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Chemistry 2012

JOHN E. MCMURRY, ROBERT C. FAY, JORDAN FANTINI

Chapter 17

Electrochemistry

Educators


Problem 1

Describe a galvanic cell that uses the reaction
$$2 \mathrm{Ag}^{+}(a q)+\mathrm{Ni}(s) \longrightarrow 2 \mathrm{Ag}(s)+\mathrm{Ni}^{2+}(a q)$$
Identify the anode and cathode half-reactions, and sketch the experimental setup. Label the anode and cathode, indicate the direction of electron and ion flow, and identify the sign of each electrode.

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Problem 2

Write a balanced equation for the overall cell reaction, and give a brief description of a galvanic cell represented by the following shorthand notation:
$$\mathrm{Pb}(s)\left|\mathrm{Pb}^{2+}(a q)\right|\left|\mathrm{Br}_{2}(l)\right| \mathrm{Br}^{-}(a q) | \mathrm{Pt}(s)$$

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Problem 3

Write the shorthand notation for a galvanic cell that uses the reaction
$$\mathrm{Fe}(s)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Fe}^{2+}(a q)+\mathrm{Sn}(s)$$

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Problem 4

Consider the following galvanic cell:
(a) Complete the drawing by adding any components essential for a functioning cell.
(b) Label the anode and cathode, and indicate the direction of ion flow.
(c) Write a balanced equation for the cell reaction.
(d) Write the shorthand notation for the cell.

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Problem 5

The standard cell potential at $25^{\circ} \mathrm{C}$ is 0.92 $\mathrm{V}$ for the reaction
$$\mathrm{Al}(s)+\mathrm{Cr}^{3+}(a q) \longrightarrow \mathrm{Al}^{3+}(a q)+\mathrm{Cr}(s)$$
What is the standard free-energy change for this reaction at $25^{\circ} \mathrm{C} ?$

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Problem 6

The standard potential for the following galvanic cell is $0.92 \mathrm{V} :$
$$\operatorname{Al}(s)\left|\mathrm{A} \mathrm{l}^{3+}(a q) \| \mathrm{Cr}^{3+}(a q)\right| \mathrm{Cr}(s)$$
Look up the standard reduction potential for the $\mathrm{Al}^{3+} /$ Al half-cell in Table $17.1,$ and calculate the standard reduction potential for the $\mathrm{Cr}^{3+} / \mathrm{Cr}$ half-cell.

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Problem 7

Which is the stronger oxidizing agent, $\mathrm{Cl}_{2}(g)$ or $\mathrm{Ag}^{+}(a q) ?$ Which is the stronger reducing agent, $\mathrm{Fe}(s)$ or Mg(s)?

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Problem 8

Predict from Table 17.1 whether each of the following reactions canoccur under standard-state
conditions:
(a) $2 \mathrm{Fe}^{3+}(a q)+2 \mathrm{I}^{-}(a q) \longrightarrow 2 \mathrm{Fe}^{2+}(a q)+\mathrm{I}_{2}(s)$
(b) $3 \mathrm{Ni}(s)+2 \mathrm{Al}^{3+}(a q) \longrightarrow 3 \mathrm{Ni}^{2+}(a q)+2 \mathrm{Al}(s)$
Confirm your predictions by calculating the value of $E^{\circ}$ for each reaction. Which reaction(s) can occur in the reverse direction under standard-state conditions?

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Problem 9

Consider the following table of standard reduction potentials:
$\begin{array}{ll}{\mathrm{A}^{3+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{A}^{+}} & {1.47} \\ {\mathrm{B}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{B}} & {0.60} \\ {\mathrm{C}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{C}} & {-0.21} \\ {\mathrm{D}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{D}} & {-1.38}\end{array}$
(a) Which substance is the strongest reducing agent? Which is the strongest oxidizing agent?
(b) Which substances can be oxidized by $\mathrm{B}^{2+}$ ? Which can be reduced by C?
(c) Write a balanced equation for the overall cell reaction that delivers the highest volt- age, and calculate $E^{\circ}$ for the reaction.

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Problem 10

Consider a galvanic cell that uses the reaction
$$\mathrm{Cu}(s)+2 \mathrm{Fe}^{3+}(a q) \longrightarrow \mathrm{Cu}^{2+}(a q)+2 \mathrm{Fe}^{2+}(a q)$$
What is the potential of a cell at $25^{\circ} \mathrm{C}$ that has the following ion concentrations?
$$\left[\mathrm{Fe}^{3+}\right]=1.0 \times 10^{-4} \mathrm{M} \quad\left[\mathrm{Cu}^{2+}\right]=0.25 \mathrm{M} \quad\left[\mathrm{Fe}^{2+}\right]=0.20 \mathrm{M}$$

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Problem 11

Consider the following galvanic cell:
(a) What is the change in the cell voltage on decreasing the ion concentrations in theanode compartment
by a factor of 100$?$
(b) What is the change in the cell voltage on decreasing the ion concentrations in the cathode compartment by a factor of 100$?$

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Problem 12

What is the pH of the solution in the anode compartment of the following cell if the measured cell potential at $25^{\circ} \mathrm{C}$ is 0.28 $\mathrm{V}$ ?
$$\operatorname{Pt}(s)\left|\mathrm{H}_{2}(1 \mathrm{atm})\right| \mathrm{H}^{+}(? \mathrm{M})\left|\mathrm{Pb}^{2+}(1 \mathrm{M})\right| \mathrm{Pb}(s)$$

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Problem 13

Use the data in Table 17.1 to calculate the equilibrium constant at $25^{\circ} \mathrm{C}$ for the reaction
$$4 \mathrm{Fe}^{2+}(a q)+\mathrm{O}_{2}(g)+4 \mathrm{H}^{+}(a q) \longrightarrow 4 \mathrm{Fe}^{3+}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)$$

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Problem 14

What is the value of $E^{\circ}$ for a redox reaction involving the transfer of 2 mol of electrons if its equilibrium constant is $1.8 \times 10^{-5} ?$

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Problem 15

Write a balanced equation for the overall cell reaction when each of the following batteries is producing current:
(a) Leclanché dry cell
(b) Alkaline dry cell
(c) Nickel–cadmium battery
(d) Lithium battery
(e) Lithium-ion battery

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Problem 16

In what ways are fuel cells and batteries similar, and in what ways are they different?

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Problem 17

What is the standard potential for the cell reaction in
(a) the hydrogen–oxygen fuel cell used in space vehicles?
(b) the PEM fuel cell used in electric automobiles?

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Problem 18

Magnesium is often attached to the steel hulls of ships to protect the steel from rusting. Write balanced equations for the corrosion reactions that occur (a) in the presence of Mg and (b) in the absence of Mg.

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Problem 19

Metallic potassium was first prepared by Humphrey Davy in 1807 by electrolysis of molten potassium hydroxide:
(a) Label the anode and cathode, and show the direction of ion flow.
(b) Write balanced equations for the anode, cathode, and overall cell reactions.

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Problem 20

Predict the half-cell reactions that occur when aqueous solutions of the following salts are electrolyzed in a cell with inert electrodes. What is the overall cell reaction in each case?
(a) LiCl
(b) $\mathrm{CuSO}_{4}$
(c) $\mathrm{K}_{2} \mathrm{SO}_{4}$

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Problem 21

Sketch an electrolytic cell suitable for electroplating a silver spoon. Describe the electrodes and the electrolyte, label the anode and cathode, and indicate the balanced equations for the anode and cathode half-reactions. What is the overall cell reaction?

