Chapter 7

Can the results of a combustion analysis ever give the true molecular formula of a compound?

A chemical reaction that is used to analyze a compound is expected to have a \(100 \%\) yield. However, when a compound is synthesized, a \(100 \%\) yield is almost never expected. Explain this difference.

A 0.100 g sample of a compound containing \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{O}\) is burned in oxygen, producing \(0.1783 \mathrm{g} \mathrm{CO}_{2}\) and \(0.0734 \mathrm{g}\) \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula of the compound?

GRAS List for Food Additives The alcohol geraniol is on the U.S. Food and Drug Administration's GRAS (generally recognized as safe) list and can be used in foods and personal care products. By itself, geraniol has a roselike odor, but it is frequently blended with other scents to produce the fruity fragrances of some personal care products. Complete combustion of 175 mg of geraniol produces \(499 \mathrm{mg} \mathrm{CO}_{2}\) and \(184 \mathrm{mg} \mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula of geraniol?

Combustion of 135.0 mg of a hydrocarbon produces \(440.0 \mathrm{mg} \mathrm{CO}_{2}\) and \(135.0 \mathrm{mg} \mathrm{H}_{2} \mathrm{O} .\) The molar mass of the hydrocarbon is \(270 \mathrm{g} / \mathrm{mol}\). What are the empirical and molecular formulas of this compound?

The combustion of 40.5 mg of a compound extracted from the bark of the sassafras tree and known to contain \(\mathrm{C}, \mathrm{H}\) and O produces \(110.0 \mathrm{mg} \mathrm{CO}_{2}\) and \(22.5 \mathrm{mg} \mathrm{H}_{2} \mathrm{O} .\) The molar mass of the compound is 162 g/mol. What are its empirical and molecular formulas?

If a reaction vessel contains equal masses of \(\mathrm{Fe}\) and \(\mathrm{S}, \mathrm{a}\) mass of FeS corresponding to which of the following could theoretically be produced? a. the sum of the masses of \(\mathrm{Fe}\) and \(\mathrm{S}\) b. more than the sum of the masses of Fe and \(S\) c. less than the sum of the masses of Fe and \(S\)

A reaction vessel contains equal masses of magnesium metal and oxygen gas. The mixture is ignited, forming MgO. After the reaction has gone to completion, the mass of the \(\mathrm{MgO}\) is less than the mass of the reactants. Is this result a violation of the law of conservation of mass? Explain your answer.

Can the percent yield of a chemical reaction ever exceed \(100 \% ?\)

If fewer moles of \(\mathrm{A}\) are present in a reaction between \(\mathrm{A}\) and B, then \(A\) must be the limiting reagent. What is wrong with this statement?

A chemical reaction produces less than the expected amount of product. Is this result a violation of the law of conservation of mass?

Making Hollandaise Sauce A recipe for 1 cup of hollandaise sauce calls for \(\frac{1}{4}\) cup of butter, \(\frac{1}{2}\) cup of hot water, 4 egg yolks, and the juice of a medium-sized lemon. How many cups of sauce can be made from a pound ( 2 cups) of butter, a dozen eggs, 4 medium-sized lemons, and an unlimited supply of hot water?

A factory making toy wagons has 13,466 wheels, 3360 handles, and 2400 wagon beds in stock. What is the maximum number of wagons with four wheels that the factory can make from these components?

Sulfur in Coal Suppose 75 metric tons of coal that is \(3.0 \%\) sulfur by mass is burned at a power plant. During combustion, the sulfur is converted into \(\mathrm{SO}_{2} .\) Antipollution scrubbers installed in the smokestacks of the power plant capture 3.9 metric tons of \(\mathrm{SO}_{2} .\) How efficient are the scrubbers in capturing \(\mathrm{SO}_{2} ?\) How many metric tons of \(\mathrm{SO}_{2}\) escape?

One reaction in the production of sulfuric acid involves the conversion of sulfur dioxide to sulfur trioxide. In the presence of excess \(\mathrm{O}_{2}, 88 \mathrm{kg} \mathrm{SO}_{2}\) produces \(106 \mathrm{kg} \mathrm{SO}_{3}\) What is the percent yield?

A reaction vessel contains \(10.0 \mathrm{g} \mathrm{CO}\) and \(10.0 \mathrm{g} \mathrm{O}_{2},\) which combine to form \(\mathrm{CO}_{2}\) : $$2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{CO}_{2}(g)$$ a. Which reactant is limiting? b. How many grams of \(\mathrm{CO}_{2}\) could be produced? c. How many grams of the nonlimiting reactant are left over?

