Chapter 4

Chromium(II) sulfate, \(\mathrm{CrSO}_{4^{\prime}}\) is a reagent that has been used in certain applications to help reduce carbon-carbon double bonds \((\mathrm{C}=\mathrm{C})\) in molecules to single bonds ( \(\mathrm{C}-\mathrm{C}\) ). The reagent can be prepared via the following reaction. $$\begin{array}{c} 4 \mathrm{Zn}(\mathrm{s})+\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}(\mathrm{aq})+7 \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \longrightarrow 4 \mathrm{ZnSO}_{4}(\mathrm{aq})+2 \mathrm{CrSO}_{4}(\mathrm{aq})+\mathrm{K}_{2} \mathrm{SO}_{4}(\mathrm{aq})+7 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \end{array}$$

Titanium tetrachloride, \(\mathrm{TiCl}_{4}\) is prepared by the reaction below. $$\begin{aligned} &3 \mathrm{TiO}_{2}(\mathrm{s})+4 \mathrm{C}(\mathrm{s})+6 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow 3 \mathrm{TiCl}_{4}(\mathrm{g})+2 \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{CO}(\mathrm{g}) \end{aligned}$$ What is the maximum mass of \(\mathrm{TiCl}_{4}\) that can be obtained from \(35 \mathrm{g} \mathrm{TiO}_{2^{\prime}} 45 \mathrm{g} \mathrm{Cl}_{2^{\prime}}\) and \(11 \mathrm{g} \mathrm{C} ?\)

In the reaction of \(277 \mathrm{g} \mathrm{CCl}_{4}\) with an excess of \(\mathrm{HF}\) \(187 \mathrm{g} \mathrm{CCl}_{2} \mathrm{F}_{2}\) is obtained. What are the (a) theoretical, (b) actual, and (c) percent yields of this reaction? $$\mathrm{CCl}_{4}+2 \mathrm{HF} \longrightarrow \mathrm{CCl}_{2} \mathrm{F}_{2}+2 \mathrm{HCl}$$

In the reaction shown, \(100.0 \mathrm{g} \mathrm{C}_{6} \mathrm{H}_{11} \mathrm{OH}\) yielded \(64.0 \mathrm{g}\) \(\mathrm{C}_{6} \mathrm{H}_{10} .\) (a) What is the theoretical yield of the reaction? (b) What is the percent yield? (c) What mass of \(\mathrm{C}_{6} \mathrm{H}_{11} \mathrm{OH}\) would produce \(100.0 \mathrm{g} \mathrm{C}_{6} \mathrm{H}_{10}\) if the percent yield is that determined in part (b)? $$\mathrm{C}_{6} \mathrm{H}_{11} \mathrm{OH} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{10}+\mathrm{H}_{2} \mathrm{O}$$

Cryolite, \(\mathrm{Na}_{3} \mathrm{AlF}_{6^{\prime}}\) is an important industrial reagent. It is made by the reaction below. $$\begin{array}{r} \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})+6 \mathrm{NaOH}(\mathrm{aq})+12 \mathrm{HF}(\mathrm{g}) \longrightarrow 2 \mathrm{Na}_{3} \mathrm{AlF}_{6}(\mathrm{s})+9 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \end{array}$$ In an experiment, \(7.81 \mathrm{g} \mathrm{Al}_{2} \mathrm{O}_{3}\) and excess \(\mathrm{HF}(\mathrm{g})\) were dissolved in 3.50 L of 0.141 M NaOH. If 28.2 g \(\mathrm{Na}_{3} \mathrm{AlF}_{6}\) was obtained, then what is the percent yield for this experiment?

Nitrogen gas, \(\mathrm{N}_{2}\), can be prepared by passing gaseous ammonia over solid copper(II) oxide, \(\mathrm{CuO}\), at high temperatures. The other products of the reaction are solid copper, \(\mathrm{Cu},\) and water vapor. In a certain experiment, a reaction mixture containing \(18.1 \mathrm{g} \mathrm{NH}_{3}\) and \(90.4 \mathrm{g}\) CuO yields \(6.63 \mathrm{g} \mathrm{N}_{2}\). Calculate the percent yield for this experiment.

