Chapter 9

The following chemical equation is unbalanced: \(\mathrm{I}_{2}+\mathrm{Cl}_{2} \rightarrow \mathrm{ICl}_{3}\) (a) Balance the equation. (b) The balanced equation is a source of many conversion factors containing the two reactants and one product. Write all of them that use the word mole(s). (c) The balanced equation is also a source of conversion factors involving the individual atoms and molecules. Write all of them that use the word mole(s).

How many \(\mathrm{H}\) atoms are there in \(2.0158 \mathrm{~g}\) of H atoms?

Consider a sample of \(24.0 \mathrm{~g}\) of \(\mathrm{O}_{2}\) molecules. (a) How many moles of \(\mathrm{O}_{2}\) molecules are present? (b) How many moles of \(\mathrm{O}\) atoms are present?

Consider a sample of \(92.5 \mathrm{~g}\) of \(\mathrm{O}_{2}\) molecules. (a) How many moles of \(\mathrm{O}_{2}\) molecules are present? (b) How many moles of \(\mathrm{O}\) atoms are present?

Consider sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4}\), used in car batteries. (a) What is the molar mass of sulfuric acid? (b) What is the mass in grams of 1 mole of \(\mathrm{H}_{2} \mathrm{SO}_{4} ?\) (c) What is the mass in grams of \(2.50\) moles of \(\mathrm{H}_{2} \mathrm{SO}_{4} ?\) (d) What is the mass in grams of 1000 molecules of \(\mathrm{H}_{2} \mathrm{SO}_{4} ?\) (Hint: Start by writing \({ }^{\prime \prime} 1000\) molecules \(\mathrm{H}_{2} \mathrm{SO}_{4}^{\prime \prime}\) and then apply conversior factors. Remember our admonition: If in doubt, convert to moles.)

How many \(\mathrm{O}_{2}\) molecules are there in \(1.00 \mathrm{~g}\) of \(\mathrm{O}_{2}\) molecules?

Suppose you wanted 1 billion \(\left(1.00 \times 10^{9}\right)\) water molecules and you didn't have time to sit and count them out. How many grams of water would you need to get 1 billion water molecules?

How many grams of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) would you need to get \(5.00 \times 10^{30}\) carbon atoms?

Consider the balanced chemical equation \(2 \mathrm{H}_{2} \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}\) (a) Given \(20.0 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}_{2}\) (hydrogen peroxide), how many grams of water will the reaction yield? (b) How many grams of hydrogen peroxide would you need to get \(20.0 \mathrm{~g}\) of water? (c) How many grams of hydrogen peroxide would you need to get \(20.0 \mathrm{~g}\) of \(\mathrm{O}_{2} ?\)

Consider the balanced chemical equation \(\mathrm{SCl}_{4}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{SO}_{2}+4 \mathrm{HCl}\) (a) How many grams of \(\mathrm{H}_{2} \mathrm{O}\) will react with \(5.000 \mathrm{~g}\) of \(\mathrm{SCl}_{4} ?\) (b) How many grams of \(\mathrm{SO}_{2}\) can you make from \(10.00 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O} ?\) (c) Suppose you react \(5.000 \mathrm{~g}\) of \(\mathrm{SCl}_{4}\) with the amount of \(\mathrm{H}_{2} \mathrm{O}\) you calculated in part (a). How many grams of \(\mathrm{HCl}\) will you form?

Suppose you run the reaction \(\mathrm{A}+2 \mathrm{~B} \rightarrow \mathrm{C}\) with \(\mathrm{B}\) as the limiting reactant and all of the reactants and products are solids. You desire to sell pure product \(C\). What problem are you going to encounter that you will have to spend money on to fix?