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Problem 22

How many kilograms of aluminum can be produced in 8.00 h by passing a constant current of $1.00 \times 10^{5}$ A through a molten mixture of aluminum oxide and cryolite?

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Problem 23

A layer of silver is electroplated on a coffee server using a constant current of 0.100 A. How much time is required to deposit 3.00 g of silver?

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Problem 24

What is the overall cell reaction and cell potential for anodizing titanium if the anode half-reaction is
$$\mathrm{Ti}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{TiO}_{2}(s)+4 \mathrm{H}^{+}(a q)+4 \mathrm{e}^{-} \quad E^{\circ}=+1.066 \mathrm{V}$$

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Problem 25

How many minutes are required to produce a 0.0100 mm thick coating of $\mathrm{Al}_{2} \mathrm{O}_{3}\left(\text { density } 3.97 \mathrm{g} / \mathrm{cm}^{3}\right)$ on a square piece of aluminum metal 10.0 $\mathrm{cm}$ on an edge if the current passed through the piece is 0.600 $\mathrm{A}$ ?

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Problem 26

The following picture of a galvanic cell has lead and zinc electrodes:
(a) Label the electrodes, and identify the ions present in the solutions.
(b) Label the anode and cathode.
(c) Indicate the direction of electron flow in the wire and ion flow in the solutions.
(d) Tell what electrolyte could be used in the salt bridge, and indicate the direction of ion flow.
(e) Write balanced equations for the electrode and overall cell reactions.

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Problem 27

Consider the following galvanic cell:
(a) Identify the anode and cathode.
(b) Write a balanced equation for the cell reaction.
(c) Write the shorthand notation for the cell.

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Problem 28

Consider the following galvanic cells:
(1) $\mathrm{Cu}(s)\left|\mathrm{Cu}^{2+}(1 \mathrm{M}) \| \mathrm{Fe}^{3+}(1 \mathrm{M}), \mathrm{Fe}^{2+}(1 \mathrm{M})\right| \mathrm{Pt}(s)$
(2) $\mathrm{Cu}(s)\left|\mathrm{Cu}^{2+}(1 \mathrm{M}) \| \mathrm{Fe}^{3+}(1 \mathrm{M}), \mathrm{Fe}^{2+}(5 \mathrm{M})\right| \operatorname{Pt}(s)$
(3) $\mathrm{Cu}(s)\left|\mathrm{Cu}^{2+}(0.1 \mathrm{M}) \| \mathrm{Fe}^{3+}(0.1 \mathrm{M}), \mathrm{Fe}^{2+}(0.1 \mathrm{M})\right| \mathrm{Pt}(s)$
(a) Write a balanced equation for each cell reaction.
(b) Sketch each cell. Label the anode and cathode, and indicate the direction of electron and ion flow.
(c) Which of the three cells has the largest cell potential? Which has the smallest cell potential? Explain.

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Problem 29

Sketch a cell with inert electrodes suitable for electrolysis of aqueous CuBr2.
(a) Label the anode and cathode.
(b) Indicate the direction of electron and ion flow.
(c) Write balanced equations for the anode, cathode, and overall cell reactions.

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Problem 30

Consider the following electrochemical cell:
(a) Is the cell a galvanic or an electrolytic cell? Explain.
(b) Label the anode and cathode, and show the direction of ion flow.
(c) Write balanced equations for the anode, cathode, and overall cell reactions.

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Problem 31

It has recently been reported that porous pellets of $\mathrm{TiO}_{2}$ can be reduced to titanium metal at the cathode of an electro-chemical cell containing molten $\mathrm{CaCl}_{2}$ as the electrolyte. When the $\mathrm{TiO}_{2}$ is reduced, the $\mathrm{O}^{2-}$ ions dissolve in the $\mathrm{CaCl}_{2}$ and are subsequently oxidized to $\mathrm{O}_{2}$ gas at the anode. This approach may be the basis for a less expensive process than the one currently used for producing titanium.
(a) Label the anode and cathode, and indicate the signs of the electrodes.
(b) Indicate the direction of electron and ion flow.
(c) Write balanced equations for the anode, cathode, and overall cell reactions.

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Problem 32

Consider a Daniell cell with 1.0 M ion concentrations:
Does the cell voltage increase, decrease, or remain the same when each of the following changes is made? Explain.
(a) 5.0 $\mathrm{M} \mathrm{CuSO}_{4}$ is added to the cathode compartment.
(b) 5.0 $\mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}$ is added to the cathode compartment.
(c) 5.0 $\mathrm{M} \mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}$ is added to the anode compartment.
(d) 1.0 $\mathrm{M} \mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}$ is added to the anode compartment.

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Problem 33

Consider the following galvanic cell with 0.10 M concentrations:
Does the cell voltage increase, decrease, or remain the same when each of the following changes is made? Explain.
(a) 0.10 $\mathrm{MNaCl}$ is added to the cathode compartment.
(b) 0.10 $\mathrm{M} \mathrm{NaCl}$ is added to the anode compartment.
(c) 1.0 $\mathrm{MNH}_{3}$ is added to the cathode compartment.
(d) 1.0 $\mathrm{M} \mathrm{NH}_{3}$ is added to the anode compartment.

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Problem 34

Consider a PEM fuel cell, consisting of a sandwich of two porous graphite electrodes and the proton-exchange membrane, with separate compartments for entrance of $\mathrm{H}_{2}$ and $\mathrm{O}_{2} :$
(a) Label the anode and cathode, and indicate the signs of the electrodes.
(b) Indicate the direction of electron and ion flow.
(c) Identify the substances that exit from each cell compartment.
(d) Write balanced equations for the anode, cathode, and overall cell reactions, and calculate the standard cell potential.

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Problem 35

Consider the following table of standard reduction potentials:
$\begin{array}{ll}{A^{+}+e^{-} \longrightarrow A} & {0.80} \\ {B^{2+}+2 e^{-} \longrightarrow B} & {0.38} \\ {C_{2}+2 e^{-} \longrightarrow 2 C^{-}} & {0.17} \\ {D^{3+}+3 e^{-} \longrightarrow D} & {-1.36}\end{array}$
(a) Which substance is the strongest oxidizing agent? Which is the strongest reducing agent?
(b) Which substances can be oxidized by $\mathrm{B}^{2+}$ ? Which can be reduced by D?
(c) Write a balanced equation for the overall cell reaction that delivers a voltage of 1.53 $\mathrm{V}$ under standard-state conditions.

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Problem 36

Why is the cathode of a galvanic cell considered to be the positive electrode?

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Problem 37

What is the function of a salt bridge in a galvanic cell?

