LESSON 4.3
Key Objectives 4.3.1 EXPLAIN what makes elements and
4.3 Distinguish g Distinguishing Among Atoms
isotopes different from each other. 4.3.2 EXPLAIN how isotopes of an element differ. 4.3.3 CALCULATE the atomic mass of an element.
CHEMISTRY
Additional Resources
YOU Y &YOU
Q: How can there be different varieties of atoms? Some things exist in many different varieties. For example, dogs can differ in many ways, such as color, size, ear shape, and length of hair. Just as there are many types of dogs, atoms come in different varieties, too.
Reading and Study Workbook, Lesson 4.3 Available Online or on Digital Media: • Teaching Resources, Lesson 4.3 Review • Small-Scale Chemistry Manual, Lab 6
Atomic Number and Mass Number What makes one element different from another? Atoms are composed of protons, neutrons, and electrons. Protons and neutrons make up the nucleus. Electrons surround the nucleus. How, then, are atoms of hydrogen, for example, different from atoms of oxygen?
Key Questions What makes one element different from another?
Atomic Number Look at Table 4.2. Notice that a hydrogen atom has Elements are one proton, but an oxygen atom has eight protons. different because they contain different numbers of protons. An element’s atomic number is the number of protons in the nucleus of an atom of that element. Since all hydrogen atoms have one proton, the atomic number of hydrogen is 1. All oxygen atoms have eight protons, so the atomic number of oxygen is 8. The atomic number identifies an element. For each element listed in Table 4.2, the number of protons equals the number of electrons. Remember that atoms are electrically neutral. Thus, the number of electrons (negatively charged particles) must equal the number of protons (positively charged particles).
How do isotopes of an element differ?
Engage
&
CHEMISTRY Y YO YOU U Direct students to look at the photograph of the dogs and to read the corresponding text. Ask What characteristics can you use to classify different dogs? (Sample answers: height, weight, color, hair length, tail, etc.) Point out that each dog in the picture is a different variety, called a breed, but they are all dogs. Tell students to keep this distinction in mind as they work through the lesson.
How do you calculate the atomic mass of an element ?
Vocabulary tBUPNJDOVNCFS tNBTTOVNCFS tJTPUPQF tBUPNJDNBTTVOJU BNV
tBUPNJDNBTT
Table 4.2
Atoms of the First Ten Elements Symbol
Atomic number
Protons
Neutrons*
Mass number
Electrons
)ZESPHFO
H
1
1
0
1
1
)FMJVN
He
2
2
2
4
2
-JUIJVN
-J
4
7
#FSZMMJVN
Be
4
4
5
9
4
#PSPO
B
5
5
6
11
5
$BSCPO
C
6
6
6
12
6
/JUSPHFO
N
7
7
7
14
7
0YZHFO
O
8
8
8
16
8
'MVPSJOF
F
9
9
10
19
9
Ne
10
10
10
20
10
Name
Activate Prior Knowledge Briefly review what students know about subatomic particles and Dalton’s atomic theory. Have a student volunteer go to the board, and draw an atom based on the description given by his or her classmates. Have the volunteer label the different parts of the atom with important characteristics, such as charge.
National Science Education Standards A-1, A-2, B-1, B-2, G-1, G-2
* Number of neutrons in the most abundant isotope. Isotopes are introduced later in Lesson 4.3.
/FPO
112 $IBQUFSt-FTTPO
Focus on ELL 1 CONTENT AND LANGUAGE Direct students’ attention to the second paragraph under the Mass Number heading on the following page. Read the second sentence aloud. Explain that this sentence describes a mathematical relationship. Have students identify the words that relate to mathematical symbols. Then demonstrate how to re-write the sentence using these signs to create a word equation. Point out that this technique can be used whenever they are having difficulty understanding similar sentences. Have students practice identifying and re-writing the other descriptions of mathematical relationships in the paragraph. 2 FRONTLOAD THE LESSON Ask students to preview Table 4.2 and the Periodic Table
of Elements. Show students how the numbers on the Periodic Table of Elements correspond to the values in Table 4.2.
112
Chapter 4 • Lesson 3
3 COMPREHENSIBLE INPUT As you write the chemical, use a black marker to write the element symbol, a red marker to represent the protons, and a blue marker to represent the number of electrons. Continue to use the corresponding color throughout the calculation. Use green to represent the neutrons.
TU
Sample Problem 4.1
TOR
Foundations for Reading
Understanding Atomic Number
BUILD VOCABULARY Have students use the vocabulary for this section to build a concept map that links and relates the vocabulary terms. READING STRATEGY Allot time at the beginning of the lesson to remind students how to read a table. Review each table in this lesson, except for the periodic table. Point out that students should read the title, the headings of each row and column, and take note of units. Relate the cells of each table to a matrix or to a spreadsheet. Students need to be able to read the text, locate the appropriate table and extract the necessary information.
