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University of British Columbia

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## Recommended Questions

Prior to 1961, the atomic mass unit was defined as 1/16 the mass of the atomic mass of oxygen; that is, the atomic mass of oxygen was defined as exactly 16 amu. What was the mass of a $^{12} \mathrm{C}$ atom prior to 1961 if the atomic mass of oxygen on today's scale is 15.9994 amu?

The mole is defined as the amount of a substance containing the same number of particles as exactly 12 $\mathrm{g}$ of $\mathrm{C}-12 .$ The amu is defined as 1$/ 12$ of the mass of an atom of $\mathrm{C}-12 .$ Why is it important that both of these definitions reference the same isotope? What would be the result, for example, of defining the mole with respect to $C-12,$ but the amu with respect to Ne- 20$?$

The mole is defined as the amount of a substance containing the same number of particles as exactly 12 g of C-12. The amu is defined as 1>12 of the mass of an atom of C-12. Why is it important that both of these definitions reference the same isotope? What would be the result, for example, of defining the mole with respect to C-12, but the amu with respect to Ne-20?

What was the mass in atomic mass units of a $^{40} \mathrm{Ca}$ atom prior to 1961 if its mass on today’s scale is 39.9626 amu? (See Problem 2.122).

A Although carbon-12 is now used as the standard for atomic masses, this has not always been the case. Farly attempts at classification used hydrogen as the standard, with the mass of hydrogen being set equal to 1.0000 u. Later attempts defined atomic masses using oxygen (with a mass of $16.0000 \mathrm{u}$ ). In each instance, the atomic masses of the other elements were defined relative to these masses. (To answer this question, you need more precise data on current atomic masses: $\mathrm{H}, 1.00794 \mathrm{u} ; \mathrm{O}$ $15.9994 \mathrm{u} .)$

(a) If $\mathrm{H}=1.0000 \mathrm{u}$ was used as a standard for atomic masses, what would the atomic mass of oxygen be? What would be the value of Avogadro's number under these circumstances?

(b) Assuming the standard is $\mathrm{O}=16.0000 \mathrm{u}$, determine the value for the atomic mass of hydrogen and the value of Avogadro's number.

Although carbon-12 is now used as the standard for atomic weights, this has not always been the case. Early attempts at classification used hydrogen as the standard, with the weight of hydrogen being set equal to 1.0000. Later attempts defined atomic weights using oxygen (with a weight of 16.0000 ). In each instance, the atomic weights of the other elements were defined relative to these masses. (To answer this question, you need more precise data on current atomic weights: $\mathrm{H}, 1.00794 ;$ O, $15.9994 .$)

(a) If $\mathrm{H}=1.0000 \mathrm{u}$ was used as a standard for atomic weights, what would the atomic weight of oxygen be? What would be the value of Avogadro's number under these circumstances?

(b) Assuming the standard is $\mathrm{O}=16.0000$, determine the value for the atomic weight of hydrogen and the value of Avogadro's number.

The mole is defined in terms of the carbon-12 atom. Use the definition to find (a) the mass in grams equal to 1 atomic mass unit; (b) the ratio of the gram to the atomic mass unit.

Use the definition of Avogadro's number to find the mass of a helium atom.

Determine the number of moles of oxygen atoms in each sample.

a. 4.88 mol H2O2

b. 2.15 mol N2O

c. 0.0237 mol H2CO3

d. 24.1 mol CO2

Avogadro's number has sometimes been described as a conversion factor between amu and grams. Use the fluorine atom $(19.00 \mathrm{amu})$ as an example to show the relationship between the atomic mass unit and the gram.

Use the definition that 1 mol of $^{12} \mathrm{C}$ (carbon-12) atoms has a mass of exactly $12 \mathrm{g}$, along with Avogadro's number, to derive the conversion between atomic mass units and kg.

Before $1961,$ the standard for atomic masses was the isotope $^{16} \mathrm{O},$ to which physicists assigned a value of exactly $16 .$ At the same time, chemists assigned a value of exactly 16 to the naturally occurring mixture of the isotopes $^{16} \mathrm{O},^{17} \mathrm{O},$ and $^{18} \mathrm{O}$. Would you expect atomic masses listed in a 60 -year-old text to be the same, generally higher, or generally lower than in this text? Explain.

Use Avogadro’s number to find the mass of a helium atom.

Avogadro' constant is used to calculate the number of particles in a mole. A mole is a basic unit in chemistry to measure the amount of a substance. The constant is $6.0221413 \times 10^{23}$ . Write Avogadro's constant in standard notation.

