Chapter 17

Fluorine, \(\mathrm{F}_{2}\), is made by the electrolysis of anhydrous \(\mathrm{HF}\). $$ 2 \mathrm{HF}(\ell) \longrightarrow \mathrm{H}_{2}(\mathrm{~g})+\mathrm{F}_{2}(\mathrm{~g}) $$ Typical electrolysis cells operate at 4000 to \(6000 \mathrm{~A}\) and 8 to \(12 \mathrm{~V}\). A large-scale plant can produce about \(9.0 \mathrm{met}-\) ric tons of \(\mathrm{F}_{2}\) gas per day. (a) Calculate the mass (g) of HF consumed. (b) Using the conversion factor of \(3.60 \times 10^{6} \mathrm{~J} / \mathrm{kWh}\), calculate how much energy in kilowatt-hours is transferred to a cell operating at \(6.0 \times 10^{3} \mathrm{~A}\) at \(12 \mathrm{~V}\) for \(24 \mathrm{~h}\).

You wish to electroplate a copper surface having an area of \(1200 \mathrm{~mm}^{2}\) with a \(1.0-\mu \mathrm{m}\) -thick coating of silver from a solution of \(\mathrm{Ag}(\mathrm{CN})_{2}^{-}\) ions. If you use a current of \(150.0 \mathrm{~mA},\) calculate how much electrolysis time you should use. The density of metallic silver is \(10.5 \mathrm{~g} / \mathrm{cm}^{3} .\)

In a mercury battery, the anode reaction is $$ \mathrm{Zn}(\mathrm{s})+2 \mathrm{OH}^{-}(\mathrm{aq}) \longrightarrow \mathrm{ZnO}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)+2 \mathrm{e}^{-} $$ and the cathode reaction is $$ \mathrm{HgO}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\ell)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Hg}(\ell)+2 \mathrm{OH}^{-}(\mathrm{aq}) $$ The cell potential is \(1.35 \mathrm{~V}\). Calculate how many hours such a battery can provide power at a rate of \(4.0 \times 10^{-4}\) watt \(\left(1\right.\) watt \(\left.=1 \mathrm{~J} \mathrm{~s}^{-1}\right)\) if \(1.25 \mathrm{~g} \mathrm{HgO}\) is available.

Four metals \(\mathrm{A}, \mathrm{B}, \mathrm{C},\) and \(\mathrm{D}\) exhibit these properties: (a) Only \(\mathrm{A}\) and \(\mathrm{C}\) react with \(1.0-\mathrm{M} \mathrm{HCl}\) to give \(\mathrm{H}_{2}\) gas. (b) When \(\mathrm{C}\) is added to solutions of ions of the other metals, metallic \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{D}\) are formed. (c) Metal D reduces \(\mathrm{B}^{n+}\) ions to give metallic \(\mathrm{B}\) and \(\mathrm{D}^{n+}\) ions. On the basis of this information, arrange the four metals in order of increasing ability to act as reducing agents.

The table below lists the cell potentials for the ten possible voltaic cells assembled from the elements \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}\) and \(\mathrm{E}\) and their respective ions in solutions. Using the data in the table, establish a standard half-cell potential table similar to Table 17.1. Assign a half-cell potential of \(0.00 \mathrm{~V}\) to the element that falls in the middle of the series. $$ \begin{array}{lcc} \hline & \mathrm{A}(\mathrm{s}) \text { in } \mathrm{A}^{n+}(\mathrm{aq}) & \mathrm{B}(\mathrm{s}) \text { in } \mathrm{B}^{n+}(\mathrm{aq}) \\ \hline \mathrm{E}(\mathrm{s}) \text { in } \mathrm{E}^{n+}(\mathrm{aq}) & +0.21 \mathrm{~V} & +0.68 \mathrm{~V} \\ \mathrm{D}(\mathrm{s}) \text { in } \mathrm{D}^{n+}(\mathrm{aq}) & +0.35 \mathrm{~V} & +1.24 \mathrm{~V} \\ \mathrm{C}(\mathrm{s}) \text { in } \mathrm{C}^{n+}(\text { aq }) & +0.58 \mathrm{~V} & +0.31 \mathrm{~V} \\ \mathrm{~B}(\mathrm{~s}) \text { in } \mathrm{B}^{n+}(\text { aq }) & +0.89 \mathrm{~V} & \- \\ \hline & \mathrm{C}(\mathrm{s}) \text { in } \mathrm{C}^{n+}(\mathrm{aq}) & \mathrm{D}(\mathrm{s}) \text { in } \mathrm{D}^{n+}(\mathrm{aq}) \\ \hline \mathrm{E}(\mathrm{s}) \text { in } \mathrm{E}^{n+}(\mathrm{aq}) & +0.37 \mathrm{~V} & +0.56 \mathrm{~V} \\ \mathrm{D}(\mathrm{s}) \text { in } \mathrm{D}^{n+}(\mathrm{aq}) & +0.93 \mathrm{~V} & \- \\ \mathrm{C}(\mathrm{s}) \text { in } \mathrm{C}^{n+}(\mathrm{aq}) & \- & \- \\ \mathrm{B}(\mathrm{s}) \text { in } \mathrm{B}^{n+}(\mathrm{aq}) & \- & \- \\ \hline \end{array} $$