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Problem 38

Describe galvanic cells that use the following reactions. In each case, write the anode and cathode half-reactions and sketch the experimental setup. Label the anode and cathode, identify the sign of each electrode, and indicate the direction of electron and ion flow.
(a) $\mathrm{Cd}(s)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Cd}^{2+}(a q)+\mathrm{Sn}(s)$
(b) $2 \mathrm{Al}(s)+3 \mathrm{Cd}^{2+}(a q) \longrightarrow 2 \mathrm{Al}^{3+}(a q)+3 \mathrm{Cd}(s)$
(c) $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+6 \mathrm{Fe}^{2+}(a q)+14 \mathrm{H}^{+}(a q) \longrightarrow$
$\quad\quad\quad\quad 2 \mathrm{Cr}^{3+}(a q)+6 \mathrm{Fe}^{3+}(a q)+7 \mathrm{H}_{2} \mathrm{O}(l)$

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Problem 39

Describe galvanic cells that use the following reactions. In each case, write the anode and cathode half-reactions and sketch the experimental setup. Label the anode and cathode, identify the sign of each electrode, and indicate the direction of electron and ion flow.
(a) $3 \mathrm{Cu}^{2+}(a q)+2 \mathrm{Cr}(s) \longrightarrow 3 \mathrm{Cu}(s)+2 \mathrm{Cr}^{3+}(a q)$
(b) $\mathrm{Pb}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Pb}^{2+}(a q)+\mathrm{H}_{2}(g)$
(c) $\mathrm{Cl}_{2}(g)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Sn}^{4+}(a q)+2 \mathrm{Cl}^{-}(a q)$

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Problem 40

Write the standard shorthand notation for each cell in Problem 17.38.

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Problem 41

Write the standard shorthand notation for each cell in Problem 17.39.

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Problem 42

Write a balanced equation for the overall cell reaction in the following galvanic cell, and tell why inert electrodes are required at the anode and cathode.
$$\operatorname{Pt}(s)\left|\mathrm{Br}^{-}(a q)\right| \mathrm{Br}_{2}(l)\left|\mathrm{Cl}_{2}(g)\right| \mathrm{Cl}^{-}(a q) | \mathrm{Pt}(s)$$

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Problem 43

Write the standard shorthand notation for a galvanic cell that uses the following cell reaction. Include inert electrodes if necessary.
$$\mathrm{Fe}(s)+\mathrm{I}_{2}(s) \longrightarrow \mathrm{Fe}^{2+}(a q)+2 \mathrm{I}^{-}(a q)$$

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Problem 44

An $\mathrm{H}_{2} / \mathrm{H}^{+}$ half-cell (anode) and an $\mathrm{Ag}^{+} / \mathrm{Ag}$ half-cell (cathode) are connected by a wire and a salt bridge.
(a) Sketch the cell, indicating the direction of electron and ion flow.
(b) Write balanced equations for the electrode and overall cell reactions.
(c) Give the shorthand notation for the cell.

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Problem 45

A galvanic cell is constructed from a $\mathrm{Zn} / \mathrm{Zn}^{2+}$ half-cell (anode) and a $\mathrm{Cl}_{2} / \mathrm{Cl}^{-}$ half-cell (cathode).
(a) Sketch the cell, indicating the direction of electron and ion flow.
(b) Write balanced equations for the electrode and overallcell reactions.
(c) Give the shorthand notation for the cell.

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Problem 46

Write balanced equations for the electrode and overall cell reactions in the following galvanic cells. Sketch each cell, labeling the anode and cathode and showing the direction of electron and ion flow.
(a) $\operatorname{Co}(s)\left|\mathrm{Co}^{2+}(a q)\right|\left|\mathrm{Cu}^{2+}(a q)\right| \mathrm{Cu}(s)$
(b) $\mathrm{Fe}(s)\left|\mathrm{Fe}^{2+}(a q)\right|\left|\mathrm{O}_{2}(g)\right| \mathrm{H}^{+}(a q), \mathrm{H}_{2} \mathrm{O}(l) | \mathrm{Pt}(s)$

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Problem 47

Write balanced equations for the electrode and overall cell reactions in the following galvanic cells. Sketch each cell, labeling the anode and cathode and showing the direction of electron and ion flow.
(a) $\operatorname{Mn}(s)\left|\operatorname{Mn}^{2+}(a q)\right|\left|\mathrm{Pb}^{2+}(a q)\right| \mathrm{Pb}(s)$
(b) $\operatorname{Pt}(s)\left|\mathrm{H}_{2}(g)\right| \mathrm{H}^{+}(a q)| | \mathrm{Cl}^{-}(a q)|\mathrm{AgCl}(\mathrm{s})| \mathrm{Ag}(s)$

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Problem 48

What conditions must be met for a cell potential $E$ to qualify as a standard cell potential $E^{\circ} ?$

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Problem 49

How are standard reduction potentials defined?

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Problem 50

The silver oxide–zinc battery used in watches delivers a voltage of 1.60 V. Calculate the free-energy change (in kilo-joules) for the cell reaction
$$\mathrm{Zn}(s)+\mathrm{Ag}_{2} \mathrm{O}(s) \longrightarrow \mathrm{ZnO}(s)+2 \mathrm{Ag}(s)$$

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Problem 51

The standard cell potential for a lead storage battery is 1.924 $\mathrm{V}$ . Calculate $\Delta G^{\circ}$ (in kilojoules) for the cell reaction
$\quad \quad \quad \quad \quad2 \mathrm{PbSO}_{4}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)$

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Problem 52

What is the value of $x$ for the following reaction if $E^{\circ}=1.43 \mathrm{V}$ and $\Delta G^{\circ}=-414 \mathrm{kJ} ?$
$$\mathrm{A}+\mathrm{B}^{x+} \longrightarrow \mathrm{A}^{x+}+\mathrm{B}$$

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Problem 53

What are the values of $x$ and $y$ for the following reaction if $E^{\circ}=0.91 \mathrm{V}$ and $\Delta G^{\circ}=-527 \mathrm{kJ} ?$
$$2 \mathrm{A}^{x+}+3 \mathrm{B} \longrightarrow 2 \mathrm{A}+3 \mathrm{B}^{y+}$$

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Problem 54

Use the standard free energies of formation in Appendix B to calculate the standard cell potential for the reaction in the hydrogen–oxygen fuel cell:
$$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)$$

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Problem 55

Consider a fuel cell that uses the reaction
$$\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$$
Given the standard free energies of formation in Appendix B, what is the value of for the cell reaction?

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Problem 56

The standard potential for the following galvanic cell is 0.40 V:
$$\mathrm{Zn}(s)\left|\mathrm{Zn}^{2+}(a q)\right| \mathrm{Eu}^{3+}(a q), \mathrm{Eu}^{2+}(a q) | \mathrm{Pt}(s)$$
(Europium, Eu, is one of the lanthanide elements.) Use the data in Table 17.1 to calculate the standard reduction potential for the $\mathrm{Eu}^{3+} / \mathrm{Eu}^{2+}$ half-cell.

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Problem 57

The following reaction has an $E^{\circ}$ value of $0.27 \mathrm{V} :$
$$\mathrm{Cu}^{2+}(a q)+2 \mathrm{Ag}(s)+2 \mathrm{Br}^{-}(a q) \longrightarrow \mathrm{Cu}(s)+2 \mathrm{AgBr}(s)$$
Use the data in Table 17.1 to calculate the standard reduction potential for the half-reaction
$$\operatorname{Ag} \operatorname{Br}(s)+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(s)+\mathrm{Br}^{-}(a q)$$

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Problem 58

Arrange the following oxidizing agents in order of increasing strength under standard-state conditions: $\mathrm{Br}_{2}(a q)$ $\mathrm{MnO}_{4}-(a q), \mathrm{Sn}^{4+}(a q)$

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Problem 59

List the following reducing agents in order of increasing strength under standard-state conditions: Al(s), $\mathrm{Pb}(s), \mathrm{Fe}(s)$ .

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Problem 60

Consider the following substances: $\mathrm{I}_{2}(s), \mathrm{Fe}^{2+}(a q),$ $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q) .$ Which is the strongest oxidizing agent? Which is the weakest oxidizing agent?

