Chapter 3

Write formulas for the compounds: (a) magnesium perchlorate; (b) lead(II) acetate; (c) tin(IV) oxide; (d) hydroiodic acid; (e) chlorous acid; (f) sodium hydrogen sulfite; (g) calcium dihydrogen phosphate; (h) aluminum phosphate; (i) dinitrogen tetroxide; (j) disulfur dichloride.

Write a formula for (a) the chloride of titanium having Ti in the O.S. \(+4 ;\) (b) the sulfate of iron having Fe in the O.S. \(+3 ;(c)\) an oxide of chlorine with Cl in the O.S. \(+7 ;\) (d) an oxoanion of sulfur in which the apparent O.S. of \(S\) is +7 and the ionic charge is \(2-\).

Write a formula for (a) an oxide of nitrogen with \(\mathrm{N}\) in the O.S. \(+5 ;\) (b) an oxoacid of nitrogen with \(\mathrm{N}\) in the O.S. \(+3 ;\) (c) an oxide of carbon in which the apparent O.S. of \(C\) is \(+4 / 3 ;\) (d) a sulfur- containing oxoanion in which the apparent O.S. of \(S\) is +2.5 and the ionic charge is \(2-\).

Name the acids: (a) \(\mathrm{HClO}_{2} ;\) (b) \(\mathrm{H}_{2} \mathrm{SO}_{3} ;\) (c) \(\mathrm{H}_{2} \mathrm{Se}\) (d) HNO \(_{2}\).

Supply the formula for the acids: (a) hydrofluoric acid; (b) nitric acid; (c) phosphorous acid; (d) sulfuric acid.

Name the following compounds and specify which ones are best described as ionic: (a) \(\mathrm{OF}_{2} ;\) (b) \(\mathrm{XeF}_{2}\) (c) \(\operatorname{CuSO}_{3} ;\) (d) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\)

Name the following compounds and specify which ones are best described as ionic: (a) \(\mathrm{KNO}_{2} ;\) (b) \(\mathrm{Br} \mathrm{F}_{3}\) (c) \(\mathrm{S}_{2} \mathrm{Cl}_{2} ;\) (d) \(\mathrm{Mg}(\mathrm{ClO})_{2} ;\) (e) \(\mathrm{Cl}_{2} \mathrm{O}\)

Without per frming detailed calculations, indicate which of the following hydrates has the greatest \% \(\mathrm{H}_{2} \mathrm{O}\) by mass: \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}, \quad \mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3} \cdot 18 \mathrm{H}_{2} \mathrm{O}, \quad \mathrm{MgCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{LiC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\)

Without per forming detailed calculations, determine the hydrate of \(\mathrm{Na}_{2} \mathrm{SO}_{3}\) that contains almost exactly \(50 \%\) \(\mathrm{H}_{2} \mathrm{O},\) by mass.

Anhydrous sodium sulfate, \(\mathrm{Na}_{2} \mathrm{SO}_{4},\) absorbs water vapor and is converted to the decahydrate, \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O} .\) How much would the mass of \(24.05 \mathrm{g}\) of anhydrous \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) increase if converted completely to the decahydrate?

A certain hydrate is found to have the composition \(20.3 \%\) Cu, \(8.95 \%\) Si, \(36.3 \%\) F, and \(34.5 \% \mathrm{H}_{2} \mathrm{O}\) by mass. What is the empirical formula of this hydrate?

An 8.129 g sample of \(\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O}\) is heated until all the water of hydration is driven off. The resulting anhydrous compound, \(\mathrm{MgSO}_{4},\) weighs \(3.967 \mathrm{g} .\) What is the formula of the hydrate?

Which of the following names is most appropriate for the molecule \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{2} \mathrm{COOH} ?\) (a) dimethyleneacetic acid; (b) propanoic acid; (c) butanoic acid; (d) oxobutylalcohol.

Write the condensed structural formulas for the organic compounds: (a) heptane (b) propanoic acid (c) 2-methyl-1-pentanol (d) fluoroethane

Write the condensed structural formulas for the organic compounds: (a) octane (b) heptanoic acid (c) 3-hexanol (d) 2 -chlorobutane

The mineral spodumene has the empirical formula \(\mathrm{LiAlSi}_{2} \mathrm{O}_{6} .\) Given that the percentage of lithium- 6 atoms in naturally occuring lithium is \(7.40 \%,\) how many lithium- 6 atoms are present in a 518 g sample of spodumene?