An electrolytic cell is set up with \(\mathrm{Cd}(\mathrm{s})\) in \(\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})\) and \(\mathrm{Zn}(\mathrm{s})\) in \(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) .\) Initially both electrodes weigh \(5.00 \mathrm{~g}\). After running the cell for several hours the electrode in the left compartment weighs \(4.75 \mathrm{~g}\). (a) Which electrode is in the left compartment? (b) Does the mass of the electrode in the right compartment increase, decrease, or stay the same? If the mass changes, what is the new mass? (c) Does the volume of the electrode in the right compartment increase, decrease, or stay the same? If the volume changes, what is the new volume? (The density of \(\mathrm{Cd}\) is \(\left.8.65 \mathrm{~g} / \mathrm{cm}^{3} .\right)\)

The permanganate ion \(\mathrm{MnO}_{4}^{-}\) can be reduced to the manganese(II) ion \(\mathrm{Mn}^{2+}\) in aqueous acidic solution, and the half- cell potential for this half-cell reaction is \(1.51 \mathrm{~V}\). If this half-cell is combined with a \(\mathrm{Zn}^{2+} \mid \mathrm{Zn}\) half-cell to form a voltaic cell at standard conditions, (a) Write the chemical equation for the half-reaction occurring at the anode. (b) Write the chemical equation for the half-reaction occurring at the cathode. (c) Write the overall balanced equation for the reaction. (d) Calculate the cell potential.

Consider two different electrolytic cells; one cell contains aqueous \(\mathrm{Zn}^{2+}\) and the other contains \(\mathrm{Cr}^{3+}\). The initial metal ion concentration is the same in each cell and the metal ions are reduced to the metal during the electrolysis. Each cell operates at the same current. Without doing calculations, predict which cell has the greater mass of metal deposited after 5 min. Explain your prediction.

To measure the \(\mathrm{Ag}^{+}\) concentration, \(25.00 \mathrm{~mL}\) of a silvercontaining solution is titrated with \(0.015 \mathrm{M} \mathrm{KI}\) at \(25^{\circ} \mathrm{C}\) by using a silver electrode immersed in the test solution and the electrical potential measured against a standard hydrogen electrode. It required \(16.7 \mathrm{~mL}\) of the KI solution to reach the equivalence point, where the potential was \(0.325 \mathrm{~V}\). (a) Calculate the molarity of \(\mathrm{Ag}^{+}\) in the solution. (b) Calculate the \(K_{\mathrm{sp}}\) of \(\mathrm{AgI}\).

Consider these unbalanced equations for two reactions: \(\mathrm{NO}_{3}^{-}(\mathrm{aq})+\mathrm{H}^{+}(\mathrm{aq})+\mathrm{Hg}(\ell) \longrightarrow \underset{\mathrm{Hg}_{2}^{2+}}(\mathrm{aq})+\mathrm{NO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\ell)\) $$ \mathrm{Hg}^{2+}(\mathrm{aq})+\mathrm{Br}^{-}(\mathrm{aq}) \longrightarrow \mathrm{Hg}_{2}^{2+}(\mathrm{aq})+\mathrm{Br}_{2}(\ell) $$ For each reaction: (a) balance the equation. (b) draw a cell diagram. (c) calculate the standard cell potential. (d) calculate the \(\Delta_{t} G^{\circ} .\) (e) determine whether each reaction is product-favored. Explain your reason.

The standard potential of a \(\mathrm{Zn}\left|\mathrm{Zn}^{2+} \| \mathrm{Cu}^{2+}\right| \mathrm{Cu}\) voltaic cell is \(1.103 \mathrm{~V}\). As the cell operates, the cell potential changes due to concentration changes of \(\mathrm{Zn}^{2+}\) and \(\mathrm{Cu}^{2+} .\) Calculate the ratio (conc. \(\left.\mathrm{Zn}^{2+}\right) /\left(\right.\) conc. \(\left.\mathrm{Cu}^{2+}\right)\) when the cell potential is \(0.050 \mathrm{~V}\).

In an electrolytic cell, a 10.0 -A direct current passes through an aqueous copper(II) nitrate solution and \(9.50 \mathrm{~g}\) metallic copper plates out. (a) Calculate how long it took for this mass of copper to be deposited at the cathode. Assume \(100 \%\) efficiency. (b) A gas is produced at the anode and collected. Identify the gas and calculate its volume. The gas was collected at \(25^{\circ} \mathrm{C}\) and \(0.945 \mathrm{~atm} .\)

This reaction occurs in a cell with \(\mathrm{H}_{2}(\mathrm{~g})\) pressure of \(1.0 \mathrm{~atm}\) and (conc. \(\left.\mathrm{Cl}^{-}\right)=1.0 \mathrm{M}\) at \(25^{\circ} \mathrm{C} ;\) the measured \(E_{\text {cell }}=0.34 \mathrm{~V}\). Calculate the \(\mathrm{pH}\) of the solution. $$ \mathrm{H}_{2}(\mathrm{~g})+2 \mathrm{AgCl}(\mathrm{s}) \longrightarrow 2 \mathrm{H}^{+}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{s}) $$

A student wanted to measure the copper(II) concentration in aqueous solution. For the cathode half-cell she used a silver electrode with a 1.00 -M solution of \(\mathrm{AgNO}_{3}\). For the anode half-cell she used a copper electrode dipped into the aqueous sample. The cell gave \(E_{\text {cell }}=\) \(0.62 \mathrm{~V}\) at \(25^{\circ} \mathrm{C}\). Calculate the copper(II) ion concentration of the solution.