Chapter 11

Challenge For each of the following, balance the chemical equation; interpret the equation in terms of particles, moles, and mass; and show that the law of conservation of mass is observed. a. ___\(\mathrm{Na}(\mathrm{s})+\)____\(\mathrm{H}_{2} \mathrm{O}(1) \rightarrow\)____\(\mathrm{NaOH}(\mathrm{aq})+\)____\(\mathrm{H}_{2}(\mathrm{g})\) b.___\(Z n(s)+\)____\(\mathrm{HNO}_{3}(\mathrm{aq}) \rightarrow\)____\(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+\)____\(\mathrm{N}_{2} \mathrm{O}(\mathrm{g})+\)____\(\mathrm{H}_{2} \mathrm{O}(\mathfrak{l})\)

Determine all possible mole ratios for the following balanced chemical equations. \begin{equation} \begin{array}{l}{\text { a. } 4 \mathrm{Al}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})} \\ {\text { b. } 3 \mathrm{Fe}(\mathrm{s})+4 \mathrm{H}_{2} \mathrm{O}\left(\mathrm{l} \rightarrow \mathrm{Fe}_{3} \mathrm{O}_{4}(\mathrm{s})+4 \mathrm{H}_{2}(\mathrm{g})\right.} \\ {\text { c. } 2 \mathrm{HgO}(\mathrm{s}) \rightarrow 2 \mathrm{Hg}(1)+\mathrm{O}_{2}(\mathrm{g})}\end{array} \end{equation}

Challenge Balance the following equations, and determine the possible mole ratios. \begin{equation} \begin{array}{l}{\text { a. } \mathrm{ZnO}(\mathrm{s})+\mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{ZnCl}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})} \\\ {\text { b. butane }\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)+\text { oxygen } \rightarrow \text { carbon dioxide }+\text { water }}\end{array} \end{equation}

Categorize the ways in which a balanced chemical equation can be interpreted.

Apply The general form of a chemical reaction is \(x A+y B \rightarrow z A B\) . In the equa- tion, \(A\) and \(B\) are elements, and \(x_{i} y\) , and \(z\) are coefficients. State the mole ratios for this reaction.

Apply Hydrogen peroxide \(\left(\mathrm{H}_{2} \mathrm{O}_{2}\right)\) decomposes to produce water and oxygen. Write a balanced chemical equation for this reaction, and determine the possible mole ratios.

Model Write the mole ratios for the reaction of hydrogen gas and oxygen gas, \(2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{H}_{2} 0 .\) Make a sketch of six hydrogen molecules reacting with the correct number of oxygen molecules. Show the water molecules produced.

Methane and sulfur react to produce carbon disulfide \(\left(\mathrm{CS}_{2}\right),\) a liquid often used in the production of cellophane. ___\(\mathrm{CH}_{4}(\mathrm{g})+\) ___ \(\mathrm{S}_{8}(\mathrm{s}) \rightarrow\) ___\(\mathrm{cs}_{2}(\mathrm{l})\) + ___ \(\mathrm{H}_{2} \mathrm{S}(\mathrm{g})\) \begin{equation} \begin{array}{l}{\text { a. Balance the equation. }} \\ {\text { b. Calculate the moles of } \mathrm{CS}_{2} \text { produced when } 1.50 \mathrm{mol} \mathrm{S}_{8} \text { is used. }} \\ {\text { c. How many moles of } \mathrm{H}_{2} \mathrm{S} \text { is produced? }}\end{array} \end{equation}

Challenge Sulfuric acid \(\left(\mathrm{H}_{2} \mathrm{SO}_{\mathfrak{4}}\right)\) is formed when sulfur dioxide \(\left(\mathrm{SO}_{2}\right)\) reacts with oxygen and water. \begin{equation} \begin{array}{l}{\text { a. Write the balanced chemical equation for the reaction. }} \\ {\text { b. How many moles of } \mathrm{H}_{2} \mathrm{SO}_{4} \text { is produced from } 12.5 \text { moles of } \mathrm{SO}_{2} \text { ? }} \\ {\text { c. How many moles of } \mathrm{O}_{2} \text { are needed? }}\end{array} \end{equation}

Challenge Titanium is a transition metal used in many alloys because it is extremely strong and lightweight. Titanium tetrachloride \((\mathrm{TiCl_{4 }})\) is extracted from titanium oxide \(\left(\mathrm{TiO}_{2}\right)\) using chlorine and coke (carbon). $$\mathrm{TiO}_{2}(\mathrm{s})+\mathrm{C}(\mathrm{s})+2 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow \mathrm{TiCl}_{4}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$$ \begin{equation} \mathrm{a. Cl}_{2} \text { gas is needed to react with } 1.25 \text { mol of } \mathrm{TIO}_{2} ? \end{equation} \begin{equation} \begin{array}{l}{\text { b. What mass of } C \text { is needed to react with } 1.25 \text { mol of TiO_{2} ? }} \\ {\text { c. What is the mass of all of the products formed by reaction with } 1.25 \text { mol of TiO_{2} ? }}\end{array} \end{equation}