The important natural sources of boron compounds are the minerals kernite, \(\mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{7} \cdot 4 \mathrm{H}_{2} \mathrm{O}\) and borax, \(\mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{7} \cdot 10 \mathrm{H}_{2} \mathrm{O} .\) How much additional mass of mineral must be processed per kilogram of boron obtained if the mineral is borax rather than kernite?

To deposit exactly one mole of \(\mathrm{Ag}\) from an aqueous solution containing \(\mathrm{Ag}^{+}\) requires a quantity of electricity known as one faraday (F). The electrodeposition requires that each \(\mathrm{Ag}^{+}\) ion gain one electron to become an Ag atom. Use appropriate physical constants listed on the inside back cover to obtain a precise value of the Avogadro constant, \(N_{A}\).

What is the molecular formula of a hydrocarbon containing \(n\) carbon atoms and only one double bond? Can such a hydrocarbon yield a greater mass of \(\mathrm{H}_{2} \mathrm{O}\) than \(\mathrm{CO}_{2}\) when burned in an excess of oxygen?

A hydrocarbon mixture consists of \(60.0 \%\) by mass of \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(40.0 \%\) of \(\mathrm{C}_{x} \mathrm{H}_{y} .\) When \(10.0 \mathrm{g}\) of this mixture is burned, \(29.0 \mathrm{g} \mathrm{CO}_{2}\) and \(18.8 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) are the only products. What is the formula of the unknown hydrocarbon?

A 0.732 g mixture of methane, \(\mathrm{CH}_{4}\), and ethane, \(\mathrm{C}_{2} \mathrm{H}_{6},\) is burned, yielding \(2.064 \mathrm{g} \mathrm{CO}_{2} .\) What is the percent composition of this mixture (a) by mass; (b) on a mole basis?

The density of a mixture of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and water is 1.78 g/mL. The percent composition of the mixture is to be determined by converting \(\mathrm{H}_{2} \mathrm{SO}_{4}\) to \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) If \(32.0 \mathrm{mL}\) of the mixture gives \(65.2 \mathrm{g}\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) then what is the percent composition of the mixture?

All the silver in a \(26.39 \mathrm{g}\) sample of impure silver is converted to silver chloride. If 31.56 g of silver chloride are obtained, then what is the mass percent of silver in the sample?

In the year 2000 , the Guinness Book of World Records called ethyl mercaptan, \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{S}\), the smelliest substance known. The average person can detect its presence in air at levels as low as \(9 \times 10^{-4} \mu \mathrm{mol} / \mathrm{m}^{3} .\) Express the limit of detectability of ethyl mercaptan in parts per billion (ppb). (Note: 1 ppb \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{S}\) means there is \(1 \mathrm{g}\) \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{S}\) per billion grams of air.) The density of air is approximately \(1.2 \mathrm{g} / \mathrm{L}\) at room temperature.

Dry air is essentially a mixture of the following entities: \(\mathrm{N}_{2}, \mathrm{O}_{2}, \mathrm{Ar},\) and \(\mathrm{CO}_{2} .\) The composition of dry air, in mole percent, is \(78.08 \% \mathrm{N}_{2}, 20.95 \% \mathrm{O}_{2}, 0.93 \% \mathrm{Ar}\) and \(0.04 \% \mathrm{CO}_{2}\). (a) What is the mass, in grams, of a sample of air that contains exactly one mole of the entities? (b) Dry air also contains other entities in much smaller amounts. For example, the mole percent of krypton (Kr) is about \(1.14 \times 10^{-4} \% .\) Given that the density of dry air is about \(1.2 \mathrm{g} / \mathrm{L}\) at room temperature, what mass of krypton could be obtained from exactly one cubic meter of dry air?

A public water supply was found to contain 1 part per billion (ppb) by mass of chloroform, \(\mathrm{CHCl}_{3}\) (a) How many \(\mathrm{CHCl}_{3}\) molecules would be present in a \(225 \mathrm{mL}\) glass of this water? (b) If the \(\mathrm{CHCl}_{3}\) in part (a) could be isolated, would this quantity be detectable on an ordinary analytical balance that measures mass with a precision of ±0.0001 g?

