Chapter 20

Write balanced equations for the following half-reactions. Specify whether each is an oxidation or reduction. (a) \(\mathrm{Cr}(\mathrm{s}) \rightarrow \mathrm{Cr}^{3+}(\mathrm{aq})\) (in acid) (b) \(\mathrm{AsH}_{3}(\mathrm{g}) \rightarrow \mathrm{As}(\mathrm{s})\) (in acid) (c) \(\mathrm{VO}_{3}^{-}(\mathrm{aq}) \rightarrow \mathrm{V}^{2+}(\mathrm{aq})\) (in acid) (d) \(\mathrm{Ag}(\mathrm{s}) \rightarrow \mathrm{Ag}_{2} \mathrm{O}(\mathrm{s})\) (in base)

Write balanced equations for the following half-reactions. Specify whether each is an oxidation or reduction. (a) \(\mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{aq}) \rightarrow \mathrm{O}_{2}(\mathrm{g})\) (in acid) (b) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})\) (in acid) (c) \(\mathrm{NO}_{3}^{-}(\mathrm{aq}) \rightarrow \mathrm{NO}(\mathrm{g})\) (in acid) (d) \(\mathrm{MnO}_{4}^{-}(\mathrm{aq}) \rightarrow \mathrm{MnO}_{2}(\mathrm{s})\) (in base)

Balance the following redox equations. All occur in acid solution. $$\text { (a) } \mathrm{Ag}(\mathrm{s})+\mathrm{NO}_{3}^{-}(\mathrm{aq}) \rightarrow \mathrm{NO}_{2}(\mathrm{g})+\mathrm{Ag}^{+}(\mathrm{aq})$$ $$\begin{aligned} &\text { (b) } \mathrm{MnO}_{4}^{-}(\mathrm{aq})+\mathrm{HSO}_{3}^{-}(\mathrm{aq}) \rightarrow\\\ &&\mathrm{Mn}^{2+}(\mathrm{aq})+\mathrm{SO}_{4}^{2-}(\mathrm{aq}) \end{aligned}$$ (c) \(\mathrm{Zn}(\mathrm{s})+\mathrm{NO}_{3}-(\mathrm{aq}) \rightarrow \mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{N}_{2} \mathrm{O}(\mathrm{g})\) (d) \(\mathrm{Cr}(\mathrm{s})+\mathrm{NO}_{3}^{-}(\mathrm{aq}) \rightarrow \mathrm{Cr}^{3+}(\mathrm{aq})+\mathrm{NO}(\mathrm{g})\)

Balance the following redox equations. All occur in acid solution. (a) \(\operatorname{Sn}(\mathrm{s})+\mathrm{H}^{+}(\mathrm{aq}) \rightarrow \mathrm{Sn}^{2+}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g})\) (b) \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq})+\mathrm{Fe}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Cr}^{3+}(\mathrm{aq})+\mathrm{Fe}^{3+}(\mathrm{aq})\) (c) \(\mathrm{MnO}_{2}(\mathrm{s})+\mathrm{Cl}^{-}(\mathrm{aq}) \rightarrow \mathrm{Mn}^{2+}(\mathrm{aq})+\mathrm{Cl}_{2}(\mathrm{g})\) (d) \(\mathrm{CH}_{2} \mathrm{O}(\mathrm{aq})+\mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{HCO}_{2} \mathrm{H}(\mathrm{aq})+\mathrm{Ag}(\mathrm{s})\)

Balance the following redox equations. All occur in basic solution. (a) \(\mathrm{Al}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{Al}(\mathrm{OH})_{4}^{-}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g})\) (b) \(\mathrm{CrO}_{4}^{2-}(\mathrm{aq})+\mathrm{SO}_{3}^{2-}(\mathrm{aq}) \rightarrow \mathrm{Cr}(\mathrm{OH})_{3}(\mathrm{s})+\mathrm{SO}_{4}^{2-}(\mathrm{aq})\) (c) \(\mathrm{Zn}(\mathrm{s})+\mathrm{Cu}(\mathrm{OH})_{2}(\mathrm{s}) \rightarrow\left[\mathrm{Zn}(\mathrm{OH})_{4}\right]^{2-}(\mathrm{aq})+\mathrm{Cu}(\mathrm{s})\) (d) \(\mathrm{HS}^{-}(\mathrm{aq})+\mathrm{ClO}_{3}^{-}(\mathrm{aq}) \rightarrow \mathrm{S}(\mathrm{s})+\mathrm{Cl}^{-}(\mathrm{aq})\)