Azobenzene, an intermediate in the manufacture of dyes, can be prepared from nitrobenzene by reaction with triethylene glycol in the presence of \(\mathrm{Zn}\) and KOH. In one reaction, 0.10 L of nitrobenzene \((d=1.20 \mathrm{g} / \mathrm{mL})\) and \(0.30 \mathrm{L}\) of triethylene glycol \((d=1.12 \mathrm{g} / \mathrm{mL})\) yields \(55 \mathrm{g}\) azobenzene. What are the (a) theoretical yield, (b) actual yield, and (c) percent yield of this reaction? $$ 2 \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NO}_{2}+4 \mathrm{C}_{6} \mathrm{H}_{14} \mathrm{O}_{4} \frac{\mathrm{Zn}}{\mathrm{KOH}} $$ nitrobenzene triethylene glycol $$ \left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{N}\right)_{2}+4 \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{4}+4 \mathrm{H}_{2} \mathrm{O} $$ azobenzene

How many grams of commercial acetic acid (97\% \(\mathrm{CH}_{3} \mathrm{COOH}\) by mass) must be allowed to react with an excess of \(\mathrm{PCl}_{3}\) to produce \(75 \mathrm{g}\) of acetyl chloride \(\left(\mathrm{CH}_{3} \mathrm{COCl}\right),\) if the reaction has a \(78.2 \%\) yield? $$\begin{aligned} \mathrm{CH}_{3} \mathrm{COOH}+\mathrm{PCl}_{3} & \longrightarrow \mathrm{CH}_{3} \mathrm{COCl}+ \mathrm{H}_{3} \mathrm{PO}_{3}(\text { not balanced }) \end{aligned}$$

Suppose that reactions (a) and (b) each have a \(92 \%\) yield. Starting with \(112 \mathrm{g} \mathrm{CH}_{4}\) in reaction \((\mathrm{a})\) and an excess of \(\mathrm{Cl}_{2}(\mathrm{g}),\) how many grams of \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) are formed in reaction (b)? (a) \(\mathrm{CH}_{4}+\mathrm{Cl}_{2} \longrightarrow \mathrm{CH}_{3} \mathrm{Cl}+\mathrm{HCl}\) (b) \(\mathrm{CH}_{3} \mathrm{Cl}+\mathrm{Cl}_{2} \longrightarrow \mathrm{CH}_{2} \mathrm{Cl}_{2}+\mathrm{HCl}\)

An essentially \(100 \%\) yield is necessary for a chemical reaction used to analyze a compound, but it is almost never expected for a reaction that is used to synthesize a compound. Explain this difference.

How ma475.15 grams \(\mathrm{HCl}\)ny grams of HCl are consumed in the reaction of \(425 \mathrm{g}\) of a mixture containing \(35.2 \% \mathrm{MgCO}_{3}\) and \(64.8 \% \mathrm{Mg}(\mathrm{OH})_{2},\) by mass? $$\begin{array}{c} \mathrm{Mg}(\mathrm{OH})_{2}+2 \mathrm{HCl} \longrightarrow \mathrm{MgCl}_{2}+2 \mathrm{H}_{2} \mathrm{O} \\ \mathrm{MgCO}_{3}+2 \mathrm{HCl} \longrightarrow \mathrm{MgCl}_{2}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}(\mathrm{g}) \end{array}$$

How many grams of \(\mathrm{CO}_{2}\) are produced in the complete combustion of \(406 \mathrm{g}\) of a bottled gas that consists of \(72.7 \%\) propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) and \(27.3 \%\) butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\) by mass?

High-purity silicon is obtained using a three-step process. The first step involves heating solid silicon dioxide, \(\mathrm{SiO}_{2^{\prime}}\) with solid carbon to give solid silicon and carbon monoxide gas. In the second step, solid silicon is converted into liquid silicon tetrachloride, \(\mathrm{SiCl}_{4}\) by treating it with chlorine gas. In the last step, \(\mathrm{SiCl}_{4}\) is treated with hydrogen gas to give ultrapure solid silicon and hydrogen chloride gas. (a) Write balanced chemical equations for the steps involved in this three- step process. (b) Calculate the masses of carbon, chlorine, and hydrogen required per kilogram of silicon.

