Chapter 3

Which of the following has the greater mass: \(0.72 \mathrm{~g}\) of \(\mathrm{O}_{2}\) or 0.0011 mole of chlorophyll \(\left(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{MgN}_{4} \mathrm{O}_{5}\right) ?\)

Analysis of a metal chloride \(\mathrm{XCl}_{3}\) show that it contains 67.2 percent \(\mathrm{Cl}\) by mass. Calculate the molar mass of \(\mathrm{X}\) and identify the element.

Hemoglobin \(\left(\mathrm{C}_{2952} \mathrm{H}_{4664} \mathrm{~N}_{812} \mathrm{O}_{832} \mathrm{~S}_{8} \mathrm{Fe}_{4}\right)\) is the oxy- gen carrier in blood. (a) Calculate its molar mass. (b) An average adult has about \(5.0 \mathrm{~L}\) of blood. Every milliliter of blood has approximately \(5.0 \times 10^{9}\) erythrocytes, or red blood cells, and every red blood cell has about \(2.8 \times 10^{8}\) hemoglobin molecules. Calculate the mass of hemoglobin molecules in grams in an average adult.

Calculate the number of cations and anions in each of the following compounds: (a) \(0.764 \mathrm{~g}\) of CsI, (b) \(72.8 \mathrm{~g}\) of \(\mathrm{K}_{2} \mathrm{Cr}_{2}\mathrm{O}_{7}\) (c) \(6.54 \mathrm{~g}\) of\(\mathrm{Hg}_{2}\left(\mathrm{NO}_{3}\right)_{2}\)

Consider the reaction \(3 \mathrm{~A}+2 \mathrm{~B} \rightarrow 3 \mathrm{C}\). A student mixed 4.0 moles of \(\mathrm{A}\) with 4.0 moles of \(\mathrm{B}\) and obtained 2.8 moles of \(\mathrm{C}\). What is the percent yield of the reaction?

Aspirin or acetyl salicylic acid is synthesized by reacting salicylic acid with aceticanhydride:$$\mathrm{C}_{7}\mathrm{H}_{6}\mathrm{O}_{3}+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3} \quad \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8}\mathrm{O}_{4}+\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}$$ (a) How much salicylic acid is required to produce \(0.400 \mathrm{~g}\) of aspirin (about the content in a tablet), assuming acetic anhydride is present in excess? (b) Calculate the amount of salicylic acid needed if only 74.9 percent of salicylic acid is converted to aspirin. (c) In one experiment, \(9.26 \mathrm{~g}\) of salicylic acid is reacted with \(8.54 \mathrm{~g}\) of acetic anhydride. Calculate the theoretical yield of aspirin and the percent yield if only \(10.9 \mathrm{~g}\) of aspirin is produced.

Calculate the percent composition by mass of all the elements in calcium phosphate \(\left[\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\right],\) a major component of bone.

Lysine, an essential amino acid in the human body, contains \(\mathrm{C}, \mathrm{H}, \mathrm{O},\) and \(\mathrm{N} .\) In one experiment, the complete combustion of \(2.175 \mathrm{~g}\) of lysine gave \(3.94 \mathrm{~g}\) \(\mathrm{CO}_{2}\) and \(1.89 \mathrm{~g} \mathrm{H}_{2} \mathrm{O} .\) In a separate experiment, \(1.873 \mathrm{~g}\) of lysine gave \(0.436 \mathrm{~g} \mathrm{NH}_{3}\). (a) Calculate the empirical formula of lysine. (b) The approximate molar mass of lysine is \(150 \mathrm{~g}\). What is the molecular formula of the compound?

Does \(1 \mathrm{~g}\) of hydrogen molecules contain as many \(\mathrm{H}\) atoms as \(1 \mathrm{~g}\) of hydrogen atoms?

Avogadro's number has sometimes been described as a conversion factor between atomic mass units and grams. Use the fluorine atom ( 19.00 amu) as an example to show the relation between the atomic mass unit and the gram.

The natural abundances of the two stable isotopes of hydrogen (hydrogen and deuterium) are \({ }_{1}^{1} \mathrm{H}\) : 99.985 percent and \({ }_{1}^{2} \mathrm{H}: 0.015\) percent. Assume that water exists as either \(\mathrm{H}_{2} \mathrm{O}\) or \(\mathrm{D}_{2} \mathrm{O} .\) Calculate the number of \(\mathrm{D}_{2} \mathrm{O}\) molecules in exactly \(400 \mathrm{~mL}\) of water. (Density \(=1.00 \mathrm{~g} / \mathrm{mL} .)\)

A compound containing only \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{Cl}\) was examined in a mass spectrometer. The highest mass peak seen corresponds to an ion mass of 52 amu. The most abundant mass peak seen corresponds to an ion mass of 50 amu and is about three times as intense as the peak at 52 amu. Deduce a reasonable molecular formula for the compound and explain the positions and intensities of the mass peaks mentioned.