Syngas An industrial process for producing hydrogen gas is based on the reaction between carbon heated to incandescence and steam that produces a mixture of \(\mathrm{CO}\) and \(\mathrm{H}_{2}\) called synthesis gas, or syngas. a. Write a balanced chemical equation for the production of syngas. b. If a reaction vessel that initially contains 66 kilograms of incandescent carbon and excess steam produces \(6.8 \mathrm{kg}\) \(\mathrm{H}_{2},\) what is the percent yield?

Baking soda (NaHCO \(_{3}\) ) is produced on an industrial scale by the Solvay process. A key reaction in the process is $$\mathrm{NaCl}(a q)+\mathrm{NH}_{3}(a q)+\mathrm{CO}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow$$ $$\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \mathrm{NaHCO}_{3}(s)+\mathrm{NH}_{4} \mathrm{Cl}(a q)$$ Suppose a reaction vessel initially contains \(58.5 \mathrm{kg} \mathrm{NaCl}\) \(18.8 \mathrm{kg} \mathrm{NH}_{3},\) and excess \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O} .\) If \(66 \mathrm{kg} \mathrm{NaHCO}_{3}\) is produced, what is the percent yield?

Chemistry of Fermentation Yeast converts glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) in aqueous solution into ethanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right.\) \(d=0.789 \mathrm{g} / \mathrm{mL})\) in a process called fermentation. Carbon dioxide is also produced. a. Write a balanced chemical equation for the fermentation reaction. b. If 100.0 grams of glucose yields \(50.0 \mathrm{mL}\) of ethanol, what is the percent yield for the reaction?

Black Powder Gunpowder, known also as black powder, is generally thought to have been invented by the Chinese in the 9 th century. The first description in English was given by Roger Bacon in the 13 th century. The basic formulation has not changed since then: \(40 \%\) potassium nitrate, \(30 \%\) carbon, and \(30 \%\) sulfur by weight. The products of the reaction that provide the explosive force when the powder is ignited are three gases: carbon monoxide, carbon dioxide, and nitrogen. An additional product is potassium sulfite. Consider a sample of \(100 \mathrm{g}\) of black powder. a. Which reagent is limiting? b. How much of each of the reagents in excess is left over after the explosion takes place?

Artificial Bones for Medical Implants The material often used to make artificial bones is the same material that gives natural bones their strength. Its common name is hydroxyapatite, and its formula is \(\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}\) a. Propose a systematic name for this compound. b. What is the mass percentage of calcium in it? c. When treated with hydrogen fluoride, hydroxyapatite becomes fluorapatite \(\left[\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F}\right]\), an even stronger substance. Does the percent mass of Ca increase or decrease as a result of this substitution?

As a solution of copper sulfate slowly evaporates, beautiful blue crystals form. Their chemical formula is \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) a. What is the percent water in this compound? b. At high temperatures the water is driven off as steam. What fraction of the original sample's mass is lost as a result?

Mining for Gold Gold can be extracted from the surrounding rock using a solution of sodium cyanide. While effective for isolating gold, toxic cyanide finds its way into watersheds, causing environmental damage and harming human health. $$\begin{array}{l} 4 \mathrm{Au}(s)+8 \mathrm{NaCN}(a q)+\mathrm{O}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \\ \quad \quad\quad\quad\quad\quad\quad\quad4 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+4 \mathrm{NaOH}(a q) \\ 2 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+\mathrm{Zn}(s) \rightarrow 2 \mathrm{Au}(s)+\mathrm{Na}_{2}\left[\mathrm{Zn}(\mathrm{CN})_{4}\right](a q) \end{array}$$ a. If a sample of rock contains \(0.009 \%\) gold by mass, how much \(\mathrm{NaCN}\) is needed to extract the gold as \(\mathrm{NaAu}(\mathrm{CN})_{2}\) from 1 metric ton \(\left(10^{3} \mathrm{kg}\right)\) of rock? b. How much zinc is needed to convert the \(\mathrm{NaAu}(\mathrm{CN})_{2}\) from part (a) to metallic gold? c. The gold recovered in part (b) is manufactured into a gold ingot in the shape of a cube. The density of gold is \(19.3 \mathrm{g} / \mathrm{cm}^{3} .\) How big is the block of gold in \(\mathrm{cm}^{3} ?\)

Phosgenite, a lead compound with the formula \(\mathrm{Pb}_{2} \mathrm{Cl}_{2} \mathrm{CO}_{3}\) is found in Egyptian cosmetics. Phosgenite was prepared by the reaction of \(\mathrm{PbO}, \mathrm{NaCl},\) and \(\mathrm{CO}_{2} .\) An unbalanced expression of the reactant mixture is $$\mathrm{PbO}(s)+\mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{CO}_{2}(g) \rightarrow $$ $$\quad\quad\quad\quad\quad \mathrm{Pb}_{2} \mathrm{Cl}_{2} \mathrm{CO}_{3}(s)+\mathrm{NaOH}(a q)$$ a. Balance the equation. b. How many grams of phosgenite can be obtained from \(10.0 \mathrm{g} \mathrm{PbO}\) and \(10.0 \mathrm{g} \mathrm{NaCl}\) in the presence of excess water and \(\mathrm{CO}_{2} ?\) c. Phosgenite can be considered a mixture of two lead compounds. Which compounds appear to be combined to make phosgenite?