An element consists of $1.40 \%$ of an isotope with mass $203.973 \mathrm{amu}, 24.10 \%$ of an isotope with mass 205.9745 amu, $22.10 \%$ of an isotope with mass 206.9759 amu, and $52.40 \%$ of an isotope with mass 207.9766 amu. Calculate the average atomic mass and identify the element.

Chemistry In chemistry, a mole is a unit of measure equal to $6.02 \times 10^{23}$ atoms of a substance. The mass of a single neon atom is about $3.35 \times 10^{-23} \mathrm{g}$. What is the mass of 2 moles of neon atoms? Write your answer in scientific notation.

What particular isotope is the basis for

defining the atomic mass unit and the mole?

Using average atomic masses for each of the following elements (see the table in the inside front cover of this book), calculate the number of atoms present in each of the following samples.

a. 10.81 amu of boron

b. 320.7 amu of sulfur

c. $19,697$ amu of gold

d. $19,695$ amu of xenon

e. 3588.3 amu of aluminum

The conversion between atomic mass units and kilograms is

$$1 \mathrm{u}=1.66 \times 10^{-27} \mathrm{kg}$$

A sample containing carbon (atomic mass 12 u), oxygen $(16 \mathrm{u}),$ and an unknown element is placed in a mass spectrometer. The ions all have the same charge and are accelerated through the same potential difference before entering the magnetic field. The carbon and oxygen lines are separated by $2.250 \mathrm{cm}$ on the photographic plate, and the unknown element makes a line between them that is $1.160 \mathrm{cm}$ from the carbon line. (a) What is the mass of the unknown clement? (b) Identify the element.

Explain how molar mass relates the mass of an atom to the mass of a mole of

atoms.

The molar mass of $\mathrm{HCl}$ is 36.5 $\mathrm{g} / \mathrm{mol}$ , and the average mass per $\mathrm{HCl}$ molecule is 36.5 $\mathrm{amu}$ . Use the fact that $1 \mathrm{amu}=1.6605 \times 10^{-24} \mathrm{g}$ to calculate Avogadro's number.

(a) What is the mass in amu of a carbon-12 atom? (b) Why is the atomic weight of carbon reported as 12.011 in the table of elements and the periodic table in the front inside cover of this text?

Using average atomic masses for each of the following elements (see the table in the inside

front cover of this book), calculate the mass, in amu, of each of the following samples.

a. 635 atoms of hydrogen

b. $1.261 \times 10^{4}$ atoms of tungsten

c. 42 atoms of potassium

d. $7.213 \times 10^{23}$ atoms of nitrogen

e. 891 atoms of iron

A certain element has a mass per mole of 196.967 g/mol. What is the mass of a single atom in (a) atomic mass units and (b) kilograms? (c) How many moles of atoms are in a 285 -g sample?

In $1860,$ Stanislao Cannizzaro showed how Avogadro's hypothesis could be used to establish the atomic masses of elements in gaseous compounds. Cannizzaro took the atomic mass of hydrogen to be exactly one and assumed that hydrogen exists as $\mathrm{H}_{2}$ molecules (molecular mass $=2$ ). Next, he determined the volume of $\mathrm{H}_{2}(\mathrm{g})$ at $0.00^{\circ} \mathrm{C}$ and $1.00 \mathrm{atm}$

that has a mass of exactly $2 \mathrm{g}$. This volume is $22.4 \mathrm{L}$ Then he assumed that 22.4 L of any other gas would have the same number of molecules as in 22.4 L of $\mathrm{H}_{2}(\mathrm{g}) .$ (Here is where Avogadro's hypothesis entered in.) Finally, he reasoned that the ratio of the mass of 22.4 Lof any other gas to the mass of 22.4 Lof $\mathrm{H}_{2}(\mathrm{g})$ should be the same as the ratio of their molecular masses. The sketch below illustrates Cannizzaro's reasoning in establishing the atomic weight of oxygen as $16 .$ The gases in the table all contain the element X. Their molecular masses were determined by Cannizzaro's method. Use the percent composition data to deduce the atomic mass of $X,$ the number of atoms of $X$ in each of the gas molecules, and the identity of X.

a. What is the molar mass of an element?

b. To two decimal places, write the molar masses of carbon, neon, iron, and uranium.

Calculate the mass in grams of one mole of each of the following (the mass of a single item is given in parentheses): electrons (9.10938 * 10-28 g), protons (1.67262 * 10-24 g), neutrons (1.67493 * 10-24 g), atoms of carbon-12 (1.992646 * 10-23 g), and doughnuts (74 g). Compare the mass of one mole of carbon-12 atoms to the sum of the masses of the particles that it contains. If the doughnut mentioned in this question were made entirely of carbon, how many atoms would it contain?

