Chapter 11

How is a mole ratio used to find the limiting reactant?

Explain why the statement, "The limiting reactant is the reactant with the lowest mass" is incorrect.

Nickel-Iron Battery In 1901 , Thomas Edison invented the nickel-iron battery. The following reaction takes place in the battery. \begin{equation} \mathrm{Fe}(\mathrm{s})+2 \mathrm{NiO}(\mathrm{OH})(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \end{equation} \begin{equation} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\mathrm{Fe}(\mathrm{OH})_{2}(\mathrm{s})+2 \mathrm{Ni}(\mathrm{OH})_{2}(\mathrm{aq}) How many mol of \(\mathrm{Fe}(\mathrm{OH})_{2}\) is produced when 5.00 \(\mathrm{mol}\) of Fe and 8.00 \(\mathrm{mol}\) of \(\mathrm{NiO}(\mathrm{OH})\) react? \end{equation}

One of the few xenon compounds that form is cesium xenon heptafluoride (CsXeF 7\() .\) How many moles of CsXeF_ can be produced from the reaction of 12.5 \(\mathrm{mol}\) of cesium fluoride with 10.0 mol of xenon hexafluoride? \begin{equation} \mathrm{CsF}(\mathrm{s})+\mathrm{XeF}_{6}(\mathrm{s}) \rightarrow \mathrm{Cs} \mathrm{XeF}_{7}(\mathrm{s}) \end{equation}

Iron Production Iron is obtained commercially by the reaction of hematite \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)\) with carbon monoxide. How many grams of iron is produced when 25.0 \(\mathrm{mol}\) of hematite reacts with 30.0 \(\mathrm{mol}\) of carbon monoxide? \begin{equation} \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{CO}(\mathrm{g}) \rightarrow 2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}_{2}(\mathrm{g}) \end{equation}

The reaction of chlorine gas with solid phosphorus (P \(_{4} )\) produces solid phosphorus pentachloride. When 16.0 \(\mathrm{g}\) of chlorine reacts with 23.0 \(\mathrm{g}\) of \(\mathrm{P}_{4},\) which reactant is limiting? Which reactant is in excess?

Alkaline Battery An alkaline battery produces electrical energy according to this equation. \begin{equation} \mathrm{Zn}(\mathrm{s})+2 \mathrm{MnO}_{2}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \end{equation} \begin{equation} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\mathrm{Zn}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{Mn}_{2} \mathrm{O}_{3}(\mathrm{s}) \end{equation} \begin{equation} \begin{array}{l}{\text { a. Determine the limiting reactant if } 25.0 \mathrm{g} \text { of } \mathrm{Zn} \text { and }} \\ {30.0 \mathrm{g} \text { of } \mathrm{MnO}_{2} \text { are used. }} \\ {\text { b. Determine the mass of } \mathrm{Zn}(\mathrm{OH})_{2} \text { produced. }}\end{array} \end{equation}

Lithium reacts spontaneously with bromine to produce lithium bromide. Write the balanced chemical equation for the reaction. If 25.0 g of lithium and 25.0 g of bromine are present at the beginning of the reaction, determine \begin{equation} \begin{array}{l}{\text { a. the limiting reactant. }} \\ {\text { b. the mass of lithium bromide produced. }} \\ {\text { c. the excess reactant and the excess mass. }}\end{array} \end{equation}

What is the difference between actual yield and theoretical yield?

Can the percent yield of a chemical reaction be more than 100\(\% ?\) Explain your answer.

What relationship is used to determine the percent yield of a chemical reaction?

Ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) is produced from the fermentation of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) in the presence of enzymes. \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow 4 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(1)+4 \mathrm{CO}_{2}(\mathrm{g})\) Determine the theoretical yield and the percent yield of ethanol if 684 \(\mathrm{g}\) of sucrose undergoes fermentation and 349 \(\mathrm{g}\) of ethanol is obtained.

Lead(II) oxide is obtained by roasting galena, lead(II) sulfide, in air. The unbalanced equation is: \begin{equation} \mathrm{PbS}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{PbO}(\mathrm{s})+\mathrm{SO}_{2}(\mathrm{g}) \end{equation} \begin{equation} \begin{array}{l}{\text { a. Balance the equation, and determine the theoretical }} \\ {\text { yield of } \mathrm{PbO} \text { if } 200.0 \mathrm{g} \text { of } \mathrm{PbS} \text { is heated. }} \\ {\text { b. What is the percent yield if } 170.0 \mathrm{g} \text { of } \mathrm{PbO} \text { is obtained? }}\end{array} \end{equation}