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Problem 61

Consider the following substances: $\mathrm{Fe}^{2+}(a q), \mathrm{Sn}^{2+}(a q), \mathrm{T}^{-}(a q)$ . Identify the strongest reducing agent and the weakest reducing agent.

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Problem 62

Given the following half-reactions, combine the two that give the cell reaction with the most positive $E^{\circ} .$ Write a balanced equation for the cell reaction, and calculate $E^{\circ}$ and $\Delta G^{\circ} .$
$$\begin{array}{ll}{\mathrm{Co}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Co}(s)} & {E^{\circ}=-0.28 \mathrm{V}} \\ {\mathrm{I}_{2}(s)+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{I}(a q)} & {E^{\circ}=0.54 \mathrm{V}} \\ {\mathrm{Cu}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Cu}(s)} & {E^{\circ}=0.34 \mathrm{V}}\end{array}$$

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Problem 63

Combine the two half-reactions in Problem 17.62 that give the spontaneous cell reaction with the smallest $E^{\circ} .$ Write a balanced equation for the cell reaction, and calculate $E^{\circ}$ and $\Delta G^{\circ} .$

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Problem 64

Calculate the standard cell potential and the standard free energy change (in kilojoules) for each reaction in Problem 17.38. (See Appendix D for standard reduction potentials.)

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Problem 65

Calculate $E^{\circ}$ and $\Delta G^{\circ}(\text { in kilojoules) for the cell reactions in }$ Problem 17.39 . (See Appendix $D$ for standard reduction potentials.)

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Problem 66

Calculate $E^{\circ}$ for each of the following reactions, and tell which are spontaneous under standard-state conditions:
(a) $2 \mathrm{Fe}^{2+}(a q)+\mathrm{Pb}^{2+}(a q) \longrightarrow 2 \mathrm{Fe}^{3+}(a q)+\mathrm{Pb}(s)$
(b) $\mathrm{Mg}(s)+\mathrm{Ni}^{2+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Ni}(s)$

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Problem 67

Calculate $E^{\circ}$ for each of the following reactions, and tell which are spontaneous under standard- state conditions:
(a) $5 \mathrm{Ag}^{+}(a q)+\mathrm{Mn}^{2+}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow$
$\quad\quad\quad\quad\quad\quad5 \mathrm{Ag}(s)+\mathrm{MnO}_{4}^{-}(a q)+8 \mathrm{H}^{+}(a q)$
(b) $2 \mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow \mathrm{O}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$

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Problem 68

Use the data in Appendix $D$ to predict whether the following reactions can occur under standard-state conditions:
(a) Oxidation of $\operatorname{Sn}^{2+}(a q)$ by $\operatorname{Br}_{2}(a q)$
(b) Reduction of $\mathrm{Ni}^{2+}(a q)$ by $\operatorname{Sn}^{2+}(a q)$
(c) Oxidation of $\mathrm{Ag}(s)$ by $\mathrm{Pb}^{2+}(a q)$
(d) Reduction of $\mathrm{I}_{2}(s)$ by $\mathrm{H}_{2} \mathrm{SO}_{3}(a q)$

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Problem 69

Use the data in Appendix $D$ to predict whether the following reactions can occur under standard-state conditions:
(a) Reduction of $\mathrm{Pb}^{2+}(a q)$ by Ni(s)
(b) Oxidation of $\mathrm{Au}^{+}(a q)$ by $\mathrm{Mn}^{2+}(a q)$
(c) Reduction of $\mathrm{I}_{2}(s)$ by $\mathrm{Mn}(s)$
(d) Oxidation of $\mathrm{Fe}^{2+}(a q)$ by $\mathrm{Br}_{2}(a q)$

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Problem 70

What reaction can occur, if any, when the following experiments are carried out under standard-state conditions?
(a) Oxygen gas is bubbled through an acidic solution of $\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}$ .
(b) A strip of lead is dipped into an aqueous solution of $\mathrm{AgNO}_{3}$ .
(c) Chlorine gas is bubbled through aqueous $\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}$
(d) A nickel wire is dipped into an aqueous solution of $\mathrm{HClO}$ .

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Problem 71

What reaction can occur, if any, when the following experiments are carried out under standard-state conditions?
(a) A strip of zinc is dipped into an aqueous solution of $\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}$
(b) An acidic solution of $\mathrm{FeSO}_{4}$ is exposed to oxygen.
(c) A silver wire is immersed in an aqueous solution of $\mathrm{NiCl}_{2}$.
(d) Hydrogen gas is bubbled through aqueous $\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}$

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Problem 72

Consider a galvanic cell that uses the reaction
$$2 \mathrm{Ag}^{+}(a q)+\mathrm{Sn}(s) \longrightarrow 2 \mathrm{Ag}(s)+\mathrm{Sn}^{2+}(a q)$$
Calculate the potential at $25^{\circ} \mathrm{C}$ for a cell that has the following ion concentrations: $\left[\mathrm{Ag}^{+}\right]=0.010 \mathrm{M},\left[\mathrm{Sn}^{2+}\right]=$ 0.020 $\mathrm{M} .$

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Problem 73

Consider a galvanic cell based on the reaction
$$2 \mathrm{Fe}^{2+}(a q)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{Fe}^{3+}(a q)+2 \mathrm{Cl}^{-}(a q)$$
Calculate the cell potential at $25^{\circ} \mathrm{C}$ when $\left[\mathrm{Fe}^{2+}\right]=$ $1.0 \mathrm{M},\left[\mathrm{Fe}^{3+}\right]=1.0 \times 10^{-3} \mathrm{M},[\mathrm{Cl}]=3.0 \times 10^{-3} \mathrm{M},$ and $P_{\mathrm{Cl}_{2}}=0.50 \mathrm{atm} .$

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Problem 74

What is the cell potential at 25 °C for the following galvanic cell?
$$\operatorname{Pb}(s)\left|\mathrm{P}^{2+}(1.0 \mathrm{M})\right|\left|\mathrm{Cu}^{2+}\left(1.0 \times 10^{-4} \mathrm{M}\right)\right| \mathrm{Cu}(\mathrm{s})$$
If the $\mathrm{Pb}^{2+}$ concentration is maintained at $1.0 \mathrm{M},$ what is the $\mathrm{Cu}^{2+}$ concentration when the cell potential drops to zero?

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Problem 75

A galvanic cell has an iron electrode in contact with 0.10 $\mathrm{M}$ $\mathrm{FeSO}_{4}$ and a copper electrode in contact with a $\mathrm{CuSO}_{4}$ solution. If the measured cell potential at $25^{\circ} \mathrm{C}$ is $0.67 \mathrm{V},$ what is the concentration of $\mathrm{Cu}^{2+}$ in the CuSO_ solution?

