Chapter 5

The following are actual student responses to the question: Why is it necessary to balance chemical equations? a. The chemicals will not react until you have added the correct mole ratios. b. The correct products will not be formed unless the right amount of reactants have been added. c. A certain number of products cannot be formed without a certain number of reactants. d. The balanced equation tells you how much reactant you need and allows you to predict how much product you'll make. e. A mole-to-mole ratio must be established for the reaction to occur as written. Justify the best choice, and for choices you did not pick, explain what is wrong with them.

What information do we get from a chemical formula? From a chemical equation?

You are making cookies and are missing a key ingredienteggs. You have most of the other ingredients needed to make the cookies, except you have only 1.33 cups of butter and no eggs. You note that the recipe calls for two cups of butter and three eggs (plus the other ingredients) to make six dozen cookies. You call a friend and have him bring you some eggs. a. What number of eggs do you need? b. If you use all the butter (and get enough eggs), what number of cookies will you make? Unfortunately, your friend hangs up before you tell him how many eggs you need. When he arrives, he has a surprise for you- -to save time, he has broken them all in a bowl for you. You ask him how many he brought, and he replies, "I can't remember." You weigh the eggs and find that they weigh \(62.1 \mathrm{g}\). Assuming that an average egg weighs \(34.21 \mathrm{g}\) a. What quantity of butter is needed to react with all the eggs? b. What number of cookies can you make? c. Which will you have left over, eggs or butter? d. What quantity is left over?

You know that chemical \(A\) reacts with chemical \(B\). You react \(10.0 \mathrm{g} A\) with \(10.0 \mathrm{g} B .\) What information do you need to determine the amount of product that will be produced? Explain.

A new grill has a mass of \(30.0 \mathrm{kg}\). You put \(3.0 \mathrm{kg}\) of charcoal in the grill. You burn all the charcoal and the grill has a mass of \(30.0 \mathrm{kg} .\) What is the mass of the gases given off? Explain.

Consider an iron bar on a balance as shown. $$75.0 \mathrm{g}$$ As the iron bar rusts, which of the following is true? Explain your answer. a. The balance will read less than \(75.0 \mathrm{g}\). b. The balance will read \(75.0 \mathrm{g}\). c. The balance will read greater than \(75.0 \mathrm{g}\). d. The balance will read greater than \(75.0 \mathrm{g},\) but if the bar is removed, the rust is scraped off, and the bar replaced, the balance will read 75.0 g.

You may have noticed that water sometimes drips from the exhaust of a car as it is running. Is this evidence that there is at least a small amount of water originally present in the gasoline? Explain.

What is the mass of the product? a. less than \(10 \mathrm{g}\) b. between 20 and 100 g c. between 100 and \(120 \mathrm{g}\) d. exactly \(120 \mathrm{g}\) e. more than \(120 \mathrm{g}\)

Is there a difference between a homogeneous mixture of hydrogen and oxygen in a 2: 1 mole ratio and a sample of water vapor? Explain.

Can the subscripts in a chemical formula be fractions? Explain. Can the coefficients in a balanced chemical equation be fractions? Explain. Changing the subscripts of chemicals can balance the equations mathematically. Why is this unacceptable?

Consider the equation \(2 A+B \longrightarrow A_{2} B\). If you mix 1.0 mole of \(A\) with 1.0 mole of \(B\), what amount (moles) of \(A_{2} B\) can be produced?

According to the law of conservation of mass, mass cannot be gained or destroyed in a chemical reaction. Why can't you simply add the masses of two reactants to determine the total mass of product?

Which of the following pairs of compounds have the same empirical formula? a. acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2},\) and benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\) b. ethane, \(\mathrm{C}_{2} \mathrm{H}_{6},\) and butane, \(\mathrm{C}_{4} \mathrm{H}_{10}\) c. nitrogen dioxide, \(\mathrm{NO}_{2}\), and dinitrogen tetroxide, \(\mathrm{N}_{2} \mathrm{O}_{4}\) d. diphenyl ether, \(\mathrm{C}_{12} \mathrm{H}_{10} \mathrm{O},\) and phenol, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\)

Atoms of three different elements are represented by \(\mathrm{O}, \square,\) and \(\Delta .\) Which compound is left over when three molecules of \(\mathrm{O}\Delta\) and three molecules of \(\square \square \Delta\) react to form \(O \square \Delta\) and \(\mathrm{O} \Delta \Delta ?\)

In chemistry, what is meant by the term "mole"? What is the importance of the mole concept?

