Chapter 3

In a combination reaction, is the number of different products equal to, less than, or greater than the number of different reactants?

In principle we could use the more familiar unit dozen in place of mole when expressing the quantities of particles (atoms, ions, or molecules) in chemical reactions. What would be the disadvantage in doing so?

In what way are the molar mass of an ionic compound and its formula mass the same, and in what ways are they different?

Do molecular compounds containing three atoms per molecule always have a molar mass greater than that of molecular compounds containing two atoms per molecule? Explain.

Without calculating their molar masses (though you may consult the periodic table), predict which of the following oxides of nitrogen has the larger molar mass: \(\mathrm{NO}_{2}\) or \(\mathrm{N}_{2} \mathrm{O}\).

Earth's atmosphere contains many volatile substances that are present in trace amounts. The following quantities of these trace gases were found in a \(1.0 \mathrm{mL}\) sample of air. Calculate the number of moles of each gas in the sample. a. \(4.4 \times 10^{14}\) atoms of \(\mathrm{Ne}(g)\) b. \(4.2 \times 10^{13}\) molecules of \(\mathrm{CH}_{4}(g)\) c. \(2.5 \times 10^{12}\) molecules of \(\mathrm{O}_{3}(g)\) d. \(4.9 \times 10^{9}\) molecules of \(\mathrm{NO}_{2}(g)\)

The following quantities of trace gases were found in a 1.0 mL sample of air. Calculate the number of moles of each compound in the sample. a. \(1.4 \times 10^{13}\) molecules of \(\mathrm{H}_{2}(g)\) b. \(1.5 \times 10^{14}\) atoms of \(\mathrm{He}(g)\) c. \(7.7 \times 10^{12}\) molecules of \(\mathrm{N}_{2} \mathrm{O}(g)\) d. \(3.0 \times 10^{12}\) molecules of \(\mathrm{CO}(g)\)

How many atoms of titanium are there in 0.125 mole of each of the following? a. ilmenite, \(\mathrm{FeTiO}_{3}\) b. titanium(IV) chloride c. \(\mathrm{Ti}_{2} \mathrm{O}_{3}\) d. \(T i_{3} O_{5}\)

How many atoms of iron are there in 2.5 moles of each of the following? a. wolframite, FeWO \(_{4}\) b. pyrite, \(\mathrm{FeS}_{2}\) c. magnetite, \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) d. hematite, \(\mathrm{Fe}_{2} \mathrm{O}_{3}\)

Which substance in each of the following pairs of quantities contains more moles of sulfur? a. 3 moles of \(\mathrm{Al}_{2} \mathrm{S}_{3}\) or 4 moles of \(\mathrm{Fe}_{2} \mathrm{S}_{3}\) b. 3 moles of \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) or 4 moles of \(\mathrm{CaS}\) c. 2 moles of \(\mathrm{SO}_{3}\) or 2 moles of \(\mathrm{SO}_{2}\)

Which substance in each of the following pairs of quantities contains more moles of nitrogen? a. 2 moles of \(\mathrm{Li}_{3} \mathrm{N}\) or 0.5 mole of \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\). b. 1 mole of \(\mathrm{NO}\) or 0.4 mole of \(\mathrm{NO}_{2}\). c. 3 moles of \(\mathrm{NF}_{3}\) or 1 mole of \(\mathrm{N}_{2} \mathrm{O}_{5}\).

Elemental Composition of Amino Acids Carbon, hydrogen, nitrogen, and oxygen are the most prevalent components of amino acids, the fundamental building blocks of proteins in living systems. How many moles of oxygen are in 1.50 mol of the following compounds? a. Glycine, the smallest amino acid: \(C_{2} H_{5} N O_{2}\) b. Lysine, essential in the diet of humans: \(C_{6} \mathrm{H}_{14} \mathrm{N}_{2} \mathrm{O}_{2}\) c. Asparagine, produced in our bodies: \(C_{4} H_{8} N_{2} O_{3}\)

Composition of Uranium Ores The uranium used for nuclear fuel exists in nature in several minerals. Calculate how many moles of uranium are in 1 mole of the following: a. carnotite, \(\mathrm{K}_{2}\left(\mathrm{UO}_{2}\right)_{2}\left(\mathrm{VO}_{4}\right)_{2}\). b. uranophane, \(\mathrm{CaU}_{2} \mathrm{Si}_{2} \mathrm{O}_{11}\). c. autunite, \(\mathrm{Ca}\left(\mathrm{UO}_{2}\right)_{2}\left(\mathrm{PO}_{4}\right)_{2}\).

How many moles of carbon are there in \(500.0 \mathrm{g}\) of carbon?

