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Introductory Chemistry

Steven S. Zumdahl, Donald J. DeCoste

Chapter 8

Chemical Composition

Educators


Problem 75

How does the molecular formula of a compound differ from the empirical formula? Can a compound's
empirical and molecular formulas be the same? Explain.

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Problem 76

What information do we need to determine the molecular formula of a compound if we know only the empirical formula?

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Problem 77

A binary compound of boron and hydrogen has the following percentage composition: 78.14$\%$ boron,
21.86$\%$ hydrogen. If the molar mass of the compound is determined by experiment to be between 27
and 28 g, what are the empirical and molecular formulas of the compound?

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Problem 78

A compound with empirical formula CH was found by experiment to have a molar mass of approximately 78 g. What is the molecular formula of the compound?

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Problem 79

A compound with the empirical formula $\mathrm{CH}_{2}$ was found to have a molar mass of approximately 84 $\mathrm{g}$ . What is the molecular formula of the compound?

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Problem 80

A compound with empirical formula $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}$ was found in a separate experiment to have a molar mass of approximately 90 $\mathrm{g}$ . What is the molecular formula of the compound?

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Problem 81

A compound having an approximate molar mass of $165-170$ g has the following percentage composition by mass: carbon, 42.87$\%$ ; hydrogen, $3.598 \% ;$ oxygen, 28.55$\%$ ; nitrogen, 25.00$\% .$ Determine the empirical and molecular formulas of the compound.

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Problem 82

$\mathrm{NO}_{2}$ (nitrogen dioxide) and $\mathrm{N}_{2} \mathrm{O}_{4}$ (dinitrogen tetroxide) have the same empirical formula, NO$_{2}$ . Confirm this by calculating the percent by mass of each element present in the two compounds.

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Problem 83

Use the periodic table inside the front 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 .
$$
\begin{array}{ll}{\text { Column } \mathbf{1}} & {\text { Column } 2} \\ {\text { (1) molybdenum }} & {\text { (a) } 33.99 \mathrm{g}} \\ {\text { (2) lanthanum }} & {\text { (b) } 79.9 \mathrm{g}} \\ {\text { (3) carbon tetrabromide }} & {\text { (c) } 95.94 \mathrm{g}} \\ {\text { (4) mercury(II) oxide }} & {\text { (d) } 125.84 \mathrm{g}}\end{array}
$$
$$
\begin{array}{l}{\text { (5) titanium(IV) oxide }} & {\text { (e) } 138.9 \mathrm{g}} \\ {\text { (6) manganese(II) chloride }} & {\text { (f) } 143.1 \mathrm{g}} \\ {\text { (7) phosphine, } \mathrm{PH}_{3}} & {\text { (g) } 156.7 \mathrm{g}} \\ {\text { (8) } \operatorname{tin}(\mathrm{II}) \text { fluoride }} & {\text { (h) } 216.6 \mathrm{g}}\end{array}
$$
$$
\begin{array}{ll}{\text { (9) lead(II) sulfide }} & {\text { (i) } 239.3 \mathrm{g}} \\ {(10) \text { copper }(\mathrm{I}) \text { oxide }} & {\text { (j) } 331.6 \mathrm{g}}\end{array}
$$

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Problem 84

Complete the following table.
Table cannot copy

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Problem 85

Complete the following table.
Table cannot copy

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Problem 86

Consider a hypothetical compound composed of elements $\mathrm{X}, \mathrm{Y},$ and $\mathrm{Z}$ with the empirical formula $\mathrm{X}_{2} \mathrm{YZ}_{3}$ . Given that the atomic masses of $\mathrm{X}, \mathrm{Y},$ and $\mathrm{Z}$ are 41.2 , 57.7, and 63.9, respectively, calculate the percentage composition by mass of the compound. If the molecular formula of the compound is found by molar mass determination to be actually $\mathrm{X}_{4} \mathrm{Y}_{2} \mathrm{Z}_{6},$ what is the percentage of each element present? Explain your results.

