Chapter 4

A One half liter \((500 . \mathrm{mL})\) of \(2.50 \mathrm{M} \mathrm{HCl}\) is mixed with \(250 .\) mL. of 3.75 M HCl. Assuming the total solution volume after mixing is \(750 .\) mL, what is the concentration of hydrochloric acid in the resulting solution? What is its pH?

A You place \(2.56 \mathrm{g}\) of \(\mathrm{CaCO}_{3}\) in a beaker containing \(250 .\) mL of \(0.125 \mathrm{M} \mathrm{HCl}\). When the reaction has ceased, does any calcium carbonate remain? What mass of \(\mathrm{CaCl}_{2}\) can be produced? \(\mathrm{CaCO}_{3}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow\) $$ \mathrm{CaCl}_{2}(\mathrm{aq})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\ell) $$

A You need to know the volume of water in a small swimming pool, but, owing to the pool's irregular shape, it is not a simple matter to determine its dimensions and calculate the volume. To solve the problem, you stir in a solution of a dye \((1.0 \mathrm{g}\) of methylene blue, \(\mathrm{C}_{16} \mathrm{H}_{18} \mathrm{ClN}_{3} \mathrm{S},\) in \(50.0 \mathrm{mL}\) of water). After the dye has mixed with the water in the pool, you take a sample of the water. Using a spectrophotometer, you determine that the concentration of the dye in the pool is \(4.1 \times 10^{-8} \mathrm{M} .\) What is the volume of water in the pool?

A Calcium and magnesium carbonates occur together in the mineral dolomite. Suppose you heat a sample of the mineral to obtain the oxides, \(\mathrm{CaO}\) and \(\mathrm{MgO},\) and then treat the oxide sample with hydrochloric acid. If \(7.695 \mathrm{g}\) of the oxide sample requires 125 mL. of 2.55 M \(\mathrm{HCl}\). $$ \begin{aligned} \mathrm{CaO}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) & \rightarrow \mathrm{CaCl}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \\ \mathrm{MgO}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) & \rightarrow \mathrm{MgCl}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \end{aligned} $$ what is the weight percent of each oxide (CaO and \(\mathrm{MgO})\) in the sample?

Gold can be dissolved from gold-bearing rock by treating the rock with sodium cyanide in the presence of oxygen. \(4 \mathrm{Au}(\mathrm{s})+8 \mathrm{NaCN}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow\) $$ 4 \mathrm{NaAu}(\mathrm{CN})_{2}(\mathrm{aq})+4 \mathrm{NaOH}(\mathrm{aq}) $$ (a) Name the oxidizing and reducing agents in this reaction. What has been oxidized, and what has been reduced? (b) If you have exactly one metric ton ( 1 metric ton \(=1000 \mathrm{kg})\) of gold-bearing rock, what volume of \(0.075 \mathrm{M} \mathrm{NaCN},\) in liters, do you need to extract the gold if the rock is \(0.019 \%\) gold?

ATOM ECONOMY: One type of reaction used in the chemical industry is a substitution, where one atom or group is exchanged for another. In this reaction, an alcohol, 1-butanol, is transformed into 1 -bromobutane by substituting Br for the -OH group in the presence of sulfuric acid. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}+\mathrm{NaBr}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow\) $$ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br}+\mathrm{NaHSO}_{4}+\mathrm{H}_{2} \mathrm{O} $$ Calculate the \(\%\) atom economy for the desired product, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br}.\)

ATOM ECONOMY: Ethylene oxide, \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O},\) is an important industrial chemical las it is the starting place to make such important chemicals as ethylene glycol (antifreeze) and various polymers \(1 .\) One way to make the compound is called the "chlorohydrin route." $$ \mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{Cl}_{2}+\mathrm{Ca}(\mathrm{OH})_{2} \rightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}+\mathrm{CaCl}_{2}+\mathrm{H}_{2} \mathrm{O} $$ Another route is the modern catalytic reaction. $$ \mathrm{C}_{2} \mathrm{H}_{4}+1 / 2 \mathrm{O}_{2} \rightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O} $$ (a) Calculate the \(\%\) atom economy for the production of \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) in each of these reactions. Which is the more efficient method? (b) What is the percent yield of \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) if \(867 \mathrm{g}\) of \(\mathrm{C}_{2} \mathrm{H}_{4}\) is used to synthesize \(762 \mathrm{g}\) of the product by the catalytic reaction?

In the Laboratory Suppose you dilute \(25.0 \mathrm{mL}\) of a \(0.110 \mathrm{M}\) solution of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) to exactly \(100.0 \mathrm{mL}\). You then take exactly \(10.0 \mathrm{mL}\) of this diluted solution and add it to a \(250-\mathrm{mL}\) volumetric flask. After filling the volumetric flask to the mark with distilled water (indicating the volume of the new solution is \(250 .\) mL.), what is the concentration of the diluted \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) solution?