In the formation of carbon monoxide, CO, it is found that \(2.445 \mathrm{~g}\) of carbon combine with \(3.257 \mathrm{~g}\) of oxygen. What is the atomic mass of oxygen if the atomic mass of carbon is 12.01 amu?

What mole ratio of molecular chlorine \(\left(\mathrm{Cl}_{2}\right)\) to molecular oxygen \(\left(\mathrm{O}_{2}\right)\) would result from the breakup of the compound \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) into its constituent elements?

Which of the following substances contains the greatest mass of chlorine? (a) \(5.0 \mathrm{~g} \mathrm{Cl}_{2},\) (b) \(60.0 \mathrm{~g}\mathrm{NaClO}_{3}\) (c) \(0.10 \mathrm{~mol} \mathrm{KCl}\), (d) \(30.0 \mathrm{~g} \mathrm{MgCl}_{2}\), (e) \(0.50 \mathrm{~mol} \mathrm{Cl}_{2}\).

A compound made up of \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{Cl}\) contains 55.0 percent \(\mathrm{Cl}\) by mass. If \(9.00 \mathrm{~g}\) of the compound contain \(4.19 \times 10^{23} \mathrm{H}\) atoms, what is the empirical formula of the compound?

Platinum forms two different compounds with chlorine. One contains 26.7 percent \(\mathrm{Cl}\) by mass, and the other contains 42.1 percent Cl by mass. Determine the empirical formulas of the two compounds.

The following reaction is stoichiometric as written$$\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Cl}+\mathrm{NaOC}_{2}\mathrm{H}_{5} \longrightarrow \mathrm{C}_{4}\mathrm{H}_{8}+\mathrm{C}_{2} \mathrm{H}_{5}\mathrm{OH}+\mathrm{NaCl}$$ but it is often carried out with an excess of \(\mathrm{NaOC}_{2} \mathrm{H}_{5}\) to react with any water present in the reaction mixture that might reduce the yield. If the reaction shown was carried out with \(6.83 \mathrm{~g}\) of \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Cl}\), how many grams of \(\mathrm{NaOC}_{2} \mathrm{H}_{5}\) would be needed to have a 50 percent molar excess of that reactant?

Compounds containing ruthenium(II) and bipyridine, \(\mathrm{C}_{10} \mathrm{H}_{8} \mathrm{~N}_{2},\) have received considerable interest because of their role in systems that convert solar energy to electricity. The compound \(\left[\mathrm{Ru}\left(\mathrm{C}_{10} \mathrm{H}_{8} \mathrm{~N}_{2}\right)_{3}\right]$$\mathrm{Cl}_{2}\) is synthesized by reacting \(\mathrm{RuCl}_{3} \cdot 3 \mathrm{H}_{2} \mathrm{O}(s)\) with three molar equivalents of \(\mathrm{C}_{10} \mathrm{H}_{8} \mathrm{~N}_{2}(s),\) along with an excess of triethylamine, \(\mathrm{N}\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{3}(l),\) to convert ruthenium(III) to ruthenium(II). The density of triethylamine is \(0.73 \mathrm{~g} / \mathrm{mL},\) and typically eight molar equivalents are used in the synthesis. (a) Assuming that you start with \(6.5 \mathrm{~g}\) of \(\mathrm{RuCl}_{3} \cdot 3 \mathrm{H}_{2} \mathrm{O},\) how many grams of \(\mathrm{C}_{10} \mathrm{H}_{8} \mathrm{~N}_{2}\) and what volume of \(\mathrm{N}\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{3}\) should be used in the reaction? (b) Given that the yield of this reaction is 91 percent, how many grams of \(\left[\mathrm{Ru}\left(\mathrm{C}_{10} \mathrm{H}_{8} \mathrm{~N}_{2}\right)_{3}\right] \mathrm{Cl}_{2}\) will be obtained?

Heating \(2.40 \mathrm{~g}\) of the oxide of metal \(\mathrm{X}\) (molar mass of \(\mathrm{X}=55.9 \mathrm{~g} / \mathrm{mol}\) ) in carbon monoxide (CO) yields the pure metal and carbon dioxide. The mass of the metal product is \(1.68 \mathrm{~g}\). From the data given, show that the simplest formula of the oxide is \(\mathrm{X}_{2} \mathrm{O}_{3}\) and write a balanced equation for the reaction.