Determine the number of moles of oxygen atoms in each sample.

\begin{equation}

\begin{array}{ll}{\text { a. } 4.88 \mathrm{mol} \mathrm{H}_{2} \mathrm{O}_{2}} & {\text { b. } 2.15 \mathrm{mol} \mathrm{N}_{2} \mathrm{O}} \\ {\mathrm{c} .0 .0237 \mathrm{mol} \mathrm{H}_{2} \mathrm{CO}_{3}} & {\text { d. } 24.1 \mathrm{mol} \mathrm{CO}_{2}}\end{array}

\end{equation}

If the mass of a gold atom is 196.97 amu,

what is the atom's molar mass?

Use the periodic table inside the back cover of this text to determine the atomic mass (per

mole) or molar mass of each of the substances in column 1, and find that mass in column 2.

(COLUMN IS NOT AVAILABLE TO COPY)

(a) What is the mass, in grams, of one mole of $^{12} \mathrm{C} ?$ (b) How many carbon atoms are present in one mole of $^{12} \mathrm{C} ?$

There are two different isotopes of bromine atoms. Under normal conditions, elemental bromine consists of Br_{2} \text molecules, and the mass of a Br $_{2}$ molecule is the sum of the masses of the two atoms in the molecule. The mass spectrum of Br_{2} consists of three peaks:(a) What is the origin of each peak (of what isotopes does each consist)? (b) What is the mass of each isotope? (c) Determine the average molecular mass of a Br_ molecule. (d) Determine the average atomic mass of a bromine atom. (e) Calculate the abundances of the two isotopes.

A mole of atoms is $6.02 \times 10^{23}$ atoms. To the nearest order of magnitude, how many moles of atoms are in a large domestic cat? The masses of a hydrogen atom, an oxygen atom, and a carbon atom are $1.0 \mathrm{u}, 16 \mathrm{u},$ and $12 \mathrm{u},$ respectively. (Hint: Cats are sometimes known to kill a mole.)

Using the average atomic masses given inside the front cover of the text, calculate the mass in grams of each of the following samples.

a. $2.21 \times 10^{-4}$ mol of calcium carbonate

b. 2.75 mol of helium

c. 0.00975 mol of oxygen gas

d. $7.21 \times 10^{-3}$ mol of carbon dioxide

e. 0.835 mol of iron(II) sulfide

f. 4.01 mol of potassium hydroxide

g. 0.0219 mol of hydrogen gas

Distinguish between Avogadro's number

and the mole.

Using the average atomic masses given in Table 8.1 , calculate the number of atoms present in each of the following samples.

a. $160,000$ amu of oxygen

b. 8139.81 amu of nitrogen

c. $13,490$ amu of aluminum

d. 5040 amu of hydrogen

e. $367,495.15$ amu of sodium

What is the mass (in amu) of a carbon- 12 atom? Why is the atomic mass of carbon listed as 12.01 amu in the table on the inside front cover of this book?

What is the approximate atomic mass of an atom if its mass is

a. 12 times that of carbon-12?

b. $\frac{1}{2}$ that of carbon-12?

Identify the quantity that is calculated by dividing the molar mass of an element by Avogadro's number.

The atomic mass of tin is 118.7 amu. What would be the mass of 35 tin atoms? How many tin atoms are

contained in a sample of tin that has a mass of 2967.5 amu?

a. What is the definition of a mole?

b. What is the abbreviation for mole?

c. How many particles are in one mole?

d. What name is given to the number of particles in a mole?

Define the term "mole." What is the unit for mole in calculations? What does the mole have in common with the pair, the dozen, and the gross? What does Avogadro's number represent?

If an average atom of sulfur weighs 32.07 amu, how many sulfur atoms are contained in a

sample with mass 8274 amu? What is the mass of $5.213 \times 10^{24}$ sulfur atoms?

The mass of the neutral tritium atom is 3.016049 amu. Find the mass of the bare nucleus, called the triton.

Find the number of moles.

a. $3.01 \times 10^{23}$ molecules $\mathrm{H}_{2} \mathrm{O}$

b. $1.000 \times 10^{23}$ atoms $\mathrm{C}$

c. $5.610 \times 10^{22}$ ions $\mathrm{Na}^{+}$

Determine the mass defect (in atomic mass units) for (a) helium $_{2}^{3} \mathrm{He}$ which has an atomic mass of $3.016030 \mathrm{u},$ and $\quad(\mathrm{b})$ the isotope of hydrogen known as tritium $_{1}^{3} \mathrm{T}$ , which has an atomic mass of 3.016050 $\mathrm{u}$ (c) On the basis of your answers to parts (a) and (b), state which nucleus

requires more energy to disassemble it into its separate and stationary

constituent nucleons. Give your reasoning.

