Average Atomic Mass

What is average atomic mass?

Average atomic mass is the weighted average of the atomic masses of the naturally occurring isotopes of an element

Calculating a Weighted Average

Example

A box contains two size of marbles. If

25.0% have masses of 2.00 g and 75.0%

have masses of 3.00 g what is the weighted

average?

(.250) (2.00) + (.750) (3.00) = .500 + 2.25 =

2.75g

Calculating Average Atomic MassEXAMPLE

Boron has two isotopes:

B-10 (mass 10.013 amu) 19.8% abundance

B-11 (mass 11.009 amu) 80.2% abundance

Calculate the average atomic mass.

(.198) (10.013) + (.802) ( 11.009) =

1.98 amu + 8.83 amu = 10.81 amu

Calculating Average Atomic Mass

Calculate the average atomic mass of Mg.

Isotope 1 - 23.985 amu (78.99%)

Isotope 2 - 24.986 amu (10.00%)

Isotope 3 – 25.982 amu (11.01%)

(23.985)(.7899)+(24.986)(.1000)+(25.982)(.1101)

18.95 amu + 2.499 amu + 2.861 amu = 24.31 amu

Average Atomic Mass

Helium has two naturally occurring isotopes, He-3 and He-4. The atomic mass of helium is 4.003 amu. Which isotope is more abundant in nature?

He-4 is more abundant in nature because the atomic mass is closer to the mass of He-4 than to the mass of He-3.

Isotopic Pennies – number of pre and post 1982

a. Let X be the number of pre-1982 pennies

b. Let 10-X be the number of post-1982 pennies

c. (X)(3.1g) + (10-X)(2.5g) = mass of 10 pennies

pre-82 post-82

EXAMPLE (Mass of a sample of pennies is 31.0g)

(X)(3.1g) + [(10-X)(2.5g)] = 31.0 g

3.1X + 25 - 2.5X = 31.0g

.6X + 25 = 31.0g

.6X = 6.0g X = 6.0g/.6

X = 10 pre-82 pennies

10-X = 0 pre-82 pennies

Isotopic Penny Lab- Average Atomic Mass

Calculate percent of pre-82 and post-82 pennies

# of pre-82 pennies x 100% # post-82 pennies x 100%

10 10

Calculate the average atomic mass of coinium

(% pre-82)(3.1g) + (% post-82)(2.5) = average atomic mass