Introductory Chemistry: An Active Learning Approach

Mark S. Cracolice, Edward I. Peters

Chapter 5

Atomic Theory: The Nuclear Model of the Atom - all with Video Answers

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Chapter Questions

Problem 1

According to Dalton's atomic theory, can more than one compound be made from atoms of the same two elements?

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Problem 2

List the major points in Dalton's atomic theory.

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Problem 3

Show that Dalton's atomic theory explains the Law of Definite Composition.

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Problem 4

How does Dalton's atomic theory account for the Law of Conservation of Mass?

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Problem 5

The chemical name for limestone, a compound of calcium, carbon, and oxygen, is calcium carbonate. When heated, limestone decomposes into solid calcium oxide and gaseous carbon dioxide. From the names of the products, tell where you might find the atoms of each element after the reaction. How does Dalton's atomic theory explain this?

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Problem 6

The brilliance with which magnesium burns makes it ideal for use in flares and flashbulbs. Compare the mass of magnesium that burns with the mass of magnesium in the magnesium oxide ash that forms. Explain this in terms of atomic theory.

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Problem 7

Sulfur and fluorine form at least two compounds $-\mathrm{SF}_{4}$ and $\mathrm{SF}_{6}$. Explain how these compounds can be used as an example of the Law of Multiple Proportions.

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Problem 8

When 10.0 g of chlorine reacts with mercury under varying conditions, the reaction consumes either $28.3 \mathrm{g}$ or $56.6 \mathrm{g}$ of mercury. No other combinations occur. Explain these observations in terms of the Law of Multiple Proportions.

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Problem 9

Compare the three major parts of an atom in charge and mass.

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Problem 10

Which of the following applies to the electron? (a) Charge $=-1 ;$ (b) Mass $\approx 1$ amu; $(c)$ Charge $=0 ;$ (d) Mass $\approx 0$ amu; (e) Charge $=+1$.

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Problem 11

How can we account for the fact that, in the Rutherford scattering experiment, some of the alpha particles were deflected from their paths through the gold foil, and some were even bounced back at various angles?

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Problem 12

How can we account for the fact that most of the alpha particles in the Rutherford scattering experiment passed directly through a solid sheet of gold?

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Problem 13

What do we call the central part of an atom?

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Problem 14

What major conclusions were drawn from the Rutherford scattering experiment?

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Problem 15

Describe the activity of electrons according to the planetary model of the atom that appeared after the Rutherford scattering experiment.

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Problem 16

The Rutherford experiment was performed and its conclusions reached before protons and neutrons were discovered. When they were found, why was it believed that they were in the nucleus of the atom?

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Problem 17

Can two different elements have the same atomic number? Explain.

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Problem 18

Compare the number of protons and electrons in an atom, the number of protons and neutrons, and the number of electrons and neutrons.

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Problem 19

Explain why isotopes of different elements can have the same mass number, but isotopes of the same element cannot.

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Problem 20

neutral atom of the isotope represented by $_{5}^{8} \mathrm{B} ?$

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Problem 21

From the information given in the following tables, fill in as many blanks as you can without looking at any reference. If there are unfilled spaces, continue by referring to your periodic table. As a last resort, check the table of elements on the Reference Page. All atoms are neutral.
(TABLE CANNOT COPY)

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Problem 22

From the information given in the following tables, fill in as many blanks as you can without looking at any reference. If there are unfilled spaces, continue by referring to your periodic table. As a last resort, check the table of elements on the Reference Page. All atoms are neutral.
(TABLE CANNOT COPY)

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Problem 23

What advantage does the atomic mass unit have over grams when speaking of the mass of an atom or a subatomic particle?

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Problem 24

What is an atomic mass unit?

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Problem 25

The mass of an average atom of a certain element is 6.66 times as great as the mass of an atom of carbon- $12 .$ Using either the periodic table or the table of elements, identify the element.

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Problem 26

The average mass of boron atoms is 10.81 amu. How would you explain what this means to a friend who had never taken chemistry?

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Problem 27

The atomic masses of the natural isotopes of neon are 19.99244 amu, 20.99395 amu, and 21.99138 amu. The average of these three masses is 20.99259 amu. The atomic mass of neon is listed as 20.1797 amu on the periodic table. Which isotope do you expect is the most abundant in nature? Explain.

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Problem 28

A certain element consists of two stable isotopes. The first has an atomic mass of 137.9068 amu and a percent natural abundance of $0.09 \% .$ The second has an atomic mass of 138.9061 amu and a percent natural abundance of $99.91 \% .$ What is the atomic mass of the element?

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Problem 29

The mass of $60.4 \%$ of the atoms of an element is 68.9257 amu. There is only one other natural isotope of that element, and its atomic mass is 70.9249 amu. Calculate the average atomic mass of the element. Using the periodic table and/or the table of the elements, write its symbol and name.

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Problem 30

Isotopic data for boron allow the calculation of its atomic mass to the number of significant figures justified by the measurement process. One analysis showed that $19.78 \%$ of boron atoms have an atomic mass of 10.0129 amu and the remainder have an atomic mass of 11.00931 amu. Find the average mass in as many significant figures as those data will allow.