Calculate the mass defect (in g/mol) for the following nuclei:

(a) $^{32}{S}$ (atomic mass $=31.97207 {amu} )$

(b)$^{40}$ Ca (atomic mass $=39.96259 {amu} )$

An element consists of 1.40$\%$ of an isotope with mass 203.973 u, 24.10$\%$ of an isotope with mass 205.9745 u, 22.10$\%$ of an isotope with mass 206.9759 u, and 52.40$\%$ of an isotope with mass 207.9766 u. Calculate the average atomic mass, and identify the element.

What is the mass in grams of each of the following? (Hint: See Sample Problems B and E.)

a. 1.00 mol $\mathrm{Li}$

b. 1.00 mol $\mathrm{Al}$

c. 1.00 molar mass $\mathrm{Ca}$

d. 1.00 molar mass $\mathrm{Fe}$

e. $6.022 \times 10^{23}$ atoms $\mathrm{C}$

f. $6.022 \times 10^{23}$ atoms $\mathrm{Ag}$

A Identify, from the list below, the information needed to calculate the number of atoms in $1 \mathrm{cm}^{3}$ of iron. Outline the procedure used in this calculation.

(a) the structure of solid iron

(b) the molar mass of iron

(c) Avogadro's number

(d) the density of iron

(e) the temperature

(f) iron's atomic number

(g) the number of iron isotopes

(a) What isotope is used as the standard in establishing the atomic mass scale? (b) The atomic weight of boron is reported as 10.81 , yet no atom of boron has the mass of 10.81

amu. Explain.

The conversion between atomic mass units and kilograms is

$$1 \mathrm{u}=1.66 \times 10^{-27} \mathrm{kg}$$

A sample containing sulfur (atomic mass 32 u), manganese $(55 \mathrm{u}),$ and an unknown element is placed in a mass spectrometer. The ions have the same charge and are accelerated through the same potential difference before entering the magnetic field. The sulfur and manganese lines are separated by $3.20 \mathrm{cm},$ and the unknown element makes a line between them that is $1.07 \mathrm{cm}$ from the sulfur line. (a) What is the mass of the unknown clement? (b) Identify the element.

An element has two naturally occurring isotopes. Isotope 1 has a mass of 120.9038 amu and a relative abundance of 57.4%, and isotope 2 has a mass of 122.9042 amu. Find the atomic mass of this element and identify it.

An element has two naturally occurring isotopes. Isotope 1 has a mass of 120.9038 amu and a relative abundance of $57.4 \%,$ and isotope 2 has a mass of 122.9042 amu. Find the atomic mass of this element and identify it.

Use the average atomic masses given inside the front cover of this book to calculate the number of moles of the element present in each of the following samples.

a. 66.50 g of fluorine atoms

b. 401.2 mg of mercury

c. 84.27 g of silicon

d. 48.78 g of platinum

e. 2431 g of magnesium

f. 47.97 g of molybdenum

An element consists of $1.40 \%$ of an isotope with mass 203.973 u, $24.10 \%$ of an isotope with mass 205.9745 u, $22.10 \%$ of an isotope with mass $206.9759 \mathrm{u},$ and $52.40 \%$ of an isotope with mass 207.9766 u. Calculate the average atomic mass, and identify the element.

Use the average atomic masses given inside the front cover of this book to calculate the number of moles of the element present in each of the following samples.

a. 4.95 g of neon

b. 72.5 g of nickel

c. 115 mg of silver

d. 6.22$\mu g$ of uranium $(\mu \text { is a standard abbreviation }$ meaning "micro")

e. 135 g of iodine

Calculate the average mass in grams of 1 atom of oxygen.

(a) Find the number of moles in one cubic meter of an ideal gas at $20.0^{\circ} \mathrm{C}$ and atmospheric pressure. (b) For air, Avogadro's number of molecules has mass 28.9 $\mathrm{g}$ . Calculate the mass of one cubic meter of air. (c) State how this result compares with the tabulated density of air at $20.0^{\circ} \mathrm{C}$ .

The atomic mass of an oxygen atom is 15.999 u. Convert this mass to units of (a) kilograms and (b) $\mathrm{MeV} / \mathrm{c}^{2}$

Oxygen-16 is one of the most stable nuclides. The mass of a 16 $\mathrm{O}$ atom is 15.994915 amu. Calculate the binding energy (a) per nucleon in MeV; (b) per atom in MeV; (c) per mole in kJ.

