Chapter 3

Is the element with the largest atomic mass always the element present in the highest percentage by mass in a compound? Explain your answer.

Sometimes the composition of a compound is expressed as a mole percentage, and sometimes as an atom percentage. Are the values of these parameters likely to be the same for a given compound, or different?

Among the naturally occurring hydrocarbons emitted by plants are three compounds named camphene, carene, and thujene. If all three of these compounds have the same percent composition and the same molar mass, do they have the same empirical formula? Do they have the same molecular formula? Are they isomers?

Gasoline consists primarily of a mixture of the hydrocarbons \(\mathrm{C}_{6} \mathrm{H}_{14}, \mathrm{C}_{7} \mathrm{H}_{16}, \mathrm{C}_{8} \mathrm{H}_{18},\) and \(\mathrm{C}_{9} \mathrm{H}_{20} .\) What is the empirical formula of each compound?

Calculate the percent composition of (a) \(\mathrm{Na}_{2} \mathrm{O},\) (b) \(\mathrm{NaOH}\) (c) \(\mathrm{NaHCO}_{3},\) and \((\mathrm{d}) \mathrm{Na}_{2} \mathrm{CO}_{3}\).

Calculate the percent composition of (a) sodium sulfate, (b) dinitrogen tetroxide, (c) strontium nitrate, and (d) aluminum sulfide.

The following compounds have been detected in space. Which of them contains the greatest percentage of carbon by mass? Do any two of the following compounds have the same empirical formula? a. naphthalene, \(\mathrm{C}_{10} \mathrm{H}_{8}\) b. chrysene, \(\mathbf{C}_{18} \mathrm{H}_{12}\) c. pentacene, \(\mathrm{C}_{22} \mathrm{H}_{14}\) d. pyrene, \(\mathrm{C}_{16} \mathrm{H}_{10}\)

Of the nitrogen oxides \(-\mathrm{N}_{2} \mathrm{O}, \mathrm{NO}, \mathrm{N}_{2} \mathrm{O}_{3}, \mathrm{N}_{2} \mathrm{O}_{2}, \mathrm{NO}_{2},\) and \(\mathrm{N}_{2} \mathrm{O}_{4}-\) which are more than \(50 \%\) oxygen by mass? Which, if any, have the same empirical formula?

Methane \(\left(\mathrm{CH}_{4}\right)\) and tetrafluoromethane \(\left(\mathrm{CF}_{4}\right)\) both contain \(20 \%\) carbon per mole. Which one has the greater percent \(C\) by mass?

Silane \(\left(\mathrm{SiH}_{4}\right)\) is used in the electronics industry to manufacture thin films of silicon. What is the percent Si by mass in \(\mathrm{SiH}_{4} ?\) Does silane have the same percent Si by mass as disilane, \(\mathrm{Si}_{2} \mathrm{H}_{6} ?\)

Surgical-Grade Titanium Medical implants and high-quality jewelry items for body piercings are frequently made of a material known as G23Ti, or surgical- grade titanium. The percent composition of the material is \(64.39 \%\) titanium,\(24.19 \%\) aluminum, and \(11.42 \%\) vanadium. What is the empirical formula for surgical-grade titanium?

A sample of an iron-containing compound is \(22.0 \%\) iron, \(50.2 \%\) oxygen, and \(27.8 \%\) chlorine by mass. What is the empirical formula of this compound?

Sour Candy Tartaric acid, \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{6},\) and citric acid, \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7},\) are both used commercially to give sour candies (Figure \(\mathrm{P} 3.87\) ) their characteristic sour taste. Which compound has the larger percent C by mass? (IMAGE CAN'T COPY)

CFCs (chlorofluorocarbons) are molecules used as refrigerants, but they also contribute to the destruction of the ozone layer. One CFC known as Freon consists of two carbon atoms, two fluorine atoms, and four chlorine atoms. What is the empirical formula of Freon? What is its molecular formula?

Asbestosis is a lung disease caused by inhaling asbestos fibers. In addition, fiber from a form of asbestos called chrysotile is considered to be a human carcinogen by the U.S. Department of Health and Human Services. Chrysotile's composition is \(26.31 \%\) magnesium, \(20.20 \%\) silicon, and \(1.45 \%\) hydrogen with the remainder of the mass as oxygen. Determine the empirical formula of chrysotile.