The following set of reactions is to be used as the basis of a method for producing nitric acid, \(\mathrm{HNO}_{3}\) Calculate the minimum masses of \(\mathrm{N}_{2}, \mathrm{H}_{2^{\prime}}\) and \(\mathrm{O}_{2}\) required per kilogram of \(\mathrm{HNO}_{3}\) $$\begin{array}{l} \mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g}) \\ 4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\ 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) \\ 3 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow 2 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{NO}(\mathrm{g}) \end{array}$$

When a solid mixture of \(\mathrm{MgCO}_{3}\) and \(\mathrm{CaCO}_{3}\) is heated strongly, carbon dioxide gas is given off and a solid mixture of \(\mathrm{Mg} \mathrm{O}\) and \(\mathrm{CaO}\) is obtained. If a \(24.00 \mathrm{g}\) sample of a mixture of \(\mathrm{MgCO}_{3}\) and \(\mathrm{CaCO}_{3}\) produces \(12.00 \mathrm{g} \mathrm{CO}_{2}\) then what is the percentage by mass of \(\mathrm{MgCO}_{3}\) in the original mixture?

Write chemical equations to represent the following reactions. (a) Limestone rock (calcium carbonate) is heated (calcined) and decomposes to calcium oxide and carbon dioxide gas. (b) Zinc sulfide ore is heated in air (roasted) and is converted to zinc oxide and sulfur dioxide gas. (Note that oxygen gas in the air is also a reactant.) (c) Propane gas reacts with gaseous water to produce a mixture of carbon monoxide and hydrogen gases. (This mixture, called synthesis gas, is used to produce a variety of organic chemicals.) (d) Sulfur dioxide gas is passed into an aqueous solution containing sodium sulfide and sodium carbonate. The reaction products are carbon dioxide and an aqueous solution of sodium thiosulfate.

Write chemical equations to represent the following reactions. (a) Calcium phosphate is heated with silicon dioxide and carbon, producing calcium silicate \(\left(\mathrm{CaSiO}_{3}\right)\) phosphorus ( \(\mathrm{P}_{4}\) ), and carbon monoxide. The phosphorus and chlorine react to form phosphorus trichloride, and the phosphorus trichloride and water react to form phosphorous acid. (b) Copper metal reacts with gaseous oxygen, carbon dioxide, and water to form green basic copper carbonate, \(\mathrm{Cu}_{2}(\mathrm{OH})_{2} \mathrm{CO}_{3}\) (a reaction responsible for the formation of the green patina, or coating, often seen on outdoor bronze statues). (c) White phosphorus and oxygen gas react to form tetraphosphorus decoxide. The tetraphosphorus decoxide reacts with water to form an aqueous solution of phosphoric acid. (d) Calcium dihydrogen phosphate reacts with sodium hydrogen carbonate (bicarbonate), producing calcium phosphate, sodium hydrogen phosphate, carbon dioxide, and water (the principal reaction occurring when ordinary baking powder is added to cakes, bread, and biscuits).

Chalkboard chalk is made from calcium carbonate and calcium sulfate, with minor impurities such as \(\mathrm{SiO}_{2} .\) Only the \(\mathrm{CaCO}_{3}\) reacts with dilute \(\mathrm{HCl}(\mathrm{aq})\) What is the mass percent \(\mathrm{CaCO}_{3}\) in a piece of chalk if a 3.28 -g sample yields \(0.981 \mathrm{g} \mathrm{CO}_{2}(\mathrm{g}) ?\) $$\begin{aligned} \mathrm{CaCO}_{3}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) & \longrightarrow \mathrm{CaCl}_{2}(\mathrm{aq}) +\mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{CO}_{2}(\mathrm{g}) \end{aligned}$$

Hydrogen gas, \(\mathrm{H}_{2}(\mathrm{g}),\) is passed over \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})\) at \(400^{\circ} \mathrm{C} .\) Water vapor is formed together with a black residue-a compound consisting of \(72.3 \% \mathrm{Fe}\) and \(27.7 \%\) O. Write a balanced equation for this reaction.

A sulfide of iron, containing \(36.5 \%\) S by mass, is heated in \(\mathrm{O}_{2}(\mathrm{g}),\) and the products are sulfur dioxide and an oxide of iron containing \(27.6 \%\) O, by mass. Write a balanced chemical equation for this reaction.