How many moles of iron are there in 1 mole of the following compounds? (a). \(\mathrm{FeO} ;\) (b) .\(\mathrm{Fe}_{2} \mathrm{O}_{3} ;\) (c) \(\mathrm{Fe}(\mathrm{OH})_{3}\) (d). \(\mathrm{Fe}_{3} \mathrm{O}_{4}\)

How many moles of sodium are there in 1 mole of the following compounds? (a) \(\mathrm{NaCl} ;\) (b) .\(\mathrm{Na}_{2} \mathrm{SO}_{4} ;(\mathrm{c}) \mathrm{Na}_{3} \mathrm{PO}_{4}\).(d) \(\mathrm{NaNO}_{3}\)

Calculate the molar masses of the following atmospheric molecules: \((\mathrm{a}) \mathrm{SO}_{2} ;(\mathrm{b}) \mathrm{O}_{3} ;(\mathrm{c}) \mathrm{CO}_{2} ;(\mathrm{d}) \mathrm{N}_{2} \mathrm{O}_{5}\).

Determine the molar masses of the following minerals: a. rhodonite, \(\mathrm{MnSiO}_{3}\) b. scheelite, CaWO \(_{4}\) c. ilmenite, FeTiO \(_{3}\) d. magnesite, \(\mathrm{Mg} \mathrm{CO}_{3}\)

Calculate the molar masses of the following common flavors in food: a. vanillin, \(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\). b. oil of cloves, \(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}_{2}\). c. anise oil, \(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}\). d. oil of cinnamon, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}\).

Calculate the molar masses of the following common sweeteners:. a. sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\). b. saccharin, \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{NO}_{3} \mathrm{S}\). c. aspartame, \(\mathrm{C}_{14} \mathrm{H}_{18} \mathrm{N}_{2} \mathrm{O}_{5}\). d. fructose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\).

Suppose pairs of balloons are filled with \(10.0 \mathrm{g}\) of the following pairs of gases. Which balloon in each pair has the greater number of particles? (a) \(\mathrm{CO}_{2}\) or \(\mathrm{NO} ;\) (b) \(\mathrm{CO}_{2}\) or \(\mathrm{SO}_{2} ;(\mathrm{c}) \mathrm{O}_{2}\) or \(\mathrm{Ar}\).

If you had equal masses of the substances in the following pairs of compounds, which of the two would contain the greater number of ions? (a) NaBr or \(\mathrm{KCl} ;\) (b) \(\mathrm{NaCl}\) or \(\mathrm{MgCl}_{2} ;\) (c) \(\mathrm{BaCl}_{2}\) or \(\mathrm{Li}_{2} \mathrm{CO}_{3}\).

How many moles of \(\mathrm{NaCl}\) are there in a crystal of halite that has a mass of \(6.82 \mathrm{g} ?\).

What is the mass of 0.122 mol \(\mathrm{Mg} \mathrm{CO}_{3} ?\)

What is the volume of 1.00 mol benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) at \(20^{\circ} \mathrm{C} ?\) The density of benzene is \(0.879 \mathrm{g} / \mathrm{mL}\).

Aluminum \((d=2.70 \mathrm{g} / \mathrm{mL})\) and strontium \((d=2.64 \mathrm{g} / \mathrm{mL})\) have nearly the same density. If we manufacture two cubes, each containing 1 mole of one element or the other, which cube will be smaller? What are the dimensions of this cube?

In a balanced chemical equation, does the number of moles of reactants always equal the number of moles of products?

In a balanced chemical equation, does the sum of the coefficients for the reactants always equal the sum of the coefficients for the products?

In a balanced chemical equation, must the sum of the masses of all the gaseous reactants always equal the sum of the masses of the gaseous products?

In a balanced chemical equation, must the sum of the volumes occupied by the gaseous reactants always equal the sum of the volumes occupied by the gaseous products?

Using different-colored spheres to represent \(\mathrm{C}\) and \(\mathrm{O}\) sketch the reaction between five C atoms and the necessary number of \(\mathrm{O}_{2}\) molecules to produce a \(50 \%\) mixture of \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\).

Fluorine is a very reactive, dangerous element, as can be seen in the following unbalanced equation: $$\mathrm{F}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{HF}(a q)+\mathrm{O}_{2}(g)$$ After balancing this chemical equation, what is the coefficient of HF?

Aluminum reacts with elemental oxygen at high temperatures to give pure aluminum oxide. What is the coefficient of \(\mathrm{O}_{2}(\mathrm{g})\) in the balanced chemical equation?