Consider the following balanced chemical equation: \(2 \mathrm{H}_{2}+\mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}\) (a) How many grams of water are formed from \(5.00 \mathrm{~g}\) of \(\mathrm{H}_{2}\) and an excess amount of \(\mathrm{O}_{2}\) ? (b) How many grams of \(\mathrm{O}_{2}\) do you need to produce \(5.00 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) ? (c) Given \(100.0 \mathrm{~g}\) of \(\mathrm{H}_{2}\), how many grams of \(\mathrm{O}_{2}\) are required to run the reaction in a stoichiometric fashion? (d) What is the theoretical yield in grams of water upon combining \(50.0 \mathrm{~g}\) of \(\mathrm{O}_{2}\) with an excess amount of \(\mathrm{H}_{2}\) ? (e) Express the answer to part (d) in terms of the number of water molecules.

Consider the following unbalanced chemical equation: \(\mathrm{P}+\mathrm{O}_{2} \rightarrow \mathrm{P}_{2} \mathrm{O}_{5}\) (a) How many grams of phosphorus (P) are required to react completely with \(20.0 \mathrm{~g}\) of \(\mathrm{O}_{2} ?\) (b) What is the theoretical yield in grams if you combine the amounts of reactants in part (a)?

Consider the following unbalanced chemical equation: \(\mathrm{H}_{2}+\mathrm{N}_{2} \rightarrow \mathrm{NH}_{3}\) (a) To run this reaction in a balanced fashion, how much nitrogen is required if you start with \(10.0 \mathrm{~g}\) of \(\mathrm{H}_{2} ?\) (b) How many grams of ammonia \(\left(\mathrm{NH}_{3}\right)\) will you produce if you run the reaction with the masses calculated in part (a)? (c) How many molecules of ammonia will you produce?

A gaseous mixture containing \(10.079 \mathrm{~g}\) of \(\mathrm{H}_{2}\) and \(7.00\) moles of \(\mathrm{Br}_{2}\) react to form HBr. (a) Write a balanced chemical equation for this reaction. (b) Which reactant is limiting? (c) What is the theoretical yield for this reaction in moles? (d) What is the theoretical yield for this reaction in grams? (e) How many moles of excess reactant are left over at the end of the reaction? (f) How many grams of excess reactant are left over at the end of the reaction?

Chlorine \(\left(\mathrm{Cl}_{2}\right)\) and fluorine \(\left(\mathrm{F}_{2}\right)\) react to form \(\mathrm{ClF}_{3}\). A reaction vessel contains \(2.50\) moles of \(\mathrm{Cl}_{2}\) and \(6.15\) moles of \(\mathrm{F}_{2}\). (a) Write a balanced chemical equation for this reaction. (b) Which reactant is limiting?

\(5.00 \mathrm{~g}\) of solid sodium (Na) and \(30.0 \mathrm{~g}\) of liquid bromine \(\left(\mathrm{Br}_{2}\right)\) react to form solid \(\mathrm{NaBr}\). (a) Write a balanced chemical equation for this reaction. (b) Which reactant is limiting? (c) What is the theoretical yield for this reaction in grams? (d) How many grams of excess reactant are left over at the end of the reaction? (e) When this reaction is actually performed, \(14.7 \mathrm{~g}\) of \(\mathrm{NaBr}\) is recovered. What is the percent yield of the reaction?

Chlorine \(\left(\mathrm{Cl}_{2}\right)\) and fluorine \(\left(\mathrm{F}_{2}\right)\) react to form \(\mathrm{ClF}_{3}\). A reaction vessel contains \(10.00 \mathrm{~g} \mathrm{Cl}_{2}\) and \(10.00 \mathrm{~g} \mathrm{~F}_{2}\). (Hint: Refer to Problem 9.82.) (a) Write a balanced chemical equation for this reaction. (b) Which reactant is limiting? (c) What is the theoretical yield for this reaction in grams? (d) How many grams of excess reactant are left over at the end of the reaction? (e) When this reaction is actually performed, \(12.50 \mathrm{~g}\) of \(\mathrm{ClF}_{3}\) is recovered. What is the percent yield of the reaction?