Water and ethanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathrm{l}),\) are miscible, that is, they can be mixed in all proportions. However, when these liquids are mixed, the total volume of the resulting solution is not equal to the sum of the pure liquid volumes, and we say that the volumes are not additive. For example, when \(50.0 \mathrm{mL}\) of water and \(50.0 \mathrm{mL}\) of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathrm{l}),\) are mixed at \(20^{\circ} \mathrm{C},\) the total volume of the solution is \(96.5 \mathrm{mL}\), not \(100.0 \mathrm{mL}\). (The volumes are not additive because the interactions and packing of water molecules are slightly different from the interactions and packing of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) molecules.) Calculate the molarity of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) in a solution prepared by mixing \(50.0 \mathrm{mL}\) of water and \(50.0 \mathrm{mL}\) of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathrm{l})\) at \(20^{\circ} \mathrm{C} .\) At this temperature, the densities of water and ethanol are 0.99821 \(\mathrm{g} / \mathrm{mL}\) and \(0.7893 \mathrm{g} / \mathrm{mL},\) respectively.

When water and methanol, \(\mathrm{CH}_{3} \mathrm{OH}(\mathrm{l}),\) are mixed, the total volume of the resulting solution is not equal to the sum of the pure liquid volumes. (Refer to Exercise 99 for an explanation.) When \(72.061 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) and \(192.25 \mathrm{g}\) \(\mathrm{CH}_{3} \mathrm{OH}\) are mixed at \(25^{\circ} \mathrm{C},\) the resulting solution has a density of \(0.86070 \mathrm{g} / \mathrm{mL} .\) At \(25^{\circ} \mathrm{C},\) the densities of water and methanol are \(0.99705 \mathrm{g} / \mathrm{mL}\) and \(0.78706\) \(\mathrm{g} / \mathrm{mL},\) respectively. (a) Calculate the volumes of the pure liquid samples and the solution, and show that the pure liquid volumes are not additive. [ Hint: Although the volumes are not additive, the masses are.] (b) Calculate the molarity of \(\mathrm{CH}_{3} \mathrm{OH}\) in this solution.

What volume of \(0.149 \mathrm{M} \mathrm{HCl}\) must be added to \(1.00 \times 10^{2} \mathrm{mL}\) of \(0.285 \mathrm{M} \mathrm{HCl}\) so that the resulting solution has a molarity of \(0.205 \mathrm{M} ?\) Assume that the volumes are additive.

What volume of \(0.0175 \mathrm{M} \mathrm{CH}_{3} \mathrm{OH}\) must be added to \(50.0 \mathrm{mL}\) of \(0.0248 \mathrm{M} \mathrm{CH}_{3} \mathrm{OH}\) so that the resulting solution has a molarity of exactly \(0.0200 \mathrm{M}\) ? Assume that the volumes are additive.

What is the molarity of \(\mathrm{NaCl}(\mathrm{aq})\) if a solution has 1.52 ppm Na? Assume that NaCl is the only source of Na and that the solution density is \(1.00 \mathrm{g} / \mathrm{mL}\) (The unit \(p p m\) is parts per million; here it can be taken to mean g Na per million grams of solution.)

How many milligrams \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) must be present in \(50.0 \mathrm{L}\) of a solution containing \(2.35 \mathrm{ppm} \mathrm{Ca} ?\) [Hint: See also Exercise 103 .]

A drop \((0.05 \mathrm{mL})\) of \(12.0 \mathrm{M} \mathrm{HCl}\) is spread over a sheet of thin aluminum foil. Assume that all the acid reacts with, and thus dissolves through, the foil. What will be the area, in \(\mathrm{cm}^{2}\), of the cylindrical hole produced? (Density of \(\mathrm{Al}=2.70 \mathrm{g} / \mathrm{cm}^{3} ;\) foil thickness \(=0.10 \mathrm{mm} .)\) \(2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \longrightarrow 2 \mathrm{AlCl}_{3}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{g})\)

A small piece of zinc is dissolved in \(50.00 \mathrm{mL}\) of \(1.035 \mathrm{M}\) HCl. At the conclusion of the reaction, the concentration of the \(50.00 \mathrm{mL}\) sample is redetermined and found to be \(0.812 \mathrm{M} \mathrm{HCl} .\) What must have been the mass of the piece of zinc that dissolved? $$\mathrm{Zn}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \longrightarrow \mathrm{ZnCl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g})$$

A seawater sample has a density of \(1.03 \mathrm{g} / \mathrm{mL}\) and \(2.8 \% \mathrm{NaCl}\)l by mass. A saturated solution of \(\mathrm{NaCl}\) in water is \(5.45 \mathrm{M} \mathrm{NaCl} .\) How many liters of water would have to be evaporated from \(1.00 \times 10^{6} \mathrm{L}\) of the seawater before \(\mathrm{NaCl}\) would begin to crystallize? (A saturated solution contains the maximum amount of dissolved solute possible.)