Uranium oxides used in the preparation of fuel for nuclear reactors are separated from other metals in minerals by converting the uranium to \(\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}\left(\mathrm{H}_{2} \mathrm{O}\right)_{z},\) where uranium has a positive charge ranging from \(3+\) to \(6+\) a. Roasting UO \(_{x}\left(\mathrm{NO}_{3}\right)_{y}\left(\mathrm{H}_{2} \mathrm{O}\right)_{z}\) at \(400^{\circ} \mathrm{C}\) leads to loss of water and decomposition of the nitrate ion to nitrogen oxides, leaving behind a product with the formula \(\mathrm{U}_{a} \mathrm{O}_{b}\) that is \(83.22 \%\) U by mass. What are the values of \(a\) and b? What is the charge on \(\mathrm{U}\) in \(\mathrm{U}_{a} \mathrm{O}_{b}\) ? b. Higher temperatures produce a different uranium oxide, \(\mathrm{U}_{c} \mathrm{O}_{d},\) which is \(84.8 \% \mathrm{U}\) by mass. What are the values of \(c\) and \(d ?\) What is the charge on \(\mathrm{U}\) in \(\mathrm{U}_{\epsilon} \mathrm{O}_{d} ?\) c. The values of \(x, y,\) and \(z\) in \(\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}\left(\mathrm{H}_{2} \mathrm{O}\right)_{z}\) are found by gently heating the compound to remove all of the water. In a laboratory experiment, \(1.328 \mathrm{g}\) \(\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}\left(\mathrm{H}_{2}\mathrm{O}\right)_{z}\) produced \(1.042\mathrm{g}\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}.\) Continued heating generated \(0.742 \mathrm{g} \mathrm{U}_{n} \mathrm{O}_{m} .\) Using the information in parts (a) and (b), calculate \(x, y,\) and \(z\)

Corn farmers in the American Midwest typically use \(5.0 \times 10^{3}\) kilograms of ammonium nitrate fertilizer per square kilometer of cornfield per year. Some of the fertilizer washes into the Mississippi River and eventually flows into the Gulf of Mexico, promoting the growth of algae and endangering other aquatic life. a. Ammonium nitrate can be prepared by the following reaction: $$\mathrm{NH}_{3}(g)+\mathrm{HNO}_{3}(a q) \rightarrow \mathrm{NH}_{4} \mathrm{NO}_{3}(a q)$$ How much nitric acid would be required to make the fertilizer needed for \(1 \mathrm{km}^{2}\) of cornfield per year? b. Ammonium ions dissolved in groundwater may be converted into \(\mathrm{NO}_{3}^{-}\) ions by bacterial action: $$\mathrm{NH}_{4}^{+}(a q)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{NO}_{3}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell)+2 \mathrm{H}^{+}(a q)$$ If \(10 \%\) of the ammonium component of \(5.0 \times 10^{3}\) kilograms of fertilizer ends up as nitrate ions, how much oxygen would be consumed?

Fiber in the Diet Dietary fiber is a mixture of many compounds, including xylose \(\left(\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{5}\right)\) and methyl galacturonate \(\left(\mathrm{C}_{7} \mathrm{H}_{12} \mathrm{O}_{7}\right)\) a. Do these compounds have the same empirical formula? b. Write balanced chemical equations for the complete combustion of xylose and methyl galacturonate.

Some catalytic converters in automobiles contain two manganese oxides: \(\mathrm{Mn}_{2} \mathrm{O}_{3}\) and \(\mathrm{MnO}_{2}.\) a. What are the names of these compounds? b. What is the manganese content of each (expressed as a percent by mass)? c. Explain how \(\mathrm{Mn}_{2} \mathrm{O}_{3}\) and \(\mathrm{MnO}_{2}\) are consistent with the law of multiple proportions.