Which (if any) of the following is (are) true regarding the limiting reactant in a chemical reaction? a. The limiting reactant has the lowest coefficient in a balanced equation. b. The limiting reactant is the reactant for which you have the fewest number of moles. c. The limiting reactant has the lowest ratio of moles available/coefficient in the balanced equation. d. The limiting reactant has the lowest ratio of coefficient in the balanced equation/moles available. Justify your choice. For those you did not choose, explain why they are incorrect.

Consider the equation \(3 \mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}+\) D. You react 4 moles of A with 2 moles of B. Which of the following is true? a. The limiting reactant is the one with the higher molar mass. b. \(A\) is the limiting reactant because you need 6 moles of \(A\) and have 4 moles. c. \(B\) is the limiting reactant because you have fewer moles of B than A. d. \(B\) is the limiting reactant because three A molecules react with each B molecule. e. Neither reactant is limiting. Justify your choice. For those you did not choose, explain why they are incorrect.

Reference Section 5-2 to find the atomic masses of \(^{12} \mathrm{C}\) and \(^{13} \mathrm{C},\) the relative abundance of \(^{12} \mathrm{C}\) and \(^{13} \mathrm{C}\) in natural carbon, and the average mass (in u) of a carbon atom. If you had a sample of natural carbon containing exactly 10,000 atoms, determine the number of \(^{12} \mathrm{C}\) and \(^{13} \mathrm{C}\) atoms present. What would be the average mass (in u) and the total mass (in u) of the carbon atoms in this 10,000 -atom sample? If you had a sample of natural carbon containing \(6.0221 \times 10^{23}\) atoms, determine the number of \(^{12} \mathrm{C}\) and \(^{13} \mathrm{C}\) atoms present. What would be the average mass (in u) and the total mass (in u) of this \(6.0221 \times\) \(10^{23}\) atom sample? Given that \(1 \mathrm{g}=6.0221 \times 10^{23} \mathrm{u},\) what is the total mass of 1 mole of natural carbon in units of grams?

Avogadro's number, molar mass, and the chemical formula of a compound are three useful conversion factors. What unit conversions can be accomplished using these conversion factors?

If you had a mole of U.S. dollar bills and equally distributed the money to all of the people of the world, how rich would every person be? Assume a world population of 7 billion.

Describe 1 mole of \(\mathrm{CO}_{2}\) in as many ways as you can.

What is the difference between the molar mass and the empirical formula mass of a compound? When are these masses the same, and when are they different? When different, how is the molar mass related to the empirical formula mass?

How is the mass percent of elements in a compound different for a 1.0-g sample versus a 100.-g sample versus a 1-mole sample of the compound?

A balanced chemical equation contains a large amount of information. What information is given in a balanced equation?

What is the theoretical yield for a reaction, and how does this quantity depend on the limiting reactant?

What does it mean to say a reactant is present "in excess" in a process? Can the limiting reactant be present in excess? Does the presence of an excess of a reactant affect the mass of products expected for a reaction?

Consider the following generic reaction: $$\mathrm{Y}_{2}+2 \mathrm{XY} \longrightarrow 2 \mathrm{XY}_{2}$$ In a limiting reactant problem, a certain quantity of each reactant is given and you are usually asked to calculate the mass of product formed. If \(10.0 \mathrm{g}\) of \(\mathrm{Y}_{2}\) is reacted with \(10.0 \mathrm{g}\) of \(\mathrm{XY}\) outline two methods you could use to determine which reactant is limiting (runs out first) and thus determines the mass of product formed.

An element consists of \(1.40 \%\) of an isotope with mass 203.973 u, \(24.10 \%\) of an isotope with mass 205.9745 u, \(22.10 \%\) of an isotope with mass \(206.9759 \mathrm{u},\) and \(52.40 \%\) of an isotope with mass 207.9766 u. Calculate the average atomic mass, and identify the element.