A 99.8 mL sample of a solution that is \(120 \%\) KI by mass \((d=1.093 \mathrm{g} / \mathrm{mL})\) is added to \(96.7 \mathrm{mL}\) of another solution that is \(14.0 \% \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) by mass \((d=1.134 \mathrm{g} / \mathrm{mL})\) How many grams of \(\mathrm{PbI}_{2}\) should form? \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+2 \mathrm{KI}(\mathrm{aq}) \longrightarrow \mathrm{PbI}_{2}(\mathrm{s})+2 \mathrm{KNO}_{3}(\mathrm{aq})\)

Solid calcium carbonate, \(\mathrm{CaCO}_{3}(\mathrm{s}),\) reacts with \(\mathrm{HCl}(\mathrm{aq})\) to form \(\mathrm{H}_{2} \mathrm{O}, \mathrm{CaCl}_{2}(\mathrm{aq}),\) and \(\mathrm{CO}_{2}(\mathrm{g}) .\) If a \(45.0 \mathrm{g}\) sample of \(\mathrm{CaCO}_{3}(\mathrm{s})\) is added to \(1.25 \mathrm{L}\) of \(\mathrm{HCl}(\mathrm{aq})\) that is \(25.7 \% \mathrm{HCl}\) by mass \((d=1.13 \mathrm{g} / \mathrm{mL})\) what will be the molarity of \(\mathrm{HCl}\) in the solution after the reaction is completed? Assume that the solution volume remains constant.

A 2.05 g sample of an iron-aluminum alloy (ferroaluminum) is dissolved in excess HCl(aq) to produce \(0.105 \mathrm{g} \mathrm{H}_{2}(\mathrm{g}) .\) What is the percent composition, by mass, of the ferroaluminum? $$\begin{array}{c} \mathrm{Fe}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \longrightarrow \mathrm{FeCl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g}) \\ 2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \longrightarrow 2 \mathrm{AlCl}_{3}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{g}) \end{array}$$

An organic liquid is either methyl alcohol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) ethyl alcohol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right),\) or a mixture of the two. A 0.220-g sample of the liquid is burned in an excess of \(\mathrm{O}_{2}(\mathrm{g})\) and yields \(0.352 \mathrm{g} \mathrm{CO}_{2}(\mathrm{g}) .\) Is the liquid a pure alcohol or a mixture of the two?

The manufacture of ethyl alcohol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) yields diethyl ether, \(\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O}\) as a by-product. The complete combustion of a \(1.005 \mathrm{g}\) sample of the product of this process yields \(1.963 \mathrm{g} \mathrm{CO}_{2} .\) What must be the mass percents of \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right),\) and of \(\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O}\) in this sample?

A mixture contains only \(\mathrm{CuCl}_{2}\) and \(\mathrm{FeCl}_{3}\). A \(0.7391 \mathrm{g}\) sample of the mixture is completely dissolved in water and then treated with \(\mathrm{AgNO}_{3}(\) aq). The following reactions occur. $$\begin{aligned} &\mathrm{CuCl}_{2}(\mathrm{aq})+2 \mathrm{AgNO}_{3}(\mathrm{aq}) \longrightarrow 2 \mathrm{AgCl}(\mathrm{s})+\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) \end{aligned}$$ $$\begin{aligned} &\mathrm{FeCl}_{3}(\mathrm{aq})+3 \mathrm{AgNO}_{3}(\mathrm{aq}) \longrightarrow 3 \mathrm{AgCl}(\mathrm{s})+\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}(\mathrm{aq})\end{aligned}$$ If it takes \(86.91 \mathrm{mL}\) of \(0.1463 \mathrm{M} \mathrm{AgNO}_{3}\) solution to precipitate all the chloride as \(\mathrm{AgCl}\), then what is the percentage by mass of copper in the mixture?

