\/td>\r\n2.02 g<\/span><\/td>\r\n<\/tr>\r\n
              Total:<\/td>\r\n<\/td>\r\n171.35 g<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n

              Because molar mass is defined as the mass for 1 mol of a substance, we can refer to molar mass as grams per mole (g\/mol). The division sign (\/) implies \u201cper,\u201d and \u201c1\u201d is implied in the denominator. Thus, the molar mass of bilirubin can be expressed as 584.05 g\/mol.<\/p>\r\n\r\n

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              Concept Review Exercises<\/h3>\r\n
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                How are molar masses of the elements determined?<\/p>\r\n\r\n<\/div><\/li>\r\n \t

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                How are molar masses of compounds determined?<\/p>\r\n\r\n<\/div><\/li>\r\n<\/ol>\r\n<\/div>\r\n

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                Answers<\/h3>\r\n[reveal-answer q=\"304125\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"304125\"]\r\n
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                1. Molar masses of the elements are the same numeric value as the masses of a single atom in atomic mass units but in units of grams instead.<\/li>\r\n \t
                2. Molar masses of compounds are calculated by adding the molar masses of their atoms.[\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
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                  Key Takeaway<\/h3>\r\n