Chapter 4

Saccharin, an artificial sweetener, has the formula \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{NO}_{3} \mathrm{S} .\) Suppose you have a sample of a saccharincontaining sweetener with a mass of \(0.2140 \mathrm{g} .\) After decomposition to free the sulfur and convert it to the \(\mathrm{SO}_{4}^{2-}\) ion, the sulfate ion is trapped as water-insoluble \(\mathrm{BaSO}_{4}\) (see Figure 4.8 ). The quantity of \(\mathrm{BaSO}_{4}\) obtained is \(0.2070 \mathrm{g}\). What is the mass percent of saccharin in the sample of sweetener?

A Boron forms an extensive series of compounds with hydrogen, all with the general formula \(\mathrm{B}_{x} \mathrm{H}_{y}\) \(\mathrm{B}_{x} \mathrm{H}_{y}(\mathrm{s})+\) excess \(\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \frac{x}{2} \mathrm{B}_{2} \mathrm{O}_{3}(\mathrm{s})+\frac{2}{2} \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) If \(0.148 \mathrm{g}\) of \(\mathrm{B}_{x} \mathrm{H}_{y}\) gives \(0.422 \mathrm{g}\) of \(\mathrm{B}_{2} \mathrm{O}_{3}\) when burned in excess \(\mathrm{O}_{2},\) what is the empirical formula of \(\mathrm{B}_{x} \mathrm{H}_{y} ?\)

Silicon and hydrogen form a series of compounds with the general formula \(\mathrm{Si}_{x} \mathrm{H}_{y}\). To find the formula of one of them, a 6.22 -g sample of the compound is burned in oxygen. All of the Si is converted to \(11.64 \mathrm{g}\) of \(\mathrm{SiO}_{2},\) and all of the \(\mathrm{H}\) is converted to \(6.980 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\). What is the empirical formula of the silicon compound?

Menthol, from oil of mint, has a characteristic odor. The compound contains only \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{O} .\) If \(95.6 \mathrm{mg}\) of menthol burns completely in \(\mathrm{O}_{2},\) and gives \(269 \mathrm{mg}\) of \(\mathrm{CO}_{2}\) and \(110 \mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O},\) what is the empirical formula of menthol?

Quinone, a chemical used in the dye industry and in photography, is an organic compound containing only \(\mathrm{C}\) H, and O. What is the empirical formula of the compound if \(0.105 \mathrm{g}\) of the compound gives \(0.257 \mathrm{g}\) of \(\mathrm{CO}_{2}\) and \(0.0350 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\) when burned completely in oxygen?

Sulfuric acid can be prepared starting with the sulfide ore, cuprite \(\left(\mathrm{Cu}_{2} \mathrm{S}\right) .\) If each \(\mathrm{S}\) atom in \(\mathrm{Cu}_{2} \mathrm{S}\) leads to one molecule of \(\mathrm{H}_{2} \mathrm{SO}_{4},\) what mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) can be produced from \(3.00 \mathrm{kg}\) of \(\mathrm{Cu}_{2} \mathrm{S} ?\)

In an experiment \(1.056 \mathrm{g}\) of a metal carbonate, containing an unknown metal \(\mathrm{M}\), is heated to give the metal oxide and \(0.376 \mathrm{g} \mathrm{CO}_{2}\) $$\mathrm{MCO}_{3}(\mathrm{s})+\text { heat } \longrightarrow \mathrm{MO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$$ What is the identity of the metal M? (a) \(\mathrm{M}=\mathrm{Ni}\) (c) \(\mathbf{M}=\mathbf{Z} \mathbf{n}\) (b) \(\mathrm{M}=\mathrm{Cu}\) (d) \(\mathrm{M}=\mathrm{Ba}\)

An unknown metal reacts with oxygen to give the metal oxide, MO \(_{2} .\) Identify the metal based on the following information: Mass of metal \(=0.356 \mathrm{g}\) Mass of sample after converting metal completely to oxide \(=0.452 \mathrm{g}\)

Titanium(IV) oxide, \(\mathrm{TiO}_{2}\), is heated in hydrogen gas to give water and a new titanium oxide, \(\mathrm{Ti}_{x} \mathrm{O}_{y} .\) If \(1.598 \mathrm{g}\) of TiO \(_{2}\) produces \(1.438 \mathrm{g}\) of \(\mathrm{Ti}_{x} \mathrm{O}_{y},\) what is the formula of the new oxide?

Potassium perchlorate is prepared by the following sequence of reactions: $$\begin{aligned}\mathrm{Cl}_{2}(\mathrm{g})+& 2 \mathrm{KOH}(\mathrm{aq}) \longrightarrow \mathrm{KCl}(\mathrm{aq})+\mathrm{KClO}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \\\& 3 \mathrm{KClO}(\mathrm{aq}) \longrightarrow 2 \mathrm{KCl}(\mathrm{aq})+\mathrm{KClO}_{3}(\mathrm{aq}) \\\& 4 \mathrm{KClO}_{3}(\mathrm{aq}) \longrightarrow 3 \mathrm{KClO}_{4(\mathrm{aq})+\mathrm{KCl}(\mathrm{aq}) \end{aligned}$$ What mass of \(\mathrm{Cl}_{2}(\mathrm{g})\) is required to produce \(234 \mathrm{kg}\) of \(\mathrm{KClO}_{4} ?\)

