Chapter 19

An acidified solution was electrolyzed using copper electrodes. A constant current of 1.18 A caused the anode to lose \(0.584 \mathrm{~g}\) after \(1.52 \times 10^{3} \mathrm{~s}\). (a) What is the gas produced at the cathode, and what is its volume at STP? (b) Given that the charge of an electron is \(1.6022 \times 10^{-19} \mathrm{C},\) calculate Avogadro's number. Assume that copper is oxidized to \(\mathrm{Cu}^{2+}\) ions.

In a certain electrolysis experiment involving \(\mathrm{Al}^{3+}\) ions, \(60.2 \mathrm{~g}\) of \(\mathrm{Al}\) is recovered when a current of \(0.352 \mathrm{~A}\) is used. How many minutes did the electrolysis last?

When an aqueous solution containing gold(III) salt is electrolyzed, metallic gold is deposited at the cathode and oxygen gas is generated at the anode. (a) If \(9.26 \mathrm{~g}\) of Au is deposited at the cathode, calculate the volume (in liters) of \(\mathrm{O}_{2}\) generated at \(23^{\circ} \mathrm{C}\) and \(747 \mathrm{mmHg}\). (b) What is the current used if the electrolytic process took \(2.00 \mathrm{~h} ?\)

In an electrolysis experiment, a student passes the same quantity of electricity through two electrolytic cells, one containing a silver salt and the other a gold salt. Over a certain period of time, the student finds that \(2.64 \mathrm{~g}\) of Ag and \(1.61 \mathrm{~g}\) of Au are deposited at the cathodes. What is the oxidation state of gold in the gold salt?

Given that: $$ \begin{array}{ll} 2 \mathrm{Hg}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{Hg}_{2}^{2+}(a q) & E^{\circ}=0.92 \mathrm{~V} \\\ \mathrm{Hg}_{2}^{2+}(a q)+2 e^{-} \longrightarrow 2 \mathrm{Hg}(l) & E^{\circ}=0.85 \mathrm{~V} \end{array} $$ calculate \(\Delta G^{\circ}\) and \(K\) for the following process at \(25^{\circ} \mathrm{C}:\) $$\mathrm{Hg}_{2}^{2+}(a q) \longrightarrow \mathrm{Hg}^{2+}(a q)+\mathrm{Hg}(l)$$ (The preceding reaction is an example of a disproportionation reaction in which an element in one oxidation state is both oxidized and reduced.)

Fluorine \(\left(\mathrm{F}_{2}\right)\) is obtained by the electrolysis of liquid hydrogen fluoride (HF) containing potassium fluoride \((\mathrm{KF})\). (a) Write the half-cell reactions and the overall reaction for the process. (b) What is the purpose of \(\mathrm{KF}\) ? (c) Calculate the volume of \(\mathrm{F}_{2}\) (in liters) collected at \(24.0^{\circ} \mathrm{C}\) and 1.2 atm after electrolyzing the solution for \(15 \mathrm{~h}\) at a current of \(502 \mathrm{~A}\).

A piece of magnesium ribbon and a copper wire are partially immersed in a \(0.1 M \mathrm{HCl}\) solution in a beaker. The metals are joined externally by another piece of metal wire. Bubbles are seen to evolve at both the \(\mathrm{Mg}\) and Cu surfaces. (a) Write equations representing the reactions occurring at the metals. (b) What visual evidence would you seek to show that Cu is not oxidized to \(\mathrm{Cu}^{2+} ?(\mathrm{c})\) At some stage, \(\mathrm{NaOH}\) solution is added to the beaker to neutralize the HCl acid. Upon further addition of \(\mathrm{NaOH},\) a white precipitate forms. What is it?

An aqueous solution of a platinum salt is electrolyzed at a current of \(2.50 \mathrm{~A}\) for \(2.00 \mathrm{~h}\). As a result, \(9.09 \mathrm{~g}\) of metallic Pt is formed at the cathode. Calculate the charge on the Pt ions in this solution.

Consider a galvanic cell consisting of a magnesium electrode in contact with \(1.0 \mathrm{M}\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) and a cadmium electrode in contact with \(1.0 \mathrm{M} \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}\). Calculate \(E^{\circ}\) for the cell, and draw a diagram showing the cathode, anode, and direction of electron flow.

Explain why most useful galvanic cells give voltages of no more than 1.5 to \(2.5 \mathrm{~V}\). What are the prospects for developing practical galvanic cells with voltages of \(5 \mathrm{~V}\) or more?