Some scientists believe that life on Earth may have originated near deep-ocean vents. Balance the following reactions, which are among those taking place near such vents: a. \(\mathrm{CH}_{3} \mathrm{SH}(a q)+\mathrm{CO}(a q) \rightarrow \mathrm{CH}_{3} \mathrm{COSCH}_{3}(a q)+\mathrm{H}_{2} \mathrm{S}(a q)\). b. \(\mathrm{H}_{2} \mathrm{S}(a q)+\mathrm{CO}(a q) \rightarrow \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(a q)+\mathrm{S}_{8}(s)\).

The oxides of nitrogen are biologically reactive substances now known to be formed endogenously in the human lung: \(\mathrm{NO}\) is a powerful agent for dilating blood vessels; \(\mathrm{N}_{2} \mathrm{O}\) is the anesthetic known as laughing gas; \(\mathrm{NO}_{2}\) has an acrid odor and is corrosive to lung tissue. Balance the following reactions for the formation of nitrogen oxides: a. \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{NO}(g)\). b. \(\mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{NO}_{2}(g)\). c. \(\mathrm{NO}(g)+\mathrm{NO}_{3}(g) \rightarrow \mathrm{NO}_{2}(g)\). d. \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{N}_{2} \mathrm{O}(g)\).

If natural gas contains significant amounts of sulfur as \(\mathrm{H}_{2} \mathrm{S}\), it is called sour natural gas. For the gas to be commercially useful as a fuel, the \(\mathrm{H}_{2} \mathrm{S}\) must be removed. Once it is separated from the natural gas, it is reacted with oxygen in two different processes to yield either elemental sulfur (S \(_{8}\) ), a commercial material that can be sold, or sulfur dioxide \(\left(\mathrm{SO}_{2}\right) .\) This sulfur dioxide product can be reacted with more \(\mathrm{H}_{2} \mathrm{S}\) to make additional elemental sulfur. Balance the following reactions that describe the production of elemental sulfur. a. \(\mathrm{H}_{2} \mathrm{S}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{S}_{8}(s)+\mathrm{H}_{2} \mathrm{O}(g)\). b. \(\mathrm{H}_{2} \mathrm{S}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{SO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\). \(^{*} \mathrm{c} . \mathrm{H}_{2} \mathrm{S}(g)+\mathrm{SO}_{2}(g) \rightarrow \mathrm{S}_{8}(s)+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\).

Write a balanced chemical equation for each of the following reactions: a. Dinitrogen pentoxide reacts with sodium metal to produce sodium nitrate and nitrogen dioxide. b. A mixture of nitric acid and nitrous acid is formed when water reacts with dinitrogen tetroxide. c. At high pressure, nitrogen monoxide decomposes to dinitrogen monoxide and nitrogen dioxide. d. Acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2},\) burns and becomes carbon dioxide and water vapor.

Write a balanced chemical equation for each of the following reactions: a. Carbon dioxide reacts with carbon to form carbon monoxide. b. Potassium reacts with water to give potassium hydroxide and hydrogen gas. c. Phosphorus, \(P_{4}\), burns in air to give diphosphorus pentoxide. d. Octane, \(\mathrm{C}_{8} \mathrm{H}_{18},\) burns and becomes carbon dioxide and water vapor.

Does the sum of the masses of the products always equal the sum of the masses of the reactants in a balanced chemical equation?

When \(\mathrm{NaHCO}_{3}\) is heated above \(270^{\circ} \mathrm{C},\) it decomposes to \(\mathrm{Na}_{2} \mathrm{CO}_{3}(s), \mathrm{H}_{2} \mathrm{O}(g),\) and \(\mathrm{CO}_{2}(g)\). a. Write a balanced chemical equation for the decomposition reaction. b. Calculate the mass of \(\mathrm{CO}_{2}\) produced from the decomposition of \(25.0 \mathrm{g}\) of \(\mathrm{NaHCO}_{3}\).

Egyptian Cosmetics \(\mathrm{Pb}\) (OH) Cl, one of the lead compounds used in ancient Egyptian cosmetics, was prepared from PbO according to the following recipe:$$\mathrm{PbO}(s)+\mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{Pb}(\mathrm{OH}) \mathrm{Cl}(s)+\mathrm{NaOH}(a q)$$.How many grams of \(\mathrm{PbO}\) and how many grams of \(\mathrm{NaCl}\) would be required to produce \(10.0 \mathrm{g}\) of \(\mathrm{Pb}(\mathrm{OH}) \mathrm{Cl} ?\)