Challenge In the formation of acid rain, sulfur dioxide \(\left(\mathrm{SO}_{2}\right)\) reacts with oxygen and water in the air to form sulfuric acid \(\left(\mathrm{H}_{2} \mathrm{SO}_{4}\right) .\) Write the balanced chemical equation for the reaction. If 2.50 \(\mathrm{g}\) of \(\mathrm{SO}_{2}\) reacts with excess oxygen and water, how much \(\mathrm{H}_{2} \mathrm{SO}_{4}\) , in grams, is produced?

Explain why a balanced chemical equation is needed to solve a stoichiometric problem.

List the four steps used in solving stoichiometric problems.

Calculate Hydrogen reacts with excess nitrogen as follows: \begin{equation} \mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{g}) \end{equation} If 2.70 gof \(H_{2}\) reacts, how many grams of \(\mathrm{NH}_{3}\) is formed?

The reaction between solid sodium and iron(llI) oxide is one in a series of reactions that inflates an automobile airbag: \(6 \mathrm{Na}(\mathrm{s})+\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s}) \rightarrow 3 \mathrm{Na}_{2} \mathrm{O}(\mathrm{s})+2 \mathrm{Fe}(\mathrm{s}) .\) If 100.0 \(\mathrm{g}\) of \(\mathrm{Na}\) and 100.0 \(\mathrm{g}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) are used in this reaction, determine the following. \begin{equation} \begin{array}{l}{\text { a. limiting reactant }} \\ {\text { b. reactant in excess }} \\ {\text { c. mass of solid iron produced }} \\ {\text { d. mass of excess reactant that remains after the reaction is complete }}\end{array} \end{equation}

Challenge Photosynthesis reactions in green plants use carbon dioxide and water to produce glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) and oxygen. A plant has 88.0 \(\mathrm{g}\) of carbon dioxide and 64.0 \(\mathrm{g}\) of water available for photosynthesis. \begin{equation} \begin{array}{l}{\text { a. Write the balanced chemical equation for the reaction. }} \\ {\text { b. Determine the limiting reactant. }} \\ {\text { c. Determine the excess reactant. }} \\ {\text { d. Determine the mass in excess. }} \\ {\text { e. Determine the mass of glucose produced. }}\end{array} \end{equation}

Analyze Tetraphosphorus trisulphide \(\left(P_{4} S_{3}\right)\) is used in the match heads of some matches. It is produced in the reaction \(8 \mathrm{P}_{4}+3 \mathrm{S}_{8} \rightarrow 8 \mathrm{P}_{4} \mathrm{S}_{3}\) . Determine which of the following statements are incorrect, and rewrite the incorrect statements to make them correct. \begin{equation} \begin{array}{l}{\text { a. } 4 \text { mol } P_{4} \text { reacts with } 1.5 \text { mol } S_{8} \text { to form } 4 \text { mol } P_{4} S_{3} \text { . }} \\\ {\text { b. Sulfur is the limiting reactant when } 4 \text { mol } P_{4} \text { and } 4 \text { mol } S_{8} \text { react. }} \\ {\text { c. } 6 \text { mol } P_{4} \text { reacts with } 6 \text { mol } S_{8} \text { forming } 1320 \text { g } P_{4} S_{3} \text { . }}\end{array} \end{equation}

Zinc reacts with iodine in a synthesis reaction: \(\mathrm{Zn}+\mathrm{I}_{2} \rightarrow \mathrm{ZnI}_{2}\) \begin{equation} \begin{array}{l}{\text { a. Determine the theoretical yield if } 1.912 \text { mol of zinc is used. }} \\ {\text { b. Determine the percent yield if } 515.6 \mathrm{g} \text { of product is recovered. }}\end{array} \end{equation}

Challenge When copper wire is placed into a silver nitrate solution \(\left(\mathrm{AgNO}_{3}\right),\) silver crystals and copper(ll) nitrate \(\left(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\right)\) solution form. \begin{equation} \begin{array}{l}{\text { a. Write the balanced chemical equation for the reaction. }} \\ {\text { b. If a } 20.0 \text { -g sample of copper is used, determine the theoretical yield }} \\ {\text { of silver. }} \\ {\text { c. If } 60.0 \text { g of silver is recovered from the reaction, determine the }} \\\ {\text { percent yield of the reaction. }}\end{array} \end{equation}

Identify which type of yield-theoretical yield, actual yield, or percent yield-is a measure of the efficiency of a chemical reaction.

List several reasons why the actual yield from a chemical reaction is not usually equal to the theoretical yield.