Sodium (Na) reacts with hydrogen \(\left(\mathrm{H}_{2}\right)\) to form sodium hydride (NaH). A reaction mixture contains \(10.00 \mathrm{~g} \mathrm{Na}\) and \(0.0235 \mathrm{~g} \mathrm{H}_{2}\). (a) Write a balanced chemical equation for this reaction. (b) Which reactant is limiting? (c) What is the theoretical yield for this reaction in grams? (d) How many grams of excess reactant are left over at the end of the reaction? (e) When this reaction is actually performed, \(0.428 \mathrm{~g}\) of \(\mathrm{NaH}\) is recovered. What is the percent yield of the reaction?

Butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\), used as the fuel in disposable lighters, reacts with oxygen \(\left(\mathrm{O}_{2}\right)\) to produce \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\). Suppose \(10.00 \mathrm{~g}\) butane is combined with \(10.00 \mathrm{~g} \mathrm{O}_{2}\). (a) Write a balanced chemical equation for the combustion of butane. (b) Which reactant is limiting? (c) What is the theoretical yield of each product for this reaction in grams? (d) How many grams of excess reactant are left over at the end of the reaction? (e) How many additional grams of the limiting reactant are required to run this reaction in a balanced fashion?

A compound has the empirical formula \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\). Its molar mass is about \(90 \mathrm{~g} / \mathrm{mol}\). What is its molecular formula?

An organic compound of carbon and hydrogen has the empirical formula CH. What is its molecular formula if its molar mass is: (a) \(26 \mathrm{~g} / \mathrm{mol}\) (b) \(52 \mathrm{~g} / \mathrm{mol}\) (c) \(78 \mathrm{~g} / \mathrm{mol}\)

A \(1.540-g\) sample of a liquid is subjected to combustion analysis, yielding \(40.00 \% \mathrm{C}\) and \(6.71 \% \mathrm{H}\). It may also contain oxygen. (a) What is the empirical formula for this compound? (b) The molar mass of this compound is determined to be about \(30 \mathrm{~g} / \mathrm{mol}\). What is the molecular formula for this compound?

A \(2.230-\mathrm{g}\) sample of a solid is subjected to combustion analysis, yielding \(76.59 \% \mathrm{C}\) and \(6.39 \% \mathrm{H}\). It may also contain oxygen. (a) What is the empirical formula for this compound? (b) The molar mass of this compound is determined to be about \(94 \mathrm{~g} / \mathrm{mol}\). What is the molecular formula for this compound?

A \(1.000-\mathrm{g}\) sample of a liquid is subjected to combustion analysis, yielding \(92.3 \% \mathrm{C}\) and \(7.7 \% \mathrm{H}\). It may or may not also contain oxygen. (a) What is the empirical formula for this compound? (b) The molar mass of this compound is determined to be about \(78 \mathrm{~g} / \mathrm{mol}\). What is the molecular formula for this compound?

A \(2.000 \mathrm{~g}\) sample of a liquid compound that contains only carbon and hydrogen in its formula is subjected to combustion analysis. From the result, the lab determines that \(0.2874 \mathrm{~g}\) of the original sample's mass is due to hydrogen. (a) What is the percent by mass hydrogen for this sample? (b) What is the empirical formula for this compound? (c) The molar mass of this compound is determined to be about \(71 \mathrm{~g} / \mathrm{mol}\). What is the molecular formula for this compound?

A compound used as an insecticide that contains only \(\mathrm{C}, \mathrm{H}\), and \(\mathrm{Cl}\) is subjected to combustion analysis, yielding \(55.55 \% \mathrm{C}\) and \(3.15 \% \mathrm{H}\). (a) What is the empirical formula of this compound? (b) What is the molecular formula if its empirical formula is \(1 / 3\) the mass of its actual formula?

A compound used as an insecticide that contains only \(C, H\), and \(C l\) is subjected to combustion analysis, yielding \(24.78 \% \mathrm{C}\) and \(2.08 \% \mathrm{H}\). (a) What is the empirical formula for this compound? (b) What is the molecular formula if its actual formula is four times the mass of its empirical formula?

Determine the empirical formula of the compound with the following mass percents of the elements present: \(66.63 \% \mathrm{C} ; 11.18 \% \mathrm{H} ; 22.19 \% \mathrm{O}\).