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Problem 87

A binary compound of magnesium and nitrogen is analyzed, and 1.2791 $\mathrm{g}$ of the compound is found to contain 0.9240 $\mathrm{g}$ of magnesium. When a second sample of this compound is treated with water and heated, the nitrogen is driven off as ammonia, leaving a compound that contains 60.31$\%$ magnesium and 39.69$\%$ oxygen by mass. Calculate the empirical formulas of the two magnesium compounds.

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Problem 88

When a 2.118 -g sample of copper is heated in an atmosphere in which the amount of oxygen present is
restricted, the sample gains 0.2666 g of oxygen in forming a reddish-brown oxide. However, when 2.118 g of copper is heated in a stream of pure oxygen, the sample gains 0.5332 $\mathrm{g}$ of oxygen. Calculate the empirical formulas of the two oxides of copper.

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Problem 89

Hydrogen gas reacts with each of the halogen elements to form the hydrogen halides (HF, HCl, HBr, HI). Calculate the percent by mass of hydrogen in each of these compounds.

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Problem 90

Calculate the number of atoms of each element present in each of the following samples.
a. 4.21 g of water
b. 6.81 g of carbon dioxide
c. 0.000221 g of benzene, $\mathrm{C}_{6} \mathrm{H}_{6}$
d. 2.26 moles of $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}$

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Problem 91

Calculate the mass in grams of each of the following samples.
a. $10,000,000,000$ nitrogen molecules
b. $2.49 \times 10^{20}$ carbon dioxide molecules
c. 7.0983 moles of sodium chloride
d. $9.012 \times 10^{-6}$ moles of $1,2$ -dichloroethane, $\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}$

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Problem 92

Calculate the mass of carbon in grams, the percent carbon by mass, and the number of individual carbon atoms present in each of the following samples.
a. 7.819 g of carbon suboxide, $\mathrm{C}_{3} \mathrm{O}_{2}$
b. $1.53 \times 10^{21}$ molecules of carbon monoxide
c. 0.200 mole of phenol, $\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}$

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Problem 93

Find the item in column 2 that best explains or completes the statement or question in column 1.
Column 1
(1) 1 amu
(2) 1008 amu
(3) mass of the "average" atom of an element
(4) number of carbon atoms in 12.01 g of carbon
(5) $6.022 \times 10^{23}$ molecules
(6) total mass of all atoms in 1 mole of a compound
(7) smallest whole-number ratio of atoms present in a molecule
(8) formula showing actual number of atoms present in a molecule
(9) product formed when any carbon-containing compound is burned in $\mathrm{O}_{2}$
(10) have the same empirical formulas, but different molecular formulas
Column 2
(a) $6.022 \times 10^{23}$
(b) atomic mass
(c) mass of 1000 hydrogen atoms
(d) benzene, $\mathrm{C}_{6} \mathrm{H}_{6, \text { and acetylene, } \mathrm{C}_{2} \mathrm{H}_{2}}$
(e) carbon dioxide
(f) empirical formula
(g) $1.66 \times 10^{-24} \mathrm{g}$
(h) molecular formula
(i) molar mass
(j) 1 mole

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Problem 94

Calculate the number of grams of iron that contain the same number of atoms as 2.24 g of cobalt.

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Problem 95

Calculate the number of grams of cobalt that contain the same number of atoms as 2.24 g of iron.

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Problem 96

Calculate the number of grams of mercury that contain the same number of atoms as 5.00 g of tellurium.

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Problem 97

Calculate the number of grams of lithium that contain the same number of atoms as 1.00 $\mathrm{kg}$ of zirconium.

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Problem 98

Given that the molar mass of carbon tetrachloride, $\mathrm{CCl}_{4},$ is $153.8 \mathrm{g},$ calculate the mass in grams of 1 molecule of $\mathrm{CCl}_{4}$ .

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Problem 99

Calculate the mass in grams of hydrogen present in 2.500 $\mathrm{g}$ of each of the following compounds.
a. benzene, $\mathrm{C}_{6} \mathrm{H}_{6}$
b. calcium hydride, CaH $_{2}$
c. ethyl alcohol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$
d. serine, $\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{O}_{3} \mathrm{N}$

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Problem 100

Calculate the mass in grams of nitrogen present in 5.000 g of each of the following compounds.
a. glycine, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}_{2} \mathrm{N}$
b. magnesium nitride, $\mathrm{Mg}_{3} \mathrm{N}_{2}$
c. calcium nitrate
d. dinitrogen tetroxide

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Problem 101

A strikingly beautiful copper compound with the common name "blue vitriol" has the following elemental composition: 25.45$\%$ Cu, $12.84 \% \mathrm{S}, 4.036 \%$ $\mathrm{H}, 57.67 \%$ O. Determine the empirical formula of the compound.