The element nitrogen (N) has an atomic number of 7. How many protons and electrons are in a neutral nitrogen atom?
Analyze Identify the relevant concepts. The atomic number gives the number of protons, which in a neutral atom equals the number of electrons. Solve
Apply the concepts to this problem.
Identify the atomic number. Then use the atomic number to find the number of protons and electrons.
16. How many protons and electrons are in each atom? a. fluorine (atomic numberâ9) b. calcium (atomic numberâ20) c. aluminum (atomic numberâ13) d. potassium (atomic numberâ19)
The atomic number of nitrogen is 7. So, a neutral nitrogen atom has 7 protons and 7 electrons.
17. Complete the table. Element
Atomic number
S
16
V e..
Protons a..
c.. f..
Electrons b..
23 g..
d.. 5
Table 4.2 shows that a fluorine atom has an atomic number of 9 and a mass number of 19. Since the atomic number equals the number of protons, which equals the number of electrons, a fluorine atom has nine protons and nine electrons. The mass number of fluorine is equal to the number of protons plus the number of neutrons. So the fluorine atom has ten neutrons, which is the difference between the mass number and the atomic number (19 Ź 9 â 10). The composition of any atom can be represented in shorthand notation using the atomic number and mass number, as in Figure 4.8. The chemical symbol for gold, Au, appears with two numbers written to its left. The atomic number is the subscript. The mass number is the superscript. You can also refer to atoms by using the mass number and the name of the element. For example, 19779Au may be written as gold-197.
Atomic Number and Mass Number USE VISUALS Have students look at Table 4.2. Point
out that the atomic number is equal to the number of protons for each element. Ask Why must the number of electrons equal the number of protons for each element? (Atoms are electrically neutral.) Ask What is the relationship between the number of protons and the number of neutrons? (The number of neutrons tends to rise with the number of protons.)
Mass Number Most of the mass of an atom is concentrated in its nucleus and depends on the number of protons and neutrons. The total number of protons and neutrons in an atom is called the mass number. For example, a helium atom has two protons and two neutrons, so its mass number is 4. A carbon atom has six protons and six neutrons, so its mass number is 12. If you know the atomic number and mass number of an atom of any element, you can determine the atom’s composition. The number of neutrons in an atom is the difference between the mass number and atomic number.
Number of neutrons ämass number ź atomic number
Explain
Sample Practice Problems A.
197 7 79
B.
Figure 4.8 Chemical Symbol Au is the chemical symbol for gold. Apply Concepts How many electrons does a gold atom have?
Identify the element that has 6 protons and 6 neutrons. (carbon) What is the atomic number of Lithium (Li)? How many electrons and protons does this element have? (atomic number = 3, 3 electrons, 3 protons)
APPLY CONCEPTS Explain that the mass number of an element is defined as the total number of protons and neutrons in the element. Explain that chemists have arbitrarily assigned a value of one atomic mass unit to represent the mass of one twelfth of a carbon-12 atom. Ask How do you find the number of neutrons in an atom? (Subtract the atomic number from the mass number.)
Atomic Structure 113
Differentiated Instruction LPR LESS PROFICIENT READERS Have students make a list of familiar elements and describe at least one real world use for each element. Have students combine their lists into a master list on the chalkboard. L1
STRUGGLING STUDENTS Have students recreate Table 4.2 in their notebooks,
omitting the Neutrons column and the Mass number. Guide students to see the pattern between the atomic number of an element and its corresponding number of protons and electrons. ELL
ENGLISH LANGUAGE LEARNERS Pair students of limited proficiency with more
advanced ELL students. Have student pairs create a poster showing how to interpret the superscript and subscript associated with an element. Display the posters in the classroom for reference.
Answers FIGURE 4.8: 79 electrons 16. a. 9 protons and 9 electrons
b. 20 protons and 20 electrons c. 13 protons and 13 electrons d. 19 protons and 19 electrons 17. a. 16
e. B
b. 16
f. 5
c. 23
g. 5
d. 23 Atomic Structure
113
LESSON 4.3
CHEM
LESSON 4.3
CHEM TU
Explain
TOR
Sample Problem 4.2
Determining the Composition of an Atom
&
CHEMISTRY Y YO YOU U Atoms of different elements have different numbers of protons. Isotopes of an element have the same number of protons, but different numbers of neutrons.
Misconception Alert
How many protons, electrons, and neutrons are in each atom? b. 20 c. 23 10Ne 11Na a. 94Be
Analyze List the knowns and the unknowns. Use the definitions of atomic number and mass number to calculate the numbers of protons, electrons, and neutrons. Calculate
Students are used to seeing subscripts and superscripts in mathematics class. Be sure to emphasize how subscripts and superscripts are used in chemical symbols. When representing elements with shorthand notation, the superscripts and subscripts are located to the left of a chemical element, and the numbers indicate important information about the element.