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Problem 76

What is the $\mathrm{Zn}^{2+} : \mathrm{Cu}^{2+}$ concentration ratio in the following cell at $25^{\circ} \mathrm{C}$ if the measured cell potential is 1.07 $\mathrm{V}$ ?
$$\mathrm{Zn}(s)\left|\mathrm{Zn}^{2+}(a q)\right|\left|\mathrm{Cu}^{2+}(a q)\right| \mathrm{Cu}(s)$$

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Problem 77

What is the $\mathrm{Fe}^{2+} : \mathrm{Sn}^{2+}$ concentration ratio in the following cell at $25^{\circ} \mathrm{C}$ if the measured cell potential is 0.35 $\mathrm{V}$ ?
$$\mathrm{Fe}(s)\left|\mathrm{Fe}^{2+}(a q) \| \mathrm{Sn}^{2+}(a q)\right| \mathrm{Sn}(s)$$

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Problem 78

The Nernst equation applies to both cell reactions and half-reactions. For the conditions specified, calculate the potential for the following half-reactions at $25^{\circ} \mathrm{C} :$
(a) $\mathrm{I}_{2}(s)+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{I}(a q) ;[\mathrm{I}]=0.020 \mathrm{M}$
(b) $\mathrm{Fe}^{3+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2+}(a q) ;\left[\mathrm{Fe}^{3+}\right]=\left[\mathrm{Fe}^{2+}\right]=0.10 \mathrm{M}$
$\begin{aligned} \text { (c) } \mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Sn}^{4+}(a q)+2 \mathrm{e}^{-} ;\left[\mathrm{Sn}^{2+}\right]=1.0 \times 10^{-3} \mathrm{M} \\ &\left[\mathrm{Sn}^{4+}\right]=0.40 \mathrm{M} \end{aligned}$
(d) $2 \mathrm{Cr}^{3+}(a q)+7 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+14 \mathrm{H}^{+}(a q)$
$+6 \mathrm{e}^{-} ;\left[\mathrm{Cr}^{3+}\right]=\left[\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\right]=1.0 \mathrm{M},\left[\mathrm{H}^{+}\right]=0.010 \mathrm{M}$

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Problem 79

What is the reduction potential at 25 °C for the hydrogen electrode in each of the following solutions? The half-reaction is
$$2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}(g, 1 \mathrm{atm})$$
(a) 1.0 M HCl
(b) A solution having pH 4.00
(c) Pure water
(d) 1.0 M NaOH

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Problem 80

The following cell has a potential of 0.27 $\mathrm{V}$ at $25^{\circ} \mathrm{C} :$
$$\operatorname{Pt}(s)\left|\mathrm{H}_{2}(1 \mathrm{atm})\right| \mathrm{H}^{+}(? \mathrm{M}) \| \mathrm{Ni}^{2+}(1 \mathrm{M}) | \mathrm{Ni}(s)$$
What is the pH of the solution in the anode compartment?

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Problem 81

What is the $\mathrm{pH}$ of the solution in the cathode compartment of the following cell if the measured cell potential at $25^{\circ} \mathrm{C}$ is 0.58 $\mathrm{V}$ ?
$$\mathrm{Zn}(s)\left|\mathrm{Zn}^{2+}(1 \mathrm{M})\right|\left|\mathrm{H}^{+}(2 \mathrm{M})\right| \mathrm{H}_{2}(1 \mathrm{atm}) | \mathrm{Pt}(s)$$

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Problem 82

Beginning with the equations that relate $E^{\circ}, \Delta G^{\circ},$ and $K,$ show that $\Delta G^{\circ}$ is negative and $K>1$ for a reaction that has a positive value of $E^{\circ} .$

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Problem 83

If a reaction has an equilibrium constant $K<1,$ is $E^{\circ}$ positive or negative? What is the value of $K$ when $E^{\circ}=0 \mathrm{V} ?$

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Problem 84

Use the data in Table 17.1 to calculate the equilibrium constant at $25^{\circ} \mathrm{C}$ for the reaction
$$\mathrm{Ni}(s)+2 \mathrm{Ag}^{+}(a q) \longrightarrow \mathrm{Ni}^{2+}(a q)+2 \mathrm{Ag}(s)$$

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Problem 85

From standard reduction potentials, calculate the equilibrium constant at $25^{\circ} \mathrm{C}$ for the reaction
$2 \mathrm{MnO}_{4}^{-}(a q)+10 \mathrm{Cl}^{-}(a q)+16 \mathrm{H}^{+}(a q) \longrightarrow$
$\quad \quad\quad\quad2 \mathrm{Mn}^{2+}(a q)+5 \mathrm{Cl}_{2}(g)+8 \mathrm{H}_{2} \mathrm{O}(l)$

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Problem 86

Calculate the equilibrium constant at $25^{\circ} \mathrm{C}$ for each reaction in Problem 17.38 .

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Problem 87

Calculate the equilibrium constant at $25^{\circ} \mathrm{C}$ for each reaction in Problem 17.39 .

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Problem 88

Calculate the equilibrium constant at $25^{\circ} \mathrm{C}$ for the reaction
$$\mathrm{Hg}_{2}^{2+}(a q) \longrightarrow \mathrm{Hg}(l)+\mathrm{Hg}^{2+}(a q)$$
See Appendix $\mathrm{D}$ for standard reduction potentials.

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Problem 89

Use standard reduction potentials to calculate the equilibrium constant at $25^{\circ} \mathrm{C}$ for decomposition of hydrogen peroxide:
$$2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)$$

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Problem 90

For a lead storage battery:
(a) Sketch one cell that shows the anode, cathode, electrolyte, direction of electron and ion flow, and sign of the electrodes.
(b) Write the anode, cathode, and overall cell reactions.
(c) Calculate the equilibrium constant for the cell reaction $\left(E^{\circ}=1.924 \mathrm{V}\right)$
(d) What is the cell voltage when the cell reaction reaches equilibrium?

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Problem 91

A mercury battery uses the following electrode half-reactions:
$\mathrm{HgO}(s)+\mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Hg}(l)+2 \mathrm{OH}^{-}(a q) \quad E^{\circ}=0.098 \mathrm{V}$
$\mathrm{ZnO}(s)+\mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Zn}(s)+2 \mathrm{OH}^{-}(a q) \quad E^{\circ}=-1.260 \mathrm{V}$
(a) Write a balanced equation for the overall cell reaction.
(b) Calculate $\Delta G^{\circ}\left(\text { in kilojoules) and } K \text { at } 25^{\circ} \mathrm{C} \text { for the cell }\right.$ reaction.
(c) What is the effect on the cell voltage of a tenfold change in the concentration of KOH in the electrolyte? Explain.

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Problem 92

Calculate the values of $E^{\circ}, \Delta G^{\circ}(\text { in kilojoules }),$ and $K$ at $25^{\circ} \mathrm{C}$ for the cell reaction in a hydrogen-oxygen fuel cell: $2 \mathrm{H}_{2}(g)+\mathrm{O}_{2 (g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) .$ What is the cell voltage at $25^{\circ} \mathrm{C}$ if the partial pressure of each gas is 25 $\mathrm{atm}$ ?

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Problem 93

Use the thermodynamic data in Appendix $\mathrm{B}$ to calculate the standard cell potential and the equilibrium constant at $25^{\circ} \mathrm{C}$ for the cell reaction in a direct methanol fuel cell:
$$2 \mathrm{CH}_{3} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)$$

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Problem 94

What is rust? What causes it to form? What can be done to prevent its formation?

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Problem 95

The standard oxidation potential for the reaction $\mathrm{Cr}(s) \longrightarrow \mathrm{Cr}^{3+}(a q)+3 \mathrm{e}^{-}$ is 0.74 $\mathrm{V}$ . Despite the large, positive oxidation potential, chromium is sometimes used as a protective coating on steel. Why doesn't the chromium corrode?

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Problem 96

What is meant by cathodic protection? Which of the following metals can offer cathodic protection to iron?
$$\mathrm{Zn}, \mathrm{Ni}, \mathrm{Al}, \mathrm{Sn}$$

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Problem 97

What is a sacrificial anode? Give an example.