Balance the following redox equations. All occur in basic solution. (a) \(\mathrm{Fe}(\mathrm{OH})_{3}(\mathrm{s})+\mathrm{Cr}(\mathrm{s}) \rightarrow \mathrm{Cr}(\mathrm{OH})_{3}(\mathrm{s})+\mathrm{Fe}(\mathrm{OH})_{2}(\mathrm{s})\) (b) \(\mathrm{NiO}_{2}(\mathrm{s})+\mathrm{Zn}(\mathrm{s}) \rightarrow \mathrm{Ni}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{Zn}(\mathrm{OH})_{2}(\mathrm{s})\) $$\begin{aligned}&\text { (c) } \mathrm{Fe}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{CrO}_{4}^{2-}(\mathrm{aq}) \rightarrow\\\&&\mathrm{Fe}(\mathrm{OH})_{3}(\mathrm{s})+\left[\mathrm{Cr}(\mathrm{OH})_{4}\right]^{-}(\mathrm{aq})\end{aligned}$$ $$\text { (d) } \mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{aq})+\mathrm{Ag}_{2} \mathrm{O}(\mathrm{s}) \rightarrow \mathrm{N}_{2}(\mathrm{g})+\mathrm{Ag}(\mathrm{s})$$

A voltaic cell is constructed using the reaction $$ \mathrm{Mg}(\mathrm{s})+2 \mathrm{H}^{+}(\mathrm{aq}) \rightarrow \mathrm{Mg}^{2+ (\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g}) $$ (a) Write equations for the oxidation and reduction half-reactions. (b) Which half-reaction occurs in the anode compartment, and which occurs in the cathode compartment? (c) Complete the following sentences: Electrons in the external circuit flow from the __________electrode to the __________ electrode. Negative ions move in the salt bridge from the________ half-cell to the_________ half-cell.The half-reaction at the anode is __________ and that at the cathode is _____________.

The half-cells \(\mathrm{Fe}^{2+}(\text { aq }) | \mathrm{Fe}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g}) | \mathrm{H}_{2} \mathrm{O}\) (in acid solution) are linked to create a voltaic cell. (a) Write equations for the oxidation and reduction half-reactions and for the overall (cell) reaction. (b) Which half-reaction occurs in the anode compartment, and which occurs in the cathode compartment? (c) Complete the following sentences: Electrons in the external circuit flow from the ________ electrode to the ___________ electrode. Negative ions move in the salt bridge from the _________ half-cell to the__________ half-cell.

The half-cells \(\operatorname{Sn}^{2+}(\text { aq }) | \operatorname{Sn}(s)\) and \(\operatorname{Cl}_{2}(g) | C l^{-}(\text {aq })\) are linked to create a voltaic cell. (a) Write equations for the oxidation and reduction half-reactions and for the overall (cell) reaction. (b) Which half-reaction occurs in the anode compartment, and which occurs in the cathode compartment? (c) Complete the following sentences: Electrons in the external circuit flow from the__________ electrode to the _________ electrode. Negative ions move in the salt bridge from the half-cell__________ to the__________ half-cell.

What are the similarities and differences between dry cells, alkaline batteries, and Ni-cad batteries?

What reactions occur when a lead storage battery is recharged?

Balance each of the following unbalanced equations; then calculate the standard potential, \(E^{\circ},\) and decide whether each is product-favored as written. (All reactions are carried out in acid solution.) (a) \(\mathrm{I}_{2}(\mathrm{s})+\mathrm{Br}^{-}(\mathrm{aq}) \rightarrow \mathrm{I}^{-}(\mathrm{aq})+\mathrm{Br}_{2}(\ell)\) (b) \(\mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{Cu}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Cu}(\mathrm{s})+\mathrm{Fe}^{3+}(\mathrm{aq})\) (c) \(\mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq}) \rightarrow \mathrm{Fe}^{3+}(\mathrm{aq})+\mathrm{Cr}^{3+}(\mathrm{aq})\) (d) \(\mathrm{MnO}_{4}^{-}(\mathrm{aq})+\mathrm{HNO}_{2}(\mathrm{aq}) \rightarrow \mathrm{Mn}^{2+}(\mathrm{aq})+\mathrm{NO}_{3}^{-}(\mathrm{aq})\)