The following quantities are placed in a container: 1.5 $\times 10^{24}$ atoms of hydrogen, 1.0 $\mathrm{mol}$ of sulfur, and 88.0 $\mathrm{g}$

of diatomic oxygen.

(a) What is the total mass in grams for the collection of all three elements?

(b) What is the total number of moles of atoms for the three elements?

(c) If the mixture of the three elements formed a compound with molecules that contain two hydrogen atoms, one

sulfur atom, and four oxygen atoms, which substance is consumed first?

(d) How many atoms of each remaining element would remain unreacted in the change described in ( $(\mathrm{c})$ )

What is the average atomic mass (in amu) of iron atoms? What would 299 iron atoms weigh? How many iron atoms are present in a sample of iron that has a mass of 5529.2 amu?

Calculate the number of atoms present in each of the following:

\begin{equation}

\begin{array}{l}{\text { a. } 2 \text { mol Fe }} \\ {\text { b. } 40.1 \text { g Ca, which has an atomic mass }} \\ {\text { of } 40.08 \text { amu }} \\ {\text { c. } 4.5 \text { mol of boron-11 }}\end{array}

\end{equation}

The atomic masses of nitrogen-14, titanium-48, and xenon-129 are 13.999234 amu, 47.935878 amu, and 128.90479 amu, respectively. For each isotope, calculate (a) the nuclear mass, (b) the nuclear binding energy, (c) the nuclear binding energy per nucleon.

Determine the mass in grams of each of the following:

(a) 0.600 mol of oxygen atoms

(b) 0.600 mol of oxygen molecules, $\mathrm{O}_{2}$

(c) 0.600 mol of ozone molecules, $\mathrm{O}_{3}$

Calculate the molecular mass or formula mass (in amu) of each of the following substances: (a) $\mathrm{CH}_{4}$ (b) $\mathrm{NO}_{2},$ (c) $\mathrm{SO}_{3},$ (d) $\mathrm{C}_{6} \mathrm{H}_{6},$ (e) $\mathrm{NaI},$ (f) $\mathrm{K}_{2} \mathrm{SO}_{4}$ (g) $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}$

(a) Find the number of moles in one cubic meter of an ideal gas at $20.0^{\circ} \mathrm{C}$ and atmospheric pressure. (b) For air, Avogadro's number of molecules has mass 28.9 $\mathrm{g}$ . Calculate the mass of one cubic meter of air. State how the result compares with the tabulated density of air.

Avogadro's number $N_{a}=6.02 \times 10^{23}$ is the number of atoms in 1 mole of an element.

a. How many atoms are in 5 moles of carbon- $12 ?$

b. If $75 \mathrm{g}$ of carbon- 12 has $4.515 \times 10^{25}$ atoms, how many moles is this?

Predict/Calculate Three moles of oxygen gas (that is, 3.0 mol of $\mathrm{O}_{2} )$ are placed in a portable container with a volume of 0.0035 $\mathrm{m}^{3} .$ If the temperature of the gas is $295^{\circ} \mathrm{C},$ find $(\mathrm{a})$ the pressure of the gas and (b) the average kinetic energy of an oxygen molecule. (c) Suppose the volume of the gas is doubled, while the temperature and number of moles are held constant. By what factor do your answers to parts (a) and (b) change? Explain.

An element has two naturally occuring isotopes. Isotope 1 has a mass

of 120.9038 amu and a relative abundance of $57.4 \%,$ and isotope 2 has

a mass of 122.9042 amu. Find the atomic mass of this clement and

identify it.

Section 2.3 describes the postulates of Dalton's atomic theory. With some modifications, these postulates hold up very well regarding how we view elements, compounds, and chemical reactions today. Answer the following questions concerning Dalton's atomic theory and the modifications made today.

a. The atom can be broken down into smaller parts. What are the smaller parts?

b. How are atoms of hydrogen identical to each other, and how can they be different from each other?

c. How are atoms of hydrogen different from atoms of helium? How can H atoms be similar to He atoms?

d. How is water different from hydrogen peroxide $\left(\mathrm{H}_{2} \mathrm{O}_{2}\right)$ even though both compounds are composed of only hydrogen and oxygen?

e. What happens in a chemical reaction, and why is mass conserved in a chemical reaction?

Calculate the molar mass for a substance given its chemical formula; use molar mass to convert between grams and moles.

