# 8.4: Atomic and Molar Masses


##### Learning Objectives
• To learn how the masses of moles of atoms and molecules are expressed.

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 $$6.022 \times 10^{23}$$ and not $$1 \times 10^{23}$$ or even $$1 \times 10^{20}$$?

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.

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

##### Example $$\PageIndex{1}$$: Moles to Mass Conversion with Elements

What is the mass of each quantity?

1. 1 mol of Al atoms
2. 2 mol of U atoms
###### Solution
1. 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.
2. According to the periodic table, 1 mol of U has a mass of 238.0 g, so the mass of 2 mol is twice that, or 476.0 g.
##### Exercise $$\PageIndex{1}$$: Moles to Mass Conversion with Elements

What is the mass of each quantity?

1. 1 mol of Au atoms
2. 5 mol of Br atoms

197.0 g

5 mol Br atoms x 79.90 g/mol = 399.5 g

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, whether the substance is an element, an ionic compound, or a covalent compound.

##### Example $$\PageIndex{2}$$: Moles to Mass Conversion with Compounds

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
1. Summing the molar masses of the atoms in the NaCl formula unit gives
Solutions to Example 6.2.2, Summing the molar masses of the atoms in the NaCl formula unit gives
1 Na molar mass: 22.99 g
1 Cl molar mass: 35.45 g
Total: 58.44 g

The mass of 1 mol of NaCl is 58.44 g.

1. Multiplying the molar mass of each atom by the number of atoms of that type in bilirubin’s formula and adding the results, we get
Solutions to Example 6.2.2, Multiplying the molar mass of each atom by the number of atoms of that type in bilirubin’s formula and adding the results, we get
33 C molar mass: 33 × 12.01 g 396.33 g
36 H molar mass: 36 × 1.01 = 36.36 g
4 N molar mass: 4 × 14.01 = 56.04 g
6 O molar mass: 6 × 16.00 = 96.00 g
Total:   584.73 g

The mass of 1 mol of bilirubin is 584.73 g.

##### Exercise $$\PageIndex{2}$$: Moles to Mass Conversion with Compounds

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

233.36 g

267.28 g

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:

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 × 137.3 g = 137.3 g
2 O molar mass: 2 × 16.00 g = 32.00 g
2 H molar mass: 2 × 1.01 g = 2.02 g
Total:   171.32 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 584.73 g/mol, which is read as “five hundred eighty four point seventy three grams per mole.”

## Key Takeaway

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

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