ChemQuest 9
Name: ____________________________
Date: _______________
Hour: _____
Information: Weighted Averages
Examine the table of student test scores for five tests they have taken.
Test
1
2
3
4
5
Average Grade
Student A
95
74
82
92
81
84.8
Student B
76
88
90
81
72
81.4
Critical Thinking Questions
1. Calculate the average grade for students A and B and enter the average in the table above.
See table above.
2. If you know a student’s average grade can you tell what the student’s individual test scores
were? Explain.
No, two students with different test scores could still end up with the same average grade.
3. Suppose student C had an average of 83%. On each of his five tests he scored either 65% or
95%. Which score occurred more often? Explain.
The score of 95% occurred more often because 95% is closer to the average of 83%.
4. What if the teacher decided that test five would count for 40% of the final grade and test four
would count for 30% of the final grade and each of the other tests would count for 10%.
Calculate the new average for each student. Note: this is called the weighted average.
Student A’s new average: ____85.1____
Student B’s new average: ____78.5_______
Student A= (0.40)(81) + (0.30)(92) + (0.10)(82) + (0.10)(74) + (0.10)(95) = 85.1
Student B = (0.40)(72) + (0.30)(81) + (0.10)(90) + (0.10)(88) + (0.10)(76) = 78.5
Note: when finding the weighted average you do not divide at the end.
Information: Average Atomic Mass
On the periodic table you can find the average atomic mass for an element. This average is a
weighted average and it tells you the average mass of all the isotopes of an element. The
periodic table does not contain mass numbers for individual atoms, instead you can find the
average mass of atoms. The average atomic mass is calculated just how you calculated the
weighted average in question 4 above.
Critical Thinking Questions
5. Neon has three different isotopes. 90.51% of neon atoms have a mass of 19.992 amu. 0.27%
of neon atoms have a mass of 20.994 amu. 9.22% of neon atoms have a mass of 21.991 amu.
What is the average atomic mass of neon?
(0.9051)(19.992) + (0.0027)(20.994) + (0.0922)(21.991) = 20.179 amu
6. Chlorine-35 is one isotope of chlorine. (35 is the mass number.) Chlorine-37 is another
isotope of chlorine. How many protons and how many neutrons are in each isotope of
chlorine?
Chlorine has an atomic number of 17, so each isotope has 17 protons. Neutrons are found by
taking the mass number and subtracting the atomic number. Chlorine-35 has 18 neutrons
(35-17) and Chlorine-37 has 20 neutrons (37-17).
7. Of all chlorine atoms, 75.771% are chlorine-35. Chlorine-35 atoms have a mass of 34.96885
amu. All other chlorine atoms are chlorine-37 and these have a mass of 36.96590. Calculate
the average atomic mass of chlorine.
Percent of chlorine atoms that are chlorine-37: 100% - 75.771% = 24.229%
(0.75771)(34.96885) + (0.24229)(36.96590) = 35.4527 amu
8. Do your answers for questions 5 and 7 agree with the average atomic masses for neon and
chlorine on the periodic table?
Yes, both answers should agree with the periodic table.
Skill Practice
9. Complete the following table.
Symbol
# of neutrons
16
# of protons
15
# of electrons
15
Atomic #
15
Mass #
31
15
13
10
13
28
42
38
38
38
80
69
50
50
50
119
Po
126
84
84
84
210
N 3
8
7
10
7
15
31
28
15
13
P
Al 3
80
38
119
50
Sr
210
84
15
7
Sn
10. A certain element has two isotopes. One isotope , which has an abundance of 72.15% has a
mass of 84.9118 amu. The other has a mass of 86.9092 amu. Calculate the average atomic
mass for this element.
% of other isotope = 100% - 72.15% = 27.85%
(0.7215)(84.9118) + (0.2785)(86.9092) = 85.468 amu
11. Given the following data, calculate the average atomic mass of magnesium.
Isotope
Magnesium-24
Magnesium-25
Magnesium-26
Mass of Isotope
23.985
24.986
25.983
(0.7870)(23.985) + (0.1013)(24.986) + (0.1117)(25.983) = 24.309 amu
Abundance
78.70%
10.13%
11.17%
Skill Practice 9
Name: ______________________________
Date: _______________
Hour: _____
1.
A certain element exists as three different isotopes. 24.1% of all the isotopes have a mass of 75.23 amu,
48.7% have a mass of 74.61 amu, and 27.2% have a mass of 75.20 amu.
a. What is the average atomic mass of this element?
74.9 amu
b.
2.
An element exists as 4 different isotopes. 4.35% have a mass of 49.9461 amu, 83.79% have a mass of
51.9405 amu, 9.50% have a mass of 52.9407 amu, and 2.36% have a mass of 53.9389 amu.
a. What is the average atomic mass of this element?
52.0 amu
b.
3.
Use your periodic table to determine which element this is.
Arsenic (As)
What is the identity of this element?
Chromium (Cr)
Calcium has three different isotopes. One has a mass of 35.00 amu; another has a mass of 41.00 amu; and
another has a mass of 40.00 amu. Which isotope is the most abundant of the three? (HINT: Look at the
periodic table at calcium’s average atomic mass.)
The most abundant is the one with a mass of 40.00 amu.
4.
Several isotopes of a certain atom “X” exist. 4.35% of all X atoms have a mass of 49.946 amu. 83.79%
have a mass of 51.941 amu, 9.50% have a mass of 52.941 amu, and 2.36% have a mass of 53.939 amu.
What is the average atomic mass of atom X?
41.7 amu