A sample of the compound MSO \(_{4}\) weighing \(0.1131 \mathrm{g}\) reacts with barium chloride and yields \(0.2193 \mathrm{g} \mathrm{BaSO}_{4}\) What must be the atomic mass of the metal M? [Hint: All the \(\mathrm{SO}_{4}^{2-}\) from the MSO \(_{4}\) appears in the \(\mathrm{BaSO}_{4}\) ]

A 0.622 g sample of a metal oxide with the formula \(\mathrm{M}_{2} \mathrm{O}_{3}\) is converted to \(0.685 \mathrm{g}\) of the sulfide, MS. What is the atomic mass of the metal M?

\(\mathrm{MgCl}_{2}\) often occurs in table salt \((\mathrm{NaCl})\) and is responsible for caking of the salt. A 0.5200 g sample of table salt is found to contain \(61.10 \%\) Cl, by mass. What is the \(\% \mathrm{MgCl}_{2}\) in the sample? Why is the precision of this calculation so poor?

When \(2.750 \mathrm{g}\) of the oxide of lead \(\mathrm{Pb}_{3} \mathrm{O}_{4}\) is strongly heated, it decomposes and produces \(0.0640 \mathrm{g}\) of oxygen gas and \(2.686 \mathrm{g}\) of a second oxide of lead. What is the empirical formula of this second oxide?

A \(1.013 \mathrm{g}\) sample of \(\mathrm{ZnSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O}\) is dissolved in water and the sulfate ion precipitated as \(\mathrm{BaSO}_{4}\). The mass of pure, dry \(\mathrm{BaSO}_{4}\) obtained is \(0.8223 \mathrm{g}\). What is the formula of the zinc sulfate hydrate?

The iodide ion in a \(1.552 \mathrm{g}\) sample of the ionic compound MI is removed through precipitation. The precipitate is found to contain \(1.186 \mathrm{g}\) I. What is the element M?

An oxoacid with the formula \(\mathrm{H}_{x} \mathrm{E}_{y} \mathrm{O}_{z}\) has a formula mass of 178 u, has 13 atoms in its formula unit, contains \(34.80 \%\) by mass, and \(15.38 \%\) by number of atoms, of the element E. What is the element \(\mathrm{E}\), and what is the formula of this oxoacid?

The insecticide dieldrin contains carbon, hydrogen, oxygen, and chlorine. When burned in an excess of oxygen, a 1.510 g sample yields \(2.094 \mathrm{g} \mathrm{CO}_{2}\) and \(0.286 \mathrm{g} \mathrm{H}_{2} \mathrm{O} .\) The compound has a molecular mass of 381 u and has half as many chlorine atoms as carbon atoms. What is the molecular formula of dieldrin?

A thoroughly dried 1.271 g sample of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is exposed to the atmosphere and found to gain \(0.387 \mathrm{g}\) in mass. What is the percent, by mass, of \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}\) in the resulting mixture of anhydrous \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) and the decahydrate?

The atomic mass of \(\mathrm{Bi}\) is to be determined by converting the compound \(\mathrm{Bi}\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{3}\) to \(\mathrm{Bi}_{2} \mathrm{O}_{3} .\) If \(5.610 \mathrm{g}\) of \(\mathrm{Bi}\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{3}\) yields \(2.969 \mathrm{g} \mathrm{Bi}_{2} \mathrm{O}_{3},\) what is the atomic mass of Bi?

A piece of gold (Au) foil measuring \(0.25 \mathrm{mm} \times\) \(15 \mathrm{mm} \times 15 \mathrm{mm}\) is treated with fluorine gas. The treatment converts all the gold in the foil to \(1.400 \mathrm{g}\) of a gold fluoride. What is the formula and name of the fluoride? The density of gold is \(19.3 \mathrm{g} / \mathrm{cm}^{3}\)

In an experiment, \(244 \mathrm{mL}\) of chlorine gas \(\left(\mathrm{Cl}_{2}, d=2.898 \mathrm{g} / \mathrm{L}\right)\) combines with iodine to give \(1.553 \mathrm{g}\) of a binary compound. In a separate experiment, the molar mass of the compound is found to be about \(467 \mathrm{g} / \mathrm{mol} .\) What is the molecular formula of this compound?