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Problem 102

A magnesium salt has the following elemental composition: 16.39$\%$ Mg, 18.89$\%$ N, 64.72$\%$ O. Determine the empirical formula of the salt.

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Problem 103

The mass $1.66 \times 10^{-24} \mathrm{g}$ is equivalent to 1 _____.

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Problem 104

Although exact isotopic masses are known with great precision for most elements, we use the average mass of an element's atoms in most chemical calculations. Explain.

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Problem 105

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

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Problem 106

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?

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Problem 107

Using the average atomic masses given inside the front cover of this text, calculate how many moles of each element the following masses represent.
a. 1.5 $\mathrm{mg}$ of chromium
b. $2.0 \times 10^{-3} \mathrm{g}$ of strontium
c. $4.84 \times 10^{4} \mathrm{g}$ of boron
d. $3.6 \times 10^{-6} \mu \mathrm{g}$ of californium
e. 1.0 ton $(2000 \text { lb) of iron }$
f. 20.4 g of barium
g. 62.8 g of cobalt

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Problem 108

Using the average atomic masses given inside the front cover of this text, calculate the mass in grams of each of the following samples.
a. 5.0 moles of potassium
b. 0.000305 mole of mercury
c. $2.31 \times 10^{-5}$ moles of manganese
d. 10.5 moles of phosphorus
e. $4.9 \times 10^{4}$ moles of iron
f. 125 moles of lithium
g. 0.01205 mole of fluorine

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Problem 109

Using the average atomic masses given inside the front cover of this text, calculate the number of atoms present in each of the following samples.
a. 2.89 g of gold
b. 0.000259 mole of platinum
c. 0.000259 g of platinum
d. 2.0 lb of magnesium
e. 1.90 mL of liquid mercury (density $=13.6 \mathrm{g} / \mathrm{mL} )$
f. 4.30 moles of tungsten
g. 4.30 g of tungsten

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Problem 110

Calculate the molar mass for each of the following substances.
a. ferrous sulfate
b. mercuric iodide
c. stannic oxide
d. cobaltous chloride
e. cupric nitrate

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Problem 111

Calculate the molar mass for each of the following substances.
a. adipic acid, $\mathrm{C}_{6} \mathrm{H}_{10} \mathrm{O}_{4}$
b. caffeine, $\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}$
c. eicosane, $\mathrm{C}_{20} \mathrm{H}_{42}$
d. cyclohexanol, $\mathrm{C}_{6} \mathrm{H}_{11} \mathrm{OH}$
e. vinyl acetate, $\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2}$
f. dextrose, $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$

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Problem 112

Calculate the number of moles of the indicated substance present in each of the following samples.
a. 21.2 g of ammonium sulfide
b. 44.3 g of calcium nitrate
c. 4.35 g of dichlorine monoxide
d. 1.0 lb of ferric chloride
e. 1.0 $\mathrm{kg}$ of ferric chloride

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Problem 113

Calculate the number of moles of the indicated substance present in each of the following samples.
a. 1.28 $\mathrm{g}$ of iron(II) sulfate
b. 5.14 $\mathrm{mg}$ of mercury(II) iodide
c. 9.21$\mu \mathrm{g}$ of tin(IV) oxide
d. 1.26 $\mathrm{lb}$ of cobalt(II) chloride
e. 4.25 $\mathrm{g}$ of copper(II) nitrate

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Problem 114

Calculate the mass in grams of each of the following samples.
a. $2.6 \times 10^{-2}$ moles of copper(II) sulfate, CuSO $_{4}$
b. $3.05 \times 10^{3}$ moles of tetrafluoroethylene, $\mathrm{C}_{2} \mathrm{F}_{4}$
c. 7.83 $\mathrm{mmol}(1 \mathrm{mmol}=0.001 \mathrm{mol})$ of $1,4$ -pentadiene, $\mathrm{C}_{5} \mathrm{H}_{8}$
d. 6.30 moles of bismuth trichloride, $\mathrm{BiCl}_{3}$
e. 12.2 moles of sucrose, $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}$

