Average Atomic Mass Beanium Lab (Teacher Notes)
PSI Chemistry
Objective:
The goals of this lab are to:
 To use the relative masses and relative abundances of the isotopes of the new element
Beanium to determine its average atomic mass.
 Understand the difference between an average and a weighted average.
Background:
Most elements have naturally occurring isotopes. Isotopes are atoms of the same element with a
different number of neutrons and therefore having different masses. The relative masses and relative
abundances of these naturally occurring isotopes are used to determine the average atomic mass of
an element. The average atomic mass is a weighted average. A weighted average unlike an average
takes into account the relative abundances of the naturally occurring isotopes and is the best
determination of the average atomic mass.
Materials:

Three or four different samples of beans, balance, pencil, and laboratory record sheet and
weighing dishes (if available).
Preparation (if possible before class):
 Prepare the beanium samples for the students by randomly adding a mixture of the three to
four types of beans. A minimum of 10 beans per type would ensure a good average mass for
the different bean types.
 Check in with the students to ensure they mass all the beans of each type at one time.
Timing: This is a one period lab. Approximate timing is as follows:
 5 minutes to sort and count the beans.
 10 minutes to mass the groups of beans. The total time spent in completing this step depend
on the number and type of balances available.
 10 minutes to complete calculations.
 15 minutes to answer additional questions.
Anticipated and Sample Results:

Students are likely to count and mass the beans
correctly.

Students will probably become confused when it
comes to determining the average atomic mass of Beanium from the relative masses and
relative abundances of its isotopes. It would be a good idea to introduce the following formula
to them the next day and have them complete their calculations going forward using this
formula.
Average Atomic Mass
= (Relative Abundance Isotope A x Relative Mass Isotope A)
+ (Relative Abundance Isotope B x Relative Mass Isotope B)
+ (Relative Abundance Isotope C x Relative Mass Isotope C)......

Understanding the difference between an
average and a weighted average is always a challenging concept for students. The easiest
way to explain may be to use an actual element, for example magnesium.
Isotope
Relative Abundance
Atomic Mass (amu)
24Mg
0.7899
23.98504
25Mg
0.1000
24.98584
26Mg
0.1101
25.98259
Have the students determine the atomic mass of magnesium using an average and a weighted
average. They will see that an average gives a value of 24.98449 amu and a weighted
average gives the actual atomic mass of 24.3050 amu. The predominance of 24Mg, nearly
80% of the total, gives rise to a smaller value for the average atomic mass for a weighted
average than if you calculated a regular average. The regular average assumes, in this case
because there are three isotopes, that each isotope has a 33.333% abundance, but this is not
true.
Follow Ups (next day):
 Its very important for students to estimate what an element's average atomic mass should be
given the relative masses and relative abundances of its naturally occurring isotopes. A good
exercise as a follow up to the lab is to give them examples such as the one below and have
them estimate the average atomic mass of the element.


Isotope
Relative Abundance
Atomic Mass (amu)
100Ohno
0.1200
99.98332
101Ohno
0.6690
100.98660
105Ohno
0.2110
104.98111
To ensure the students can complete the actual mathematical computation have them calculate
the average atomic mass. It is good idea to make up fictitious elements made from your name,
school name, or their names so that they can practice and not be able to look up the actual
answer.
Challenge: Have the students determine the relative mass of an isotope of an element that
has two or more naturally occurring isotopes. Give the students the average atomic mass of
the element, the relative abundance of each of the isotopes and the relative masses of the
other one or two naturally occurring isotopes and see if they can solve for the relative mass of
the remaining isotope.
Presentation and Handout Materials
Smart Notebook class presentation and lab handouts for this lab are available through teacher access
to the PSI Chemistry website in the Atomic Structure Unit.