Apply In an experiment, you combine 83.77 \(\mathrm{g}\) of iron with an excess of sulfur and then heat the mixture to obtain iron(lil) sulfide. $$2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{S}(\mathrm{s}) \rightarrow \mathrm{Fe}_{2} \mathrm{S}_{3}(\mathrm{s})$$ What is the theoretical yield, in grams, of iron(III) sulfide?

Why must a chemical equation be balanced before you can determine mole ratios?

What relationships can be determined from a balanced chemical equation?

Explain why mole ratios are central to stoichiometric calculations.

Why are coefficients used in mole ratios instead of subscripts?

Explain how the conservation of mass allows you to interpret a balanced chemical equation in terms of mass.

When heated by a flame, ammonium dichromate decomposes, producing nitrogen gas, solid chromium(III) oxide, and water vapor \begin{equation} \left(\mathrm{NH}_{4}\right) 2 \mathrm{Cr}_{2} \mathrm{O}_{7} \rightarrow \mathrm{N}_{2}+\mathrm{Cr}_{2} \mathrm{O}_{3}+4 \mathrm{H}_{2} \mathrm{O} \end{equation} Write the mole ratios for this reaction that relate ammonium dichromate to the products.

Interpret the following equation in terms of particles, moles, and mass. \begin{equation} 4 \mathrm{Al}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s}) \end{equation}

Smelting When tin(IV) oxide is heated with carbon in a process called smelting, the element tin can be extracted. \begin{equation} \mathrm{SnO}_{2}(\mathrm{s})+2 \mathrm{C}(\mathrm{s}) \rightarrow \mathrm{Sn}(1)+2 \mathrm{CO}(\mathrm{g}) \end{equation} Interpret the chemical equation in terms of particles, moles, and mass.

When solid copper is added to nitric acid, copper(II) nitrate, nitrogen dioxide, and water are produced. Write the balanced chemical equation for the reaction. List six mole ratios for the reaction.

When hydrochloric acid solution reacts with lead(II) nitrate solution, lead(II) chloride precipitates and a solution of nitric acid is produced. \begin{equation} \begin{array}{l}{\text { a. Write the balanced chemical equation for the reaction. }} \\ {\text { b. Interpret the equation in terms of molecules and }} \\ {\text { formula units, moles, and mass. }}\end{array} \end{equation}

When aluminum is mixed with iron (III) oxide, iron metal and aluminum oxide are produced, along with a large quantity of heat. What mole ratio would you use to determine moles of Fe if moles of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is known? \begin{equation} \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Al}(\mathrm{s}) \rightarrow 2 \mathrm{Fe}(\mathrm{s})+\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})+ heat\end{equation}

Chrome The most important commercial ore of chromium is chromite \(\left(\mathrm{FeCr}_{2} \mathrm{O}_{4}\right) .\) One of the steps in the process used to extract chromium from the ore is the reaction of chromite with coke (carbon) to produce ferrochrome (FeCr_ ). \begin{equation} 2 \mathrm{C}(\mathrm{s})+\mathrm{FeCr}_{2} \mathrm{O}_{4}(\mathrm{s}) \rightarrow \mathrm{FeCr}_{2}(\mathrm{s})+2 \mathrm{CO}_{2}(\mathrm{g}) \end{equation} What mole ratio would you use to convert from moles of chromite to moles of ferrochrome?

Antacids Magnesium hydroxide is an ingredient in some antacids. Antacids react with excess hydrochloric acid in the stomach to relieve indigestion. \begin{equation} \underline\ \mathrm{Mg}(\mathrm{OH})_{2}+\longrightarrow \mathrm{HCl} \rightarrow \underline{} \mathrm{MgCl}_{2}+\underline{} \mathrm{H}_{2} \mathrm{O} \end{equation} \begin{equation} \begin{array}{l}{\text { a. Balance the reaction of Mg }(\mathrm{OH})_{2} \text { with HCl. }} \\ {\text { b. Write the mole ratio that would be used to determine }} \\ {\text { the number of moles of MgCl produced when HCl }} \\\ {\text { reacts with } \mathrm{Mg}(\mathrm{OH})_{2} \text { . }}\end{array} \end{equation}

What is the first step in all stoichiometric calculations?

What information does a balanced equation provide?

On what law is stoichometry based, and how do the calculations support this law?

How is molar mass used in some stoichiometric calculations?

What information must you have in order to calculate the mass of product formed in a chemical reaction?

Ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right),\) also known as grain alcohol, can be made from the fermentation of sugar \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right) .\)The unbalanced chemical equation for the reaction is shown below. \begin{equation} -\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \rightarrow_{-} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+_{-} \mathrm{CO}_{2} \end{equation} \begin{equation} \begin{array}{l}{\text { Balance the chemical equation and determine the mass }} \\ {\text { of } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \text { produced from } 750 \mathrm{g} \text { of } \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \text { . }}\end{array} \end{equation}

Welding If 5.50 mol of calcium carbide \(\left(\mathrm{CaC}_{2}\right)\) reacts with an excess of water, how many moles of acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right),\) a gas used in welding, will be produced? \begin{equation} \mathrm{CaC}_{2}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})+\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g}) \end{equation}

Antacid Fizz When an antacid tablet dissolves in water, the fizz is due to a reaction between sodium hydrogen carbonate \(\left(\mathrm{NaHCO}_{3}\right),\) also called sodium bicarbonate, and citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right)\) \begin{equation} 3 \mathrm{NaHCO}_{3}(\mathrm{aq})+\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq}) \rightarrow \end{equation} \begin{equation} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad3 \mathrm{CO}_{2}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(1)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq})\end{equation} How many moles of \(\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\) can be produced if one tablet containing 0.0119 \(\mathrm{mol}\) of \(\mathrm{NaHCO}_{3}\) is dissolved?

Greenhouse Gas Carbon dioxide is a greenhouse gas that is linked to global warming. It is released into the atmosphere through the combustion of octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) in gasoline. Write the balanced chemical equation for the combustion of octane and calculate the mass of octane needed to release 5.00 \(\mathrm{mol}\) of \(\mathrm{CO}_{2} .\)

A solution of potassium chromate reacts with a solution of lead(II) nitrate to produce a yellow precipitate of lead(II) chromate and a solution of potassium nitrate. \begin{equation} \begin{array}{l}{\text { a. Write the balanced chemical equation. }} \\\ {\text { b. Starting with } 0.250 \text { mol of potassium chromate, }} \\\ {\text { determine the mass of lead chromate formed. }}\end{array} \end{equation}

Rocket Fuel The exothermic reaction between liquid hydrazine \(\left(\mathrm{N}_{2} \mathrm{H}_{2}\right)\) and liquid hydrogen peroxide \(\left(\mathrm{H}_{2} \mathrm{O}_{2}\right)\) is used to fuel rockets. The products of this reaction are nitrogen gas and water. \begin{equation} \begin{array}{l}{\text { a. Write the balanced chemical equation. }} \\\ {\text { b. How much hydrazine, in grams, is needed to produce }} \\ {10.0 \text { mol of nitrogen gas? }}\end{array} \end{equation}

Gasohol is a mixture of ethanol and gasoline. Balance the equation, and determine the mass of \(\mathrm{CO}_{2}\) produced from the combustion of 100.0 g of ethanol. \begin{equation} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \end{equation}

Car Battery Car batteries use lead, lead(IV) oxide, and a sulfuric acid solution to produce an electric current. The products of the reaction are lead(II) sulfate in solution and water. \begin{equation} \begin{array}{l}{\text { a. Write the balanced equation for the reaction. }} \\\ {\text { b. Determine the mass of lead(II) sulfate produced }} \\ {\text { when } 25.0 \text { g of lead reacts with an excess of lead(IV) }} \\\ {\text { oxide and sulfuric acid. }}\end{array} \end{equation}

To extract gold from its ore, the ore is treated with sodium cyanide solution in the presence of oxygen and water. \begin{equation} 4 \mathrm{Au}(\mathrm{s})+8 \mathrm{NaCN}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(1) \rightarrow \end{equation} \begin{equation} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad4 \mathrm{NaAu}(\mathrm{CN})_{2}(\mathrm{aq})+4 \mathrm{NaOH}(\mathrm{aq}) \end{equation} \begin{equation} \begin{array}{l}{\text { a. Determine the mass of gold that can be extracted if }} \\ {25.0 \text { g of sodium cyanide is used. }} \\ {\text { b. If the mass of the ore from which the gold was }} \\ {\text { extracted is } 150.0 \mathrm{g}, \text { what percentage of the ore is gold? }}\end{array} \end{equation}

Film Photographic film contains silver bromide in gelatin. Once exposed, some of the silver bromide decomposes, producing fine grains of silver. The unexposed silver bromide is removed by treating the film with sodium thiosulfate. Soluble sodium silver thiosulfate \(\left(\mathrm{Na}_{3} \mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}\right)\) is produced. \begin{equation} \mathrm{AgBr}(\mathrm{s})+2 \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(\mathrm{aq}) \rightarrow \end{equation} \begin{equation} \quad\quad\quad\quad\quad\quad\quad\mathrm{Na}_{3} \mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}(\mathrm{aq})+\mathrm{NaBr}(\mathrm{aq}) \end{equation} Determine the mass of \(\mathrm{Na}_{3} \mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}\) produced if 0.275 \(\mathrm{g}\) of \(\mathrm{AgBr}\) is removed.