How do we calculate for the Average Atomic Mass of an element?

Question

How do we calculate for the average atomic mass of an element?

The hard part actually is determining what we have to put there like the mol fraction, or the atomic mass. Help!!??

Answer 1

Take chlorine for an example.

There are 2 common isotopes of chlorine:  Cl-35 and Cl-37

They are found in the approximate ratio of 3 Cl-35s to 1 Cl-37s.

We multiply each by its % (75% = 075 and 25% - 0.25):

0.75 x 35 = 26.25

0.25 x 37 = 9.25

Add them together:  26.25 + 9.25 = 35.5

35.5 is the atomic mass quoted for chlorine.  In practice, the %s listed above are oversimplified and the actual atomic mass of Cl is nearer 35.45, but that's how you work it out.

Answer 2

Many elements consist of more than one naturally occurring isotope.  The average atomic mass of an element is the "weighted" average.  This means that more "weight" or importance is given to the isotope which is in greater natural abundance.  

We know the percentages of each isotope.  To do the calculation we will express each percentage as its corresponding decimal fraction.

Average atomic mass = (fraction1 x atomic mass1) + (fraction2 x atomic mass2) + (fraction3 x atomic mass3) ...

Cstspeedy has given you the gist of the calculation, and has mentioned that the numbers used will only produce an approximation of the average atomic mass.  What should be used are more precise measurements of the percent abundances and the actual masses of the isotopes.

This is the important part.  The mass numbers are NOT the actual masses of the isotopes.  They are close, but not the same.  The actual isotopic masses are known very precisely.

For instance, Cl-37 has a mass of 36.965902591 amu.  We don't need to use all those digits, but they represent the actual mass of the isotope.

So for the chlorine example, where there are only two naturally occurring isotopes, you would use the following.  75.58 percent of chlorine atoms are chlorine-35 and 24.22 percent of chlorine atoms are chlorine-37.

The average atomic mass = 0.7578 x 34.9689 + 0.2422 x 36.9659 = 35.453 amu