Calculate the number of moles in $4.00 \mathrm{g}$ of each of the following:

a. He

b. $\mathrm{SnO}_{2}$

c. $\operatorname{Cr}(\mathrm{OH})_{3}$

$\mathbf{d .} \mathrm{Ca}_{3} \mathrm{N}_{2}$

What is the molar mass of an atom? What are the commonly used units for molar mass?

Calculate the quantity of energy produced per mole of U-235 (atomic mass = 235.043922 amu) for the neutron-induced fission of U-235 to produce Te-137 (atomic mass = 136.9253 amu) and Zr-97 (atomic mass = 96.910950 amu) (discussed in Problem 58).

Define the amu. What is one amu equivalent to in grams?

Calculate the mass of an atom of (a) helium, (b) iron, and (c) lead. Give your answers in kilograms. The atomic masses of these atoms are 4.00 u, 55.9 u, and 207 u, respectively.

Calculate the mass defect and nuclear binding energy per nucleon of each nuclide.

a. O-16 (atomic mass = 15.994915 amu)

b. Ni-58 (atomic mass = 57.935346 amu)

c. Xe-129 (atomic mass = 128.904780 amu)

The mass of a hydrogen atom $\left(_{1}^{1} \mathrm{H}\right)$ is 1.007825 amu; that of a tritium atom $\left(\begin{array}{c}{3} \\ {1}\end{array}\right)$ is 3.01605 amu; and that of an a particle is 4.00150 amu. How much energy in killojoules per mole of $\frac{4}{2}$ He produced is released by the following fusion reaction: $1 \mathrm{H}+_{1}^{3} \mathrm{H} \longrightarrow_{2}^{4} \mathrm{He}$

How many moles are represented by each of the following.

\begin{equation}

\begin{array}{l}{\text { a. } 11.5 \mathrm{g} \text { Na which has an atomic mass of }} \\ {22.99 \text { amu }} \\ {\text { b. } 150 \mathrm{g} \text { S which has an atomic mass of }} \\ {32.07 \text { amu }}\end{array}

\end{equation}

\begin{equation}

\begin{array}{l}{\text { c. } 5.87 \text { g Ni which has an atomic mass of }} \\ {58.69 \text { amu }}\end{array}

\end{equation}

Suppose that atomic masses were based on the assignment of a mass of 12.000 $\mathrm{g}$ to 1 $\mathrm{mol}$ of carbon, rather than 1 $\mathrm{mol}$ of 12 $\mathrm{C}$ What would the atomic mass of oxygen be? (The atomic masses of carbon and oxygen based on the assignment of 12.000 g to

1 mol of $^{12} \mathrm{C}$ are 12.011 amu and 15.9994 amu, respectively.)

Section 2.3 describes the postulates of Dalton’s atomic theory. With some modifications, these postulates hold up very well regarding how we view elements, compounds, and chemical reactions today. Answer the following questions concerning Dalton’s atomic theory and the modifications made today.

a. The atom can be broken down into smaller parts. What are the smaller parts?

b. How are atoms of hydrogen identical to each other, and how can they be different from each other?

c. How are atoms of hydrogen different from atoms of helium? How can H atoms be similar to He atoms?

d. How is water different from hydrogen peroxide $\left(\mathrm{H}_{2} \mathrm{O}_{2}\right)$even though both compounds are composed of only hydrogen and oxygen?

e. What happens in a chemical reaction, and why is mass conserved in a chemical reaction?

Calculate the mass defect (in g/mol) for the following nuclei:

(a) $^{52} \mathrm{Fe}$ (atomic mass $=51.94811 \mathrm{amu} )$

(b) $^{92} \mathrm{Mo}$ (atomic mass $=91.90681 \mathrm{amu} )$

Calculate the quantity of energy produced per mole of $\mathrm{U}-235$ (atomic mass $-235.043922$ amu) for the neutron-induced fission of $\mathrm{U}-235$ to produce Te-137 (atomic mass $=136.9253$ amu) and $\mathrm{Zr-97}$ (atomic mass $=96.910950$ amu) (discussed in Problem 58 ).