A number of chemical reactions have been proposed for the formation of organic compounds from inorganic precursors, including the following: $$\mathrm{H}_{2} \mathrm{S}(g)+\mathrm{FeS}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{FeS}_{2}(s)+\mathrm{HCO}_{2} \mathrm{H}(\ell)$$ a. Identify the ions in \(\mathrm{FeS}\) and \(\mathrm{FeS}_{2}\) b. What are the names of \(\mathrm{FeS}\) and \(\mathrm{FeS}_{2} ?\) c. How much \(\mathrm{HCO}_{2} \mathrm{H}\) is obtained by reacting \(1.00 \mathrm{g}\) FeS, \(0.50 \mathrm{g} \mathrm{H}_{2} \mathrm{S},\) and \(0.50 \mathrm{g} \mathrm{CO}_{2}\) if the reaction results in a \(50.0 \%\) yield?

Organic compounds called carbobydrates may be formed in reactions between iron(II) sulfide and carbonic acid: $$2 \mathrm{FeS}+\mathrm{H}_{2} \mathrm{CO}_{3} \rightarrow 2 \mathrm{FeO}+\frac{1}{n}\left(\mathrm{CH}_{2} \mathrm{O}\right)_{n}+2 \mathrm{S}$$ a. What is the empirical formula of these carbohydrates? b. How much carbohydrate is produced from a reaction mixture that initially contains \(211 \mathrm{g}\) FeS and excess \(\mathrm{H}_{2} \mathrm{CO}_{3}\) if the reaction results in a \(78.5 \%\) yield? c. If the carbohydrate product has a molecular mass of 300 amu, what is its molecular formula?

Marine Chemistry of Iron On the seafloor, solid iron(II) oxide may react with water to form solid \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) and hydrogen gas. a. Write a balanced chemical equation for the reaction. b. When \(\mathrm{CO}_{2}\) is also present, the product of the reaction is methane, not hydrogen. Write a balanced chemical equation for this reaction.

Titanium dioxide and zinc oxide are common names of two of the active ingredients approved by the U.S. FDA for use in sunscreens. a. What are the chemical formulas of these compounds? b. What are the proper names of the compounds based on the rules for naming described in Chapter \(4 ?\) c. Which of the two compounds contains the higher percentage of oxygen by mass?

You are given a \(0.6240 \mathrm{g}\) sample of a substance with the generic formula \(\mathrm{MCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O} .\) After completely drying the sample (which means removing the 2 mol of \(\mathrm{H}_{2} \mathrm{O}\) per mole of \(\mathrm{MCl}_{2}\), , the sample has a mass of \(0.5471 \mathrm{g}\). What is the identity of element M?

A compound found in crude oil is \(93.71 \%\) C and \(6.29 \%\) H by mass. The molar mass of the compound is \(128 \mathrm{g} / \mathrm{mol}\). What is its molecular formula?

A reaction vessel for synthesizing ammonia by reacting nitrogen and hydrogen is charged with \(6.04 \mathrm{kg} \mathrm{H}_{2}\) and excess \(\mathrm{N}_{2} .\) If \(28.0 \mathrm{kg} \mathrm{NH}_{3}\) is produced, what is the percent yield of the reaction?

Reducing \(\mathrm{SO}_{2}\) Emissions One way in which \(\mathrm{SO}_{2}\) is removed from the "stack" gases of coal-burning power plants is by spraying the gases with fine particles of solid calcium oxide suspended in \(\mathrm{O}_{2}\) gas. The product of the reaction of \(\mathrm{SO}_{2}\) \(\mathrm{CaO},\) and \(\mathrm{O}_{2}\) is calcium sulfate. a. Write a balanced chemical equation for this reaction. b. How many metric tons of calcium sulfate would be produced from each ton of \(\mathrm{SO}_{2}\) that is trapped?

Gas Grill Reaction The burner in a gas grill mixes 24 volumes of air for every one volume of propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) fuel. Like all gases, the volume that propane occupies is directly proportional to the number of moles of it at a given temperature and pressure. Air is \(21 \%\) (by volume) \(\mathrm{O}_{2} .\) Is the flame produced by the burner fuel-rich (excess propane in the reaction mixture), fuel-lean (not enough propane), or stoichiometric (just right)?

A common mineral in Earth's crust has the chemical composition \(34.55 \% \mathrm{Mg}, 19.96 \% \mathrm{Si},\) and \(45.49 \%\) O. What is its empirical formula?

Some indoor air-purification systems work by converting a little of the oxygen in the air to ozone, which kills mold and mildew spores and other biological air pollutants. The chemical equation for the ozone generation reaction is $$3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{O}_{3}(g)$$ It is claimed that one such system generates \(4.0 \mathrm{g} \mathrm{O}_{3}\) per hour from dry air passing through the purifier at a flow of \(5.0 \mathrm{L} / \mathrm{min.}\) If exactly 1 liter of indoor air contains \(0.28 \mathrm{g}\) \(\mathrm{O}_{2},\) what percentage of the \(\mathrm{O}_{2}\) is converted to \(\mathrm{O}_{3}\) by the air purifier?