A compound X contains 63.3 percent manganese (Mn) and 36.7 percent O by mass. When \(X\) is heated, oxygen gas is evolved and a new compound Y containing 72.0 percent \(\mathrm{Mn}\) and 28.0 percent \(\mathrm{O}\) is formed. (a) Determine the empirical formulas of X and Y. (b) Write a balanced equation for the conversion of \(\mathrm{X}\) to \(\mathrm{Y}\)

The formula of a hydrate of barium chloride is \(\mathrm{BaCl}_{2} \cdot x \mathrm{H}_{2} \mathrm{O} .\) If \(1.936 \mathrm{~g}\) of the compound gives\(1.864 \mathrm{~g}\) of anhydrous \(\mathrm{BaSO}_{4}\) upon treatment with sulfuric acid, calculate the value of \(x\).

A mixture of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\) is heated until all the water is lost. If \(5.020 \mathrm{~g}\) of the mixture gives \(2.988 \mathrm{~g}\) of the anhydrous salts, what is the percent by mass of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) in the mixture?

When \(0.273 \mathrm{~g}\) of \(\mathrm{Mg}\) is heated strongly in a nitrogen \(\left(\mathrm{N}_{2}\right)\) atmosphere, a chemical reaction occurs. The product of the reaction weighs 0.378 g. Calculate the empirical formula of the compound containing \(\mathrm{Mg}\) and \(\mathrm{N}\). Name the compound.

A mixture of methane \(\left(\mathrm{CH}_{4}\right)\) and ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) of mass \(13.43 \mathrm{~g}\) is completely burned in oxygen. If the total mass of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) produced is \(64.84 \mathrm{~g},\) calculate the fraction of \(\mathrm{CH}_{4}\) in the mixture.

Because of its detrimental effect on the environment, the lead compound described in Problem 3.148 has been replaced by methyl tert-butyl ether (a compound of \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{O}\) ) to enhance the performance of gasoline. (This compound is also being phased out because of its contamination of drinking water.) When \(12.1 \mathrm{~g}\) of the compound are burned in an apparatus like the one shown in Figure \(3.6,30.2 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(14.8 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) are formed. What is the empirical formula of the compound?

A certain sample of coal contains 1.6 percent sulfur by mass. When the coal is burned, the sulfur is converted to sulfur dioxide. To prevent air pollution, this sulfur dioxide is treated with calcium oxide \((\mathrm{CaO})\) to form calcium sulfite \(\left(\mathrm{CaSO}_{3}\right)\). Calculate the daily mass (in kilograms) of CaO needed by a power plant that uses \(6.60 \times 10^{6} \mathrm{~kg}\) of coal per day.

A major industrial use of hydrochloric acid is in metal pickling. This process involves the removal of metal oxide layers from metal surfaces to prepare them for coating. (a) Write an equation between iron(III) oxide, which represents the rust layer over iron, and \(\mathrm{HCl}\) to form iron(III) chloride and water. (b) If 1.22 moles of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) and \(289.2 \mathrm{~g}\) of HCl react, how many grams of \(\mathrm{FeCl}_{3}\) will be produced?

Octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) is a component of gasoline. Complete combustion of octane yields \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{CO}_{2} .\) Incomplete combustion produces \(\mathrm{H}_{2} \mathrm{O}\) and CO, which not only reduces the efficiency of the engine using the fuel but is also toxic. In a certain test run, 1.000 gal of octane is burned in an engine. The total mass of \(\mathrm{CO}, \mathrm{CO}_{2},\) and \(\mathrm{H}_{2} \mathrm{O}\) produced is \(11.53 \mathrm{~kg} .\) Calculate the efficiency of the process; that is, calculate the fraction of octane converted to \(\mathrm{CO}_{2}\). The density of octane is \(2.650 \mathrm{~kg} / \mathrm{gal}\)

In a natural product synthesis, a chemist prepares a complex biological molecule entirely from nonbiological starting materials. The target molecules are often known to have some promise as therapeutic agents, and the organic reactions that are developed along the way benefit all chemists. The overall synthesis, however, requires many steps, so it is important to have the best possible percent yields at each step. What is the overall percent yield for such a synthesis that has 24 steps with an 80 percent yield at each step?

What is wrong or ambiguous with each of the statements here? (a) \(\mathrm{NH}_{4} \mathrm{NO}_{2}\) is the limiting reactant in the reaction$$\mathrm{NH}_{4} \mathrm{NO}_{2}(s) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ (b) The limiting reactants for the reaction shown here are \(\mathrm{NH}_{3}\) and \(\mathrm{NaCl}\). $$\begin{aligned}\mathrm{NH}_{3}(a q)+\mathrm{NaCl}(a q) &+\mathrm{H}_{2} \mathrm{CO}_{3}(a q) & \longrightarrow \\ & \mathrm{NaHCO}_{3}(a q)+\mathrm{NH}_{4} \mathrm{Cl}(a q) \end{aligned}$$