A silver rod and a SHE are dipped into a saturated aqueous solution of silver oxalate \(\left(\mathrm{Ag}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\), at \(25^{\circ} \mathrm{C}\). The measured potential difference between the rod and the SHE is \(0.589 \mathrm{~V},\) the rod being positive. Calculate the solubility product constant for silver oxalate.

Zinc is an amphoteric metal; that is, it reacts with both acids and bases. The standard reduction potential is \(-1.36 \mathrm{~V}\) for the reaction: $$ \mathrm{Zn}(\mathrm{OH})_{4}^{2-}(a q)+2 e^{-} \longrightarrow \mathrm{Zn}(s)+4 \mathrm{OH}^{-}(a q)$$ Calculate the formation constant \(\left(K_{\mathrm{f}}\right)\) for the reaction: $$ \mathrm{Zn}^{2+}(a q)+4 \mathrm{OH}^{-}(a q) \rightleftharpoons \mathrm{Zn}(\mathrm{OH})_{4}^{2-}(a q) $$

The magnitudes (but not the signs) of the standard reduction potentials of two metals \(\mathrm{X}\) and \(\mathrm{Y}\) are: $$ \begin{aligned} \mathrm{Y}^{2+}+2 e^{-} \longrightarrow & \mathrm{Y} & &\left|E^{\circ}\right|=0.34 \mathrm{~V} \\\ \mathrm{X}^{2+}+2 e^{-} \longrightarrow & \mathrm{X} & &\left|E^{\circ}\right|=0.25 \mathrm{~V} \end{aligned}$$ where the \(\|\) notation denotes that only the magnitude (but not the sign) of the \(E^{\circ}\) value is shown. When the half-cells of \(X\) and \(Y\) are connected, electrons flow from \(X\) to \(Y\). When \(X\) is connected to a SHE, electrons flow from \(\mathrm{X}\) to SHE. (a) Are the \(E^{\circ}\) values of the halfreactions positive or negative? (b) What is the standard emf of a cell made up of \(X\) and \(Y ?\)

A galvanic cell using \(\mathrm{Mg} / \mathrm{Mg}^{2+}\) and \(\mathrm{Cu} / \mathrm{Cu}^{2+}\) half-cells operates under standard-state conditions at \(25^{\circ} \mathrm{C},\) and each compartment has a volume of \(218 \mathrm{~mL}\). The cell delivers 0.22 A for 31.6 h. (a) How many grams of \(\mathrm{Cu}\) are deposited? (b) What is the \(\left[\mathrm{Cu}^{2+}\right]\) remaining?

Given the following standard reduction potentials, calculate the ion-product, \(K_{\mathrm{w}},\) for water at \(25^{\circ} \mathrm{C}:\) $$ \begin{array}{ll} 2 \mathrm{H}^{+}(a q)+2 e^{-} \longrightarrow \mathrm{H}_{2}(\mathrm{~g}) & E^{\circ}=0.00 \mathrm{~V} \\ 2 \mathrm{H}_{2} \mathrm{O}(l)+2 e^{-} \longrightarrow \mathrm{H}_{2}(g)+2 \mathrm{OH}^{-}(a q) & E^{\circ}=-0.83 \mathrm{~V} \end{array} $$

Consider a Daniell cell operating under non-standardstate conditions. Suppose that the cell's reaction is multiplied by 2 . What effect does this have on each of the following quantities in the Nernst equation: (a) \(E\) (b) \(E^{\circ},(\mathrm{c}) Q\) (d) \(\ln Q\), (e) \(n\) ?

A spoon was silver-plated electrolytically in an \(\mathrm{AgNO}_{3}\) solution. (a) Sketch a diagram for the process. (b) If \(0.884 \mathrm{~g}\) of Ag was deposited on the spoon at a constant current of \(18.5 \mathrm{~mA}\), how long (in min) did the electrolysis take?

Comment on whether \(\mathrm{F}_{2}\) will become a stronger oxidizing agent with increasing \(\mathrm{H}^{+}\) concentration.

Explain why chlorine gas can be prepared by electrolyzing an aqueous solution of \(\mathrm{NaCl}\) but fluorine gas cannot be prepared by electrolyzing an aqueous solution of NaF.

Calculate the pressure of \(\mathrm{H}_{2}\) (in atm) required to maintain equilibrium with respect to the following reaction at \(25^{\circ} \mathrm{C}:\) $$\mathrm{Pb}(s)+2 \mathrm{H}^{+}(a q) \rightleftarrows \mathrm{Pb}^{2+}(a q)+\mathrm{H}_{2}(g)$$ given that \(\left[\mathrm{Pb}^{2+}\right]=0.035 M\) and the solution is buffered at \(\mathrm{pH} 1.60\).