Solve for the unknowns.
KNOWNS t #FSZMMJVN #F
BUPNJDOVNCFSä4 NBTTOVNCFSä9 t /FPO /F
BUPNJDOVNCFSä10 NBTTOVNCFSä20 t 4PEJVN /B
BUPNJDOVNCFSä11 NBTTOVNCFSä23
UNKNOWNS OVNCFSPG QSPUPOTä
Use the atomic number to find the number of protons.
atomic numberänumber of protons a. 4 b. 10 c. 11
Use the atomic number to find the number of electrons.
atomic numberänumber of electrons a. 4 b. 10 c. 11
Use the mass number and atomic number to find the number of neutrons.
number of neutronsämass numberźatomic number a. number of neutronsä9ź4ä5 b. number of neutronsä20ź10ä10 c. number of neutronsä23ź11ä12
FMFDUSPOTä OFVUSPOTä
Sample Practice Problems A.
How many neutrons are in the each atom?
a.
40 20 Ca
B.
Use Table 4.2 to express the composition of each atom below in shorthand form.
(20)
b.
204 81
a.
oxygen-16 ( 168O)
b.
helium-4 ( 42He)
Te (123)
c.
127 53
I (74)
Evaluate Do the results make sense? For each atom, the mass number equals the number of protons plus the number of neutrons. The results make sense. 18. How many neutrons are in each atom? 80 a. 35Br
32 b. 16S
c.
108 47
Ag
d.
207 82
Pb
19. Use Table 4.2 to express the composition of each atom below in shorthand form. a. carbon-12 b. boron-11
c. nitrogen-14 ( 147N )
Explore CHEMISTRY
Student Activity PURPOSE To learn about practical applications of isotopes MATERIALS Library or Internet access PROCEDURE Have students use the library or Internet to find an isotope of an element that has a practical or everyday use. EXPECTED OUTCOME Students’ research will most likely focus on applications of radioisotopes such as carbon-14 (used in archaeological dating), americium-241 (used in smoke alarms), iodine-131 (used in the treatment of thyroid disorders), and cobalt-60 (used in the treatment of some cancers). Point out that the instability of these isotopes is what makes them useful. Radioisotopes and radioactivity are discussed in Chapter 25.
&YYOU
Q: How are atoms of one element different from the atoms of another element? How are isotopes of the same element different?
c. beryllium-9 d. oxygen-16
Isotopes How do isotopes of an element differ? Figure 4.9 shows that there are three different kinds of neon atoms. How do these atoms differ? All have the same number of protons (10) and electrons (10), but they each have different numbers of neutrons. Isotopes are atoms that have the same number of protons but different numbers of Because isotopes of an element have different numbers of neutrons. neutrons, they also have different mass numbers. Despite these differences, isotopes are chemically alike because they have identical numbers of protons and electrons, which are the subatomic particles responsible for chemical behavior. Remember the dogs at the beginning of the lesson. Their color or size doesn’t change the fact that they are all dogs. Similarly, the number of neutrons in isotopes of an element doesn’t change which element it is because the atomic number doesn’t change.
114 $IBQUFSt-FTTPO
Check for Understanding The Essential Question How are atoms of one element different from atoms of another element? Have students create an acrostic poem using either atomic number or mass number that answers this Essential Question. Poems should demonstrate that students understand that the number of protons is a key determinant of difference between elements, but should also make note of differences in numbers of electrons and neutrons, and the fact that most of the atom’s mass is concentrated in its nucleus. ADJUST INSTRUCTION If students are having problems answering the Essential Question, have them review and analyze the differences between the atoms in the elements listed in Table 4.2.
114
Chapter 4 • Lesson 3
10p+ 12n0
10p+ 11n0
Figure 4.9 Isotopes Neon-20, neon-21, and neon22 are three isotopes of neon.
Compare and Contrast _
_
_
10e
10e
10e
Neon -20 10 protons 10 neutrons 10 electrons
Neon -21 10 protons 11 neutrons 10 electrons
Neon -22 10 protons 12 neutrons 10 electrons
How are these isotopes different? How are they similar?
Isotopes START A CONVERSATION Explain that isotopes of an atom all have the same number of protons and electrons. Ask What do you know about subatomic particles that explains why different isotopes of an atom exhibit almost identical chemical behavior? (Sample answer: The electrons, not the neutrons, determine the atom’s chemical properties.)
There are three known isotopes of hydrogen. Each isotope of hydrogen has one proton in its nucleus. The most common hydrogen isotope has no neutrons. It has a mass number of 1 and is called hydrogen-1 ( 11H) or hydrogen. The second isotope has one neutron and a mass number of 2. It is called either hydrogen-2 ( 21H) or deuterium. The third isotope has two neutrons and a mass number of 3. This isotope is called hydrogen-3 ( 31H) or tritium.