Which of the following elements is the best reducing agent under standard conditions? (a) Cu (b) \(\mathrm{Zn}\) (c) Fe (d) \(\mathrm{Ag}\) (e) \(\mathrm{Cr}\)

Calculate the potential delivered by a voltaic cell using the following reaction if all dissolved species are \(2.5 \times 10^{-2} \mathrm{M}\) and the pressure of \(\mathrm{H}_{2}\) is 1.0 bar. $$\begin{aligned} \mathrm{Zn}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\ell)+2 \mathrm{OH}^{-}(\mathrm{aq}) & \rightarrow \\ &\left[\mathrm{Zn}(\mathrm{OH})_{4}\right]^{2-}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g}) \end{aligned}$$

One half-cell in a voltaic cell is constructed from a copper wire electrode in a \(4.8 \times 10^{-3} \mathrm{M}\) solution of \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2} .\) The other half-cell consists of a zinc electrode in a \(0.40 \mathrm{M}\) solution of \(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2} .\) Calculate the cell potential.

One half-cell in a voltaic cell is constructed from a silver wire electrode in a AgNO \(_{3}\) solution of unknown concentration. The other half-cell consists of a zinc electrode in a \(1.0 \mathrm{M}\) solution of \(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2} .\) A potential of \(1.48 \mathrm{V}\) is measured for this cell. Use this information to calculate the concentration of \(\mathrm{Ag}^{+}(\mathrm{aq})\)

One half-cell in a voltaic cell is constructed from an iron electrode in an \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{2}\) solution of unknown concentration. The other half-cell is a standard hydrogen electrode. A potential of \(0.49 \mathrm{V}\) is measured for this cell. Use this information to calculate the concentration of \(\mathrm{Fe}^{2+}(\mathrm{aq})\)

Which product, \(\mathrm{O}_{2}\) or \(\mathrm{F}_{2}\), is more likely to form at the anode in the electrolysis of an aqueous solution of KF? Explain your reasoning.

Which product, Ca or \(\mathrm{H}_{2}\), is more likely to form at the cathode in the electrolysis of \(\mathrm{CaCl}_{2} ?\) Explain your reasoning.

An aqueous solution of KBr is placed in a beaker with two inert platinum electrodes. When the cell is attached to an external source of electrical energy, electrolysis occurs. (a) Hydrogen gas and hydroxide ion form at the cathode. Write an equation for the half-reaction that occurs at this electrode. (b) Bromine is the primary product at the anode. Write an equation for its formation.

An aqueous solution of \(\mathrm{Na}_{2} \mathrm{S}\) is placed in a beaker with two inert platinum electrodes. When the cell is attached to an external battery, electrolysis occurs. (a) Hydrogen gas and hydroxide ion form at the cathode. Write an equation for the half-reaction that occurs at this electrode. (b) Sulfur is the primary product at the anode. Write an equation for its formation.

In the electrolysis of a solution containing \(\mathrm{Ni}^{2+}(\mathrm{aq})\) metallic \(\mathrm{Ni}(\mathrm{s})\) deposits on the cathode. Using a current of 0.150 A for 12.2 minutes, what mass of nickel will form?

In the electrolysis of a solution containing \(\mathrm{Ag}^{+}(\mathrm{aq})\) metallic Ag(s) deposits on the cathode. Using a current of 1.12 A for 2.40 hours, what mass of silver forms?

Electrolysis of a solution of \(\mathrm{CuSO}_{4}(\mathrm{aq})\) to give copper metal is carried out using a current of 0.66 A. How long should electrolysis continue to produce 0.50 g of copper?

Electrolysis of a solution of \(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})\) to give zinc metal is carried out using a current of 2.12 A. How long should electrolysis continue in order to prepare \(2.5 \mathrm{g}\) of zinc?

A voltaic cell can be built using the reaction between Al metal and \(\mathrm{O}_{2}\) from the air. If the Al anode of this cell consists of \(84 \mathrm{g}\) of aluminum, how many hours can the cell produce 1.0 A of electricity, assuming an unlimited supply of \(\mathrm{O}_{2} ?\)

Assume the specifications of a Ni-Cd voltaic cell include delivery of 0.25 A of current for 1.00 hour. What is the minimum mass of the cadmium that must be used to make the anode in this cell?

