Download Calculating Average Atomic Mass Objective C.6D: Use isotopic

Calculating Average Atomic Mass
Objective C.6D: Use isotopic composition to calculate average atomic mass of an element
Section 1
Suppose that you wanted to find the average mass of students in a chemistry class. How would you go
about it? The most straightforward way would be to find out each person’s mass, add them together
and divide by the total number of people. This method of averaging works well for small groups. You
could probably accomplish this task in one class period or less. But what if your chemistry class had
3,000 students? Or 3,000,000? How would you go about finding the average mass then?
Let’s simplify the problem for a moment. For the class of 3,000 students, imagine that each of the girls
has a mass of 50 kg and each of the boys has a mass of 64 kg. Does this information help? Well, you
might find the average of 50 and 64. This gives 57 kg as an average mass. But this only works under one
condition-equal numbers of girls and boys. What if there were only two girls in the class of 3,000.
Would 57kg be an accurate average? Why/Why not?
Obviously, the average mass is dependent on the relative abundance of objects of different mass. Try to
analyze the situation presented below.
A very large box contains 100,000 red marbles, all the same size. You want to know the mass of an
“average” marble. They all look the same, so you measure the mass of one marble and find it to be 14 g.
However, your lab partner measures the mass of a different marble and finds his marble to have a mass
of 12 g. Because of the large number of marbles, the mass of the filled box is very large, and the box
can’t be moved to a balance. Besides, there are no balances available in your classroom to measure a
mass as large as that of the filled box. The two of you are resigned to measuring the mass of each
marble, when you see some writing on the side of the box. It reads:
Mass
12 g
13 g
14 g
Relative Abundance
98.890%
1.108%
0.002%
Can this information help you to find the average mass? Try to answer the following questions:
1. How many marbles have a mass of 14 g?
2. What is the total mass of all of the 14 g marbles in the box?
3. How many marbles have a mass of 13 g?
4. What is the total mass of all of the 13 g marbles in the box?
5. How many marbles have a mass of 12 g?
6. What is the total mass of all of the 12 g marbles in the box?
7. What is the total mass of all of the marbles in the box?
8. What is the average mass of all of the marbles in the box?
You have found the average mass of a marble without doing any measuring at all! Try another
similar example of finding an average value. This time, summarize your work in the table provided.
Section 2
2000 students take the Chemistry State test and do very well. The relative abundance of scores is
shown below:
Score
92 Points
94 Points
95 Points
96 Points
97 Points
98 Points
100 Points
Relative Abundance
14.8%
9.3%
15.9%
16.7%
9.6%
24.1%
9.6%
Analyze this data and fill in the following table:
Score
Number of Students
X
X
X
X
X
X
X
Total =
Total Score
=
=
=
=
=
=
=
Total =
What was the average score on this test?
Atoms of the same element can have different masses due to different numbers of neutrons present
in the nucleus; these atoms are called isotopes of the particular element. Like the marbles in the
box, or the students in the class, when millions of atoms are involved, it is likely that there will be
some with different masses. Therefore, when the mass of an atom or element is discussed, it is
usually assumed to be the average atomic mass, or the weighted average of all of the isotopes of
that element based on relative abundance.
An isotope is usually identified by its mass number. Mass number is the sum of the protons and
neutrons in the nucleus of a particular atom. The mass number for an oxygen atom with eleven
neutrons is nineteen, so the name of the isotope is written oxygen-19. How many protons and
neutrons would an atom of the isotope bromine-82 contain?
The mass number for an isotope is very close to the actual mass of that isotope. In the following
exercise, the mass number is used to designate the mass of a particular isotope.
Finding the average atomic mass for a sample containing different isotopes is very similar to the
marble and test examples above. In fact, you have already found the average mass for two
elements. See if this data set doesn’t look familiar:
Isotope
Carbon-12
Carbon-13
Carbon-14
Mass
12 u
13 u
14 u
Relative Abundance
98.890%
1.108%
0.002%
In the first example, you actually calculated the average atomic mass of carbon. What is the average
atomic mass of carbon using the proper units (Hint:Look at your answers in section 1)?
Likewise, in the test example in section 2, which element did you calculate the average atomic mass
for?
In the next example, the relative abundances of isotopes of copper are provided. However, there is
no indication as to how many copper atoms are present in the sample. One way around this
problem is to assume that there are always 100 atoms total. The total abundance will always equal
100 percent. So by using 100 atoms, the number of atoms present for a given isotope is simply
equal to the percent of abundance. Since the percent of abundance never changes, the number of
atoms is really unimportant. Choosing 100 simply makes calculations easier.
Isotope
Relative Abundance
Copper-63
69.2%
Copper-65
30.8%
The calculations for this element are summarized in the table below. Notice how the percent
abundance was used for the number of atoms in each case.
Mass Number
63
65
X
X
Total=
Number of Atoms
69.2
30.8
100
What is the average atomic mass for Copper?
=
=
Total =
Total Mass
4359.6
2002
6361.6