An element has the following natural abundances and isotopic masses: 90.92% abundance with 19.99 amu, 0.26% abundance with 20.99 amu, and 8.82% abundance with 21.99 amu. Calculate the average atomic mass of this element

Using the average atomic masses given inside the front cover of this book, calculate the number of atoms present in each of the following samples.

a. 1.50 g of silver, Ag

b. 0.0015 mole of copper, Cu

c. 0.0015 g of copper, Cu

d. 2.00 $\mathrm{kg}$ of magnesium, Mg

e. 2.34 oz of calcium, Ca

f. 2.34 g of calcium, Ca

g. 2.34 moles of calcium, Ca

You learned in Chapter 42 that the binding energy of the electron in a hydrogen atom is $13.6 \mathrm{eV}$

a. By how much does the mass decrease when a hydrogen atom is formed from a proton and an electron? Give your answer both in atomic mass units and as a percentage of the mass of the hydrogen atom.

b. By how much does the mass decrease when a helium nucleus is formed from two protons and two neutrons? Give your answer both in atomic mass units and as a percentage of the mass of the helium nucleus.

c. Compare your answers to parts a and b. Why do you hear it said that mass is "lost" in nuclear reactions but not in chemical reactions?

If an average sodium atom weighs 22.99 amu, how many sodium atoms are contained in $1.98 \times 10^{13}$ amu of sodium? What will $3.01 \times 10^{23}$ sodium atoms weigh?

Calculate the number of atoms in 2.0 $\mathrm{g}$

of hydrogen atoms. The atomic mass of

hydrogen is 1.01 amu.

Iodine-131 is one of the most important isotopes used in the diagnosis of thyroid cancer. One atom has a mass of 130.906114 amu. Calculate the binding energy (a) per nucleon in MeV; (b) per atom in MeV;(c) per mole in $\mathrm{kJ}$ .

Calculate the quantity of energy produced per mole of U- 235 (atomic

mass $=235.043922$ amu for the neutron-induced fission of $U-235$ to

produce Te-137 (atomic mass $=136.9253$ amu) and $Z r-97$

(atomic mass $=96.910950$ amu) (discussed in Problem 58 )

Avogadro’s number, molar mass, and the chemical formula of a compound are three useful conversion factors. What unit conversions can be accomplished using these conversion factors?

Avogadro's number, molar mass, and the chemical formula of a compound are three useful conversion factors. What unit conversions can be accomplished using these conversion factors?

How many moles are equal to $3.6 \times 10^{23}$

molecules of oxygen gas, $\mathrm{O}_{2} ?$

Sulfur has four naturally occurring stable isotopes. The one with the lowest mass number is sulfur-32, which is also the most abundant (95.02%).

(a) What percentage of the $\mathrm{S}$ atoms in a matchhead are $^{32} \mathrm{S}$ ?

(b) The isotopic mass of 31.972070 amu. Is the atomic mass of S larger, smaller, or equal to this mass? Explain.

Mass spectrometry is more often applied to molecules than to atoms. We will see in Chapter 3 that the molecular weight of a molecule is the sum of the atomic weights of the

atoms in the molecule. The mass spectrum of $\mathrm{H}_{2}$ is taken under conditions that prevent decomposition into $\mathrm{H}$ atoms.The two naturally occurring isotopes of hydrogen are $^{1} \mathrm{H}$ (atomic mass $=1.00783$ amu; abundance 99.9885$\% )$ and 2H (atomic mass $=2.01410$ amu; abundance 0.0115$\% ) .$ (a) How many peaks will the mass spectrum have? (b) Give the relative atomic masses of each of these peaks. (c) Which peak will be the largest, and which the smallest?

The most abundant elements by mass in the body of a healthy human adult are oxygen $(61.4 \%),$ carbon $(22.9 \%),$ hydrogen $(10.0 \%),$ and nitrogen $(2.6 \%)$

(a) Calculate the mass percent D if all the hydrogen atoms in a human were deuterium atoms.

(b) Calculate the mass percent C if all the carbon atoms were atoms of the isotope having a mass of 13 amu $\left(^{13}_{6} \mathrm{C}\right)$

(c) How much weight would a 150-pound person gain if all $^{2} \mathrm{H}$ atoms were replacedby $^{2} \mathrm{H}$ atoms?

How do you find the average atomic mass of atoms of an element? What unit of measure is this given in?

Explain the difference between the average atomic mass given on the periodic table and the mass of an atom.

A Calculate the mass of an atom of (a) helium, (b) iron, and (c) lead. Give your answers in grams. The atomic masses of these atoms are $4.00 \mathrm{u}, 55.9 \mathrm{u},$ and 207 $\mathrm{u}$ , respectively.

Calculate the molar mass of the following substances.

a.

b. $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}$

c. $\mathrm{Na}_{2} \mathrm{HPO}_{4}$

What is the difference between an atom’s atomic number and its mass number?