A candle flame produces easily seen specks of soot near the edges of the flame, especially when the candle is moved. A piece of glass held over a candle flame will become coated with soot, which is the result of the incomplete combustion of candle wax. Elemental analysis of a compound extracted from a sample of this soot gave these results: \(92.26 \% \mathrm{C}\) and \(7.74 \%\) H by mass. Calculate the empirical formula of the compound.

Adenine (135.14 g/mol; 44.44\% \(\mathrm{C}, 3.73 \% \mathrm{H}, \text { and } 51.84 \% \mathrm{N})\) was detected in mixtures of HCN, ammonia, and water under conditions that simulate early Earth. This observation suggests a possible origin for one of the bases found in DNA. What are the empirical and molecular formulas for adenine?

Ribose, the sugar found in RNA, has been detected in experiments designed to mimic the conditions of early Earth. If ribose contains \(40.00 \% \mathrm{C}\) \(6.71 \% \mathrm{H},\) and \(53.28 \%\) O, with a molar mass of \(150.13 \mathrm{g} / \mathrm{mol}\).What are the empirical and molecular formulas for ribose?

Explain why it is important for combustion analysis to be carried out in an excess of oxygen.

Why is the quantity of \(\mathrm{CO}_{2}\) obtained in a combustion analysis not a direct measure of the oxygen content of the starting compound?

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

What additional information is needed to determine a molecular formula from the results of an elemental analysis of an organic compound?

If a compound containing nitrogen is subjected to combustion analysis in excess oxygen, what is the most likely molecular formula for the nitrogen- containing product?

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

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

The compound geraniol is on the Food and Drug Administration's GRAS (generally recognized as safe) list and can be used in foods and personal care products. By itself, geraniol smells like roses but it is frequently blended with other fragrances on the GRAS list and then added to products to produce a pleasant peach-or lemon-like aroma. In an analysis, the complete combustion of 175 mg of geraniol produced \(499 \mathrm{mg}\) of \(\mathrm{CO}_{2}\) and \(184 \mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula for geraniol?

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

One of the ingredients in the Native American stomachache remedy derived from common chokecherry is caffeic acid. Combustion of \(1.00 \times 10^{2} \mathrm{mg}\) of caffeic acid yielded \(220 \mathrm{mg}\) of \(\mathrm{CO}_{2}\) and \(40.3 \mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O}\) Determine the empirical formula of caffeic acid.

Coniine, a substance isolated from poison hemlock, contains only carbon, hydrogen, and nitrogen. Combustion of 5.024 mg of coniine yields \(13.90 \mathrm{mg} \mathrm{CO}_{2}\) and \(6.048 \mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula of coniine?

If a reaction vessel contains equal masses of Fe and \(\mathrm{S}\), 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 \(S\)..

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

Give two reasons why the actual yield from a chemical reaction is usually less than the theoretical yield.

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

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

Given the amounts of reactants shown, calculate the theoretical yield in grams of the product indicated by the question mark for each of these unbalanced chemical reactions. a. \(\mathrm{Cu}_{2} \mathrm{O}(s)+\mathrm{H}_{2}(g) \rightarrow \mathrm{Cu}(s)+\mathrm{H}_{2} \mathrm{O}(\ell)\) \(30.0 \mathrm{g} \quad 12.0 \mathrm{g} \quad\) ? \(\mathrm{g}\) b. \(\mathrm{Mg}(s)+\mathrm{HCl}(g) \rightarrow \mathrm{MgCl}_{2}(s)+\mathrm{H}_{2}(g)\) \(24.3 \mathrm{g} \quad 10.0 \mathrm{g}\) \(? \mathrm{g}\) c. \(\mathrm{CuCl}_{2}(a q)+\mathrm{Zn}(s) \rightarrow \mathrm{Cu}(s)+\mathrm{ZnCl}_{2}(a q)\) \(11.6 \mathrm{g} \quad 10.0 \mathrm{g}\) \(? \mathrm{g}\)

Ammonia rapidly reacts with hydrogen chloride, making ammonium chloride. Write a balanced chemical equation for the reaction, and calculate the number of grams of excess reactant when \(3.0 \mathrm{g}\) of \(\mathrm{NH}_{3}\) reacts with \(5.0 \mathrm{g}\) of \(\mathrm{HCl}\).