All-purpose fertilizers contain the essential elements nitrogen, phosphorus, and potassium. A typical fertilizer carries numbers on its label, such as "5-10-5". These numbers represent the \% \(\mathrm{N}, \% \mathrm{P}_{2} \mathrm{O}_{5},\) and \(\% \mathrm{K}_{2} \mathrm{O},\) respectively. The \(\mathrm{N}\) is contained in the form of a nitrogen compound, such as \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}, \mathrm{NH}_{4} \mathrm{NO}_{3}\) or \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}\) (urea). The \(\mathrm{P}\) is generally present as a phosphate, and the \(K\) as \(K C\). The expressions \(\% \mathrm{P}_{2} \mathrm{O}_{5}\) and \(\% \mathrm{K}_{2} \mathrm{O}\) were devised in the nineteenth century, before the nature of chemical compounds was fully understood. To convert from \% \(\mathrm{P}_{2} \mathrm{O}_{5}\) to \% \(\mathrm{P}\) and from \% \(\mathrm{K}_{2} \mathrm{O}\) to \% \(\mathrm{K}\), the factors \(2 \mathrm{mol} \mathrm{P} / \mathrm{mol}\) \(\mathrm{P}_{2} \mathrm{O}_{5}\) and \(2 \mathrm{mol} \mathrm{K} / \mathrm{mol} \mathrm{K}_{2} \mathrm{O}\) must be used, together with molar masses. (a) Assuming three-significant-figure precision, what is the percent composition of the "5-10-5" fertilizer in \% \(\mathrm{N}, \% \mathrm{P},\) and \(\% \mathrm{K} ?\) (b) What is the \(\% \mathrm{P}_{2} \mathrm{O}_{5}\) in the following compounds (both common fertilizers)? (i) \(\mathrm{Ca}\left(\mathrm{H}_{2} \mathrm{PO}_{4}\right)_{2}\) (ii) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\) (c) In a similar manner to the "5-10-5" fertilizer described in this exercise, how would you describe a fertilizer in which the mass ratio of \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\) to KCl is 5.00:1.00? (d) Can a "5-10-5" fertilizer be prepared in which \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\) and \(\mathrm{KCl}\) are the sole fertilizer components, with or without inert nonfertilizer additives? If so, what should be the proportions of the constituents of the fertilizer mixture? If this "5-10-5" fertilizer cannot be prepared, why not?

A hydrate of copper(II) sulfate, when heated, goes through the succession of changes suggested by the photograph. In this photograph, (a) is the original fully hydrated copper(II) sulfate; (b) is the product obtained by heating the original hydrate to \(140^{\circ} \mathrm{C}\) (c) is the product obtained by further heating to \(400^{\circ} \mathrm{C}\) and (d) is the product obtained at \(1000^{\circ} \mathrm{C}\) A \(2.574 \mathrm{g}\) sample of \(\mathrm{CuSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O}\) was heated to \(140^{\circ} \mathrm{C},\) cooled, and reweighed. The resulting solid was reheated to \(400^{\circ} \mathrm{C},\) cooled, and reweighed. Finally, this solid was heated to \(1000^{\circ} \mathrm{C},\) cooled, and reweighed for the last time. $$ \text {Original sample } \quad \quad\quad\quad\quad \text {\(2.574 \mathrm{g}\) } $$ $$ \text {After heating to \(140^{\circ} \mathrm{C}\) } \quad \quad\quad\quad\quad \text {\(1.833 \mathrm{g}\) } $$ $$ \text {After reheating to \(400^{\circ} \mathrm{C}\)} \quad \quad\quad\quad\quad \text {\(1.647 \mathrm{g}\) } $$ $$ \text {After reheating to \(1000^{\circ} \mathrm{C}\)} \quad \quad\quad\quad\quad \text {\(0.812 \mathrm{g}\)} $$ (a) Assuming that all the water of hydration is driven off at \(400^{\circ} \mathrm{C},\) what is the formula of the original hydrate? (b) What is the formula of the hydrate obtained when the original hydrate is heated to only \(140^{\circ} \mathrm{C} ?\) (c) The black residue obtained at \(1000^{\circ} \mathrm{C}\) is an oxide of copper. What is its percent composition and empirical formula?

