Average Atomic Mass (review lesson)

Average Atomic Mass

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Isotopes of chlorine

• Chlorine has 2 stable isotopes

• Chlorine-35

• Chlorine-37

• A real-world sample that contains chlorine (ex: NaCl ) will involve billions and billions of chlorines.

• Some Cl-35 and some are Cl-37

35 based on Cl-35 ?
37 based on Cl-37 ?
or an average of them?

​

The mass of formula NaCl for table salt involves the mass of Na and the mass of Cl... but what number do we use for Cl?

Multiple Choice

What is the average atomic mass of chlorine?

Chlorine has 2 isotopes: Cl-35 and Cl-37

• 35

• 36

• 37

• none of these

That question was not fair!!

Indeed. You do not have complete information.

That is why this is only a participation grade.

Atomic Mass of chlorine is...

35.45 u

number below element name in boxes of your Periodic Table.

(17 is Atomic Number)

Atomic Mass is a

Weighted Average

often called the "Average Atomic Mass"

Your course grade is also a weighted average

Not every grade category is given the same weight

Math Response

A student in Honors Chemistry has an 50 for classwork because some is missing and some was late... they have an 80 for labs , and they have a 95 on exams.

What is their course average ("their grade") if classwork is weighted at 40%, labs at 40%, and exams at 20%?

Type answer here

Correct Answer: 71

Deg^°

Rad

The simple average of 50, 80, and 95 is 75

​But... that assumes each category is given the same weight (which it is not)

The weighted average of 50, 80, and 95 based on the category weights is 71

EACH VALUE IS MULTIPLED BY ITS WEIGHT , AND THEN DIVIDED BY 100


You DO NOT divide by 3 at the end.

Percent Abundance of each isotope for an element determines how its mass is weighted in the average

the math of Weighted Average Atomic Mass

Example of element with 2 isotopes

​unit of mass for atoms is "u" ... unified atomic mass unit

So the mass of a magnesium-25 atom is approximately 25 u.

Multiple Choice

The element magnesium, Mg, has 3 naturally-occuring isotopes.

The Atomic Mass of magnesium is 24.305 u

Which Isotope would you predict is the most abundant?

Mg-24 , Mg-25, or Mg-26

(hint... that atomic mass is weighted toward it)

• Mg-24

• Mg-25

• Mg-26

Atomic Mass is not a whole number, but it is usually closest to the weight of its most abundant isotope

​weighted average calculation to get Atomic Mass

Other Numerical Setup styles
(my preference)

• Divide each percentage by 100 and simplify them... which switches from the values to decimal numbers before putting in the setup

• Use 0.10 instead of 10% ; Use 0.11 instead of 11% ; Use 0.79 instead of 79%

• (24 u x 0.79) + (25 u x 0.10) + (26 u x 0.11) = 24.305

Other Numerical Setup styles

Other Numerical Setup styles

Conclusion

• Every element has an average atomic mass and is listed on the Periodic Table

• It is a weighted average based on the percent abundances of its isotopes.

• This average is usually nearest its most abundant isotope's mass (weighted toward it)

• sometimes the term average is dropped and it is just called atomic mass.

Multiple Choice

Which of the following is an acceptable (and accurate) numerical setup for calculating the atomic mass of gallium based on the provided data table?

(NOTE! the mass values in the table are very precisely measured. Yes, the mass of atoms are just a tad smaller than their mass numbers... notice how Ga-71 has a mass of 70.925 u)

Math Response

Element J has two isotopes. J-35 has an abundance of 75.78%; and J-37 has an abundance of 24.22%. What is the average atomic mass of this element?

Type answer here

Correct Answer: 35.48

Deg^°

Rad