6.2 Atomic and Molar Masses

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 number of things? Why is it 6.022 × 1023 and not 1 × 1023 or even 1 × 1020?

The number in a mole, Avogadro’s 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. And whereas one sodium atom has an approximate mass of 23 u, 1 mol of Na atoms has an approximate mass of 23 grams.

One mole of a substance has the same mass in grams that one atom or molecule has in atomic mass units. 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.

Note

One mole of a substance has the same mass in grams that one atom or molecule has in atomic mass units.

Example 3

What is the mass of each quantity?

  1. 1 mol of Al atoms
  2. 2 mol of U atoms

Solution

Skill-Building Exercise

What is the mass of each quantity?

  1. 1 mol of Au atoms

  2. 5 mol of Br atoms

 

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 has a mass of 32.00 u, and 1 mol of O2 molecules has a mass of 32.00 g. As with atomic mass unit–based 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, the mass of 1 mol of atoms, molecules, or formula units, depending on  whether the substance is an element, a covalent compound, or an ionic compound.

Example 4

What is the mass of 1 mol of each substance?

  1. NaCl
  2. bilirubin (C33H36N4O6), the principal pigment present in bile (a liver secretion)

Solution

Skill-Building Exercise

What is the mass of 1 mol of each substance?

  1. barium sulfate (BaSO4), used to take X rays of the gastrointestional tract

  2. adenosine (C10H13N5O4), a component of cell nuclei crucial for cell division

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 requires the sum of 1 mass of Ba, 2 masses of O, and 2 masses of H:

1 Ba molar mass: 1 × 137.33 g = 137.33 g
2 O molar mass: 2 × 16.00 g = 32.00 g
2 H molar mass: 2 × 1.01 g = 2.02 g
Total: 171.35 g

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 “per,” and “1” is implied in the denominator. Thus, the molar mass of bilirubin can be expressed as 584.05 g/mol.

Concept Review Exercises

  1. How are molar masses of the elements determined?

  2. How are molar masses of compounds determined?

Answers

Key Takeaway

  • The mass of moles of atoms and molecules is expressed in units of grams.

Exercises

  1. What is the molar mass of Si? What is the molar mass of U?

  2. What is the molar mass of Mn? What is the molar mass of Mg?

  3. What is the molar mass of FeCl2? What is the molar mass of FeCl3?

  4. What is the molar mass of C6H6? What is the molar mass of C6H5CH3?

  5. What is the molar mass of (NH4)2S? What is the molar mass of Ca(OH)2?

  6. What is the molar mass of (NH4)3PO4? What is the molar mass of Sr(HCO3)2?

  7. Aspirin (C9H8O4) is an analgesic (painkiller) and antipyretic (fever reducer). What is the molar mass of aspirin?

  8. Ibuprofen (C13H18O2) is an analgesic (painkiller). What is the molar mass of ibuprofen?

  9. Morphine (C17H19NO3) is a narcotic painkiller. What is the mass of 1 mol of morphine?

  10. Heroin (C21H23NO5) is a narcotic drug that is a derivative of morphine. What is the mass of 1 mol of heroin?

Answers