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Problem 98

Magnesium metal is produced by the electrolysis of molten magnesium chloride using inert electrodes.
(a) Sketch the cell, label the anode and cathode, indicate the sign of the electrodes, and show the direction of electron and ion flow.
(b) Write balanced equations for the anode, cathode, and overall cell reactions.

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Problem 99

(a) Sketch a cell with inert electrodes suitable for the electrolysis of an aqueous solution of sulfuric acid. Label the anode and cathode, and indicate the direction of electron and ion flow. Identify the positive and negative electrodes.
(b) Write balanced equations for the anode, cathode, and overall cell reactions.

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Problem 100

List the anode and cathode half-reactions that might occur when an aqueous solution of MgCl $_{2}$ is electrolyzed in a cell having inert electrodes. Predict which half-reactions will occur, and justify your answers.

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Problem 101

What products should be formed when the following reac- tants are electrolyzed in a cell having inert electrodes? Account for any differences.
(a) Molten KCl (b) Aqueous KCl

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Problem 102

Predict the anode, cathode, and overall cell reactions when an aqueous solution of each of the following salts is electrolyzed in a cell having inert electrodes:
$\begin{array}{llll}{\text { (a) NaBr }} & {\text { (b) } \mathrm{CuCl}_{2}} & {\text { (c) LiOH }}\end{array}$

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Problem 103

Predict the anode, cathode, and overall cell reactions when an aqueous solution of each of the following salts is electrolyzed in a cell having inert electrodes:
$\begin{array}{llll}{\text { (a) } \mathrm{Ag}_{2} \mathrm{SO}_{4}} & {\text { (b) } \mathrm{Ca}(\mathrm{OH})_{2}} & {\text { (c) } \mathrm{KI}}\end{array}$

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Problem 104

How many grams of silver will be obtained when an aqueous silver nitrate solution is electrolyzed for 20.0 $\mathrm{min}$ with a constant current of 2.40 $\mathrm{A}$ ?

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Problem 105

A constant current of 100.0 $\mathrm{A}$ is passed through an electrolytic cell having an impure copper anode, a pure copper cathode, and an aqueous CuSO_ electrolyte. How many kilograms of copper are refined by transfer from the anode to the cathode in a 24.0 $\mathrm{h}$ period?

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Problem 106

How many hours are required to produce $1.00 \times 10^{3} \mathrm{kg}$ of sodium by the electrolysis of molten NaCl with a constant current of $3.00 \times 10^{4} \mathrm{A} ?$ How many liters of $\mathrm{Cl}_{2}$ at STP will be obtained as a byproduct?

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Problem 107

What constant current (in amperes) is required to produce aluminum by the Hall-Heroult process at a rate of 40.0 $\mathrm{kg} / \mathrm{h}$ ?

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Problem 108

Electrolysis of a metal nitrate solution $\mathrm{M}\left(\mathrm{NO}_{3}\right)_{2}(a q)$ for 325 min with a constant current of 20.0 $\mathrm{A}$ gives 111 $\mathrm{g}$ of the metal. Identify the metal ion $\mathrm{M}^{2+}$

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Problem 109

What is the metal ion in a metal nitrate solution $\mathrm{M}\left(\mathrm{NO}_{3}\right)_{3}(a q)$ if 90.52 $\mathrm{g}$ of metal was recovered from a 4.00 $\mathrm{h}$ electrolysis at a constant current of 35.0 $\mathrm{A}$ ?

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Problem 110

Consider a galvanic cell that uses the following half-reactions:
$\mathrm{MnO}_{4}^{-}(a q)+8 \mathrm{H}^{+}(a q)+5 \mathrm{e}^{-} \longrightarrow \mathrm{Mn}^{2+}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l)$
$\mathrm{Sn}^{4+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Sn}^{2+}(a q)$
(a) Write a balanced equation for the overall cell reaction.
(b) What is the oxidizing agent, and what is the reducing agent?
(c) Calculate the standard cell potential.

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Problem 111

Given the following half-reactions and $E^{\circ}$ values,
$\mathrm{Mn}^{3+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Mn}^{2+}(a q) \qquad E^{\circ}=1.54 \mathrm{V}$
$\mathrm{MnO}_{2}(s)+4 \mathrm{H}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Mn}^{3+}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) E^{\circ}=0.95 \mathrm{V}$
write a balanced equation for the formation of $\mathrm{Mn}^{2+}$ and $\mathrm{MnO}_{2}$ from $\mathrm{Mn}^{3+},$ and calculate the value of $E^{\circ}$ for this reaction. Is the reaction spontaneous under standard-state conditions?

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Problem 112

Consider the following half-reactions and values:
$$\begin{array}{ll}{\mathrm{Ag}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(s)} & {E^{\circ}=0.80 \mathrm{V}} \\ {\mathrm{Cu}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Cu}(s)} & {E^{\circ}=0.34 \mathrm{V}} \\ {\mathrm{Pb}^{2}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Pb}(s)} & {E^{\circ}=-0.13 \mathrm{V}}\end{array}$$
(a) Which of these metals or ions is the strongest oxidizing agent? Which is the strongest reducing agent?
(b) The half-reactions can be used to construct three different galvanic cells. Tell which cell delivers the highest voltage, identify the anode and cathode, and tell the direction of electron and ion flow.
(c) Write the cell reaction for part (b), and calculate the val-ues of $E^{\circ}, \Delta G^{\circ}(\text { in kilojoules), and } K \text { for this reaction at }$ $25^{\circ} \mathrm{C}$
(d) Calculate the voltage for the cell in part (b) if both ion concentrations are 0.010 $\mathrm{M} .$

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Problem 113

Standard reduction potentials for the $\mathrm{Pb}^{2+} / \mathrm{Pb}$ and $\mathrm{Cd}^{2+} / \mathrm{Cd}$ half-reactions are $-0.13 \mathrm{V}$ and $-0.40 \mathrm{V},$ respectively. At what relative concentrations of $\mathrm{Pb}^{2+}$ and $\mathrm{Cd}^{2+}$ will these half-reactions have the same reduction potential?

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Problem 114

Consider a galvanic cell that uses the following half-reactions:
$$\begin{array}{l}{2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}(g)} \\ {\mathrm{Al}^{3+}(a q)+3 \mathrm{e}^{-} \longrightarrow \mathrm{Al}(s)}\end{array}$$
(a) What materials are used for the electrodes? Identify the anode and cathode, and indicate the direction of electron and ion flow.
(b) Write a balanced equation for the cell reaction, and calculate the standard cell potential.
(c) Calculate the cell potential at $25^{\circ} \mathrm{C}$ if the ion concentra- tions are 0.10 $\mathrm{M}$ and the partial pressure of $\mathrm{H}_{2}$ is 10.0 atm.
(d) Calculate $\Delta G^{\circ}$ (in kilojoules) and $K$ for the cell reaction at $25^{\circ} \mathrm{C}$ .
(e) Calculate the mass change (in grams) of the aluminum electrode after the cell has supplied a constant current of 10.0 $\mathrm{A}$ for 25.0 $\mathrm{min}$ .