Misconception Alert Many students associate the term isotope with radioactivity. Reinforce the point that an isotope is simply one form of an element. Explain that isotopes can be stable or unstable, and that only unstable isotopes are radioactive. Tell students that they will explore radioactivity and nuclear chemistry in more detail in Chapter 25.
Sample Problem 4.3 Writing Chemical Symbols for Isotopes Diamonds are a naturally occurring form of elemental carbon. Two stable isotopes of carbon are carbon-12 and carbon-13. Write the symbol for each isotope using superscripts and subscripts to represent the mass number and the atomic number.
Sample Practice Problems A.
Analyze Identify the relevant concepts. Isotopes are atoms that have the same number of protons but different numbers of neutrons. The composition of an atom can be expressed by writing the chemical symbol, with the atomic number as a subscript and the mass number as a superscript. Solve
Explain
Apply the concepts to this problem.
B.
Use Table 4.2 to identify the symbol and the atomic number for carbon.
The symbol for carbon is C. The atomic number of carbon is 6.
Look at the name of the isotope to find the mass number.
For carbon-12, the mass number is 12. For carbon-13, the mass number is 13.
Use the symbol, atomic number, and mass number to write the symbol of the isotope.
For carbon-12, the symbol is 126C. For carbon-13, the symbol is 136C.
20. Three isotopes of oxygen are oxygen-16, oxygen-17, and oxygen-18. Write the symbol for each, including the atomic number and mass number.
The element cesium has numerous isotopes, including these four: cesium-126, cesium-129, cesium-131, and cesium-132. Given that cesium has an atomic number of 55, how many neutrons are in each of these isotopes? (71,74, 76, 77) How does the number of neutrons in carbon-14 differ from the number of neutrons in carbon-12 and carbon-13? (Carbon-14 has one more neutron than carbon-13, and two more neutrons than carbon-12.)
21. Three chromium isotopes are chromium-50, chromium-52, and chromium-53. How many neutrons are in each isotope, given that chromium has an atomic number of 24? Atomic Structure 115
Nuclear Chemistry Answers Isotopes and nuclides are both similar in the fact that they have negligible effects on the chemical properties of the element. Chemical reactivity depends on the electron structure of an atom, not its nuclear makeup. In nuclear technology, however, the emphasis is on the neutron number because of its drastic effect on the nuclear properties of the element. Because neutrons help bind protons together in the nucleus, the ratio of protons to neutrons is a major factor in determining stability. It is not uncommon for a nuclide to be unstable. Isotopes with unstable nuclides are referred to as radioisotopes. In order for these radioisotopes to gain stability, they do not gain or lose electrons, they undergo changes in the nucleus that involve large amounts of energy. This is the stepping stone into nuclear chemistry.
FIGURE 4.9 They have different numbers of neutrons
but the same number of protons: hydrogen-1, hydrogen-2, hydrogen-3 18. a. 8 b. 16 c. 61 d. 125 9 19 80 12 19. a. 6 C b. 6 F c. 6 Be d. 35 Br 20. 16O 17O 18O 8
,
8
,
8
21. Chromium-50 has 26 neutrons; chromium-52
has 28 neutrons; chromium-53 has 29 neutrons. Atomic Structure
115
LESSON 4.3
10p+ 10n0
LESSON 4.3
Atomic Mass How do you calculate the atomic mass of an element ?
Explain
A glance back at Table 4.1 on page 107 shows that the actual mass of a proton or a neutron is very small (1.67ñ10Ź24 g). The mass of an electron is 9.11ñ10Ź28 g, which is negligible in comparison. Given these values, the mass of even the largest atom is incredibly small. Since the 1920s, it has been possible to determine these tiny masses by using a mass spectrometer. With this instrument, the mass of a fluorine atom was found to be 3.155ñ10Ź23 g, and the mass of an arsenic atom was found to be 1.244ñ10Ź22 g. Such data about the actual masses of individual atoms can provide useful information, but in general, these values are inconveniently small and impractical to work with. Instead, it is more useful to compare the relative masses of atoms using a reference isotope as a standard. The reference isotope chosen is carbon-12. This isotope of carbon has been assigned a mass of exactly 12 atomic mass units. An atomic mass unit (amu) is defined as one twelfth of the mass of a carbon-12 atom. Using these units, a helium-4 atom has one third the mass of a carbon-12 atom. On the other hand, a nickel-60 atom has five times the mass of a carbon-12 atom.