The manufacture of aluminum includes the production of cryolite (Na_AIF_ ) from the following reaction: \(6 \mathrm{HF}(g)+3 \mathrm{NaAlO}_{2}(s) \rightarrow \mathrm{Na}_{3} \mathrm{AlF}_{6}(s)+3 \mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{Al}_{2} \mathrm{O}_{3}(s)\). How much NaAlO, (sodium aluminate) is required to produce \(1.00 \mathrm{kg}\) of \(\mathrm{Na}_{3} \mathrm{AlF}_{6} ?\)

Chromium metal can be produced from the high-temperature reaction of \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) [chromium(III) oxide] with silicon or aluminum by each of the following reactions:$$\begin{aligned} \mathrm{Cr}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(\ell) & \rightarrow 2 \mathrm{Cr}(\ell)+\mathrm{Al}_{2} \mathrm{O}_{3}(s) \\\2 \mathrm{Cr}_{2} \mathrm{O}_{3}(s)+3 \mathrm{Si}(\ell) & \rightarrow 4 \mathrm{Cr}(\ell)+3 \mathrm{SiO}_{2}(s)\end{aligned}$$.a. Calculate the number of grams of aluminum required to prepare \(400.0 \mathrm{g}\) of chromium metal by the first reaction. b. Calculate the number of grams of silicon required to prepare \(400.0 \mathrm{g}\) of chromium metal by the second reaction.

Suppose 25 metric tons of coal that is \(3.0 \%\) sulfur by mass is burned at an electric power plant ( 1 metric ton \(=10^{3} \mathrm{kg}\) ). During combustion, the sulfur is converted into sulfur dioxide. How many tons of sulfur dioxide are produced?

The uranium minerals found in nature must be refined and enriched in \(^{235} \mathrm{U}\) before the uranium can be used as a fuel in nuclear reactors. One procedure for enriching uranium relies on the reaction of \(\mathrm{UO}_{2}\) with HF to form UF \(_{4}\), which is then converted into UF \(_{6}\) by reaction with fluorine: $$\begin{array}{c}\mathrm{UO}_{2}(g)+4 \mathrm{HF}(a q) \rightarrow \mathrm{UF}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \\\\\mathrm{UF}_{4}(g)+\mathrm{F}_{2}(g) \rightarrow \mathrm{UF}_{6}(g) \end{array}$$.a. How many kilograms of HF are needed to completely react with \(5.00 \mathrm{kg}\) of \(\mathrm{UO}_{2} ?\) b. How much UF \(_{6}\) can be produced from \(850.0 \mathrm{g}\) of \(\mathrm{UO}_{2} ?\)

In Brazil automobiles use ethanol, \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O},\) as fuel, whereas in the United States we rely on gasoline. Using \(\mathrm{C}_{8} \mathrm{H}_{18}\) (octane) to represent gasoline, write balanced chemical equations for the complete combustion of ethanol and octane. Which fuel produces more \(\mathrm{CO}_{2}\) per gram of fuel?

Driving 1000 miles a month is not unusual for a short-distance commuter. If your vehicle gets 25 mpg, you would use 40 gallons \((\approx 150 \mathrm{L})\) of gasoline every month. If gasoline is approximated as \(\mathrm{C}_{8} \mathrm{H}_{18}(d=0.703 \mathrm{g} / \mathrm{mL}),\) how much carbon dioxide does your vehicle emit every month? The unbalanced chemical equation for the reaction is$$ \mathrm{C}_{8} \mathrm{H}_{18}(\ell)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$.

Mining for Gold Unlike most metals, gold is found in nature as the pure element. Miners in California in 1849 searched for gold nuggets and gold dust in stream beds, where the denser gold could be easily separated from sand and gravel. However, larger deposits of gold are found in veins of rock and can be separated chemically in a two-step process:$$\begin{aligned}&\text { (1) } 4 \mathrm{Au}(s)+8 \mathrm{NaCN}(a q)+\mathrm{O}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow\\\&4 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+4 \mathrm{NaOH}(a q)\end{aligned}$$.$$\begin{aligned}&\text { (2) } 2 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+\mathrm{Zn}(s) \rightarrow\\\&2 \mathrm{Au}(s)+\mathrm{Na}_{2}\left[\mathrm{Zn}(\mathrm{CN})_{4}\right](a q)\end{aligned}$$.If a \(1.0 \times 10^{3} \mathrm{kg}\) sample of rock is \(0.019 \%\) gold by mass, how much \(\mathrm{Zn}\) is needed to react with the gold extracted from the rock? Assume that reactions (1) and (2) are \(100 \%\) efficient.

What is the difference between an empirical formula and a molecular formula?

Do the empirical and molecular formulas of a compound always have the same percent composition values? Explain your answer.