In some laboratory analyses, the preferred technique is to dissolve a sample in an excess of acid or base and then "back-titrate" the excess with a standard base or acid. This technique is used to assess the purity of a sample of \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\). Suppose you dissolve a 0.475 -g sample of impure \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) in aqueous \(\mathrm{KOH}\) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}(\mathrm{aq})+2 \mathrm{KOH}(\mathrm{aq}) \rightarrow\) $$ 2 \mathrm{NH}_{3}(\mathrm{aq})+\mathrm{K}_{2} \mathrm{SO}_{4}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\ell) $$ The NH ated in the reaction is distilled from the solution into a flask containing \(50.0 \mathrm{mL}\) of \(0.100 \mathrm{M}\) HCl. The ammonia reacts with the acid to produce \(\mathrm{NH}_{4} \mathrm{Cl},\) but not all of the \(\mathrm{HCl}\) is used in this reaction. The amount of excess acid is determined by titrating the solution with standardized NaOH. This titration consumes \(11.1 \mathrm{mL}\) of \(0.121 \mathrm{M} \mathrm{NaOH}\). What is the weight percent of \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) in the \(0.475-\mathrm{g}\) sample?

You wish to determine the weight percent of copper in a copper-containing alloy. After dissolving a \(0.251-\mathrm{g}\) sample of the alloy in acid, an excess of KI is added, and the \(\mathrm{Cu}^{2+}\) and \(1^{-}\) ions undergo the reaction $$ 2 \mathrm{Cu}^{2+}(\mathrm{aq})+5 \mathrm{I}^{-}(\mathrm{aq}) \rightarrow 2 \mathrm{CuI}(\mathrm{s})+\mathrm{I}_{3}^{-}(\mathrm{aq}) $$ The liberated \(I_{3}^{-}\) is titrated with sodium thiosulfate according to the equation \(\mathrm{I}_{3}^{-}(\mathrm{aq})+2 \mathrm{S}_{2} \mathrm{O}_{3}^{2-}(\mathrm{aq}) \rightarrow \mathrm{S}_{4} \mathrm{O}_{6}^{2-}(\mathrm{aq})+3 \mathrm{I}^{-}(\mathrm{aq})\) (a) Designate the oxidizing and reducing agents in the two reactions above. (b) If 26.32 mL of \(0.101 M N a_{2} S_{2} O_{3}\) is required for titration to the equivalence point, what is the weight percent of Cu in the alloy?

A A compound has been isolated that can have either of two possible formulas: (a) \(\mathrm{K}\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]\) or (b) \(\mathrm{K}_{3}\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right] .\) To find which is correct, you dissolve a weighed sample of the compound in acid, forming oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\). You then titrate this acid with potassium permanganate, \(\mathrm{KMnO}_{4}\) (the source of the \(\left.\mathrm{MnO}_{4}-\text { ion }\right) .\) The balanced, net ionic equation for the titration is $$ \begin{aligned} 5 \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq})+& 2 \mathrm{MnO}_{4}-(\mathrm{aq})+6 \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq}) \rightarrow \\ & 2 \mathrm{Mn}^{2+}(\mathrm{aq})+10 \mathrm{CO}_{2}(\mathrm{g})+14 \mathrm{H}_{2} \mathrm{O}(\ell) \end{aligned} $$ Titration of \(1.356 \mathrm{g}\) of the compound requires \(34.50 \mathrm{mL}\) of \(0.108 \mathrm{M} \mathrm{KMnO}_{4} .\) Which is the correct formula of the iron-containing compound: (a) or (b)?

A Chromium(III) chloride forms many compounds with ammonia. To find the formula of one of these compounds, you titrate the \(\mathrm{NH}_{3}\) in the compound with standardized acid. \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{\mathrm{x}} \mathrm{Cl}_{3}(\mathrm{aq})+\times \mathrm{HCl}(\mathrm{aq}) \rightarrow\) $$ x \mathrm{NH}_{4}+(\mathrm{aq})+\mathrm{Cr}^{3+}(\mathrm{aq})+(x+3) \mathrm{Cl}^{-}(\mathrm{aq}) $$ Assume that \(24.26 \mathrm{mL}\) of \(1.500 \mathrm{M} \mathrm{HCl}\) is used to tirate \(1.580 \mathrm{g}\) of \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{3} .\) What is the value of \(x ?\)

A Sulfuric acid is listed in a catalog with a concentration of \(95-98 \% .\) A bottle of the acid in the stockroom states that 1.00 I. has a mass of \(1.84 \mathrm{kg} .\) To determine the concentration of sulfuric acid in the stockroom bottle, a student dilutes \(5.00 \mathrm{mL}\) to \(500 .\) mL. She then takes four \(10.00-\mathrm{mL}\). samples and titrates each with standardized sodium hydroxide \((c=0.1760 \mathrm{M}).\) \(\begin{array}{lcccc}\text { Sample } & 1 & 2 & 3 & 4 \\ \text { Volume NaOH (mL) } & 20.15 & 21.30 & 20.40 & 20.35\end{array}\) (a) What is the average concentration of the diluted sulfuric acid sample? (b) What is the mass percent of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in the original bottle of the acid?

