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6.4: Molar Mass

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    289385
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    ⚙️ Learning Objectives

    • Calculate the molar mass of an element or compound.
    • Determine the number of atoms, formula units, or molecules in one mole of a substance.


    Molar Mass of an Element

    According to the periodic table, the atomic mass of aluminum is 26.98 amu, copper is 63.55 amu, and carbon is 12.01 amu. Since 1 amu is only 1.674 × 10−24 g, these masses would be way too small to measure on ordinary laboratory equipment. However, if we have 6.022 × 1023 atoms, or 1 mole of each of these elements, we would have 26.98 g Al, 63.55 g Cu, and 12.01 g C. In other words, one mole of any element will have a mass that is numerically equal to its atomic mass and expressed in units of grams. This mass is called the molar mass.
     

    fig-ch01_patchfile_01.jpg
    Figure \(\PageIndex{1}\): One mole of aluminum, copper, and carbon. (R. Press/N. Hanacek/NIST)


    We might find these easier to use if the relationships are written out like this (recall that mole is abbreviated as mol):

    • 1 mol Al = 26.98 g Al = 6.022 × 1023 atoms Al
    • 1 mol Cu = 63.55 g Cu = 6.022 × 1023 atoms Cu
    • 1 mol C = 12.01 g C = 6.022 × 1023 atoms C
          

    Molar Mass of a Compound

    One mole of any compound will have a mass that is numerically equal to its molecular mass or formula mass and expressed in units of grams. This mass is also called the molar mass.

    In Section 6.2, the formula mass for NaCl was calculated to be 58.44 amu. This means that the molar mass of NaCl is 58.44 g and it will contain 6.022 × 1023 formula units of NaCl, or one mole of NaCl. We also calculated the molecular mass for C12H22O11 to be 342.3 amu. This means that the molar mass of C12H22O11 is 342.3 g and it will contain 6.022 × 1023 molecules of C12H22O11, or one mole of C12H22O11

    We might find these easier to use if the relationships are written out like this (recall that mole is abbreviated as mol):

    • 1 mol NaCl = 58.44 g NaCl = 6.022 × 1023 formula units NaCl
    • 1 mol C12H22O11 = 342.3 g C12H22O11 = 6.022 × 1023 molecules C12H22O11
           
    fig-ch01_patchfile_01.jpg
    Figure \(\PageIndex{2}\): One mole table salt (NaCl) and sugar (C12H22O11). (Lance S. Lund)


    Summary of Relevant Terminology

    Keeping the terminology straight (see Table \(\PageIndex{1}\)) is essential to understanding the mole concept and correctly performing mole calculations.
         

    Table \(\PageIndex{1}\): Relevant Terminology
    Substance Fundamental Unit Atomic, Molecular, or Formula Mass Molar Mass
    aluminum (Al) atom atomic mass = 26.98 amu molar mass = 26.98 g
    sucrose (C12H22O11) molecule molecular mass = 342.3 amu molar mass = 342.3 g
    sodium chloride (NaCl) formula unit formula mass = 58.44 amu molar mass = 58.44 g

         

    ✅ Example \(\PageIndex{1}\)

    Find the molar mass of each element. Then determine how many atoms are contained in the calculated molar mass. (Periodic Table)

    1. K
    2. Pb

    Solution

    1. Since the atomic mass of K is 39.10 amu, it has a molar mass of 39.10 g. There are 6.022 × 1023 atoms K, which is also 1 mole of K, in 39.10 g K.
    2. Since the atomic mass of Pb is 207.2 amu, it has a molar mass of 207.2 g. There are 6.022 × 1023 atoms Pb, which is also 1 mole of Pb, in 207.2 g Pb.

     

    ✅ Example \(\PageIndex{2}\)

    Calculate the molar mass for each compound. Then determine how many formula units or molecules are contained in the calculated molar mass. (Periodic Table)

    1. H2O
    2. Ca(NO3)2

    Solution

      H2O Ca(NO3)2
    1. Determine how many atoms of each element are present in the compound. Multiply the number of atoms of each element by its atomic mass and express in units of grams.
    2 H = 2(1.008) =   2.016 g H
    1 O = 1(16.00) = 16.00   g O
    1 Ca = 1(40.08) = 40.08 g Ca
    2 N = 2(14.01) = 28.02 g N
    6 O = 6(16.00) = 96.00 g O
    1. Sum the masses to find the molar mass.
    molar mass = 18.02 g molar mass = 164.10 g
    1. Determine whether the compound is ionic or molecular.
    H2O is a molecular compound. Ca(NO3)2 is an ionic compound.
    1. Formula units or molecules contained in the molar mass.
    6.022 × 1023 molecules H2O, which is also 1 mol H2O, are in 18.02 g H2O. 6.022 × 1023 formula units Ca(NO3)2, which is also 1 mol Ca(NO3)2, are in 164.10 g Ca(NO3)2.

     

    ✏️ Exercise \(\PageIndex{1}\)

    Calculate the molar mass for each substance. Then show the number of grams in 1 mol of the substance, as well as the number of atoms, molecules, or formula units that are contained 1 mol of the substance. (Periodic Table)

    1. Na
    2. Na2S
    3. N2O
    Answer A
    molar mass = 22.99 g; Therefore, 1 mol Na = 22.99 g Na = 6.022 × 1023 atoms Na.
    Answer B
    molar mass = 78.05 g; Therefore, 1 mol Na2S = 78.05 g Na2S = 6.022 × 1023 formula units Na2S.
    Answer C
    molar mass = 44.02 g; Therefore, 1 mol N2O = 44.02 g N2O = 6.022 × 1023 molecules N2O.


    Summary

    • A mole is defined as exactly 6.02214076 × 1023 particles, e.g., atoms, molecules, ions or electrons.
    • There are 6.02214076 × 1023 particles in 1 mole. This number is called Avogadro's number.
    • The molar mass of an element can be found by referring to the atomic mass on a periodic table with units of grams.  
    • The molar mass of compounds can be determined by the molar masses of the atoms in their formulas.

     

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