Industrially, copper is purified by electrolysis. The impure copper acts as the anode, and the cathode is made of pure copper. The electrodes are immersed in a \(\mathrm{CuSO}_{4}\) solution. During electrolysis, copper at the anode enters the solution as \(\mathrm{Cu}^{2+}\) while \(\mathrm{Cu}^{2+}\) ions are reduced at the cathode. (a) Write half-cell reactions and the overall reaction for the electrolytic process. (b) Suppose the anode was contaminated with \(\mathrm{Zn}\) and Ag. Explain what happens to these impurities during electrolysis. (c) How many hours will it take to obtain \(1.00 \mathrm{~kg}\) of \(\mathrm{Cu}\) at a current of \(18.9 \mathrm{~A} ?\)

Gold will not dissolve in either concentrated nitric acid or concentrated hydrochloric acid. However, the metal does dissolve in a mixture of the acids (one part \(\mathrm{HNO}_{3}\) and three parts \(\mathrm{HCl}\) by volume \()\), called aqua regia. (a) Write a balanced equation for this reaction. (Hint: Among the products are \(\mathrm{HAuCl}_{4}\) and \(\mathrm{NO}_{2} .\) ) (b) What is the function of \(\mathrm{HCl} ?\)

To remove the tarnish \(\left(\mathrm{Ag}_{2} \mathrm{~S}\right)\) on a silver spoon, a student carried out the following steps. First, she placed the spoon in a large pan filled with water so the spoon was totally immersed. Next, she added a few tablespoonfuls of baking soda (sodium bicarbonate), which readily dissolved. Finally, she placed some aluminum foil at the bottom of the pan in contact with the spoon and then heated the solution to about \(80^{\circ} \mathrm{C}\). After a few minutes, the spoon was removed and rinsed with cold water. The tarnish was gone, and the spoon regained its original shiny appearance. (a) Describe with equations the electrochemical basis for the procedure. (b) Adding \(\mathrm{NaCl}\) instead of \(\mathrm{NaHCO}_{3}\) would also work because both compounds are strong electrolytes. What is the added advantage of using \(\mathrm{NaHCO}_{3}\) ?

A construction company is installing an iron culvert (a long cylindrical tube) that is \(40.0 \mathrm{~m}\) long with a radius of \(0.900 \mathrm{~m}\). To prevent corrosion, the culvert must be galvanized. This process is carried out by first passing an iron sheet of appropriate dimensions through an electrolytic cell containing \(\mathrm{Zn}^{2+}\) ions, using graphite as the anode and the iron sheet as the cathode. If the voltage is \(3.26 \mathrm{~V}\), what is the cost of electricity for depositing a layer \(0.200 \mathrm{~mm}\) thick if the efficiency of the process is 95 percent? The electricity rate is \(\$ 0.12\) per kilowatt hour \((\mathrm{kWh})\), where \(1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s}\) and the density of \(\mathrm{Zn}\) is \(7.14 \mathrm{~g} / \mathrm{cm}^{3}\).

The concentration of sulfuric acid in the lead-storage battery of an automobile over a period of time has decreased from 38.0 percent by mass (density \(=1.29 \mathrm{~g} / \mathrm{mL}\) ) to 26.0 percent by mass ( \(1.19 \mathrm{~g} / \mathrm{mL}\) ). Assume the volume of the acid remains constant at \(724 \mathrm{~mL}\). (a) Calculate the total charge in coulombs supplied by the battery. (b) How long (in hours) will it take to recharge the battery back to the original sulfuric acid concentration using a current of \(22.4 \mathrm{~A}\) ?

Compare the pros and cons of a fuel cell, such as the hydrogen-oxygen fuel cell, and a coal-fired power station for generating electricity.

Oxalic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) is present in many plants and vegetables. (a) Balance the following equation in acid solution: $$\mathrm{MnO}_{4}^{-}+\mathrm{C}_{2} \mathrm{O}_{4}^{2-} \longrightarrow \mathrm{Mn}^{2+}+\mathrm{CO}_{2}$$ (b) If a \(1.00-\mathrm{g}\) sample of plant matter requires \(24.0 \mathrm{~mL}\) of \(0.0100 \mathrm{M} \mathrm{KMnO}_{4}\) solution to reach the equivalence point, what is the percent by mass of \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) in the sample?

The ingestion of a very small quantity of mercury is not considered too harmful. Would this statement still hold if the gastric juice in your stomach were mostly nitric acid instead of hydrochloric acid? Explain.