Determine the empirical formula of the compound with the following mass percents of the elements present: \(58.5 \% \mathrm{C} ; 4.91 \% \mathrm{H} ; 19.5 \% \mathrm{O} ; 17.1 \% \mathrm{~N}\).

Determine the empirical formula of the compound that is \(26.4 \%\) by mass \(\mathrm{Na}, 36.8 \%\) by mass \(\mathrm{S}\), and also contains oxygen.

Determine the empirical formula of the compound that is \(43.2 \%\) by mass \(\mathrm{K}, 39.1 \%\) by \(\mathrm{mass} \mathrm{Cl}\), and also contains oxygen.

Ethanol, the alcohol in beer and wine, has the molecular formula \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O} .\) Calculate the mass percent of each element in ethanol.

Ethylene glycol, used for antifreeze, has the molecular formula \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\). Calculate the mass percent of each element in ethylene glycol.

The compound \(\mathrm{P}_{4} \mathrm{O}_{10}\) has an empirical formula of \(\mathrm{P}_{2} \mathrm{O}_{5} .\) By what factor will the percent by mass composition differ for each element between these two formulas? Explain your answer.

The thyroid hormone thyroxine has the molecular formula \(\mathrm{C}_{15} \mathrm{H}_{11} \mathrm{NO}_{4} \mathrm{I}_{4} .\) Calculate the mass percent of each element in thyroxine.

(a) What is the molar mass of ribose \(\left(\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{5}\right)\) ? (b) What is the mass of \(3.87\) moles of ribose? (c) How many ribose molecules are there in \(3.87\) moles? (d) How many oxygen atoms are there in \(3.87\) moles of ribose? (e) What is the mass in grams of the oxygen atoms in part (d)?

Can the actual yield ever be greater than the theoretical yield for a chemical reaction?

Sodium metal reacts with water to form aqueous sodium hydroxide and hydrogen gas. (a) Write a balanced chemical equation for this reaction. (b) Which reactant is limiting if \(100.0 \mathrm{~g}\) of \(\mathrm{Na}\) and \(4.00\) moles of water are used?

Which has the greatest mass: 1 mole of ethylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right), 1\) mole of carbon monoxide gas, or 1 mole of nitrogen gas \(\left(\mathrm{N}_{2}\right) ?\)

What is the maximum possible value of the percent yield of a chemical reaction?

(a) What is the molar mass of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right) ?\) (b) What is the mass of \(1.25\) moles of sucrose? (c) How many sucrose molecules are in \(1.25\) moles? (d) How many hydrogen atoms are in \(1.25\) moles of sucrose? (e) What is the mass in grams of the hydrogen atoms in part (d)?

Aluminum metal burns in chlorine gas to form aluminum chloride. (a) Write a balanced chemical equation for this reaction. (b) Which reactant is limiting if \(100.0 \mathrm{~g}\) of \(\mathrm{Al}\) and \(5.00\) moles of \(\mathrm{Cl}_{2}\) are used?

Copper(I) oxide reacts with solid carbon to form copper metal. Carbon dioxide gas is the other product of this reaction. (a) Write the balanced chemical equation for this reaction. (b) Coke is a cheap, impure form of solid carbon that is often used industrially. If a sample of coke is \(95 \%\) C by mass, determine the mass in kilograms of coke needed to react completely with \(1.000\) ton of copper(I) oxide. \([1\) ton \(=2000 \mathrm{lb} ; 1 \mathrm{~kg}=2.205 \mathrm{lb}]\)

What is the empirical formula of a compound that is \(17.552 \% \mathrm{Na}, 39.696 \% \mathrm{Cr}\), and \(42.752 \% \mathrm{O} ?\)