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Problem 115

Calculate the mass in grams of each of the following samples.
a. 3.09 moles of ammonium carbonate
b. $4.01 \times 10^{-6}$ moles of sodium hydrogen carbonate
c. 88.02 moles of carbon dioxide
d. 1.29 mmol of silver nitrate
e. 0.0024 mole of chromium(III) chloride

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Problem 116

Calculate the number of molecules present in each of the following samples.
a. 3.45 $\mathrm{g}$ of $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$
b. 3.45 moles of $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$
c. 25.0 $\mathrm{g}$ of $\mathrm{ICl}_{5}$
d. 1.00 $\mathrm{g}$ of $\mathrm{B}_{2} \mathrm{H}_{6}$
e. 1.05 $\mathrm{mmol}$ of $\mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}$

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Problem 117

Calculate the number of moles of hydrogen atoms present in each of the following samples.
a. 2.71 g of ammonia
b. 0.824 mole of water
c. 6.25 $\mathrm{mg}$ of sulfuric acid
d. 451 g of ammonium carbonate

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Problem 118

Calculate the percent by mass of each element in the following compounds.
a. calcium phosphate
b. cadmium sulfate
c. iron(III) sulfate
d. manganese(II) chloride
e. ammonium carbonate
f. sodium hydrogen carbonate
g. carbon dioxide
h. silver(I) nitrate

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Problem 119

Calculate the percent by mass of the element mentioned first in the formulas for each of the following compounds.
a. sodium azide, NaN $_{3}$
b. copper (II) sulfate, CuSO $_{4}$
c. gold(ili) chloride, AuCl$_{3}$
d. silver nitrate, $\mathrm{AgNO}_{3}$
e. rubidium sulfate, $\mathrm{Rb}_{2} \mathrm{SO}_{4}$
f. sodium chlorate, $\mathrm{NaClO}_{3}$
g. nitrogen triiodide, $\mathrm{NI}_{3}$
h. cesium bromide, CsBr

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Problem 120

Calculate the percent by mass of the element mentioned first in the formulas for each of the following compounds.
a. iron(II) sulfate
b. silver (I) oxide
c. strontium chloride
d. vinyl acetate, $\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2}$
e. methanol, $\mathrm{CH}_{3} \mathrm{OH}$
f. aluminum oxide
g. potassium chlorite
h. potassium chloride

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Problem 121

A 1.2569 -g sample of a new compound has been analyzed and found to contain the following masses of elements: carbon, 0.7238 g; hydrogen, 0.07088 g; nitrogen, 0.1407 g; oxygen, 0.3214 g. Calculate the empirical formula of the compound.

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Problem 122

A 0.7221 -g sample of a new compound has been analyzed and found to contain the following masses of elements: carbon, $0.2990 \mathrm{~g} ;$ hydrogen, $0.05849 \mathrm{~g} ; $ nitrogen, $0.2318 \mathrm{~g} ;$ oxygen, $0.1328 \mathrm{~g} .$ Calculate the empirical formula of the compound.

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Problem 123

When 2.004 $\mathrm{g}$ of calcium is heated in pure nitrogen gas, the sample gains 0.4670 $\mathrm{g}$ of nitrogen. Calculate the empirical formula of the calcium nitride formed.

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Problem 124

When 4.01 $\mathrm{g}$ of mercury is strongly heated in air, the resulting oxide weighs 4.33 g. Calculate the empirical formula of the oxide.

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Problem 125

When 1.00 $\mathrm{g}$ of metallic chromium is heated with elemental chlorine gas, 3.045 $\mathrm{g}$ of a chromium chloride salt results. Calculate the empirical formula of the compound.

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Problem 126

When barium metal is heated in chlorine gas, a binary compound forms that consists of 65.95$\%$ Ba and 34.05$\%$ Cl by mass. Calculate the empirical formula of the compound.

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