The nitrite ion \(\left(\mathrm{NO}_{2}^{-}\right)\) in soil is oxidized to the nitrate ion \(\left(\mathrm{NO}_{3}^{-}\right)\) by the bacterium Nitrobacter agilis in the presence of oxygen. The half-reactions are: \(\mathrm{NO}_{3}^{-}+2 \mathrm{H}^{+}+2 e^{-} \longrightarrow \mathrm{NO}_{2}^{-}+\mathrm{H}_{2} \mathrm{O} \quad E^{\circ}=0.42 \mathrm{~V}\) $$\mathrm{O}_{2}+4 \mathrm{H}^{+}+4 e^{-} \longrightarrow 2 \mathrm{H}_{2} \mathrm{O} \quad E^{\circ}=1.23 \mathrm{~V}$$ Calculate the yield of ATP synthesis per mole of nitrite oxidized.

In recent years, there has been much interest in electric cars. List some advantages and disadvantages of electric cars compared to automobiles with internal combustion engines.

The \(\mathrm{SO}_{2}\) present in air is mainly responsible for the phenomenon of acid rain. The concentration of \(\mathrm{SO}_{2}\) can be determined by titrating against a standard permanganate solution as follows: \(5 \mathrm{SO}_{2}+2 \mathrm{MnO}_{4}^{-}+2 \mathrm{H}_{2} \mathrm{O} \longrightarrow 5 \mathrm{SO}_{4}^{2-}+2 \mathrm{Mn}^{2+}+4 \mathrm{H}^{+}\) Calculate the number of grams of \(\mathrm{SO}_{2}\) in a sample of air if \(7.37 \mathrm{~mL}\) of \(0.00800 \mathrm{M} \mathrm{KMnO}_{4}\) solution is required for the titration.

The zinc-air battery shows much promise for electric cars because it is lightweight and rechargeable: The net transformation is \(\mathrm{Zn}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{ZnO}(s)\) (a) Write the half-reactions at the zinc-air electrodes, and calculate the standard emf of the battery at \(25^{\circ} \mathrm{C}\). (b) Calculate the emf under actual operating conditions when the partial pressure of oxygen is 0.21 atm. (c) What is the energy density (measured as the energy in kilojoules that can be obtained from \(1 \mathrm{~kg}\) of the metal) of the zinc electrode? (d) If a current of \(2.1 \times 10^{5} \mathrm{~A}\) is to be drawn from a zinc-air battery system, what volume of air (in liters) would need to be supplied to the battery every second? Assume that the temperature is \(25^{\circ} \mathrm{C}\) and the partial pressure of oxygen is 0.21 atm.

A current of 6.00 A passes through an electrolytic cell containing dilute sulfuric acid for \(3.40 \mathrm{~h}\). If the volume of \(\mathrm{O}_{2}\) gas generated at the anode is \(4.26 \mathrm{~L}\) (at STP), calculate the charge (in coulombs) on an electron.

A \(9.00 \times 10^{2} \mathrm{~mL}\) amount of \(0.200 \mathrm{M} \mathrm{MgI}_{2}\) solution was electrolyzed. As a result, hydrogen gas was generated at the cathode and iodine was formed at the anode. The volume of hydrogen collected at \(26^{\circ} \mathrm{C}\) and \(779 \mathrm{mmHg}\) was \(1.22 \times 10^{3} \mathrm{~mL}\). (a) Calculate the charge in coulombs consumed in the process. (b) How long (in min) did the electrolysis last if a current of 7.55 A was used? (c) A white precipitate was formed in the process. What was it, and what was its mass in grams? Assume the volume of the solution was constant.

When \(25.0 \mathrm{~mL}\) of a solution containing both \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) ions is titrated with \(23.0 \mathrm{~mL}\) of \(0.0200 \mathrm{M} \mathrm{KMnO}_{4}\) (in dilute sulfuric acid), all the \(\mathrm{Fe}^{2+}\) ions are oxidized to \(\mathrm{Fe}^{3+}\) ions. Next, the solution is treated with Zn metal to convert all the \(\mathrm{Fe}^{3+}\) ions to \(\mathrm{Fe}^{2+}\) ions. Finally, \(40.0 \mathrm{~mL}\) of the same \(\mathrm{KMnO}_{4}\) solution is added to the solution to oxidize the \(\mathrm{Fe}^{2+}\) ions to \(\mathrm{Fe}^{3+}\). Calculate the molar concentrations of \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) in the original solution.