Online Introductory Chemistry

Isotopes and average atomic masses

Dr. Walt Volland revised July 5, 2010

Example of a weighted average calculation: Assume you have taken five quizzes with the following scores out of 10 possible points. 10 pts, 5 pts, 10 pts, 10 pts, 10 pts. The average score will be 9 pts. average = (1/5)( 10 pts + 5 pts + 10 pts + 10 pts + 10 pts) = 45 points total / 5 = 9 pts The low score doesn't shift the average down much because the four 10 point scores weight the average toward nine. Here the high scores occurred 4 out of 5 times or 80% of the time. Only one out of five scores was low at 5. The abundant high scores have more influence on the average. You can calculate the weighted average in the following way. Literally what happens in the calculation is average score = [40 points + 5 points][1/5] = [45 points] = 9 points

Example weighted average calculation using isotope abundances:

What is the average atomic weight for chlorine if it has two isotopes? The percent abundance for chlorine-35 is 75.53%. The percent abundance for chlorine-37 is 24.4%. The mass for Cl-35 is 35.0 amu and for Cl-37 it is 37.0 amu.

Average atomic weight = 26.4 amu + 9.05 amu = 35.5 amu

Notice that the average is determined by the more abundant Chlorine-35. Because chlorine-35 is more common, the average is closer to 35 amu than 37 amu. Clearly no atoms of chlorine actually have a mass of 35.5 amu. The tabulated value in the periodic table is a statistical creation and matches no real chlorine atoms at all.