Average Atomic Mass

Isotopes are different atoms of the same element that have:
- The same number of protons
- A different number of neutrons
- A different mass number
Most naturally occurring elements have more than one isotope
The percentage of each isotope in a sample is called relative abundance
The average atomic mass of an element is a weighted average of the masses of all of the naturally occurring isotopes of that element

$average atomic mass = \sum_{}^{} {(isotope mass \times relative abundance)}_{1 . . n}$

The relative abundance percentage must be converted to a decimal value by dividing by 100 before proceeding with an average atomic mass calculation
In decimal form, the sum of the relative abundances will equal 1

The average atomic mass of boron is 10.81 amu. The two naturally occurring isotopes of boron are listed in the table below.

Using the information provided, calculate the percent abundance of each isotope.

Answer:

The sum of the relative abundances in decimal form is
- x + y = 1
Rearranging the equation to solve for x
- x = 1 – y
The average atomic mass of boron is
- average atomic mass = (isotope mass × relative abundance)₁ + (isotope mass × relative abundance)₂
- 10.81 = 10.01x + 11.01y
Substituting the value of x
- 10.81 = 10.01(1–y) + 11.01y
- 10.81 = 10.01 – 10.01y + 11.01y
- 10.81 = 10.01 + 1y
- 0.80 = y
Substituting y into the equation for x
- x = 1 – 0.80
- x = 0.20
The percent abundance of boron-10 is 20% and the percent abundance of boron-11 is 80%

The results of the analysis of a pure sample of AgF using mass spectroscopy are shown in the

table above. Fluorine only has one naturally occurring isotope. Based on this information, what is the average atomic mass of silver?

Answer:

The average atomic mass of fluorine is 19.00 amu
The mass of each silver isotope must be
- isotope mass₁ = 125.91 amu - 19.00 amu
- isotope mass₁ = 106.91 amu
- isotope mass₂ = 127.90 amu - 19.00 amu
- isotope mass₂ = 108.90 amu

The average atomic mass of silver is
- average atomic mass = (isotope mass × relative abundance)₁ + (isotope mass × relative abundance)₂
- average atomic mass = (106.91 amu × 0.5180) + (108.90 amu × 0.4820)
- average atomic mass = 55.38 amu + 52.49 amu
- average atomic mass = 107.87 amu

Average Atomic Mass (College Board AP Chemistry)