(a) For molecules having small molecular masses, mass spectrometry can be used to identify their formulas. To illustrate this point, identify the molecule that most likely accounts for the observation of a peak in a mass spectrum at 16 amu, 17 amu, 18 amu, and 64 amu. (b) Note that there are (among others) two likely molecules that would give rise to a peak at 44 amu, namely, \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(\mathrm{CO}_{2} .\) In such cases, a chemist might try to look for other peaks generated when some of the molecules break apart in the spectrometer. For example, if a chemist sees a peak at 44 amu and also one at 15 amu, which molecule is producing the 44 -amu peak? Why? (c) Using the following precise atomic masses \(-\mathrm{H}\) ( 1.00797 amu), \({ }^{12} \mathrm{C}(12.00000 \mathrm{amu}),\) and \({ }^{16} \mathrm{O}(15.99491 \mathrm{amu})-\) how precisely must the masses of \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(\mathrm{CO}_{2}\), be measured to distinguish between them?

Potash is any potassium mineral that is used for its potassium content. Most of the potash produced in the United States goes into fertilizer. The major sources of potash are potassium chloride \((\mathrm{KCl})\) and potassium sulfate \(\left(\mathrm{K}_{2} \mathrm{SO}_{4}\right) .\) Potash production is often reported as the potassium oxide \(\left(\mathrm{K}_{2} \mathrm{O}\right)\) equivalent or the amount of \(\mathrm{K}_{2} \mathrm{O}\) that could be made from a given mineral. (a) If \(\mathrm{KCl}\) costs \(\$ 0.55\) per \(\mathrm{kg}\), for what price (dollar per \(\mathrm{kg}\) ) must \(\mathrm{K}_{2} \mathrm{SO}_{4}\) be sold to supply the same amount of potassium on a per dollar basis? (b) What mass (in kg) of \(\mathrm{K}_{2} \mathrm{O}\) contains the same number of moles of \(\mathrm{K}\) atoms as \(1.00 \mathrm{~kg}\) of KCl?

A certain metal M forms a bromide containing 53.79 percent Br by mass. What is the chemical formula of the compound?

A sample of iron weighing \(15.0 \mathrm{~g}\) was heated with potassium chlorate \(\left(\mathrm{KClO}_{3}\right)\) in an evacuated container. The oxygen generated from the decomposition of \(\mathrm{KClO}_{3}\) converted some of the Fe to \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). If the combined mass of Fe and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) was \(17.9 \mathrm{~g}\), calculate the mass of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) formed and the mass of \(\mathrm{KClO}_{3}\) decomposed.

A sample containing \(\mathrm{NaCl}, \mathrm{Na}_{2} \mathrm{SO}_{4},\) and \(\mathrm{NaNO}_{3}\) gives the following elemental analysis: Na: 32.08 percent; O: 36.01 percent; Cl: 19.51 percent. Calculate the mass percent of each compound in the sample.

Without doing any detailed calculations, arrange the following substances in the increasing order of number of moles: \(20.0 \mathrm{~g} \mathrm{Cl}, 35.0 \mathrm{~g} \mathrm{Br},\) and\(94.0 \mathrm{~g} \mathrm{I}\)

Without doing any detailed calculations, estimate which element has the highest percent composition by mass in each of the following compounds: (a) \(\mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}\) (b) \(\mathrm{NF}_{3}\) (c) \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) (d) \(\mathrm{C}_{2952} \mathrm{H}_{4664} \mathrm{~N}_{812} \mathrm{O}_{832} \mathrm{~S}_{8} \mathrm{Fe}_{4}\)

Consider the reaction $$6 \mathrm{Li}(s)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{Li}_{3} \mathrm{~N}(s)$$ Without doing any detailed calculations, choose one of the following combinations in which nitrogen is the limiting reactant: (a) \(44 \mathrm{~g} \mathrm{Li}\) and \(38 \mathrm{~g} \mathrm{~N}_{2}\) (b) \(1380 \mathrm{~g} \mathrm{Li}\) and \(842 \mathrm{~g} \mathrm{~N}_{2}\) (c) \(1.1 \mathrm{~g} \mathrm{Li}\) and \(0.81 \mathrm{~g} \mathrm{~N}_{2}\)

The following is a crude but effective method for estimating the order of magnitude of Avogadro's number using stearic acid \(\left(\mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}\right)\) shown here. When stearic acid is added to water, its molecules collect at the surface and form a monolayer; that is, the layer is only one molecule thick. The crosssectional area of each stearic acid molecule has been measured to be \(0.21 \mathrm{nm}^{2}\). In one experiment it is found that \(1.4 \times 10^{-4} \mathrm{~g}\) of stearic acid is needed to form a monolayer over water in a dish of diameter \(20 \mathrm{~cm} .\) Based on these measurements, what is A vogadro's number?