Weighted Averages and Isotopes
Do Now:
Write the nuclear symbols (symbolic notation) for the 7 problems on your homework.
Walk through the room, look at last problem, make sure everybody got all the answers correct. If there
was a lot of trouble, go stepwise through each problem until the class seems to understand the
information.
If the class got the information correct, call on students to give all of the answers to one row until the
problems are all completed.
Instruction:
Let’s review weighted averages. You’ve all seen weighted averages in terms of grades for classes. In this
class, your grade is 10% homework, 55% tests/quizzes, and 35% labs/projects. If a fictional student had
a 95 on homework, a 77 on quizzes/tests, and an 84 on projects, what would their grade be?
To figure out the grade, you take the actual score, and multiply it by the weight percentage in decimal
notation:
Homework – 95 x 0.10 = 9.5
Test/Quiz – 77 x 0.55 = 42.35
Lab/Project – 84 x 0.35 = 29.4
Then you just add up the resulting numbers: 9.5 + 42.35 + 29.4 = 81.25
What would the non-weighted average be?
(95+77+84)/3 = 85.333
Practice Problem. A fictional student in chemistry has a homework score of 88, a test/quiz score of 67
and a lab/project score of 92. What’s their final grade (using the weights above)?
HW – 88(0.10) = 8.8
T/Q – 67(0.55) = 36.85
L/P – 92(0.35) = 32.2
8.8+36.85+32.2 = 77.85
The type of atom is defined by what? Protons. So, all hydrogen atoms have 1 proton. But there are
three different types of hydrogen atoms; hydrogen atoms with 1, 2, or 3 neutrons. These are all
isotopes.
Isotopes are atoms that have the same number of protons but different neutrons.
Do Isotopes have the same or different atomic number?
Do Isotopes have the same or different mass number?
The mass of a proton and neutron are essentially the same, and are incredibly small, 1.67 x 10-24 g. The
mass of an electron is 1840 times smaller than a proton or neutron, which is negligible in comparison to
the protons and neutrons.
Since the 1920’s, mass spectrometry has been able to the masses of atoms. The mass of a fluorine atom
was found to be 3.1 x 10-23 g.
In order to be more practical and useful, carbon-12 was chosen as a reference and this isotope of carbon
was defined as having a mass of exactly 12 amu (atomic mass units).
Since the 6 protons and 6 neutrons in the carbon-12 atom account for essentially all of it’s mass, and
since neutrons and protons have essentially the same mass, the mass of one proton or one neutron is
about 1 amu.
Take out your agenda and turn to R-15, look up the atomic mass of carbon. What is the atomic mass of
carbon?
12.011
Since we just defined carbon-12 as having a mass of 12 amu, why do you think that the atomic mass of
carbon is listed as 12.011?
In nature, most elements exist as 2 or more stable isotopes.
Each isotope of an element has a fixed mass and a natural percent abundance.
The atomic mass of an element is the weighted average mass of the atom in a naturally occurring
sample of the element.
Sample problem:
Chlorine has 2 naturally occurring isotopes. Chlorine-35 in 75.77% with a mass of 34.969 amu and
chlorine-37 in 24.23% abundance with a mass of 36.966 amu. What’s the atomic mass (weighted
average) of chlorine?
Chlorine-35 -> 34.969 amu x 0.7577 = 26.4960113 amu
Chlorine-37 -> 36.966 x 0.2423 = 8.9568618 amu
Atomic mass = 26.4960113 amu + 8.9568618 amu = 35.453 amu
Problems for the class:
1) Nitrogen has 2 naturally occurring isotopes:
Isotope
% abundance
Nitrogen-14
99.63
Nitrogen-15
0.37
Nitrogen-14 14.003(0.9963) = 13.9511889
Mass (amu)
14.003
15.000
Nitrogen-15 15.000(0.0037) = 0.0555
What’s the atomic mass (weighted average) of nitrogen? 14.007 amu
2) Oxygen has 3 naturally occurring isotopes:
Isotope
% abundance
Oxygen-16
99.759
Oxygen-17
0.037
Oxygen-18
0.204
Oxygen-16 15.995(0.99759) = 15.95645205
Oxygen-17 16.995(0.00037) = 0.00628815
Oxygen-18 17.999(0.00204) = 0.03671796
Mass (amu)
15.995
16.995
17.999
What’s the atomic mass (weighted average) of oxygen? 15.999 amu
3) Iron has 4 naturally occurring isotopes:
Isotope
Iron-54
Iron-56
Iron-57
Iron-58
% abundance
5.845
91.754
2.119
0.282
Iron-54 53.939(0.05845) = 3.152793
Mass (amu)
53.940
55.935
56.935
57.933
Iron-56 55.935(0.91754) = 51.3225999
Iron-57 56.935(0.02119) = 1.20645265
Iron-58 57.933(0.00282) = 0.16337106
What’s the atomic mass (weighted average) of iron? 55.845 amu