Atomic Mass USE VISUALS Direct students to Table 4.3. Point out that the average atomic masses listed in Table 4.3 are based on the masses of stable isotopes and their percent abundance in Earth’s crust. Have students study the average atomic masses in the table. Ask Which elements exist predominantly as one natural isotope? (those with atomic masses closest to a whole number) Ask Which element has substantial amounts of each of its natural isotopes? (chlorine) MAKE A CONNECTION Students may ask why the masses (in amu) of most of the isotopes in Table 4.3 are not whole-number values like the mass numbers that are used to seeing. Explain that although the mass number of carbon-12 exactly equals its mass in amu, this is generally not the case for other isotopes due to the mass defect. Point out that the mass defect is the difference between the mass of a nucleus and the sum of the masses of its component protons and neutrons. Mass defect also varies with different elements. As a result the masses of isotopes other than carbon-12 in amu (a unit based on the mass of a carbon-12 atom) will generally not be whole numbers. For example, the mass of hydrogen-2 is 2.0141 amu; the mass of oxygen-16 is 15.995 amu. (NOTE: Assessment problem 79 asks students to calculate the mass defect of an atom in grams by comparing the actual mass of the atom to the sum of the masses of the atom’s component protons, neutrons, and electrons.)
Interpret Data Natural Percent Abundance of Stable Isotopes of Some Elements Name
Natural percent abundance
Symbol
99.985 0.015 OFHMJHJCMF
1 1
)ZESPHFO
)FMJVN $BSCPO
H H 1H 2 1
He He
2 4 2
12
C C
14 7
Mass (amu)
1.0078 2.0141
0.0001 99.9999
98.89 1.11
Atomic mass
1.0079
12.000
12.011
15.000
14.007
15.999
N N
0YZHFO
O O 18 8O
99.759 0.204
15.995 17.999
4VMGVS
S S S S
95.002 4.22 0.014
75.77
/JUSPHFO
15 7 8
17 8
$IMPSJOF
17
$M $M
17
Table 4.3 The atomic mass of an element is calculated using the percent abundance and mass of its isotopes. a. Identify Which isotope of oxygen is the most abundant? b. Describe How could you use the atomic mass of helium to determine which isotope of helium is most abundant?
Hint: The natural percent abundance of hydrogen-3 is “negligible” because the amount of naturally occurring hydrogen-3 is so small that it doesn’t affect the atomic mass of hydrogen.
116 $IBQUFSt-FTTPO
Check for Understanding How do you calculate the atomic mass of an element? To assess students’ understanding of atomic mass, ask students to write a few sentences, create an example, or write a step-by-step explanation of how to determine the atomic mass of an element. Students’ products should indicate an understanding of how the natural abundance of each isotope affects the atomic weight of an element.
116
ADJUST INSTRUCTION To reinforce this concept, perform a probability experiment in your class. Survey 10 students in your class. Ask them to select one sandwich from tuna, turkey, or jelly, one fruit from apple or pear, and one drink from milk or water. Tally the results and create a weighted probability tree diagram. Point out how each selection of the tree is weighted. Show students how this is similar to understanding weighted average mass.
Chapter 4 • Lesson 3
17p 18n0
35 17
Cl +
17p 18n0
35 17
Cl
37 17
Cl
+
17p 18n0
Total number of protons in three 35 17Cl atoms and one 37 17Cl atom (17 + 17 +17 + 17)
Cl
USE VISUALS Direct students to Figure 4.10. Explain that atomic mass is the weighted average mass of the atoms in a naturally occurring sample of the element. Relate students’ knowledge of calculating the mean of a data set or calculating weighted probability to help them understand how this concept is related to chemistry.
+
17p 20n0
Total number of neutrons in three 35 17Cl atoms and one 37 17Cl atom (18 + 18 +18 + 20) 68 + 74 = 35.5 amu 4
Weighted Average Mass of a Chlorine Atom
A carbon-12 atom has six protons and six neutrons in its nucleus, and its mass is set as 12 amu. The six protons and six neutrons account for nearly all of this mass. Therefore, the mass of a single proton or a single neutron is about one twelfth of 12 amu, or about 1 amu. Because the mass of any single atom depends mainly on the number of protons and neutrons in the nucleus of the atom, you might predict that the atomic mass of an element should be a whole number. However, that is not usually the case. In nature, most elements occur as a mixture of two or more isotopes. Each isotope of an element has a fixed mass and a natural percent abundance. Consider the three isotopes of hydrogen discussed earlier in this section. According to Table 4.3, almost all naturally occurring hydrogen (99.985 percent) is hydrogen-1. The other two isotopes are present in trace amounts. Notice that the atomic mass of hydrogen listed in Table 4.3 (1.0079 amu) is very close to the mass of hydrogen-1 (1.0078 amu). The slight difference takes into account the larger masses, but much smaller amounts, of the other two isotopes of hydrogen. Now consider the two stable isotopes of chlorine listed in Table 4.3: chlorine-35 and chlorine-37. If you calculate the arithmetic mean of these two masses ((34.969 amu à 36.966 amu)/2), you get an average atomic mass of 35.968 amu. However, this value is higher than the actual value of 35.453. To explain this difference, you need to know the natural percent abundance of the isotopes of chlorine. Chlorine-35 accounts for 75 percent of the naturally occurring chlorine atoms; chlorine-37 accounts for only 25 percent. See Figure 4.10. The atomic mass of an element is a weighted average mass of the atoms in a naturally occurring sample of the element. A weighted average mass reflects both the mass and the relative abundance of the isotopes as they occur in nature.