Write balanced equations for the following half-reactions. (a) \(\mathrm{UO}_{2}^{+}(\mathrm{aq}) \rightarrow \mathrm{U}^{4+}(\mathrm{aq})\) (acid solution) (b) \(\mathrm{ClO}_{3}^{-}(\mathrm{aq}) \rightarrow \mathrm{Cl}^{-}(\mathrm{aq})\) (acid solution) (c) \(\mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{aq}) \rightarrow \mathrm{N}_{2}(\mathrm{g})\) (basic solution) (d) \(\mathrm{ClO}^{-}(\mathrm{aq}) \rightarrow \mathrm{Cl}^{-}(\mathrm{aq})\) (basic solution)

Balance the following equations. $$\begin{aligned} &\text { (a) } \mathrm{Zn}(\mathrm{s})+\mathrm{VO}^{2+}(\mathrm{aq}) \rightarrow\\\ &&\mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{V}^{3+}(\mathrm{aq}) \quad \text { (acid solution) } \end{aligned}$$ $$\begin{aligned} &\text { (b) } \mathrm{Zn}(\mathrm{s})+\mathrm{VO}_{3}^{-}(\mathrm{aq}) \rightarrow\\\ &&\mathrm{V}^{2+}(\mathrm{aq})+\mathrm{Zn}^{2+}(\mathrm{aq}) \quad \text { (acid solution) } \end{aligned}$$ $$\begin{aligned} &\text { (c) } \mathrm{Zn}(\mathrm{s})+\mathrm{ClO}^{-}(\mathrm{aq}) \rightarrow\\\ &&\mathrm{Zn}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{Cl}^{-}(\mathrm{aq}) \text { (basic solution) }\end{aligned}$$ $$\begin{aligned} &\text { (d) } \mathrm{ClO}^{-}(\mathrm{aq})+\left[\mathrm{Cr}(\mathrm{OH})_{4}\right]^{-}(\mathrm{aq}) \rightarrow\\\ &&\mathrm{Cl}^{-}(\mathrm{aq})+\mathrm{CrO}_{4}^{2-}(\mathrm{aq}) \quad \text { (basic solution) } \end{aligned}$$

Magnesium metal is oxidized, and silver ions are reduced in a voltaic cell using \(\mathrm{Mg}^{2+}(\mathrm{aq}, 1 \mathrm{M}) | \mathrm{Mg}\) and \(\mathrm{Ag}^{+}(\mathrm{aq}, 1 \mathrm{M}) |\) Ag half-cells.(a) Label each part of the cell. (b) Write equations for the half-reactions occurring at the anode and the cathode, and write an equation for the net reaction in the cell. (c) Trace the movement of electrons in the external circuit. Assuming the salt bridge contains \(\mathrm{NaNO}_{3},\) trace the movement of the \(\mathrm{Na}^{+}\) and \(\mathrm{NO}_{3}^{-}\) ions in the salt bridge that occurs when a voltaic cell produces current. Why is a salt bridge required in a cell?

You want to set up a series of voltaic cells with specific cell potentials. The \(\mathrm{Ag}^{+}(\mathrm{aq}, 1.0 \mathrm{M}) | \mathrm{Ag}(\mathrm{s})\) half-cell is one of the compartments. Identify several half-cells that you could use so that the cell potential will be close to (a) \(1.7 \mathrm{V}\) and (b) \(0.50 \mathrm{V} .\) Consider cells in which the silver cell can be either the cathode or the anode.

The reaction occurring in the cell in which \(\mathrm{Al}_{2} \mathrm{O}_{3}\) and aluminum salts are electrolyzed is \(\mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \rightarrow\) Al(s). If the electrolysis cell operates at \(5.0 \mathrm{V}\) and \(1.0 \times 10^{5} \mathrm{A},\) what mass of aluminum metal can be produced in a 24 -hour day?