Commercial sodium "hydrosulfite" is \(90.1 \%\) pure \(\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{4} .\) The sequence of reactions used to prepare the compound is $$\begin{aligned} \mathrm{Zn}(\mathrm{s})+2 \mathrm{SO}_{2}(\mathrm{g}) & \longrightarrow \mathrm{ZnS}_{2} \mathrm{O}_{4}(\mathrm{s}) \\ \mathrm{ZnS}_{2} \mathrm{O}_{4}(\mathrm{s})+\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq}) & \longrightarrow \mathrm{ZnCO}_{3}(\mathrm{s})+\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{4}(\mathrm{aq}) \end{aligned}$$ (a) What mass of pure \(\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{4}\) can be prepared from \(125 \mathrm{kg}\) of \(\mathrm{Zn}, 500 \mathrm{g}\) of \(\mathrm{SO}_{2},\) and an excess of \(\mathrm{Na}_{2} \mathrm{CO}_{3} ?\) (b) What mass of the commercial product would contain the \(\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{4}\) produced using the amounts of reactants in part (a)?

What mass of lime, CaO, can be obtained by heating \(125 \mathrm{kg}\) of limestone that is \(95.0 \%\) by mass \(\mathrm{CaCO}_{3} ?\) $$\mathrm{CaCO}_{3}(\mathrm{s}) \longrightarrow \mathrm{CaO(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$$

Sulfuric acid can be produced from a sulfide ore such as iron pyrite by the following sequence of reactions: $$\begin{aligned} 4 \mathrm{FeS}_{2}(\mathrm{s})+11 \mathrm{O}_{2}(\mathrm{g}) & \longrightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+8 \mathrm{SO}_{2}(\mathrm{g}) \\ 2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) & \longrightarrow 2 \mathrm{SO}_{3}(\mathrm{g}) \\ \mathrm{SO}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\ell) & \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(\ell) \end{aligned}$$ Starting with \(525 \mathrm{kg}\) of \(\mathrm{FeS}_{2}\) (and an excess of other reactants), what mass of pure \(\mathrm{H}_{2} \mathrm{SO}_{4}\) can be prepared?

The elements silver, molybdenum, and sulfur combine to form \(\mathrm{Ag}_{2} \mathrm{MoS}_{4} .\) What is the maximum mass of \(\mathrm{Ag}_{2} \mathrm{MoS}_{4}\) that can be obtained if \(8.63 \mathrm{g}\) of silver, \(3.36 \mathrm{g}\) of molybdenum, and \(4.81 \mathrm{g}\) of sulfur are combined?

A mixture of butene, \(C_{4} H_{8},\) and butane, \(C_{4} H_{10},\) is burned in air to give \(\mathrm{CO}_{2}\) and water. Suppose you burn \(2.86 \mathrm{g}\) of the mixture and obtain \(8.80 \mathrm{g}\) of \(\mathrm{CO}_{2}\) and \(4.14 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\). What is the weight percents of butene and butane in the mixture?

A Cloth can be waterproofed by coating it with a silicone layer. This is done by exposing the cloth to \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiCl}_{2}\) vapor. The silicon compound reacts with OH groups on the cloth to form a waterproofing film (density = \(\left.1.0 \mathrm{g} / \mathrm{cm}^{3}\right)\) of \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiO}\right]_{n},\) where \(n\) is a large integer number. $$\begin{aligned}n\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiCl}_{2}+2 n \mathrm{OH}^{-} & \longrightarrow \\\& 2 n \mathrm{Cl}^{-}+n \mathrm{H}_{2} \mathrm{O}+\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiO}\right]_{n}\end{aligned}$$ The coating is added layer by layer, each layer of \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiO}\right]_{n}\) being \(0.60 \mathrm{nm}\) thick. Suppose you want to waterproof a piece of cloth that is \(3.00 \mathrm{m}\) square, and you want 250 layers of waterproofing compound on the cloth. What mass of \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiCl}_{2}\) do you need?

Sodium hydrogen carbonate, \(\mathrm{NaHCO}_{3},\) can be decomposed quantitatively by heating. $$2 \mathrm{NaHCO}_{3}(\mathrm{s}) \longrightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$ A 0.682 -g sample of impure NaHCO \(_{3}\) yielded a solid residue (consisting of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) and other solids) with a mass of \(0.467 \mathrm{g} .\) What was the mass percent of \(\mathrm{NaHCO}_{3}\) in the sample?

Copper metal can be prepared by roasting copper ore, which can contain cuprite \(\left(\mathrm{Cu}_{2} \mathrm{S}\right)\) and copper (II) sulfide. $$\begin{array}{c}\mathrm{Cu}_{2} \mathrm{S}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{Cu}(\mathrm{s})+\mathrm{SO}_{2}(\mathrm{g}) \\ \mathrm{CuS}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{Cu}(\mathrm{s})+\mathrm{SO}_{2}(\mathrm{g})\end{array}$$ Suppose an ore sample contains \(11.0 \%\) impurity in addition to a mixture of CuS and \(\mathrm{Cu}_{2} \mathrm{S}\). Heating \(100.0 \mathrm{g}\) of the mixture produces \(75.4 \mathrm{g}\) of copper metal with a purity of \(89.5 \% .\) What is the weight percent of CuS in the ore? The weight percent of \(\mathrm{Cu}_{2} \mathrm{S} ?\)