Sulfur trioxide dissolves in water, producing \(\mathrm{H}_{2} \mathrm{SO}_{4} .\) How much sulfuric acid can be produced from \(10.0 \mathrm{mL}\) of water \((d=1.00 \mathrm{g} / \mathrm{mL})\) and \(25.6 \mathrm{g}\) of \(\mathrm{SO}_{3} ?\)

Phosgenite, a lead compound with the formula \(\mathrm{Pb}_{2} \mathrm{Cl}_{2} \mathrm{CO}_{3},\) is found in ancient Egyptian cosmetics. Phosgenite was prepared by the reaction of \(\mathrm{Pb} \mathrm{O}, \mathrm{NaCl}\) \(\mathrm{H}_{2} \mathrm{O},\) and \(\mathrm{CO}_{2} .\) An unbalanced equation of the reaction is \(\mathrm{PbO}(s)+\mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{CO}_{2}(g) \rightarrow\).$$\mathrm{Pb}_{2} \mathrm{Cl}_{2} \mathrm{CO}_{3}(s)+\mathrm{NaOH}(a q)$$,a. Balance the equation. b. How many grams of phosgenite can be obtained from \(10.0 \mathrm{g}\) of \(\mathrm{PbO}\) and \(10.0 \mathrm{g}\) of \(\mathrm{NaCl}\) in the presence of excess water and \(\mathrm{CO}_{2} ?\) c. If 2.72 g of phosgenite is produced in the laboratory from the amounts of starting materials stated in part (b), what is the percent yield of the reaction?

Potassium superoxide, \(\mathrm{KO}_{2},\) reacts with carbon dioxide to form potassium carbonate and oxygen:\(4 \mathrm{KO}_{2}(s)+2 \mathrm{CO}_{2}(g) \rightarrow 2 \mathrm{K}_{2} \mathrm{CO}_{3}(s)+3 \mathrm{O}_{2}(g)\).This reaction makes potassium superoxide useful in a self-contained breathing apparatus. How much \(\mathrm{O}_{2}\) could be produced from \(2.50 \mathrm{g}\) of \(\mathrm{KO}_{2}\) and \(4.50 \mathrm{g}\) of \(\mathrm{CO}_{2} ?\)

Baking soda (NaHCO \(_{3}\) ) can be made in large quantities by the following reaction: \(\mathrm{NaCl}(a q)+\mathrm{NH}_{3}(a q)+\mathrm{CO}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow\).$$\mathrm{NaHCO}_{3}(s)+\mathrm{NH}_{4} \mathrm{Cl}(a q)$$ If \(10.0 \mathrm{g}\) of \(\mathrm{NaCl}\) reacts with excesses of the other reactants and \(4.2 \mathrm{g}\) of \(\mathrm{NaHCO}_{3}\) is isolated, what is the percent yield of the reaction?

Yeast converts glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) into ethanol \((d=0.789 \mathrm{g} / \mathrm{mL})\) in a process called fermentation. An equation for the reaction can be written as follows: $$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q) \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+\mathrm{CO}_{2}(g)$$ a. Write a balanced chemical equation for this fermentation reaction. b. If \(100.0 \mathrm{g}\) of glucose yields \(50.0 \mathrm{mL}\) of ethanol, what is the percent yield for the reaction?

A 1 -liter sample of seawater contains \(19.4 \mathrm{g}\) of \(\mathrm{Cl}^{-}, 10.8 \mathrm{g}\) of \(\mathrm{Na}^{+},\) and \(1.29 \mathrm{g}\) of \(\mathrm{Mg}^{2+}\) a. How many moles of each ion are present? b. If we evaporated the seawater, would there be enough Cl "present to form the chloride salts of all the sodium and magnesium present?

As a solution of copper sulfate slowly evaporates, beautiful blue crystals made of copper(II) and sulfate ions form such that water molecules are trapped inside the crystals. The overall formula of the compound 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 in the compound is driven off as steam. What mass percentage of the original sample of the blue solid is lost as a result?