A potential of \(0.142 \mathrm{V}\) is recorded (under standard conditions) for a voltaic cell constructed using the following half reactions: $$\begin{aligned} &\text { Cathode: } \quad \mathrm{Pb}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{Pb}(\mathrm{s})\\\ &\begin{array}{ll} \text { Anode: } & \mathrm{PbCl}_{2}(\mathrm{s})+2 \mathrm{e}^{-} \rightarrow \mathrm{Pb}(\mathrm{s})+2 \mathrm{Cl}^{-}(\mathrm{aq}) \\ \text { Net: } & \mathrm{Pb}^{2+}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq}) \rightarrow \mathrm{PbCl}_{2}(\mathrm{s}) \end{array} \end{aligned}$$ (a) What is the standard reduction potential for the anode reaction? (b) Calculate the solubility product, \(K_{\mathrm{sp}},\) for \(\mathrm{PbCl}_{2}\)

The standard potential, \(E^{\circ},\) for the reaction of \(\mathrm{Zn}(\mathrm{s})\) and \(\mathrm{Cl}_{2}(\mathrm{g})\) is \(+2.12 \mathrm{V}\). What is the standard free energy change, \(\Delta_{\mathrm{r}} G^{\circ},\) for the reaction?

A An electrolysis cell for aluminum production operates at \(5.0 \mathrm{V}\) and a current of \(1.0 \times 10^{5} \mathrm{A}\). Calculate the number of kilowatt-hours of energy required to produce 1 metric ton \(\left(1.0 \times 10^{3} \mathrm{kg}\right)\) of aluminum. \(\left(1 \mathrm{kWh}=3.6 \times 10^{6} \mathrm{J} \text { and } 1 \mathrm{J}=1 \mathrm{C} \cdot \mathrm{V}\right)\)

A Electrolysis of molten \(\mathrm{NaCl}\) is done in cells operating at \(7.0 \mathrm{V}\) and \(4.0 \times 10^{4} \mathrm{A} .\) What mass of \(\mathrm{Na}(\mathrm{s})\) and \(\mathrm{Cl}_{2}(\mathrm{g})\) can be produced in 1 day in such a cell? What is the energy consumption in kilowatt-hours? \(\left(1 \mathrm{kWh}=3.6 \times 10^{6} \mathrm{J} \text { and } 1 \mathrm{J}=1 \mathrm{C} \cdot \mathrm{V}\right)\)

A current of \(0.44 \mathrm{A}\) is passed through a solution of ruthenium nitrate causing reduction of the metal ion to the metal. After 25.0 minutes, \(0.345 \mathrm{g}\) of Ru has been deposited. What is the charge on the ruthenium ion, \(\mathrm{Ru}^{n+} ?\) What is the formula for ruthenium nitrate?

Chlorine gas is obtained commercially by electrolysis of brine (a concentrated aqueous solution of \(\mathrm{NaCl}\) ). If the electrolysis cells operate at \(4.6 \mathrm{V}\) and \(3.0 \times 10^{5} \mathrm{A},\) what mass of chlorine can be produced in a 24 -hour day?

Write equations for the half-reactions that occur at the anode and cathode in the electrolysis of \(molten\) KBr. What are the products formed at the anode and cathode in the electrolysis of \(aqueous\) KBr?

The products formed in the electrolysis of aqueous \(\mathrm{CuSO}_{4}\) are \(\mathrm{Cu}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g}) .\) Write equations for the anode and cathode reactions.

In the electrolysis of \(\mathrm{HNO}_{3}(\mathrm{aq}),\) hydrogen is produced at the cathode. According to a table of reduction potentials, \(\mathrm{NO}_{3}^{-}(\mathrm{aq})\) is easier to reduce than \(\mathrm{H}^{+}(\mathrm{aq}) .\) Suggest a possible reason why \(\mathrm{H}_{2}\) formed rather than NO. What is the product formed at the anode? Write an equation for the anode reaction.

The metallurgy of aluminum involves electrolysis of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) dissolved in molten cryolyte \(\left(\mathrm{Na}_{3} \mathrm{AlF}_{6}\right)\) at about \(950^{\circ} \mathrm{C} .\) Aluminum metal is produced at the cathode. Predict the anode product and write equations for the reactions occurring at both electrodes.

A voltaic cell set up utilizing the reaction \(\mathrm{Cu}(\mathrm{s})+2 \mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{s})\) has a cell potential of 0.45 at \(298 \mathrm{K}\). Describe how the potential of this cell will change as the cell is discharged. At what point does the cell potential reach a constant value? Explain your answer.

