Chapter 3

A bottling plant has 121,515 bottles with a capacity of $355\mathrm{mL},122,500$ caps, and 40,875 L of beverage. (a) How many bottles can be filled and capped? (b) How much of each item is left over? (c) Which component limits the production?

Sodium hydroxide reacts with carbon dioxide as follows: $$2\mathrm{NaOH}(s)+{\mathrm{CO}}_2(g)⟶{\mathrm{Na}}_2{\mathrm{CO}}_3(s)+{\mathrm{H}}_2\mathrm{O}(l)$$ Which reagent is the limiting reactant when $1.85\mathrm{mol}$ $\mathrm{NaOH}$ and $1.00\mathrm{mol}{\mathrm{CO}}_2$ are allowed to react? How many moles of ${\mathrm{Na}}_2{\mathrm{CO}}_3$ can be produced? How many moles of the excess reactant remain after the completion of the reaction?

Aluminum hydroxide reacts with sulfuric acid as follows: $2\mathrm{Al}(\mathrm{OH}{)}_3(s)+3{\mathrm{H}}_2{\mathrm{SO}}_4(aq)$ ${\mathrm{Al}}_2{\left({\mathrm{SO}}_4\right)}_3(aq)+6{\mathrm{H}}_2\mathrm{O}(l)$ Which reagent is the limiting reactant when $0.500\mathrm{mol}$ $\mathrm{Al}(\mathrm{OH}{)}_3$ and $0.500\mathrm{mol}{\mathrm{H}}_2{\mathrm{SO}}_4$ are allowed to react? How many moles of ${\mathrm{Al}}_2{\left({\mathrm{SO}}_4\right)}_3$ can form under these conditions? How many moles of the excess reactant remain after the completion of the reaction?

One of the steps in the commercial process for converting ammonia to nitric acid is the conversion of ${\mathrm{NH}}_3$ to $\mathrm{NO}$ : $$4{\mathrm{NH}}_3(g)+5{\mathrm{O}}_2(g)⟶4\mathrm{NO}(g)+6{\mathrm{H}}_2\mathrm{O}(g)$$ In a certain experiment, $1.50\mathrm{g}$ of ${\mathrm{NH}}_3$ reacts with $2.75\mathrm{g}$ of ${\mathrm{O}}_2$ (a) Which is the limiting reactant? (b) How many grams of $\mathrm{NO}$ and of ${\mathrm{H}}_2\mathrm{O}$ form? (c) How many grams of the excess reactant remain after the limiting reactant is completely consumed? (d) Show that your calculations in parts (b) and (c) are consistent with the law of conservation of mass.

Solutions of sodium carbonate and silver nitrate react to form solid silver carbonate and a solution of sodium nitrate. A solution containing $3.50\mathrm{g}$ of sodium carbonate is mixed with one containing $5.00\mathrm{g}$ of silver nitrate. How many grams of sodium carbonate, silver nitrate, silver carbonate, and sodium nitrate are present after the reaction is complete?

Solutions of sulfuric acid and lead(II) acetate react to form solid lead(II) sulfate and a solution of acetic acid. If $7.50\mathrm{g}$ of sulfuric acid and $7.50\mathrm{g}$ of lead(II) acetate are mixed, calculate the number of grams of sulfuric acid, lead(II) acetate, lead(II) sulfate, and acetic acid present in the mixture after the reaction is complete.

When benzene $\left({\mathrm{C}}_6{\mathrm{H}}_6\right)$ reacts with bromine $\left({\mathrm{Br}}_2\right)$, bromobenzene $\left({\mathrm{C}}_6{\mathrm{H}}_5\mathrm{Br}\right)$ is obtained: $${\mathrm{C}}_6{\mathrm{H}}_6+{\mathrm{Br}}_2⟶{\mathrm{C}}_6{\mathrm{H}}_5\mathrm{Br}+\mathrm{HBr}$$ (a) What is the theoretical yield of bromobenzene in this reaction when $30.0\mathrm{g}$ of benzene reacts with $65.0\mathrm{g}$ of bromine? (b) If the actual yield of bromobenzene was $42.3\mathrm{g}$, what was the percentage yield?

When ethane $\left({\mathrm{C}}_2{\mathrm{H}}_6\right)$ reacts with chlorine $\left({\mathrm{Cl}}_2\right)$, the main product is ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{Cl}$; but other products containing $\mathrm{Cl}$. such as ${\mathrm{C}}_2{\mathrm{H}}_4{\mathrm{Cl}}_2$, are also obtained in small quantities. The formation of these other products reduces the yield of ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{Cl}$. (a) Calculate the theoretical yield of ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{Cl}$ when $125\mathrm{g}$ of ${\mathrm{C}}_2{\mathrm{H}}_6$ reacts with $255\mathrm{g}$ of ${\mathrm{Cl}}_2$, assuming that ${\mathrm{C}}_2{\mathrm{H}}_6$ and ${\mathrm{Cl}}_2$ react only to form ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{Cl}$ and $\mathrm{HCl}$. (b) Calculate the percent yield of ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{Cl}$ if the reaction produces $206\mathrm{g}$ of ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{Cl}$

Hydrogen sulfide is an impurity in natural gas that must be removed. One common removal method is called the Claus process, which relies on the reaction: $$8{\mathrm{H}}_2\mathrm{S}(g)+4{\mathrm{O}}_2(g)⟶{\mathrm{S}}_8(l)+8{\mathrm{H}}_2\mathrm{O}(g)$$ Under optimal conditions the Claus process gives $98\mathrm{\%}$ yield of ${\mathrm{S}}_8$ from ${\mathrm{H}}_2\mathrm{S}$. If you started with 300 grams of ${\mathrm{H}}_2\mathrm{S}$ and $50.0$ grams of ${\mathrm{O}}_2$, how many grams of ${\mathrm{S}}_{\mathrm{g}}$ would be produced, assuming $98\mathrm{\%}$ yield?

Write the balanced chemical equations for (a) the complete combustion of acetic acid $\left({\mathrm{CH}}_3\mathrm{COOH}\right)$, the main active ingredient in vinegar; (b) the decomposition of solid calcium hydroxide into solid calcium(II) oxide (lime) and water vapor; (c) the combination reaction between nickel metal and chlorine gas.