Upon heating, calcium carbonate \(\left(\mathrm{CaCO}_{3}\right)\) decomposes to calcium oxide \((\mathrm{CaO})\) and carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) \begin{equation} \begin{array}{l}{\text { a. Determine the theoretical yield of } \mathrm{CO}_{2} \text { if } 235.0 \mathrm{g} \text { of }} \\\ {\mathrm{CaCO}_{3} \text { is heated. }}\end{array} \end{equation} \begin{equation} \begin{array}{l}{\text { b. What is the percent yield of } \mathrm{CO}_{2} \text { if } 97.5 \mathrm{g} \text { of } \mathrm{CO}_{2} \text { is }} \\\ {\text { collected? }}\end{array} \end{equation}

Hydrofluoric acid solutions cannot be stored in glass containers because HF reacts readily with silica dioxide in glass to produce hexafluorosilicic acid \(\left(\mathrm{H}_{2} \mathrm{SiF}_{6}\right)\) \begin{equation} \mathrm{SiO}_{2}(\mathrm{s})+6 \mathrm{HF}(\mathrm{aq}) \rightarrow \mathrm{H}_{2} \mathrm{SiF}_{6}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(1) \end{equation} 40.0 \(\mathrm{g} \mathrm{SiO}_{2}\) and 40.0 \(\mathrm{g}\) HF react to yield 45.8 \(\mathrm{g} \mathrm{H}_{2} \mathrm{SiF}_{6}\) \begin{equation} \begin{array}{l}{\text { a. What is the limiting reactant? }} \\ {\text { b. What is the mass of the excess reactant? }}\end{array} \end{equation} \begin{equation} \begin{array}{l}{\text { c. What is the theoretical yield of } \mathrm{H}_{2} \mathrm{SiF}_{6} \text { ? }} \\ {\text { d. What is the percent yield? }}\end{array} \end{equation}

Van Arkel Process Pure zirconium is obtained using the two-step Van Arkel process. In the first step, impure zirconium and iodine are heated to produce zirconium iodide \(\left(Z r I_{4}\right) .\) In the second step, ZrI \(_{4}\) is decomposed to produce pure zirconium. \begin{equation} \mathrm{ZrI}_{4}(\mathrm{s}) \rightarrow \mathrm{Zr}(\mathrm{s})+2 \mathrm{I}_{2}(\mathrm{g}) \end{equation} Determine the percent yield of zirconium if 45.0 \(\mathrm{g}\) of \(\mathrm{ZrI}_{4}\) is decomposed and 5.00 \(\mathrm{g}\) of pure Zr is obtained.

Phosphorus (P. ) is commercially prepared by heating a mixture of calcium phosphate \(\left(\mathrm{Ca} \mathrm{SiO}_{3}\right),\) sand \(\left(\mathrm{SiO}_{2}\right)\) and coke \((\mathrm{C})\) in an electric furnace. The process involves two reactions. \begin{equation} 2 \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(\mathrm{s})+6 \mathrm{SiO}_{2}(\mathrm{s}) \rightarrow 6 \mathrm{CaSiO}_{3}(\mathrm{l})+\mathrm{P}_{4} \mathrm{O}_{10}(\mathrm{g}) \end{equation} \begin{equation} \mathrm{P}_{4} \mathrm{O}_{10}(\mathrm{g})+10 \mathrm{C}(\mathrm{s}) \rightarrow \mathrm{P}_{4}(\mathrm{g})+10 \mathrm{CO}(\mathrm{g}) \end{equation} The P \(_{4} \mathrm{O}_{10}\) produced in the first reaction reacts with an excess of coke \((\mathrm{C})\) in the second reaction. Determine the theoretical yield of \(\mathrm{P}_{4}\) if 250.0 \(\mathrm{g}\) of \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) and 400.0 \(\mathrm{g}\) of \(\mathrm{SiO}_{2}\) are heated. If the actual yield of \(\mathrm{P}_{4}\) is \(45.0 \mathrm{g},\) determine the percent yield of \(\mathrm{P}_{4} .\)

Chlorine forms from the reaction of hydrochloric acid with manganese(IV) oxide. The balanced equation is: \begin{equation} \mathrm{MnO}_{2}+4 \mathrm{HCl} \rightarrow \mathrm{MnCl}_{2}+\mathrm{Cl}_{2}+2 \mathrm{H}_{2} \mathrm{O} \end{equation} Calculate the theoretical yield and the percent yield of chlorine if 86.0 \(\mathrm{g}\) of \(\mathrm{MnO}_{2}\) and 50.0 \(\mathrm{g}\) of \(\mathrm{HCl}\) react. The actual yield of \(\mathrm{Cl}_{2}\) is 20.0 \(\mathrm{g}\) .

