Moles of Atoms

The atomic mass of an element is a relative quantity. Originally the atomic mass of hydrogen, the lightest of the elements, was taken to be one and the atomic masses of all other elements were measured in relation to the atomic mass of hydrogen. This later proved to have been a poor choice. Not only does hydrogen naturally consist of more than one isotope, but there was the additional question (particularly among early chemists) as to whether monatomic hydrogen or diatomic hydrogen should be taken as having atomic mass one.

After some effort, and one major false start with oxygen, chemists and physicists agreed on a common relative scale of atomic mass. Carbon of isotopic mass twelve was assigned an atomic mass of exactly twelve, and all other atomic masses whether of isotopes or of elements were specified relative to carbon of atomic mass twelve. This had the effect of making the relative atomic mass of hydrogen 1.0079...rather than exactly 1.0000.... The difference of less than 1% is too small to matter in many approximate chemical calculations, but it is large enough to be significant when accurate work must be done.

Physicists, and some chemists, measure the masses of individual atoms in kg, g, or atomic mass units. For most chemists, however, the mass of a single atom is inconveniently small and the molar mass of a substance is used. The molar mass of an atom is the mass of a very large number of identical atoms-- one mole of atoms. One mole of atoms is by definition that number of atoms which exist in exactly twelve grams of carbon of isotopic mass twelve (12C). This number is called the Avogadro number, NA, and the best current determination of its value is 6.02 x 10+23.  Moles of atoms and molecules are so central to chemistry that several of the following sections are devoted to introducing them, and they will be used continually throughout all courses in chemistry.  This mole is just a number.  If someone asked you how many in a dozen, the answer would be an almost automatic 12. How many in a gross?  Again an automatic answer of 144!  This number is vital to chemists.  1 mole = 6.02 x 1023 particles (either atoms or molecules).   It would be in your best interest to memorize this number!

Molar Atomic Masses of Elements

The molar mass of an atom is simply the mass of one mole of identical atoms. However, most of the chemical elements are found on earth not as one isotope but as a mixture of isotopes, so the atoms of one element do not all have the same mass. Chemists therefore distinguish the molar atomic mass of an isotope, which is the mass of one mole of the identical atoms which form that isotope, from the molar atomic mass of an element, which is the mass of one mole of the atoms of the various isotopes of that element having the natural abundances as they are found on earth. For many elements the variation found in the natural abundances limits the accuracy with which the molar atomic mass of that element can be known. Those elements for which this is true are indicated in the periodic table.

Chemists deal with elements as they are naturally found. In actual fact it is very difficult to separate isotopes. Chemists like to deal with the atomic mass or atomic weight of 1 mole of a substance. The weighted molar atomic mass of an element as it naturally occurs will be referred to simply as the atomic mass of the element from now on.

What is the atomic mass of Pb?   Look on the periodic table and find Pb. You'll find the mass number listed as 207.2

One atom of Pb weights 207.2 amu. (atomic mass units)

One mole of Pb atoms weights 207.2 grams. That is 1 mole or 207.2 grams of Pb contains 602,000,000,000,000,000,000,000 atoms of Pb.

The sum of individual atoms can be used to find the mass of a molecule.

The mass of hydrogen peroxide, H2O2 would be calculated like this:

H2O2 has 2 hydrogen atoms and 2 oxygen atoms in it.

Therefore the mass is 2 X H  + 2 X O = 2 X 1.01 amu + 2 X 16.00 amu = 2.02 + 32.00 = 34.02 amu. So one molecule of hydrogen peroxide weighs in at 34.02 amu. A mole of hydrogen peroxide would weigh 34.02 grams.

The periodic table provides you with individual atomic masses.  If you know the number and type of elements in a molecule you can add up the individual masses to find the molecular mass or molecular weight.

Find the molecular mass of calcium phosphate, Ca3(PO4)2

The molecule has 3 calcium atoms, 2 phosphate atoms and 8 O atoms in it. Stop and verify this for yourself. The Ca has a subscript 3 with it. The P has an assumed 1 and the O has a 4. However the PO4  group has a set of brackets around it with a subscript 2. The 2 means multiply everything inside the brackets by 2. So we end up with the 2 P and 8 O atoms.

Calculation:  3 X Ca = 3 X 40.08 amu = 120.24 amu

      2 X P   = 2 X 30.97 amu =   61.94 amu

      8 X O  = 8 X 16.00 amu = 128.00 amu

The total of the individual types of atoms is 120.24 amu + 61.94 amu + 128.00 amu = 310.18 amu.

One molecule of calcium phosphate weighs 310.18 amu and a mole of it would weigh 310.18 grams.

Stop here and do the  Atomic Weights & Masses Exercise

Click here to go to a molecular mass calculator site.

Percent Composition

Percent composition is a simple little calculation that has a large impact on chemistry. When a brand new substance is discovered one of the first things that is determined is its chemical make-up. That means how much of each type of atom is in the molecule. What is the percent composition of strontium oxide? SrO

There is 1 atom of Sr and 1 atom of O.

The mass of 1 Sr is 87.62 amu and the mass of an O is 16.00 amu.

The percent composition is the fraction of the SrO that is just Sr.  This fraction is:

Percentage of Sr = mass of Sr in the molecule / molecular mass X 100%

            = 87.62 amu / 103.62 amu X 100%

            = 0.8456 X 100%

            =  84.56%

Strontium makes up 84.56% of the molecule. The oxygen makes up 100% - 84.56% = 15.44%. The amu's are units that cancel out. The % sign means out of 100.

The general equation for finding the percentage composition of an element is:

percentage of an element = the total mass of just that element / molecular mass X 100%

Stop here and do the  Percent Composition Exercise

Click here to go to a percent composition calculator.