Two \(\mathrm{Ag}^{+}\) (aq) \(|\) Ag half-cells are constructed. The first has \(\left[\mathrm{Ag}^{+}\right]=1.0 \mathrm{M},\) the second has \(\left[\mathrm{Ag}^{+}\right]=1.0 \times 10^{-5} \mathrm{M}\) When linked together with a salt bridge and external circuit, a cell potential is observed. (This kind of voltaic cell is referred to as a concentration cell.) (a) Draw a picture of this cell, labeling all components. Indicate the cathode and the anode, and indicate in which direction electrons flow in the external circuit. (b) Calculate the cell potential at \(298 \mathrm{K}\)

A Write balanced equations for the following reduction half-reactions involving organic compounds. (a) \(\mathrm{HCO}_{2} \mathrm{H} \rightarrow \mathrm{CH}_{2} \mathrm{O} \quad\) (acid solution) (b) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H} \rightarrow \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3} \quad\) (acid solution) (c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO} \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH} \quad\) (acid solution) (d) \(\mathrm{CH}_{3} \mathrm{OH} \rightarrow \mathrm{CH}_{4}\) (acid solution)

A Balance the following equations involving organic compounds. $$\begin{aligned} &\text { (a) } \mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CHO}(\mathrm{aq}) \rightarrow\\\ &&\mathrm{Ag}(\mathrm{s})+\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq}) \quad \text { (acid solution) } \end{aligned}$$ $$\begin{aligned} &\text { (b) } \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq}) \rightarrow\\\ &&\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq}) \quad+\mathrm{Cr}^{3+}(\mathrm{aq}) \quad \text { (acid solution) } \end{aligned}$$

A voltaic cell is constructed in which one half-cell consists of a silver wire in an aqueous solution of \(\mathrm{AgNO}_{3}\) The other half-cell consists of an inert platinum wire in an aqueous solution containing \(\mathrm{Fe}^{2+}(\mathrm{aq})\) and \(\mathrm{Fe}^{3+}(\mathrm{aq})\) (a) Calculate the cell potential, assuming standard conditions. (b) Write the net ionic equation for the reaction occurring in the cell. (c) Which electrode is the anode and which is the cathode? (d) If \(\left[\mathrm{Ag}^{+}\right]\) is \(0.10 \mathrm{M},\) and \(\left[\mathrm{Fe}^{2+}\right]\) and \(\left[\mathrm{Fe}^{3+}\right]\) are both 1.0 M, what is the cell potential? Is the net cell reaction still that used in part (a)? If not, what is the net reaction under the new conditions?

A You want to use electrolysis to plate a cylindrical object (radius \(=2.50 \text { and length }=20.00 \mathrm{cm})\) with a coating of nickel metal, \(4.0 \mathrm{mm}\) thick. You place the object in a bath containing a salt \(\left(\mathrm{Na}_{2} \mathrm{SO}_{4}\right) .\) One electrode is impure nickel, and the other is the object to be plated. The electrolyzing potential is \(2.50 \mathrm{V}\) (a) Which is the anode and which is the cathode in the experiment? What half- reaction occurs at each electrode? (b) Calculate the number of kilowatt-hours (kWh) of energy required to carry out the electrolysis. \(\left(1 \mathrm{kWh}=3.6 \times 10^{6} \mathrm{J} \text { and } 1 \mathrm{J}=1 \mathrm{C} \times 1 \mathrm{V}\right)\)

An old method of measuring the current flowing in a circuit was to use a "silver coulometer." The current passed first through a solution of \(\mathrm{Ag}^{+}(\mathrm{aq})\) and then into another solution containing an electroactive species. The amount of silver metal deposited at the cathode was weighed. From the mass of silver, the number of atoms of silver was calculated. since the reduction of a silver ion requires one electron, this value equaled the number of electrons passing through the circuit. If the time was noted, the average current could be calculated. If, in such an experiment, \(0.052 \mathrm{g}\) of \(\mathrm{Ag}\) is deposited during \(450 \mathrm{s},\) what was the current flowing in the circuit?

A "silver coulometer" (Study Question 94) was used in the past to measure the current flowing in an electrochemical cell. Suppose you found that the current flowing through an electrolysis cell deposited \(0.089 \mathrm{g}\) of Ag metal at the cathode after exactly 10 min. If this same current then passed through a cell containing gold(III) ion in the form of \(\left[\mathrm{AuCl}_{4}\right]^{-}\), how much gold was deposited at the cathode in that electrolysis cell?