Aluminum is mined as the mineral bauxite, which consists primarily of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) (alumina). a. How much aluminum is produced from 1 metric ton. $$\begin{array}{r}\left(1 \text { metric ton }=10^{3} \mathrm{kg}\right) \text { of } \mathrm{Al}_{2} \mathrm{O}_{3} ? \\\2 \mathrm{Al}_{2} \mathrm{O}_{3}(s) \rightarrow 4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \end{array}$$.b. The oxygen produced in part (a) is allowed to react with carbon to produce carbon monoxide:$$\mathrm{O}_{2}(g)+2 \mathrm{C}(s) \rightarrow 2 \mathrm{CO}(g)$$.Balance the following equation describing the reaction of alumina with carbon:$$\mathrm{Al}_{2} \mathrm{O}_{3}(s)+\mathrm{C}(s) \rightarrow \mathrm{Al}(s)+\mathrm{CO}(g)$$. c. How much CO can be produced from the \(\mathrm{O}_{2}\) made in part (a)?

Gold can be extracted from the surrounding rock by 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.\(4 \mathrm{Au}(s)+8 \mathrm{NaCN}(a q)+\mathrm{O}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow\).\(4 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+4 \mathrm{NaOH}(a q)\) \(2 \mathrm{NaAu}(\mathrm{CN})_{2}(a q)+\mathrm{Zn}(s) \rightarrow 2 \mathrm{Au}(s)+\mathrm{Na}_{2}\left[\mathrm{Zn}(\mathrm{CN})_{4}\right](a q)\).a. If a sample of rock contains \(0.009 \%\) gold by mass, how much \(\mathrm{NaCN}\) is needed to extract the gold from 1 metric ton ( 1 metric ton \(=10^{3} \mathrm{kg}\) ) of rock as \(\mathrm{NaAu}(\mathrm{CN})_{2} ?\) 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 cube of gold?

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 itrogen oxides, leaving behind a product with the formula \(\mathrm{U}_{a} \mathrm{O}_{b}\) that is \(83.22 \% \mathrm{U}\) 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, \(\mathrm{U}_{c} \mathrm{O}_{d},\) with a higher uranium content, \(84.8 \% \mathrm{U} .\) What are the values of \(c\) and \(d ?\) What is the charge on \(\mathrm{U}\) in \(\mathrm{U}_{a} \mathrm{O}_{b} ?\) 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, \(1.328 \mathrm{g}\) of \(\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}\left(\mathrm{H}_{2} \mathrm{O}\right)_{z}\) produced \(1.042 \mathrm{g}\) of \(\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}\) Continued heating generated \(0.742 \mathrm{g}\) of \(\mathrm{U}_{n} \mathrm{O}_{m} .\) Using the information in parts (a) and (b), calculate \(x, y,\) and \(z\).

Large quantities of fertilizer are washed into the Mississippi River from agricultural land in the Midwest. The excess nutrients collect in the Gulf of Mexico, promoting the growth of algae and endangering other aquatic life.a. One commonly used fertilizer is ammonium nitrate. What is the chemical formula of ammonium nitrate? b. Corn farmers typically use \(5.0 \times 10^{3} \mathrm{kg}\) of ammonium nitrate per square kilometer of cornfield per year. Ammonium nitrate can be prepared by the following reaction: $$\mathrm{NH}_{3}(a q)+\mathrm{HNO}_{3}(a q) \rightarrow \mathrm{NH}_{4} \mathrm{NO}_{3}(a q)$$ How much nitric acid would be required to make the fertilizer needed for \(1 \mathrm{km}^{2}\) of cornfield per year? c. The ammonium ions can be converted into \(\mathrm{NO}_{3}^{-}\) 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 \(5.0 \times 10^{2} \mathrm{kg}\) of fertilizer ends up as nitrate, how much oxygen would be consumed?

Composition of Over-the-Counter Medicines Calculate the number of molecules or formula units of compound in each of the following common, over-the-counter medications: a. ibuprofen, a pain reliever and fever reducer that contains \(200.0 \mathrm{mg}\) of the active ingredient, \(\mathrm{C}_{13} \mathrm{H}_{18} \mathrm{O}_{2}\) b. an antacid containing 500.0 mg of calcium carbonate c. an allergy tablet containing 4 mg of chlorpheniramine $$\left(\mathrm{C}_{16} \mathrm{H}_{19} \mathrm{ClN}_{2}\right)$$.

The common pain relievers aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right),\) acetaminophen \(\left(\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{NO}_{2}\right),\) and naproxen sodium \(\left(\mathrm{C}_{14} \mathrm{H}_{13} \mathrm{O}_{3} \mathrm{Na}\right)\) are all available in tablets containing \(200.0 \mathrm{mg}\) of the active ingredient. Which compound contains the greatest number of molecules per tablet? How many molecules of the active ingredient are present in each tablet?