# 4.2: Molar Mass

As we described in Section 4.1, in chemistry, the term mole can be used to describe a particular number. The number of things in a mole is large, very large (6.0221415 x 1023). We are all familiar with common copy-machine paper that comes in 500 sheet reams. If you stacked up 6.02 x 1023 sheets of this paper, the pile would reach from the earth to the moon 80 billion times! The mole is a huge number, and by appreciating this, you can also gain an understanding of how small molecules and atoms really are.

Chemists work simultaneously on the level of individual atoms, and on the level of samples large enough to work with in the laboratory. In order to go back and forth between these two scales, they often need to know how many atoms or molecules there are in the sample they’re working with. The concept that allows us to bridge these two scales is molar mass. Molar mass is defined as the mass in grams of one mole of a substance. The units of molar mass are grams per mole, abbreviated as g/mol.

The mass of a single isotope of any given element (the isotopic atomic mass) is a value relating the mass of that isotope to the mass of the isotope carbon-12 (${\displaystyle {}_{6}^{12}{\text{C}}}$); a carbon atom with six proton and six neutrons in its’ nucleus, surrounded by six electrons. The atomic mass of an element is the relative average of all of the naturally occurring isotopes of that element and atomic mass is the number that appears in the periodic table. We have defined a mole based on the isotopic atomic mass of carbon-12. By definition, the molar mass of carbon-12 is numerically the same, and is therefore exactly 12 grams. Generalizing this definition, the molar mass of any substance in grams per mole is numerically equal to the mass of that substance expressed in atomic mass units. For example, the atomic mass of an oxygen atom is 16.00 amu; that means the molar mass of an oxygen atom is 16.00 g/mol. Further, if you have 16.00 grams of oxygen atoms, you know from the definition of a mole that your sample contains 6.022 x 1023 oxygen atoms.

The concept of molar mass can also be applied to compounds. For a molecule (for example, nitrogen, N2) the mass of molecule is the sum of the atomic masses of the two nitrogen atoms. For nitrogen, the mass of the N2 molecule is simply (14.01 + 14.01) = 28.02 amu. This is referred to as the molecular mass and the molecular mass of any molecule is simply the sum of the atomic masses of all of the elements in that molecule. The molar mass of the N2 molecule is therefore 28.02 g/mol. For compounds that are not molecular (ionic compounds), it is improper to use the term “molecular mass” and “formula mass” is generally substituted. This is because there are no individual molecules in ionic compounds. However when talking about a mole of an ionic compound we will still use the term molar mass. Thus, the formula mass of calcium hydrogen carbonate is 117.10 amu and the molar mass of calcium hydrogen carbonate is 117.10 grams per mole (g/mol).

Exercise $$\PageIndex{1}$$

Find the molar mass of each of the following compounds:

Sand, silicon dioxide (SiO2) Draino™, sodium hydroxide (NaOH) Nutrasweet™, Aspartame (C14H18N2O5) Bone phosphate, calcium phosphate Ca3(PO4)2

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