Calculate the molecular mass (in amu) of each of the following substances: (a) $\mathrm{CH}_{3} \mathrm{Cl},$ (b) $\mathrm{N}_{2} \mathrm{O}_{4},$ (c) $\mathrm{SO}_{2},$ (d) $\mathrm{C}_{6} \mathrm{H}_{12},$ (e) $\mathrm{H}_{2} \mathrm{O}_{2}$

(f) $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11},(\mathrm{g}) \mathrm{NH}_{3}$.

Using the average atomic masses given inside the front cover of this book, calculate the indicated quantities.

a. the mass in grams of 125 iron atoms

b. the mass in amu of 125 iron atoms

c. the number of moles of iron atoms in 125 g of iron

d. the mass in grams of 125 moles of iron

e. the number of iron atoms in 125 of iron

f. the number of iron atoms in 125 moles of iron

Challenge Calculate the number of oxygen atoms in 5.0 mol of

oxygen molecules. Oxygen is a diatomic molecule, $\mathrm{O}_{2}$ .

Calculate the mass, in grams, of each sample.

a. 1.1 * 1023 gold atoms

b. 2.82 * 1022 helium atoms

c. 1.8 * 1023 lead atoms

d. 7.9 * 1021 uranium atoms

How many moles are represented by 118 $\mathrm{g}$ of cobalt? Cobalt has an atomic mass of 58.93 amu.

The common Eastern mole, a mammal, typically has a mass of 75 g, which corresponds to about 7.5 moles of atoms. (A mole of atoms is $6.02 \times 10^{23}$ atoms.) In atomic mass units (u), what is the average mass of the atoms in the common Eastern mole?

The atomic mass of sulfur is 32 atomic mass units. How many grams of sulfur are needed to have an Avogadro's number of sulfur atoms?

Reference Section 5-2 to find the atomic masses of $^{12} \mathrm{C}$ and $^{13} \mathrm{C},$ the relative abundance of $^{12} \mathrm{C}$ and $^{13} \mathrm{C}$ in natural carbon, and the average mass (in u) of a carbon atom. If you had a sample of natural carbon containing exactly 10,000 atoms, determine the number of $^{12} \mathrm{C}$ and $^{13} \mathrm{C}$ atoms present. What would be the average mass (in u) and the total mass (in u) of the carbon atoms in this 10,000 -atom sample? If you had a sample of natural carbon containing $6.0221 \times 10^{23}$ atoms, determine the number of $^{12} \mathrm{C}$ and $^{13} \mathrm{C}$ atoms present. What would be the average mass (in u) and the total mass (in u) of this $6.0221 \times$ $10^{23}$ atom sample? Given that $1 \mathrm{g}=6.0221 \times 10^{23} \mathrm{u},$ what is the total mass of 1 mole of natural carbon in units of grams?

Indium oxide contains 4.784 g of indium for every 1.000 g of oxygen. In $1869,$ when Mendeleev first presented his version of the periodic table, he proposed the formula $\operatorname{In}_{2} \mathrm{O}_{3}$ for indium oxide. Before that time, it was thought that the formula was InO. What values for the atomic mass of indium are obtained using these two formulas? Assume that oxygen has an atomic mass of 16.00

Determine the mass number of (a) a fluorine atom with 10 neutrons, (b) a sulfur atom with 18 neutrons, (c) an arsenic atom with 42 neutrons, and (d) a platinum atom with 114 neutrons.

Use the average atomic masses given inside the front cover of this book to calculate the mass in grams of each of the following samples.

a. 0.00552 mole of calcium

b. 6.25 mmol of boron $(1 \mathrm{mmol}=1 / 000 \text { mole) }$

c. 135 moles of aluminum

d. $1.34 \times 10^{-7}$ moles of barium

e. 2.79 moles of phosphorus

f. 0.0000997 mole of arsenic

Indium oxide contains 4.784 $\mathrm{g}$ of indium for every 1.000 $\mathrm{g}$ of oxygen. In $1869,$ when Mendeleev first presented his version of the periodic table, he proposed the formula $\operatorname{In}_{2} \mathrm{O}_{3}$ for indium oxide. Before that time it was thought that the formula was InO. What values for the atomic mass of indium are obtained using these two formulas? Assume that oxygen has an atomic mass of 16.00 .

Indium oxide contains $4.784 \mathrm{g}$ of indium for every $1.000 \mathrm{g}$ of oxygen. In $1869,$ when Mendeleev first presented his version of the periodic table, he proposed the formula $\operatorname{In}_{2} \mathrm{O}_{3}$ for indium oxide. Before that time it was thought that the formula was InO. What values for the atomic mass of indium are obtained using these two formulas? Assume that oxygen has an atomic mass of $16.00 .$