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Problem 31

Percentage abundances and atomic masses (amu) of the natural isotopes of an element are given.
(a) Calculate the atomic mass of each element from these data.
(b) Using other information that is available to you, identify the element.
Percentage Abundance
51.82
48.18
Atomic Mass $(a m u)$
106.9041
108.9047

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Problem 32

Percentage abundances and atomic masses (amu) of the natural isotopes of an element are given.
(a) Calculate the atomic mass of each element from these data.
(b) Using other information that is available to you, identify the element.
(TABLE CANNOT COPY)

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Problem 33

Percentage abundances and atomic masses (amu) of the natural isotopes of an element are given.
(a) Calculate the atomic mass of each element from these data.
(b) Using other information that is available to you, identify the element.
(TABLE CANNOT COPY)

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Problem 34

Percentage abundances and atomic masses (amu) of the natural isotopes of an element are given.
(a) Calculate the atomic mass of each element from these data.
(b) Using other information that is available to you, identify the element.
(TABLE CANNOT COPY)

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Problem 35

Percentage abundances and atomic masses (amu) of the natural isotopes of an element are given.
(a) Calculate the atomic mass of each element from these data.
(b) Using other information that is available to you, identify the element.
(TABLE CANNOT COPY)

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Problem 36

Percentage abundances and atomic masses (amu) of the natural isotopes of an element are given.
(a) Calculate the atomic mass of each element from these data.
(b) Using other information that is available to you, identify the element.
(TABLE CANNOT COPY)

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Problem 37

How many elements are in Period 5 of the periodic table? Write the atomic numbers of the elements in Group $3 \mathrm{B} / 3$.

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Problem 38

Write the symbol of the element in each given group and period. (a) Group $1 \mathrm{A} / 1,$ Period $6 ;$ (b) Group $6 \mathrm{A} / 16,$ Period 3 (c) Group $7 \mathrm{B} / 7,$ Period $4 ;$ (d) Group $1 \mathrm{A} / 1,$ Period 2

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Problem 39

Locate in the periodic table each element whose atomic number is given, and identify first the number of the period it is in and then the number of the group: (a) $20 ;$ (b) $14 ;$ (c) 43.

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Problem 40

List the symbols of the elements of each of the following:
(a) transition metals in the fourth period; (b) metals in the third period; (c) nonmetals in Group $6 \mathrm{A} / 16$ or $7 \mathrm{A} / 17$ with $\mathrm{Z}<40$;
(d) main group metals in the sixth period.

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Problem 41

Using only a periodic table for reference, list the atomic masses of the elements whose atomic numbers are $29,55,$ and $82 .$

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Problem 42

Write the atomic number of the element in each given group and period. (a) Group $4 \mathrm{A} / 14,$ Period 3; (b) Group $4 \mathrm{A} / 14$, Period $2 ;$ (c) Group $1 \mathrm{B} / 11,$ Period $4 ;$ (d) Group $2 \mathrm{A} / 2,$ Period 3.

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Problem 43

Write the atomic masses of helium and aluminum.

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Problem 44

Give the atomic mass of the element in each given group and period. (a) Group $8 \mathrm{A} / 18,$ Period $3 ;$ (b) Group $3 \mathrm{A} / 13,$ Period 4 (c) Group $4 \mathrm{B} / 4,$ Period $4 ;$ (d) Group $2 \mathrm{A} / 2,$ Period 3.

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Problem 45

The names, atomic numbers, or symbols of some of the elements in Figure 5.9 are given in Table $5.4 .$ Fill in the open spaces, referring only to a periodic table for any information that you need.
(TABLE CANNOT COPY)

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Problem 46

The names, atomic numbers, or symbols of some of the elements in Figure 5.9 are given in Table $5.5 .$ Fill in the open spaces, referring only to a periodic table for any information you need.
(TABLE CANNOT COPY)

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Problem 47

Distinguish precisely and in scientific terms the differences among items in each of the following groups.
a) Atom, subatomic particle
b) Electron, proton, neutron
c) Nuclear model of the atom, planetary model of the atom
d) Atomic number, mass number
e) Chemical symbol of an element, nuclear symbol
f) Atom, isotope
g) Atomic mass, atomic mass unit
h) Atomic mass of an element, atomic mass of an isotope
i) Period, group, or family (in the periodic table)
j) Main group element, transition element

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Problem 48

Determine whether each statement that follows is true or false.
a) Dalton proposed that atoms of different elements always combine on a one-to-one basis.
b) According to Dalton, all oxygen atoms have the same diameter.
c) The mass of an electron is about the same as the mass of a proton.
d) There are subatomic particles in addition to the electron, proton, and neutron.
e) The mass of an atom is uniformly distributed throughout the atom.
f) Most of the particles fired into the gold foil in the Rutherford experiment were not deflected.
g) The masses of the proton and electron are equal but opposite in sign.
h) Isotopes of an element have different electrical charges.
i) The atomic number of an element is the number of particles in the nucleus of an atom of that element.
j) An oxygen-16 atom has the same number of protons as an oxygen-17 atom.
k) The nuclei of nitrogen atoms have a different number of pro-
I) Neutral atoms of sulfur have a different number of electrons from neutral atoms of any other element.
m) Isotopes of different elements that exhibit the same mass number exhibit similar chemical behavior.
n) The mass number of a carbon- 12 atom is exactly $12 \mathrm{g}$.
o) Periods are arranged vertically in the periodic table.
p) The atomic mass of the second element in the farthest right column of the periodic table is 10 amu.
q) Nb is the symbol of the element for which $Z=41$.
r) Elements in the same column of the periodic table have similar properties.
s) The element for which $Z=38$ is in both Group $2 A / 2$ and the fifth period.