Fertilizer The compound calcium cyanamide \((\) CaNCN) is used as a nitrogen source for crops. To obtain this compound, calcium carbide is reacted with nitrogen at high temperatures. \begin{equation} \mathrm{CaC}_{2}(\mathrm{s})+\mathrm{N}_{2}(\mathrm{g}) \rightarrow \mathrm{CaNCN}(\mathrm{s})+\mathrm{C}(\mathrm{s}) \end{equation} What mass of CaNCN can be produced if 7.50 mol of CaC \(_{2}\) reacts with 5.00 mol of \(N_{2} ?\)

When copper(II) oxide is heated in the presence of hydrogen gas, elemental copper and water are produced. What mass of copper can be obtained if 32.0 \(\mathrm{g}\) of copper(II) oxide is used?

Air Pollution Nitrogen oxide, which is present in urban air pollution, immediately converts to nitrogen dioxide as it reacts with oxygen. \begin{equation} \begin{array}{l}{\text { a. Write the balanced chemical equation for the forma- }} \\ {\text { tion of nitrogen dioxide from nitrogen oxide. }} \\\ {\text { b. What mole ratio would you use to convert from }} \\ {\text { moles of nitrogen oxide to moles of nitrogen dioxide? }}\end{array} \end{equation}

Electrolysis Determine the theoretical and percent yield of hydrogen gas if 36.0 g of water undergoes electrolysis to produce hydrogen and oxygen and 3.80 g of hydrogen is collected.

Analyze and Conclude In an experiment, you obtain a percent yield of product of 108\(\% .\) Is such a percent yield possible? Explain. Assuming that your calculation is correct, what reasons might explain such a result?

Design an Experiment Design an experiment that can be used to determine the percent yield of anhydrous copper(II) sulfate when copper(II) sulfate pentahydrate is heated to remove water.

Apply When a campfire begins to die down and smolder, you can rekindle the flame by fanning the fire. Explain, in terms of stoichiometry, why the fire again begins to flare up when fanned.

Apply Students conducted a lab to investigate limiting and excess reactants. The students added different volumes of sodium phosphate solution \(\left(\mathrm{Na}_{3} \mathrm{PO}_{4}\right)\) to a beaker. They then added a constant volume of cobalt(II) nitrate solution \(\left(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}\right),\) stirred the contents, and allowed the beakers to sit overnight. The next day, each beaker had a purple precipitate at the bottom. The students decanted the supernatant from each beaker, divided it into two samples, and added one drop of sodium phosphate solution to one sample and one drop of cobalt(II) nitrate solution to the second sample. Their results are shown in Table \(11.5 .\) \begin{equation} \begin{array}{l}{\text { a. Write a balanced chemical equation for the reaction. }} \\ {\text { b. Based on the results, identify the limiting reactant }} \\ {\text { and the excess reactant for each trial. }}\end{array} \end{equation}

When 9.59 g of a certain vanadium oxide is heated in the presence of hydrogen, water and a new oxide of vanadium are formed. This new vanadium oxide has a mass of 8.76 g. When the second vanadium oxide undergoes additional heating in the presence of hydrogen, 5.38 g of vanadium metal forms. \begin{equation} \begin{array}{l}{\text { a. Determine the empirical formulas for the two }} \\\ {\text { vanadium oxides. }} \\ {\text { b. Write balanced equations for the steps of the reaction. }} \\ {\text { c. Determine the mass of hydrogen needed to complete }} \\ {\text { the steps of this reaction. }}\end{array} \end{equation}

You observe that sugar dissolves more quickly in hot tea than in iced tea. You state that higher temperatures increase the rate at which sugar dissolves in water. Is this statement a hypothesis or a theory? Why? (Chapter 1)

Write the electron configuration for each of the following atoms. (Chapter 5) \begin{equation} \begin{array}{ll}{\text { a. fluorine }} & {\text { c. titanium }} \\ {\text { b. aluminum }} & {\text { d. radon }}\end{array} \end{equation}

Explain why the gaseous nonmetals exist as diatomic molecules, but other gaseous elements exist as single atoms. (Chapter 8)

Write a balanced equation for the reaction of potassium with oxygen. (Chapter 9)

What is the molecular mass of \(\mathrm{UF}_{6} ?\) What is the molar mass of \(\mathrm{UF}_{6}?\) (Chapter 10)

Air Pollution Research the air pollutants produced by combustion of gasoline in internal combustion engines. Discuss the common pollutants and the reaction that produces them. Show, through the use of stoichiometry, how each pollutant could be reduced if more people used mass transit.

Haber Process The percent yield of ammonia produced when hydrogen and nitrogen are combined under ordinary conditions is extremely small. However, the Haber Process combines the two gases under a set of conditions designed to maximize yield. Research the conditions used in the Haber Process, and find out why the development of the process was of great importance.