Figure 4.10 Isotopes of Chlorine Chlorine is a reactive element used to disinfect swimming pools. Chlorine occurs as two isotopes: chlorine-35 and chlorine-37. Because there is more chlorine-35 than chlorine-37 in nature, the atomic mass of chlorine, 35.453 amu, is closer to 35 than to 37. Evaluate How does a weighted average differ from an arithmetic mean?
Atomic Structure 117
Carbon-14 Dating All living organisms contain carbon-12 and carbon-14 in a fixed ratio. After an organism dies, this ratio changes as the carbon-14 decays. Paleontologists and archaeologists use this fact to establish the age of fossils and ancient artifacts.
Answers TABLE 4.3
a. b.
oxygen-16 Helium has two isotopes, helium-3 and helium-4. The atomic mass of helium is very close to 4 amu, therefore helium-4 must be most abundant.
FIGURE 4.10 In an arithmetic mean, all the numbers
in the calculation are weighted equally. A weighted average takes into account the varying weights of the numbers in the data set. Atomic Structure
117
LESSON 4.3
35 17
+
LESSON 4.3
Sample Problem 4.4
Explain MAKE A CONNECTION Explain to the class that
some teachers evaluate a student’s performance based on the weighted average for different work. For example, homework and quizzes might be worth 20%, a term paper might be worth 30%, and an exam might be worth 50%. Have students calculate a grade for a student who receives an 84 on homework and quizzes, a 79 on the term paper, and an 86 on the exam. (The student would receive a final grade of 83.5 for the grading period.) Then, explain your own weighting strategy for grading, and have students identify which items have the most influence over the grade that appears on their grade reports.
Sample Practice Problem Argon has three isotopes with mass numbers 36, 38, and 40, respectively. Which of these isotopes is the most abundant? (argon-40)
Understanding Relative Abundance of Isotopes The atomic mass of copper is 63.546 amu. Which of copper’s two isotopes is more abundant: copper-63 or copper-65?
Analyze Identify the relevant concepts. The atomic mass of an element is the weighted average mass of the atoms in a naturally occurring sample of the element. Solve
Apply the concepts to this problem.
Compare the atomic mass to the mass of each isotope.
The atomic mass of 63.546 amu is closer to 63 than it is to 65.
Determine the most abundant isotope based on which isotope’s mass is closest to the atomic mass.
Because the atomic mass is a weighted average of the isotopes, copper-63 must be more abundant than copper-65.
22. Boron has two isotopes: boron-10 and boron-11. Which is more abundant, given that the atomic mass of boron is 10.81 amu?
23. There are three isotopes of silicon; they have mass numbers of 28, 29, and 30. The atomic mass of silicon is 28.086 amu. Comment on the relative abundance of these three isotopes.
Now that you know that the atomic mass of an element is a weighted average of the masses of its isotopes, you can determine atomic mass based on relative abundance. To do this, you must know three things: the number of stable isotopes of the element, the mass of each isotope, and the natural To calculate the atomic mass of percent abundance of each isotope. an element, multiply the mass of each isotope by its natural abundance, expressed as a decimal, and then add the products. The resulting sum is the weighted average mass of the atoms of the element as they occur in nature. You can calculate the atomic masses listed in Table 4.3 based on the given masses and natural abundances of the isotopes for each element. For example, carbon has two stable isotopes: carbon-12, which has a natural abundance of 98.89 percent, and carbon-13, which has a natural abundance of 1.11 percent. The mass of carbon-12 is 12.000 amu; the mass of carbon-13 is 13.003 amu. The atomic mass of carbon is calculated as follows: Atomic mass of carbon â (12.000 amu ñ 0.9889) à (13.003 amu ñ 0.0111) â (11.867 amu) à (0.144 amu) â12.011 amu 118 $IBQUFSt-FTTPO
Foundations for Math PERCENTAGES Tell students they will need to have a basic understanding of percents in order to calculate atomic mass. Atomic mass is a weighted average that takes into account natural percent abundance.
In Sample Problem 4.5, show students that the values given for natural abundance total 100%. In order to use these values to correctly calculate the atomic mass, remind students how to convert a percent to a decimal. Tell students to check the reasonableness of their answer by comparing it to the mass of the isotopes. The atomic mass of the element should be close to the mass of the isotope with the greatest percent of abundance.