Under appropriate conditions, copper sulfate, potassium chromate, and water react to form a product containing \(\mathrm{Cu}^{2+},\) \(\mathrm{CrO}_{4}{^2}{^-},\) and \(\mathrm{OH}^{-}\) ions. Analysis of the compound yields \(48.7 \% \mathrm{Cu}^{2+}, 35.6 \% \mathrm{CrO}_{4}{^2}{-},\) and \(15.7 \% \mathrm{OH}^{-}\). (a) Determine the empirical formula of the compound. (b) Write a plausible equation for the reaction.

Write a chemical equation to represent the complete combustion of malonic acid, a compound with \(34.62 \% \mathrm{C}, 3.88 \% \mathrm{H},\) and \(61.50 \% \mathrm{O},\) by mass.

Aluminum metal and iron(III) oxide react to give aluminum oxide and iron metal. What is the maximum mass of iron that can be obtained from a reaction mixture containing \(2.5 \mathrm{g}\) of aluminum and \(9.5 \mathrm{g}\) of iron(III) oxide. What mass of the excess reactant remains?

Silver nitrate is a very expensive chemical. For a particular experiment, you need \(100.0 \mathrm{mL}\) of \(0.0750 \mathrm{M}\) \(\mathrm{AgNO}_{3},\) but only \(60 \mathrm{mL}\) of \(0.0500 \mathrm{M} \mathrm{AgNO}_{3}\) is available. You decide to pipet exactly \(50.00 \mathrm{mL}\) of the solution into a \(100.0 \mathrm{mL}\) flask, add an appropriate mass of \(\mathrm{AgNO}_{3},\) and then dilute the resulting solution to exactly \(100.0 \mathrm{mL}\). What mass of \(\mathrm{AgNO}_{3}\) must you use?

A method for eliminating oxides of nitrogen (e.g., \(\mathrm{NO}_{2}\) ) from automobile exhaust gases is to pass the exhaust gases over solid cyanuric acid, \(\mathrm{C}_{3} \mathrm{N}_{3}(\mathrm{OH})_{3}\) When the hot exhaust gases come in contact with cyanuric acid, solid \(\mathrm{C}_{3} \mathrm{N}_{3}(\mathrm{OH})_{3}\) decomposes into isocyanic acid vapor, HNCO(g), which then reacts with \(\mathrm{NO}_{2}\) in the exhaust gases to give \(\mathrm{N}_{2}, \mathrm{CO}_{2^{\prime}}\) and \(\mathrm{H}_{2} \mathrm{O}\) How many grams of \(\mathrm{C}_{3} \mathrm{N}_{3}(\mathrm{OH})_{3}\) are needed per gram of \(\mathrm{NO}_{2}\) in this method? [Hint: To balance the equation for reaction between HNCO and \(\mathrm{NO}_{2}\), balance with respect to each kind of atom in this order: \(\mathrm{H}, \mathrm{C}, \mathrm{O}, \text { and } \mathrm{N} .]\)

For a specific reaction, ammonium dichromate is the only reactant and chromium(III) oxide and water are two of the three products. What is the third product and how many grams of this product are produced per kilogram of ammonium dichromate decomposed?

It is desired to produce as large a volume of \(1.25 \mathrm{M}\) urea \(\left[\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(\mathrm{aq})\right]\) as possible from these three sources: \(345 \mathrm{mL}\) of \(1.29 \mathrm{M} \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}, 485 \mathrm{mL}\) of \(0.653 \mathrm{M}\) \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2},\) and \(835 \mathrm{mL}\) of \(0.775 \mathrm{M} \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2} .\) How can this be done? What is the maximum volume of this solution obtainable?

It is often difficult to determine the concentration of a species in solution, particularly if it is a biological species that takes part in complex reaction pathways. One way to do this is through a dilution experiment with labeled molecules. Instead of molecules, however, we will use fish. An angler wants to know the number of fish in a particular pond, and so puts an indelible mark on 100 fish and adds them to the pond's existing population. After waiting for the fish to spread throughout the pond, the angler starts fishing, eventually catching 18 fish. Of these, five are marked. What is the total number of fish in the pond?