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Problem 115

When the nickel–zinc battery, used in digital cameras, is recharged, the following cell reaction occurs
$$2 \mathrm{Ni}(\mathrm{OH})_{2}(s)+\mathrm{Zn}(\mathrm{OH})_{2}(s) \longrightarrow 2 \mathrm{Ni}(\mathrm{OH})_{3}(s)+\mathrm{Zn}(s)$$:
(a) How many grams of zinc are formed when $3.35 \times 10^{-2} \mathrm{g}$ of $\mathrm{Ni}(\mathrm{OH})_{2}$ are consumed?
(b) How many minutes are required to fully recharge a dead battery that contains $6.17 \times 10^{-2} \mathrm{g}$ of $\mathrm{Zn}$ with a constant current of 0.100 $\mathrm{A}$ ?

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Problem 116

Chlorine can be prepared in the laboratory by the reaction of hydrochloric acid and potassium permanganate.
(a) Use data in Appendix D to write a balanced equation for the reaction. The reduction product is $\mathrm{Mn}^{2+}$
(b) Calculate $E^{\circ}$ and $\Delta G^{\circ}$ for the reaction.
(c) How many liters of $\mathrm{Cl}_{2}$ at 1.0 atm and $25^{\circ} \mathrm{C}$ will result from the reaction of 179 $\mathrm{g} \mathrm{KMnO}_{4}$ with an excess of $\mathrm{HCl}$ ?

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Problem 117

The following cell reactions occur spontaneously:
$$\begin{array}{l}{\mathrm{B}+\mathrm{A}^{+} \longrightarrow \mathrm{B}^{+}+\mathrm{A}} \\ {\mathrm{C}+\mathrm{A}^{+} \longrightarrow \mathrm{C}^{+}+\mathrm{A}} \\ {\mathrm{B}+\mathrm{C}^{+} \longrightarrow \mathrm{B}^{+}+\mathrm{C}}\end{array}$$
(a) Arrange the following reduction half-reactions in order of decreasing tendency to occur: $A^{+}+\mathrm{e}^{-} \rightarrow \mathrm{A}$ $\mathrm{B}^{+}+\mathrm{e}^{-} \rightarrow \mathrm{B},$ and $\mathrm{C}^{+}+\mathrm{e}^{-} \rightarrow \mathrm{C} .$
(b) Which of these substances $\left(\mathrm{A}, \mathrm{A}^{+}, \mathrm{B}, \mathrm{B}^{+}, \mathrm{C}, \mathrm{C}^{+}\right)$ is the strongest oxidizing agent? Which is the strongest reducing agent?
(c) Which of the three cell reactions delivers the highest voltage?

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Problem 118

Consider the following substances: $\mathrm{Fe}(s), \mathrm{PbO}_{2}(s), \mathrm{H}^{+}(a q)$ $\mathrm{Al}(s), \mathrm{Ag}(s), \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)$
(a) Look at the $E^{\circ}$ values in Appendix $D,$ and classify each substance as an oxidizing agent or a reducing agent.
(b) Which is the strongest oxidizing agent? Which is the weakest oxidizing agent?
(c) Which is the strongest reducing agent? Which is the weakest reducing agent?
(d) Which substances can be oxidized by $\mathrm{Cu}^{2+}(a q)$ ? Which can be reduced by $\mathrm{H}_{2} \mathrm{O}_{2}(a q) ?$

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Problem 119

The sodium-sulfur battery has molybdenum electrodes with anode and cathode compartments separated by $\beta$ -alumina, a ceramic through which sodium ions can pass. Because the battery operates at temperatures above $300^{\circ} \mathrm{C},$ all the reactants and products are present in a molten solution. The cell voltage is about 2.0 $\mathrm{V}$ .
(a) What is the cell reaction if the shorthand notation is $\mathrm{Mo}(s)|\mathrm{Na}(s o l n)| \mathrm{Na}^{+}(\mathrm{soln}) \| \mathrm{S}^{2-}(\mathrm{soln}) | \mathrm{Mo}(s) ?$
(b) How many kilograms of sodium are consumed when a 25 $\mathrm{kW}$ sodium-sulfur battery produces current for 32 minutes?

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Problem 120

When suspected drunk drivers are tested with a Breathalyzer, the alcohol (ethanol) in the exhaled breath is oxidized to acetic acid with an acidic solution of potassium dichromate:
$3 \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(a q)+2 \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-(a q)}+16 \mathrm{H}^{+}(a q) \longrightarrow$
$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad 3 \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(a q)+4 \mathrm{Cr}^{3+}(a q)+11 \mathrm{H}_{2} \mathrm{O}(l)$
The color of the solution changes because some of the orange $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}$ is converted to the green $\mathrm{Cr}^{3+}$ . The Breathalyzer measures the color change and produces a meter reading calibrated in blood alcohol content.
(a) What is $E^{\circ}$ for the reaction if the standard half-cell potential for the reduction of acetic acid to ethanol is 0.058 $\mathrm{V}$ ?
(b) What is the value of $E$ for the reaction when the concen- trations of ethanol, acetic acid, $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-},$ and $\mathrm{Cr}^{3+}$ are 1.0 $\mathrm{M}$ and the $\mathrm{pH}$ is 4.00$?$

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Problem 121

Consider the addition of the following half-reactions:
$$\begin{array}{ll}{\text { (1) } \mathrm{Fe}^{3+}(a q)+3 \mathrm{e}^{-} \longrightarrow \mathrm{Fe}(s)} & {E_{1}^{\circ}=-0.04 \mathrm{V}} \\ {\text { (2) } \mathrm{Fe}(s) \longrightarrow \mathrm{Fe}^{2+}(a q)+2 \mathrm{e}^{-}} & {E_{2}^{\circ}=0.45 \mathrm{V}} \\ {\text { (3) } \mathrm{Fe}^{3+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2+}(a q)} & {E_{3}^{\circ}=?}\end{array}$$
(a) Starting with the relationship between $\Delta G^{\circ}$ and $E^{\circ},$ derive a general equation that relates the $E^{\circ}$ values for half-reactions $(1),(2),$ and $(3) .$
(b) Calculate the value of $E_{3}^{\circ}$ for the $\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+} / \mathrm{Fe}^{2+}$ half-reaction.
(c) Explain why the $E^{\circ}$ values would be additive $\left(E_{3}^{\circ}=E_{1}^{\circ}+E_{2}^{\circ}\right)$ if reaction $(3)$ were an overall cell reaction rather than a half-reaction.

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Problem 122

The following galvanic cell has a potential of 0.578 $\mathrm{V}$ at $25^{\circ} \mathrm{C} :$
$$\operatorname{Ag}(s)|\operatorname{Ag} \mathrm{Cl}(s)| \mathrm{Cl}^{-}(1.0 \mathrm{M})| | \mathrm{Ag}^{+}(1.0 \mathrm{M}) | \mathrm{Ag}(s)$$
Use this information to calculate $K_{\mathrm{sp}}$ for $\mathrm{AgCl}$ at $25^{\circ} \mathrm{C}$

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Problem 123

A galvanic cell has a silver electrode in contact with 0.050 $\mathrm{M} \mathrm{AgNO}_{3}$ and a copper electrode in contact with 1.0 $\mathrm{M} \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}$
(a) Write a balanced equation for the cell reaction, and calculate the cell potential at $25^{\circ} \mathrm{C}$ .
(b) Excess $\mathrm{NaBr}(a q)$ is added to the AgNO_ solution to pre- cipitate AgBr. What is the cell potential at $25^{\circ} \mathrm{C}$ after the precipitation of AgBr if the concentration of excess $\mathrm{Br}^{-}$ is 1.0 $\mathrm{M}$ ? Write a balanced equation for the cell reaction under these conditions. $\left(K_{\mathrm{sp}} \text { for AgBr at } 25^{\circ} \mathrm{C} \text { is }\right.$ $5.4 \times 10^{-13}$ )
(c) Use the result in part (b) to calculate the standard reduction potential $E^{\circ}$ for the half-reaction
$$\operatorname{Ag} \operatorname{Br}(s)+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(s)+\mathrm{Br}^{-}(a q)$$