Some substances that are only very slightly soluble in water will spread over the surface of water to produce a film that is called a monolayer because it is only one molecule thick. A practical use of this phenomenon is to cover ponds to reduce the loss of water by evaporation. Stearic acid forms a monolayer on water. The molecules are arranged upright and in contact with one another, rather like pencils tightly packed and standing upright in a coffee mug. The model below represents an individual stearic acid molecule in the monolayer. (a) How many square meters of water surface would be covered by a monolayer made from \(10.0 \mathrm{g}\) of stearic acid? [Hint: What is the formula of stearic acid?] (b) If stearic acid has a density of \(0.85 \mathrm{g} / \mathrm{cm}^{3}\), estimate the length (in nanometers) of a stearic acid molecule. [Hint: What is the thickness of the monolayer described in part a?] (c) A very dilute solution of oleic acid in liquid pentane is prepared in the following way: $$\begin{aligned} &1.00 \mathrm{mL} \text { oleic acid }+9.00 \mathrm{mL} \text { pentane } \rightarrow \text { solution }(1)\\\ &1.00 \mathrm{mL} \text { solution }(1)+9.00 \mathrm{mL} \text { pentane } \rightarrow \text { solution }(2)\\\ &1.00 \mathrm{mL} \text { solution }(2)+9.00 \mathrm{mL} \text { pentane } \rightarrow \text { solution }(3)\\\ &1.00 \mathrm{mL} \text { solution }(3)+9.00 \mathrm{mL} \text { pentane } \rightarrow \text { solution }(4) \end{aligned}$$ A 0.10 mL sample of solution (4) is spread in a monolayer on water. The area covered by the monolayer is \(85 \mathrm{cm}^{2} .\) Assume that oleic acid molecules are arranged in the same way as described for stearic acid, and that the cross-sectional area of the molecule is \(4.6 \times 10^{-15} \mathrm{cm}^{2}\). The density of oleic acid is \(0.895 \mathrm{g} / \mathrm{mL} .\) Use these data to obtain an approximate value of Avogadro's number.

In your own words, define or explain the following terms or symbols: (a) formula unit; (b) \(\mathrm{P}_{4} ;\) (c) molecular compound; (d) binary compound; (e) hydrate.

Briefly describe each of the following ideas or methods: (a) mole of a compound; (b) structural formula; (c) oxidation state; (d) carbon-hydrogen- oxygen determination by combustion analysis.

Explain the important distinctions between each pair of terms: (a) molecular mass and molar mass; (b) empirical and molecular formulas; (c) systematic and trivial, or common, name; (d) hydroxyl and carboxyl functional group.

Explain each term as it applies to the element nitrogen. (a) atomic mass; (b) molecular mass; (c) molar mass.

Which answer is correct? One mole of liquid bromine, \(\mathrm{Br}_{2},\) (a) has a mass of \(79.9 \mathrm{g} ;\) (b) contains \(6.022 \times 10^{23}\) Br atoms; (c) contains the same number of atoms as in \(12.01 \mathrm{g} \mathrm{H}_{2} \mathrm{O} ;\) (d) has twice the mass of 0.500 mole of gaseous \(\mathrm{Cl}_{2}\)

Three of the following formulas might be either an empirical or a molecular formula. The formula that must be a molecular formula is (a) \(\mathrm{N}_{2} \mathrm{O} ;\) (b) \(\mathrm{N}_{2} \mathrm{H}_{4}\) (c) \(\mathrm{NaCl} ;\) (d) \(\mathrm{NH}_{3}\)

The compound \(\mathrm{C}_{7} \mathrm{H}_{7} \mathrm{NO}_{2}\) contains (a) 17 atoms per mole; (b) equal percents by mass of \(\mathrm{C}\) and \(\mathrm{H} ;\) (c) about twice the percent by mass of \(\mathrm{O}\) as of \(\mathrm{N} ;\) (d) about twice the percent by mass of \(\mathrm{N}\) as of \(\mathrm{H}\).

The greatest number of \(\mathrm{N}\) atoms is found in (a) \(50.0 \mathrm{g}\) \(\mathrm{N}_{2} \mathrm{O} ;\) (b) \(17.0 \mathrm{g} \mathrm{NH}_{3} ;\) (c) \(150 \mathrm{mL}\) of liquid pyridine, \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}(d=0.983 \mathrm{g} / \mathrm{mL}) ;\) (d) \(1.0 \mathrm{mol} \mathrm{N}_{2}\)

\(\mathrm{XF}_{3}\) consists of \(65 \%\) F by mass. The atomic mass of the element X must be (a) 8 u; (b) 11 u; (c) 31 u; (d) 35 u.