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Problem 49

The first experiment to suggest that an atom consisted of smaller particles showed that one particle had a negative charge. From that fact, what could be said about the charge of other particles that might be present?

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Problem 50

Sodium oxide and sodium peroxide are two compounds made up of the elements sodium and oxygen. Sixty-two grams of sodium oxide contains $46 \mathrm{g}$ of sodium and $16 \mathrm{g}$ of oxygen; $78 \mathrm{g}$ of sodium peroxide has $46 \mathrm{g}$ of sodium and $32 \mathrm{g}$ of oxygen. Show how these figures confirm the Law of Multiple Proportions.

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Problem 51

Two compounds of mercury and chlorine are mercury(I) chloride and mercury(II) chloride. The amount of mercury(I) chloride that contains $71 \mathrm{g}$ of chlorine has $402 \mathrm{g}$ of mercury; the amount of mercury(II) chloride that has 71 g of chlorine has 201 g of mercury. Show how the Law of Multiple Proportions is illustrated by these quantities.

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Problem 52

The $C R C$ Handbook, a large reference book of chemical and physical data from which many of the values in this book are taken, lists two isotopes of rubidium $(Z=37) .$ The atomic mass of $72.15 \%$ of rubidium atoms is 84.9118 amu. Through a typographical oversight, the atomic mass of the second isotope is not printed. Calculate that atomic mass.

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Problem 53

The element lanthanum has two stable isotopes, lanthanum-138 with an atomic mass of 137.9071 amu and lanthanum-139 with an atomic mass of 138.9063 amu. From the atomic mass of La, 138.9 amu, what conclusion can you make about the relative percent abundance of the isotopes?

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Problem 54

The atomic mass of lithium on a four-significant-figure periodic table is 6.941 amu. Lithium has two natural isotopes with atomic masses of 6.10512 amu and 7.01600 amu. Calculate the percentage distribution between the two isotopes.

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Problem 55

When Thomson identified the electron, he found that the ratio of its charge to its mass (the e/m ratio) was the same regardless of the element from which the electron came. This showed that the electron is a unique particle that is found in atoms of all elements. Positively charged particles found at about the same time did not all have the same e/m ratio. (Later it was found that even different atoms of the same element contain positive particles that have different e/m ratios.) What does that suggest about the mass, particle charge, and minimum number of positive particles from different elements?

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Problem 56

Why were scientists inclined to think of an atom as a miniature solar system in the planetary model of the atom? What are the similarities and differences between electrons in orbit around a nucleus and planets in orbit around the sun?

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Problem 57

Isotopes were unknown until nearly a century after Dalton proposed the atomic theory. When they were discovered, it was through experiments more closely associated with physics than with chemistry. What does this suggest about the chemical properties of isotopes?

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Problem 58

A carbon-12 atom contains six electrons, six protons, and six neutrons. Assuming the mass of the atom is the sum of the masses of those parts, as given in Table $5.1,$ calculate the mass of the atom. Why is it not exactly 12 amu, as the definition of the atomic mass unit would suggest?

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Problem 59

Using the figures in Question $58,$ calculate the percentage each kind of subatomic particle contributes to the mass of a carbon-12 atom. What percentage of the total mass of the atom is in the nucleus?

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Problem 60

The element carbon occurs in two crystal forms, diamond and graphite. The density of the diamond form is $3.51 \mathrm{g} / \mathrm{cm}^{3},$ and of graphite, $2.25 \mathrm{g} / \mathrm{cm}^{3} .$ The volume of a carbon atom is
$1.9 \times 10^{-24} \mathrm{cm}^{3} .$ As stated in Section $5.5,$ one atomic mass unit is $\frac{1}{6.02 \times 10^{23}} \mathrm{g}$.
a) Calculate the average density of a carbon atom.
b) Suggest a reason for the density of the atom being so much larger than the density of either form of carbon.
c) The radius of a carbon atom is roughly $1 \times 10^{5}$ times larger than the radius of the nucleus. What is the volume of that nucleus? (Hint: Volume is proportional to the cube of the radius.)
d) Calculate the average density of the nucleus.
e) The radius of a period on this page is about $0.02 \mathrm{cm} .$ The volume of a sphere that size is $4 \times 10^{-5} \mathrm{cm}^{3} .$ Calculate the mass of that sphere if it were completely filled with carbon nuclei. Express the mass in tons.

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