Lead nitrate and potassium iodide react in aqueous solution to form a yellow precipitate of lead iodide. In one series of experiments, the masses of the two reactants were varied, but the total mass of the two was held constant at \(5.000 \mathrm{g}\). The lead iodide formed was filtered from solution, washed, dried, and weighed. The table gives data for a series of reactions. $$\begin{array}{lll} \hline & \text { Mass of Lead } & \text { Mass of Lead } \\ \text { Experiment } & \text { Nitrate, } g & \text { lodide, } g \\ \hline 1 & 0.500 & 0.692 \\ 2 & 1.000 & 1.388 \\ 3 & 1.500 & 2.093 \\ 4 & 3.000 & 2.778 \\ 5 & 4.000 & 1.391 \\ \hline \end{array}$$ (a) Plot the data in a graph of mass of lead iodide versus mass of lead nitrate, and draw the appropriate curve(s) connecting the data points. What is the maximum mass of precipitate that can be obtained? (b) Explain why the maximum mass of precipitate is obtained when the reactants are in their stoichiometric proportions. What are these stoichiometric proportions expressed as a mass ratio, and as a mole ratio? (c) Show how the stoichiometric proportions determined in part (b) are related to the balanced equation for the reaction.

Baking soda, \(\mathrm{NaHCO}_{3}\), is made from soda ash, a common name for sodium carbonate. The soda ash is obtained in two ways. It can be manufactured in a process in which carbon dioxide, ammonia, sodium chloride, and water are the starting materials. Alternatively, it is mined as a mineral called trona (left photo). Whether the soda ash is mined or manufactured, it is dissolved in water and carbon dioxide is bubbled through the solution. Sodium bicarbonate precipitates from the solution. As a chemical analyst you are presented with two samples of sodium bicarbonate-one from the manufacturing process and the other derived from trona. You are asked to determine which is purer and are told that the impurity is sodium carbonate. You decide to treat the samples with just sufficient hydrochloric acid to convert all the sodium carbonate and bicarbonate to sodium chloride, carbon dioxide, and water. You then precipitate silver chloride in the reaction of sodium chloride with silver nitrate. A \(6.93 \mathrm{g}\) sample of baking soda derived from trona gave \(11.89 \mathrm{g}\) of silver chloride. A \(6.78 \mathrm{g}\) sample from manufactured sodium carbonate gave \(11.77 \mathrm{g}\) of silver chloride. Which sample is purer, that is, which has the greater mass percent \(\mathrm{NaHCO}_{3} ?\)

In your own words, define or explain these terms or symbols. (a) \(\stackrel{\Delta}{\longrightarrow}\) (b) (aq) (c) stoichiometric coefficient (d) overall equation

Briefly describe (a) balancing a chemical equation; (b) preparing a solution by dilution; (c) determining the limiting reactant in a reaction.

Explain the important distinctions between (a) chemical formula and chemical equation; (b) stoichiometric coefficient and stoichiometric factor; (c) solute and solvent; (d) actual yield and percent yield; (e) consecutive and simultaneous reactions.

When the equation below is balanced, the correct set of stoichiometric coefficients is (a) \(1,6 \longrightarrow 1,3,4;\) (b) \(1,4 \longrightarrow 1,2,2 ;\) (c) \(2,6 \longrightarrow 2,3,2;\) (d) \(3,8 \longrightarrow 3,4,2\) \(\begin{aligned} ? \mathrm{Cu}(\mathrm{s})+? \mathrm{HNO}_{3}(\mathrm{aq}) & \longrightarrow ? \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+? \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+? \mathrm{NO}(\mathrm{g}) \end{aligned}\)

A reaction mixture contains \(1.0 \mathrm{mol} \mathrm{CaCN}_{2}\) (calcium cyanamide) and \(1.0 \mathrm{mol} \mathrm{H}_{2} \mathrm{O}\). The maximum number of moles of \(\mathrm{NH}_{3}\) produced is (a) \(3.0 ;\) (b) 2.0 (c) between 1.0 and 2.0; (d) less than 1.0. $$\mathrm{CaCN}_{2}(\mathrm{s})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow \mathrm{CaCO}_{3}+2 \mathrm{NH}_{3}(\mathrm{g})$$