Molar Mass of An Element and Avogadro's Number

This page will describes molar mass of an element and avogadro's number.

Atomic mass units provide a relative scale for the masses of the elements. But since atoms have such small masses, no usable scale can be devised to weigh them in calibrated units of atomic mass units. In any real situation, we deal with macroscopic samples containing enormous numbers of atoms. Therefore it is convenient to have a special unit to describe a very large number of atoms. The idea of a unit to denote a particular number of objects is not new. For example, the pair (2 items), the dozen (12 items), and the gross (144 items) are all familiar units. Chemists measure atoms and molecules in moles.

In the SI system the mole (mol) is the amount of a substance that contains as many elementary entities (atoms, molecules, or other particles) as there are atoms in exactly 12 grams (or 0.012 kilogram) of the carbon-12 isotope. The actual number of atoms in 12 g of carbon-12 is determined experimentally. The currently accepted value is

1 mole = 6.022045 x 10²³ particles

This number is called Avogadro’s number, in honor of the Italian scientist Amedeo Avogadro. Generally, we round Avogadro’s number to 6.022 x 10²³. Thus, just as one dozen oranges contains twelve oranges, 1  mole of hydrogen atoms contains 6.022 x 10²³ H atoms. (The Chemistry in Three Dimensions essay on p. 106 describes a method for determining Avogadro’s number.)

We have seen that 1 mole of carbon-12 atoms has a mass of exactly 12 grams and contains 6.022 x 10²³ atoms. This mass of carbon-12 is its molar mass, defined as the mass (in grams or kilograms) of 1 mole of units (such as atoms or molecules) of a substance. Note that the molar mass of carbon-12 (in grams) is numerically equal to its atomic mass in amu. Likewise, the atomic mass of sodium (Na) is 22.99 amu and its molar mass is 22.99 grams; the atomic mass of phosphorus is 30.97 amu and its molar mass is 30.97 grams; and so on. If we know the atomic mass of an element, we also know its molar mass. Using atomic mass and molar mass, we can calculate the mass in grams of a single carbon-12 atom. From our discussion we know that 1 mole of carbon-12 atoms weighs exactly 12 grams. This allows us to write the equality

12.00 g carbon-12 = 1 mol carbon-12 atoms

Therefore, we can write the unit factor as

(12.00 g carbon-12) / (1 mol carbon-12 atoms)  =1

(Note that we use the unit “mol” to represent “mole” in calculations.) Similarly, since there are 6.022 x 10²³ atoms in 1 mole of carbon-12 atoms, we have

1 mol carbon-12 atoms 6.022 x 10²³ carbon-12 atoms 

and the unit factor is

(1 mol carbon-12 atoms) / (6.022 x 10²³  carbon-12 atoms) = 1