Average Atomic Mass

Chapter 7.4Average Atomic Mass

• Objective:(1) To calculate the average atomic mass for an

atom.

Average Atomic Mass

• Weighted average of the masses of the existing isotopes of an element.

Recall: Atomic Mass Unit

• The unit that describes the mass of an atom

• Symbol: amu

Example #1

• The mass of a Cu-63 atom is 62.94 amu, and that of a Cu-65 atom is 64.93 amu. The percent abundance of Cu-63 is 69.17% and the percent abundance of Cu-65 is 30.83%. What is the average atomic mass of Cu?

Example #1• The mass of a Cu-63 atom is 62.94 amu, and that of a Cu-65 atom

is 64.93 amu. The percent abundance of Cu-63 is 69.17% and the percent abundance of Cu-65 is 30.83%. What is the average atomic mass?

• Step 1: Find the contribution of each isotope:Cu-63: (62.94 amu) x (0.6917) = 43.535598 amu

Cu-65: (64.93 amu) x (0.3083) = 20.017919 amu

• Step 2: Add the relative abundances from each isotope together.43.535598 amu + 20.017919 amu = 63.553517 amu

Round answer to two numbers after the decimal: 63.55 amu

Example #2

• Calculate the average atomic mass of chromium. It is made up of isotopes with the following percent compositions and atomic masses: 83.79% with a mass of 51.94 amu; 9.50% with a mass of 52.94 amu; 4.35% with a mass of 49.95 amu; 2.36 % with a mass of 53.94 amu.

Example #2• Calculate the average atomic mass of chromium. It is made up of

isotopes with the following percent compositions and atomic masses: 83.79% with a mass of 51.94 amu; 9.50% with a mass of 52.94 amu; 4.35% with a mass of 49.95 amu; 2.36 % with a mass of 53.94 amu.

• Step 1: Find the contribution of each isotope:(51.94 amu) x (0.8379) = 43.520526 amu

(52.94 amu) x (0.0950) = 5.0293 amu (49.95 amu) x (0.0435) = 2.172825 amu (53.94 amu) x (0.0236) = 1.272984 amu

• Step 2: Add the relative abundances from each isotope together.43.520526 amu + 5.0293 amu + 2.172825 amu + 1.272984 amu =

51.995635 amu

Round answer to two numbers after the decimal: 52.00 amu

Example #3

• Calculate the average atomic mass of iron if its abundance in nature is 15% iron-55 and 85% iron-56.

Example #3

• Calculate the average atomic mass of iron if its abundance in nature is 15% iron-55 and 85% iron-56.

• Step 1: Calculate the contribution of each isotope:Iron-55: (55 amu) x (0.15) = 8.25 amuIron-56: (56 amu) x (0.85) = 47.6 amu

• Step 2: Add the contribution from each isotope together:8.25 amu + 47.6 amu = 55.85 amu

The element with an atomic mass of 10.8 amu is Boron.

Example #4

• Chlorine exists as chlorine-35, which has a mass of 34.969 amu and makes up 75.8% of chlorine atoms. The rest of naturally occurring chlorine is chlorine-37, with a mass of 36.996 amu. What is the average atomic mass of chlorine?

Example #4• Chlorine exists as chlorine-35, which has a mass of 34.969 amu

and makes up 75.8% of chlorine atoms. The rest of naturally occurring chlorine is chlorine-37, with a mass of 36.996 amu. What is the average atomic mass of chlorine?

• Step 1: Find the contribution of each isotope:Cl-35: (34.969 amu) x (0.758) = 26.506502 amu

Cl-37: (36.996 amu) x (0.242) = 8.953032 amu

• Step 2: Add the relative abundances from each isotope together.26.506502 amu + 8.953032 amu = 35.459534 amu

Round answer to two numbers after the decimal: 35.46 amu

Example #5

• Element X has two isotopes. One has a mass of 10.0 amu and an abundance of 20.0%. The other has a mass of 11.0 amu and an abundance of 80.0%. Estimate the average atomic mass. What element is it?

Example #5• Element X has two isotopes. One has a mass of 10.0 amu

and an abundance of 20.0%. The other has a mass of 11.0 amu and an abundance of 80.0%. Estimate the average atomic mass. What element is it?

• Step 1: Calculate the contribution of each isotope:Isotope 1: (10.0 amu) x (0.20) = 2 amuIsotope 2: (11.0 amu) x (0.80) = 8.8 amu

• Step 2: Add the contribution from each isotope together:2 amu + 8.8 amu = 10.8 amu

The element with an atomic mass of 10.8 amu is Boron.