118
Chapter 4 • Lesson 3
5PmOEBMMUIFLOPXOT DIBOHFUIFQFSDFOU BCVOEBODFUPEFDJNBMT"QFSDFOUJTB TIPSUIBOEXBZPGFYQSFTTJOHBGSBDUJPO XIPTFEFOPNJOBUPSJTJT FRVJWBMFOUUPPS
Calculating Atomic Mass Element X has two naturally occurring isotopes. The isotope with a mass of 10.012 amu (10X) has a relative abundance of 19.91 percent. The isotope with a mass of 11.009 amu (11X) has a relative abundance of 80.09 percent. Calculate the atomic mass of element X.
Analyze List the knowns and the unknown. The mass each isotope contributes to the element’s atomic mass can be calculated by multiplying the isotope’s mass by its relative abundance. The atomic mass of the element is the sum of these products. Calculate
KNOWNS t JTPUPQF100X: NBTTäBNV SFMBUJWFBCVOEBODFää t JTPUPQF11X: NBTTäBNV SFMBUJWFBCVOEBODFää UNKNOWN
Add the atomic mass contributions for all the isotopes.
for 10X: for 11X:
10.012 amu ò 0.1991 ä 1.993 amu 11.009 amu ò 0.8009 ä 8.817 amu
For element X, atomic mass ä 1.993 amu á 8.817 amu ä 10.810 amu
PR
S
E
O
24. The element copper has naturally occurring isotopes with mass numbers of 63 and 65. The relative abundance and atomic masses are 69.2% for massâ62.93 amu, and 30.8% for massâ64.93 amu. Calculate the average atomic mass of copper.
M
OBLE
25. Calculate the atomic mass of bromine. The two isotopes of bromine have atomic masses and relative abundance of 78.92 amu (50.69%) and 80.92 amu (49.31%).
4.3 LessonCheck
26.
Explain What distinguishes the atoms of one element from the atoms of another?
31. Use Models What does the number represent in the isotope platinum-194?
27.
Compare and Contrast How do the isotopes of a given element differ from one another?
32. Explain The atomic masses of elements are generally not whole numbers. Explain why.
28.
Explain How is atomic mass calculated?
29. Identify What equation tells you how to calculate the number of neutrons in an atom? 30. Compare How is atomic number different from mass number?
Evaluate Informal Assessment
Evaluate Does the result make sense? The calculated value is closer to the mass of the more abundant isotope, as would be expected.
NLIN
The element antimony (Sb) has naturally occurring isotopes with mass numbers of 121 and 123. The relative abundance and atomic masses are 57.21% for mass ⫽ 120.90 amu, and 42.79% for mass ⫽ 122.90 amu. Calculate the atomic mass of antimony. (121.76 amu)
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Solve for the unknown.
Use the atomic mass and the decimal form of the percent abundance to the find the mass contributed by each isotope.
Sample Practice Problem
Write the symbols for isotopes of an element not described in the chapter. Ask How does changing the value of the subscript change the chemical properties of the atom? (The subscript designates the number of protons in the atoms of that isotope. Changing the number of protons would change the chemical identity of the isotope to that of another element.) Then have students complete the 4.3 Lesson Check.
Reteach Review the concept of weighted averages. Work through the following calculations. If 75% of chlorine atoms are 35Cl species and 25% are 37Cl species, this implies that for a sample of 100 atoms, 75 atoms are 35Cl and 25 atoms are 37Cl species. The combined masses of these atoms would be (75 ⫻ 35 amu) ⫹ (25 ⫻ 37 amu) ⫽ 3550 amu for 100 atoms, or 35.5 amu for one atom.
33. Identify Which of argon’s three isotopes is most abundant: argon-36, argon-38, or argon-40? (Hint: the atomic mass of argon is 39.948 amu.) 34. Calculate List the number of protons, neutrons, and electrons in each pair of isotopes. 44 78 b. 42 c. 34 Se, 8034Se a. 63Li, 73Li 20Ca, 10Ca Atomic Structure 119
Lesson Check Answers 26. Atoms of different elements contain different numbers of protons. 27. mass number ⫺ atomic number ⫽ number of neutrons 28. They have different mass numbers and different numbers of neutrons. 29. For each isotope, multiply its atomic mass by its percent abundance, then add the products. 30. It allows you to compare the properties of the elements.
194
31. Mass number, 78Pt 32. The atomic mass is the weighted average of the masses of its isotopes. 33. a. lithium-6: 3 p⫹, 3 e⫺, 3 n0 ; lithium-7: 3 p⫹, 3 e–, 4 n0 b. calcium-42: 20 p⫹, 20 e⫺, 22 n0; calcium-44: 20 p⫹, 20 e⫺, 24 n0 c. selenium-78: 34 p⫹, 34 e⫺, 44 n0; selenium-80: 34 p⫹, 34 e⫺, 46 n0 34. any two: beryllium (Be), magnesium (Mg), strontium (Sr), barium (Ba), radium (Ra)
Answers 22. boron-11 23. Silicon-28 must be by far the most abundant.
