6.4: Molar Mass

⚙️ 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.
 

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
       

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
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
Sum the masses to find the molar mass.	molar mass = 18.02 g	molar mass = 164.10 g
Determine whether the compound is ionic or molecular.	H2O is a molecular compound.	Ca(NO3)2 is an ionic compound.
Formula units or molecules contained in the molar mass.	6.022 × 10^23 molecules H2O, which is also 1 mol H2O, are in 18.02 g H2O.	6.022 × 10^23 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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This page is shared under a CK-12 license and was authored, remixed, and/or curated by Vicki MacMurdo (Anoka-Ramsey Community College), Lance S. Lund (Anoka-Ramsey Community College), Melissa Alviar-Agnew, Henry Agnew, and Wikipedia.

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