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### Calculations in Chemistry:

Average Atomic Mass

Isotopes

- An element can exist in a number of forms, called isotopes. Isotopes are forms of the same atom that vary in mass as a result of a different number of neutrons.

For example, there are two different types (isotopes) of copper atoms. One type of copper atoms weighs in at 62.93 amu, the other has a mass of 64.94 amu.

- These two isotopes have different proportions in a natural sample of copper.
- The lighter isotope is more common with 69.09% of the naturally occurring copper having a mass of 62.93 amu per atom.
- What is the percent abundance of the other isotope?

Average Atomic Mass

- To find the AVERAGE ATOMIC MASS of an atom, we take into account all of the isotopes that exist and the percentage of each type.
- The calculation of the average atomic mass is a WEIGHTED AVERAGE.

Calculation of Average Mass

Average atomic mass =

Σ (mass of isotope × relative abundance)

Σ = sum or to add them all together

Calculation of Average Mass

- The bottom line is that to find the average atomic mass of copper, we insert the information about copper’s isotopes into the formula and solve.
- There are two isotopes, so we will be adding the contributions of 2 isotopes. (That’s where the Σ sign comes in. )
- The relative abundance is simply the percentage of the isotope, but in decimal format. 69.09% corresponds to a relative abundance of 0.6909.

Calculation of Average Mass

Average atomic mass of copper =

(62.93 amu × 0.6909)

[the mass and abundance of isotope #1]

+

(64.94 amu × 0.3091)

[the mass and abundance of isotope #2]

=

63.55

Calculation of Average Mass

- From the calculation, we know that an AVERAGE atom of copper has a mass of 63.55 amu.
- Notice that in this problem, we would predict that the average is closer to the weight of the lighter isotope.
- This is because the lighter form of copper is more abundant.

Check Your Answers

- Silver = 107.87 amu
- Silicon = 28.09 amu
- Iron = 55.84 amu

Homework

- Read section 1.4 in the text to support what we did in class today.
- pg27 #1
- Pg 29 #1-5,9

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