The other two isotopes must be present in very small amounts. 24. 63.6 amu 25. 79.91 amu
Atomic Structure
119
LESSON 4.3
Sample Problem 4.5
SMALL-SCALE LAB
Small-Scale Lab
Explore PURPOSE Students make measurements to calculate
the relative abundances of three types of candy in a mixture and use their data to calculate the atomic mass of a candium particle. MATERIALS mass balance, coated candies (3 different brands), small plastic cups or containers ADVANCE PREP Prepare in advance a large mixture of the three candies and half fill a clean 3.5-ounce plastic cup for each student. Each sample will contain about 50 total pieces. SAFETY Discourage students from eating the candies after the experiment. Contamination can easily occur in a lab even if you have taken every precaution to keep the candy free of contamination. TEACHING TIPS This lab is similar to the longer SmallScale Lab “Isotopes and Atomic Mass” found in the Small-Scale Chemistry Laboratory Manual. EXPECTED OUTCOME Sample data are listed below. Total Mass: 13.16 g; 13.83 g; 15.40 g; 42.39 g (total).
The Atomic Mass of “Candium” Purpose To analyze the isotopes of “candium” and to calculate its atomic mass
Materials r sample of candium
Procedure Obtain a sample of “candium” that contains three different brands of round, coated candy. Treat each brand of candy as an isotope of candium. Separate the three isotopes into groups labeled A, B, and C, and measure the mass of each isotope. Count the number of atoms in each sample. Make a table similar to the one below to record your measured and calculated data. A
Percent abundance
ANALYZE
1–5. See Expected Outcome. 6. Percent abundance is parts per hundred. Relative abundance is parts per one, or the decimal form of percent. The individual percent abundances add up to 100. The individual relative abundances add up to 1. 7. Relative abundance tells you the decimal fraction of particles. 8. The total in row 3 is an average that ignores the relative abundances of particles. The total in row 6 is a weighted average that best represents atomic mass because it considers differences in mass and abundance among the particles. 9. Another student might not have had the same relative abundance of each candy. YOU’RE THE CHEMIST
1.
2.
Any differences are probably due to small variations in the numbers of each kind of candy in the samples, which affects the relative abundances. The larger the samples, the better the results with any of the methods. Mass is likely to provide better results than volume.
120
Chapter 4 • Small-Scale Lab
Totals
Average mass (grams)
Average mass (grams): 0.8773 g; 1.064 g; 0.7700 g; 0.8831 g (total).
Relative mass: 0.2742 g; 0.2883 g; 0.3208 g; 0.8833 g (total).
C
Number
Relative abundance
Percent abundance: 31.25%; 27.08%; 41.67%; 100% (total).
B
Total mass (grams)
Number: 15; 13; 20; 48 (total).
Relative abundance: 0.3125; 0.2708; 0.4167; 1.000 (total).
r balance
Relative mass
Analyze l Using the experimental data, record the answers to the following questions below your data table. 1. Calculate Calculate the average mass of each isotope by dividing its total mass by the number of particles of that isotope. 2. Calculate Calculate the relative abundance of each isotope by dividing its number of particles by the total number of particles. 3. Calculate Calculate the percent abundance of each isotope by multiplying the relative abundance from Step 2 by 100.
4. Calculate Calculate the relative mass of each isotope by multiplying its relative abundance from Step 2 by its average mass. 5. Calculate Calculate the weighted average mass of all candium particles by adding the relative masses. This weighted average mass is the atomic mass of candium. 6. Explain What is the difference between percent abundance and relative abundance? What is the result when you total the individual relative abundances? The individual percent abundances? 7. Identify The percent abundance of each kind of candy tells you how many of each kind of candy there are in every 100 particles. What does relative abundance tell you? 8. Analyze Data Compare the total values for rows 3 and 6 in the table. Explain why the totals differ and why the value in row 6 best represents atomic mass. 9. Analyze Data Explain any differences between the atomic mass of your candium sample and that of your neighbor. Explain why the difference would be smaller if larger samples were used.
You’re the Chemist The following small-scale activity allows you to develop your own procedures and analyze the results. 1. Analyze Data Determine the atomic mass of a second sample of candium. How does it compare with the first? Suggest reasons for any differences between the samples.
120 $IBQUFSt4NBMM4DBMF-BC
Focus on ELL 4 LANGUAGE PRODUCTION Have students work in groups of three to complete the lab. Make sure each group has ELLs of varied language proficiencies, so that more proficient students can help less proficient ones. Have students work according to their proficiency level. BEGINNING: LOW/HIGH Paraphrase the procedural steps and group students with higher language proficiency partners. INTERMEDIATE: LOW/HIGH Have students brainstorm what they think they may
observe, prior to performing each step. Allow students to orally present their results. ADVANCED: LOW/HIGH Have students write a bulleted list stating the procedure, their
findings, and their conclusions.