An element "X" has five major isotopes, which are listed below along with their abundances. What is the element? $$\begin{aligned} &\begin{array}{|ccc|}\hline \text { Isotope } & \text { Percent Natural Abundance } & \text { Mass (u) } \\\\\hline 46 \mathrm{X} & 8.00 \% & 45.95232 \\\^{47} \mathrm{X} & 7.30 \% & 46.951764 \\\^{48} \mathrm{X} & 73.80 \% & 47.947947 \\\^{49} \mathrm{X} & 5.50 \% & 48.947841 \\\^{50} \mathrm{X} & 5.40 \% & 49.944792 \\\\\hline\end{array}\\\&\end{aligned}$$

The element rhenium (Re) has two naturally occurring isotopes, \(^{185} \mathrm{Re}\) and \(^{187} \mathrm{Re},\) with an average atomic mass of 186.207 u. Rhenium is \(62.60 \%\) is \(^{187} \mathrm{Re},\), and the atomic mass of \(^{187}\)Re is 186.956 u. Calculate the mass of \(^{185} \mathrm{Re}\).

The element europium exists in nature as two isotopes: \(^{151} \mathrm{Eu}\) has a mass of 150.9196 u and \(^{153} \mathrm{Eu}\) has a mass of 152.9209 u. The average atomic mass of europium is 151.96 u. Calculate the relative abundance of the two europium isotopes.

The element silver (Ag) has two naturally occurring isotopes: \(^{109} \mathrm{Ag}\) and \(^{107} \mathrm{Ag}\) with a mass of 106.905 u. Silver consists of \(51.82 \%^{107} \mathrm{Ag}\) and has an average atomic mass of \(107.868 \mathrm{u}\) Calculate the mass of \(^{109} \mathrm{Ag.}\)

The mass spectrum of bromine \(\left(\mathrm{Br}_{2}\right)\) consists of three peaks with the following characteristics: $$\begin{array}{|lc|}\hline \text { Mass }(\mathrm{u}) & \text { Relative Size } \\\\\hline 157.84 & 0.2534 \\\159.84 & 0.5000 \\\161.84 & 0.2466 \\\\\hline\end{array}$$ How do you interpret these data?

What number of Fe atoms and what amount (moles) of Fe atoms are in \(500.0 \mathrm{g}\) of iron?

Diamond is a natural form of pure carbon. What number of atoms of carbon are in a 1.00-carat diamond \((1.00 \text { carat }=\) \(0.200 \mathrm{g}) ?\)

A diamond contains \(5.0 \times 10^{21}\) atoms of carbon. What amount (moles) of carbon and what mass (grams) of carbon are in this diamond?

Aluminum metal is produced by passing an electric current through a solution of aluminum oxide \(\left(\mathrm{Al}_{2} \mathrm{O}_{3}\right)\) dissolved in molten cryolite \(\left(\mathrm{Na}_{3} \mathrm{AlF}_{6}\right) .\) Calculate the molar masses of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) and \(\mathrm{Na}_{3} \mathrm{AlF}_{6}.\)

The Freons are a class of compounds containing carbon, chlorine, and fluorine. While they have many valuable uses, they have been shown to be responsible for depletion of the ozone in the upper atmosphere. In 1991, two replacement compounds for Freons went into production: HFC-134a \(\left(\mathrm{CH}_{2} \mathrm{FCF}_{3}\right)\) and HCFC-124 \(\left(\mathrm{CHClFCF}_{3}\right)\). Calculate the molar masses of these two compounds.

Freon-12 \(\left(\mathrm{CCl}_{2} \mathrm{F}_{2}\right)\) is used as a refrigerant in air conditioners and as a propellant in aerosol cans. Calculate the number of molecules of Freon-12 in 5.56 mg of Freon-12. What is the mass of chlorine in 5.56 mg of Freon-12?