Anhydrous calcium chloride is a good drying agent because it will rapidly pick up water. Suppose you have stored some carefully dried \(\mathrm{CaCl}_{2}\) in a desiccator. Unfortunately, someone did not close the top of the desiccator tightly, and the \(\mathrm{CaCl}_{2}\) became partially hydrated. A \(150-\mathrm{g}\) sample of this partially hydrated material was dissolved in \(80 \mathrm{g}\) of hot water. When the solution was cooled to \(20^{\circ} \mathrm{C}, 74.9 \mathrm{g}\) of \(\mathrm{CaCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) precipitated. Knowing the solubility of calcium chloride in water at \(20^{\circ} \mathrm{C}\) is \(74.5 \mathrm{g} \mathrm{CaCl}_{2} / 100 \mathrm{g}\) water, determine the water content of the \(150-\mathrm{g}\) sample of partially hydrated calcium chloride (in moles of water per mole of \(\mathrm{CaCl}_{2}\) ).

A Phosphate in urine can be determined by spectrophotometry. After removing protein from the sample, it is treated with a molybdenum compound to give, ultimately, a deep blue polymolybdate. The absorbance of the blue polymolybdate can be measured at \(650 \mathrm{nm}\) and is directly related to the urine phosphate concentration. A 24 -hour urine sample was collected from a patient; the volume of urine was 1122 mL. The phosphate in a \(1.00 \mathrm{mL}\), portion of the urine sample was converted to the blue polymolybdate and diluted to \(50.00 \mathrm{mL} .\) A calibration curve was prepared using phosphate-containing solutions. (Concentrations are reported in grams of phosphorus (P) per liter of solution.) $$\begin{array}{lc} \text { Solution (mass P/L) } & \begin{array}{c} \text { Absorbance at } 650 \mathrm{nm} \\ \text { in a } 1.0-\mathrm{cm} \text { cell } \end{array} \\ \hline 1.00 \times 10^{-6} \mathrm{g} & 0.230 \\ 2.00 \times 10^{-6} \mathrm{g} & 0.436 \\ 3.00 \times 10^{-6} \mathrm{g} & 0.638 \\ 4.00 \times 10^{-6} \mathrm{g} & 0.848 \\ \text { Urine sample } & 0.518 \\ \hline \end{array}$$ (a) What are the slope and intercept of the calibration curve? (b) What is the mass of phosphorus per liter of urine? (c) What mass of phosphate did the patient excrete in the one-day period?

\(A A .000-g\) sample containing \(K C l\) and \(K C 1 O_{4}\) was dis. solved in sufficient water to give \(250.00 \mathrm{mL}\) of solution. A \(50.00-\mathrm{mL}\) portion of the solution required \(41.00 \mathrm{mL}\) of \(0.0750 \mathrm{M} \mathrm{AgNO}_{3}\) in a Mohr titration (page 187 ). Next, a \(25.00-\mathrm{mL}\), portion of the original solution was treated with \(\mathrm{V}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) to reduce the perchlorate ion to chloride, \(8 \mathrm{V}^{3+}(\mathrm{aq})+\mathrm{ClO}_{4}^{-}(\mathrm{aq})+12 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow\) $$ \mathrm{Cl}^{-}(\mathrm{aq})+8 \mathrm{VO}^{2+}(\mathrm{aq})+8 \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq}) $$ and the resulting solution was tirrated with AgNO, This titration required \(38.12 \mathrm{mL}\) of \(0.0750 \mathrm{M} \mathrm{AgNO}_{3} .\) What is the mass percent of \(\mathrm{KCl}\) and \(\mathrm{KClO}_{4}\) in the mixture?

The following questions may use concepts from this and previous chapters. Two beakers sit on a balance; the total mass is \(167.170 \mathrm{g} .\) One beaker contains a solution of \(\mathrm{KI}\) the other contains a solution of \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} .\) When the solution in one beaker is poured completely into the other, the following reaction occurs: $$ 2 \mathrm{KI}(\mathrm{aq})+\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) \rightarrow 2 \mathrm{KNO}_{3}(\mathrm{aq})+\mathrm{PbI}_{2}(\mathrm{s}) $$ (IMAGE CANNOT COPY) What is the total mass of the beakers and solutions after reaction? Explain completely.

Awo students titrate different samples of the same solution of HCl using \(0.100 \mathrm{M} \mathrm{NaOH}\) solution and phenolphthalein indicator (Figure 4.14). The first student pipets \(20.0 \mathrm{mL}\) of the HCl solution into a flask, adds \(20 \mathrm{mL}\) of distilled water and a few drops of phenolphthalein solution, and titrates until a lasting pink color appears. The second student pipets \(20.0 \mathrm{mL}\) of the HCl solution into a flask, adds \(60 \mathrm{mL}\) of distilled water and a few drops of phenolphthalein solution, and titrates to the first lasting pink color. Each student correctly calculates the molarity of an HCl solution. What will the second student's result be? (a) four times less than the first student's result (b) four times greater than the first student's result (c) two times less than the first student's result (d) two times greater than the first student's result (e) the same as the first student's result