1. Average Atomic Mass

2. Chapter 7.4 Average Atomic Mass
Objective:
(1) To calculate the average atomic mass for an atom.

3. Average Atomic Mass
Weighted average of the masses of the existing isotopes of an element.

4. Recall: Atomic Mass Unit
The unit that describes the mass of an atom
Symbol: amu

5. Example #1
The mass of a Cu-63 atom is amu, and that of a Cu-65 atom is 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?

6. Example #1
The mass of a Cu-63 atom is amu, and that of a Cu-65 atom is 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) = amu
Cu-65: (64.93 amu) x (0.3083) = amu
Step 2: Add the relative abundances from each isotope together.
amu amu = amu
Round answer to two numbers after the decimal: amu

7. 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 amu; 9.50% with a mass of amu; 4.35% with a mass of amu; 2.36 % with a mass of amu.

8. 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 amu; 9.50% with a mass of amu; 4.35% with a mass of amu; 2.36 % with a mass of amu.
Step 1: Find the contribution of each isotope:
(51.94 amu) x (0.8379) = amu
(52.94 amu) x (0.0950) = amu
(49.95 amu) x (0.0435) = amu
(53.94 amu) x (0.0236) = amu
Step 2: Add the relative abundances from each isotope together.
amu amu amu amu = amu
Round answer to two numbers after the decimal: amu

9. Example #3
Calculate the average atomic mass of iron if its abundance in nature is 15% iron-55 and 85% iron-56.

10. 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 amu
Iron-56: (56 amu) x (0.85) = 47.6 amu
Step 2: Add the contribution from each isotope together:
8.25 amu amu = amu
The element with an atomic mass of 10.8 amu is Boron.

11. Example #4
Chlorine exists as chlorine-35, which has a mass of amu and makes up 75.8% of chlorine atoms. The rest of naturally occurring chlorine is chlorine-37, with a mass of amu. What is the average atomic mass of chlorine?

12. Example #4
Chlorine exists as chlorine-35, which has a mass of amu and makes up 75.8% of chlorine atoms. The rest of naturally occurring chlorine is chlorine-37, with a mass of amu. What is the average atomic mass of chlorine?
Step 1: Find the contribution of each isotope:
Cl-35: ( amu) x (0.758) = amu
Cl-37: ( amu) x (0.242) = amu
Step 2: Add the relative abundances from each isotope together.
amu amu = amu
Round answer to two numbers after the decimal: amu
1 – 0.758

13. 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?

14. 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 amu
Isotope 2: (11.0 amu) x (0.80) = 8.8 amu
Step 2: Add the contribution from each isotope together:
2 amu amu = 10.8 amu
The element with an atomic mass of 10.8 amu is Boron.