Bauxite, the principal ore used in the production of aluminum, has a molecular formula of \(\mathrm{Al}_{2} \mathrm{O}_{3} \cdot 2 \mathrm{H}_{2} \mathrm{O} .\) The \(\cdot \mathrm{H}_{2} \mathrm{O}\) in the formula are called waters of hydration. Each formula unit of the compound contains two water molecules. a. What is the molar mass of bauxite? b. What is the mass of aluminum in 0.58 mole of bauxite? c. How many atoms of aluminum are in 0.58 mole of bauxite? d. What is the mass of \(2.1 \times 10^{24}\) formula units of bauxite?

What amount (moles) is represented by each of these samples? a. \(150.0 \mathrm{g} \mathrm{Fe}_{2} \mathrm{O}_{3}\) b. \(10.0 \mathrm{mg} \mathrm{NO}_{2}\) c. \(1.5 \times 10^{16}\) molecules of \(\mathrm{BF}_{3}\)

What amount (moles) is represented by each of these samples? a. 20.0 mg caffeine, \(C_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\) b. \(2.72 \times 10^{21}\) molecules of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) c. \(1.50 \mathrm{g}\) of dry ice, \(\mathrm{CO}_{2}\)

What number of atoms of nitrogen are present in \(5.00 \mathrm{g}\) of each of the following? a. glycine, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}_{2} \mathrm{N}\) b. magnesium nitride c. calcium nitrate d. dinitrogen tetroxide

Ascorbic acid, or vitamin \(\mathrm{C}\left(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\right),\) is an essential vitamin. It cannot be stored by the body and must be present in the diet. What is the molar mass of ascorbic acid? Vitamin C tablets are taken as a dietary supplement. If a typical tablet contains \(500.0 \mathrm{mg}\) vitamin \(\mathrm{C},\) what amount (moles) and what number of molecules of vitamin C does it contain?

The molecular formula of acetylsalicylic acid (aspirin), one of the most commonly used pain relievers, is \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) a. Calculate the molar mass of aspirin. b. A typical aspirin tablet contains \(500 . \mathrm{mg} \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} .\) What amount (moles) of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) molecules and what number of molecules of acetylsalicylic acid are in a 500.-mg tablet?

Chloral hydrate \(\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}_{3} \mathrm{O}_{2}\right)\) is a drug formerly used as a sedative and hypnotic. It is the compound used to make "Mickey Finns" in detective stories. a. Calculate the molar mass of chloral hydrate. b. What amount (moles) of \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}_{3} \mathrm{O}_{2}\) molecules are in \(500.0 \mathrm{g}\) chloral hydrate? c. What is the mass in grams of \(2.0 \times 10^{-2}\) mole of chloral hydrate? d. What number of chlorine atoms are in 5.0 g chloral hydrate? e. What mass of chloral hydrate would contain 1.0 g Cl? f. What is the mass of exactly 500 molecules of chloral hydrate?

Dimethylnitrosamine, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{N}_{2} \mathrm{O},\) is a carcinogenic (cancercausing) substance that may be formed in foods, beverages, or gastric juices from the reaction of nitrite ion (used as a food preservative) with other substances. a. What is the molar mass of dimethylnitrosamine? b. How many moles of \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{N}_{2} \mathrm{O}\) molecules are present in \(250 \mathrm{mg}\) dimethylnitrosamine? c. What is the mass of 0.050 mole of dimethylnitrosamine? d. How many atoms of hydrogen are in 1.0 mole of dimethylnitrosamine? e. What is the mass of \(1.0 \times 10^{6}\) molecules of dimethylnitrosamine? f. What is the mass in grams of one molecule of dimethylnitrosamine?

Calculate the percent composition by mass of the following compounds that are important starting materials for synthetic polymers: a. \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{2}\) (acrylic acid, from which acrylic plastics are made) b. \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2}\) (methyl acrylate, from which Plexiglas is made) c. \(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}\) (acrylonitrile, from which Orlon is made)

In 1987 the first substance to act as a superconductor at a temperature above that of liquid nitrogen \((77 \mathrm{K})\) was discovered. The approximate formula of this substance is \(\mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7}\) Calculate the percent composition by mass of this material.

Arrange the following substances in order of increasing mass percent of carbon. a. caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\) b. sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) c. ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)