Consider the balanced chemical equation $$ \begin{aligned} &\mathrm{Fe}(\mathrm{CO})_{5}(s)+2 \mathrm{PF}_{3}(l)+\mathrm{H}_{2}(g) \rightarrow \\ &\mathrm{Fe}(\mathrm{CO})_{2}\left(\mathrm{PF}_{3}\right)_{2} \mathrm{H}_{2}(s)+3 \mathrm{CO}(g) \end{aligned} $$ (a) How many grams of \(\mathrm{CO}\) could be produced from \(10.0 \mathrm{~g}\) of \(\mathrm{PF}_{3}\), excess \(\mathrm{Fe}(\mathrm{CO})_{5}\), and excess \(\mathrm{H}_{2} ?\) (b) How many grams of \(\mathrm{CO}\) could be produced from \(5.0\) moles of \(\mathrm{Fe}(\mathrm{CO})_{5}, 8.0\) moles of \(\mathrm{PF}_{3}\), and \(6.0\) moles of \(\mathrm{H}_{2}\) ? (c) How many moles of \(\mathrm{CO}\) could be produced from \(25.0 \mathrm{~g}\) of \(\mathrm{Fe}(\mathrm{CO})_{5}, 10.0 \mathrm{~g}\) of \(\mathrm{PF}_{3}\), and excess \(\mathrm{H}_{2} ?\) (d) The density of hydrogen gas at room temperature and atmospheric pressure is \(0.0820 \mathrm{~g} / \mathrm{L}\). When \(5.00 \mathrm{~L}\) of hydrogen gas at room temperature and atmospheric pressure is mixed with excess \(\mathrm{Fe}(\mathrm{CO})_{5}\) and excess \(\mathrm{PF}_{3}\), the mass of \(\mathrm{CO}\) collected is \(13.5 \mathrm{~g}\). What is the theoretical yield (in grams) and the percent yield of \(\mathrm{CO}\) ?

(a) Write a balanced chemical equation for the combustion of \(\mathrm{CH}_{4}(\mathrm{~g})\) with \(\mathrm{O}_{2}(g)\) to form \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\) (b) Consider the reaction of three molecules of \(\mathrm{CH}_{4}(g)\) with four molecules of \(\mathrm{O}_{2}(g)\). The following boxes represent before and after pictures of the tiny, sealed container in which this reaction takes place. Draw pictures to show the contents of this container before and after the reaction happens:

Consider a \(5.00-\mathrm{g}\) sample of silver nitrate, \(\mathrm{AgNO}_{3}(s)\) (a) How many moles of \(\mathrm{AgNO}_{3}\) are in this sample? (b) How many moles of \(\mathrm{O}\) are in this sample? (c) How many grams of \(\mathrm{N}\) are in this sample? (d) How many Ag atoms are in this sample?

Nitrogen and fluorine react to form nitrogen trifluoride according to the balanced chemical equation \(\mathrm{N}_{2}(g)+3 \mathrm{~F}_{2}(g) \rightarrow 2 \mathrm{NF}_{3}(g)\) For each of the following reaction mixtures, choose the limiting reactant: (a) \(0.50 \mathrm{~mol} \mathrm{~N}_{2}(g)\) and \(0.50 \mathrm{~mol} \mathrm{~F}_{2}(g)\) (b) \(12.0 \mathrm{~mol} \mathrm{~N}_{2}(g)\) and \(20.0 \mathrm{~mol} \mathrm{~F}_{2}(g)\) (c) \(2.5 \mathrm{~mol} \mathrm{~N}_{2}(g)\) and \(7.5 \mathrm{~mol} \mathrm{~F}_{2}(g)\) (d) 100 molecules \(\mathrm{N}_{2}(g)\) and 500 molecules \(\mathrm{F}_{2}(g)\) (e) \(5.00 \mathrm{~g} \mathrm{~N}_{2}(g)\) and \(15.0 \mathrm{~g} \mathrm{~F}_{2}(g)\) (f) \(20.0 \mathrm{mg} \mathrm{N}_{2}(g)\) and \(70.0 \mathrm{mg} \mathrm{F}_{2}(g)\)

When you bring your piggy bank of pennies into the bank, instead of counting them individually, the teller measures the mass of a single penny on a scale and then measures the mass of the entire contents of your piggy bank. If a single penny has a mass of \(2.49 \mathrm{~g}\) and your entire penny collection has a mass of \(5789.25 \mathrm{~g}\), how much money in dollars do you receive?