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Problem 124

At one time on Earth, iron was present mostly as iron(II). Later, once plants had produced a significant quantity of oxygen in the atmosphere, the iron became oxidized to iron(III). Show that $\mathrm{Fe}^{2+}(a q)$ can be spontaneously oxidized to Fe $^{3+}(a q)$ by $\mathrm{O}_{2}(g)$ at $25^{\circ} \mathrm{C}$ assuming the following reasonable environmental conditions: [Fe $^{2+} ]=\left[\mathrm{Fe}^{3+}\right]=$ $1 \times 10^{-7} \mathrm{M} ; \mathrm{pH}=7.0 ; P_{\mathrm{O}_{2}}=160 \mathrm{mm} \mathrm{Hg}$

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Problem 125

Given the following standard reduction potentials at $25^{\circ} \mathrm{C}$ , (a) balance the equation for the reaction of $\mathrm{H}_{2} \mathrm{MoO}_{4}$ with elemental arsenic in acidic solution to give $\mathrm{Mo}^{3+}$ and $\mathrm{H}_{3} \mathrm{AsO}_{4}$ and (b) calculate $E^{\circ}$ for this reaction.
$\overline{\mathrm{H}_{3} \mathrm{AsO}_{4}(a q)+2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{3} \mathrm{AsO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+0.560}$
$\mathrm{H}_{3} \mathrm{AsO}_{3}(a q)+3 \mathrm{H}^{+}(a q)+3 \mathrm{e}^{-} \longrightarrow \mathrm{As}(s)+3 \mathrm{H}_{2} \mathrm{O}(l) \quad+0.240$
$\mathrm{H}_{2} \mathrm{MoO}_{4}(a q)+2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{MoO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)+0.646$
$\mathrm{MoO}_{2}(s)+4 \mathrm{H}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Mo}^{3+}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \quad+0.008$

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Problem 126

The following galvanic cell has a potential of 1.214 $\mathrm{V}$ at $25^{\circ} \mathrm{C} :$
$\begin{aligned} \operatorname{Hg}(l)\left|\mathrm{Hg}_{2} \mathrm{Br}_{2}(s)\right| \mathrm{Br}^{-}(0.10 \mathrm{M})| | \mathrm{MnO}_{4}^{-}(0.10 \mathrm{M}) \\ & \mathrm{Mn}^{2+}(0.10 \mathrm{M}), \mathrm{H}^{+}(0.10 \mathrm{M}) | \mathrm{Pt}(s) \end{aligned}$
Calculate the value of $K_{\mathrm{sp}}$ for $\mathrm{Hg}_{2} \mathrm{Br}_{2}$ at $25^{\circ} \mathrm{C}$

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Problem 127

For the following half-reaction, $E^{\circ}=1.103 \mathrm{V} :$
$$\mathrm{Cu}^{2+}(a q)+2 \mathrm{CN}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Cu}(\mathrm{CN})_{2}^{-}(a q)$$
Calculate the formation constant $K_{f}$ for $\mathrm{Cu}(\mathrm{CN})_{2}$ .

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Problem 128

Accidentally chewing on a stray fragment of aluminum foil can cause a sharp tooth pain if the aluminum comes in contact with an amalgam filling. The filling, an alloy of silver, tin, and mercury, acts as the cathode of a tiny galvanic cell, the aluminum behaves as the anode, and saliva serves as the electrolyte. When the aluminum and the filling come in contact, an electric current passes from the aluminum to the filling, which is sensed by a nerve in the tooth. Aluminum is oxidized at the anode, and $\mathrm{O}_{2}$ gas is reduced to water at the cathode.
(a) Write balanced equations for the anode, cathode, and overall cell reactions.
(b) Write the Nernst equation in a form that applies at body temperature $\left(37^{\circ} \mathrm{C}\right)$
(c) Calculate the cell voltage at $37^{\circ} \mathrm{C}$ . You may assume that $\left[\mathrm{Al}^{3+}\right]=1.0 \times 10^{-9} \mathrm{M}, P_{\mathrm{O}_{2}}=0.20 \mathrm{atm},$ and that saliva has a pH of 7.0 . Also assume that the $E^{\circ}$ values in Appendix D apply at $37^{\circ} \mathrm{C}$ .

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Problem 129

Copper reduces dilute nitric acid to nitric oxide (NO) but reduces concentrated nitric acid to nitrogen dioxide (NO2):
$\begin{aligned}(1) 3 \mathrm{Cu}(s)+2 \mathrm{NO}_{3}(a q)+& 8 \mathrm{H}^{+}(a q) \longrightarrow \\ & 3 \mathrm{Cu}^{2+}(a q)+2 \mathrm{NO}(g)+4 \mathrm{H}_{2} \mathrm{O}(l) \quad E^{\circ}=0.62 \mathrm{V} \end{aligned}$
$\begin{array}{l}{\text { (2) } \mathrm{Cu}(s)+2 \mathrm{NO}_{3}(a q)+4 \mathrm{H}^{+}(a q) \longrightarrow} \\ {\quad \qquad\qquad\qquad\qquad\qquad \mathrm{Cu}^{2+}(a q)+2 \mathrm{NO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \quad E^{\circ}=0.45 \mathrm{V}}\end{array} $
Assuming that $\left[\mathrm{Cu}^{2+}\right]=0.10 \mathrm{M}$ and that the partial pres- sures of $\mathrm{NO}$ and $\mathrm{NO}_{2}$ are $1.0 \times 10^{-3}$ atm, calculate the potential $(E)$ for reactions $(1)$ and $(2)$ at $25^{\circ} \mathrm{C}$ and show which reaction has the greater thermodynamic tendency to occur when the concentration of $\mathrm{HNO}_{3}$ is
(a) 1.0 $\mathrm{M}$
(b) 10.0 $\mathrm{M}$
(c) At what $\mathrm{HNO}_{3}$ concentration do reactions (1) and (2) have the same value of $E$ ?

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Problem 130

Adiponitrile, a key intermediate in the manufacture of nylon, is made industrially by an electrolytic process that reduces acrylonitrile:
Anode (oxidation): $\quad 2 \mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{O}_{2}+4 \mathrm{H}^{+}+4 \mathrm{e}^{-}$
Cathode (reduction):
$$2 \mathrm{CH}_{2}=\mathrm{CHCN}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{NC}\left(\mathrm{CH}_{2}\right)_{4} \mathrm{CN}$$
(a) Write a balanced equation for the overall cell reaction.
(b) How many kilograms of adiponitrile are produced in 10.0 $\mathrm{h}$ in a cell that has a constant current of $3.00 \times 10^{3} \mathrm{A}$ ?
(c) How many liters of $\mathrm{O}_{2}$ at 740 $\mathrm{mm} \mathrm{Hg}$ and $25^{\circ} \mathrm{C}$ are produced as a byproduct?

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Problem 131

The reaction of MnO - with oxalic acid $\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)$ in acidic solution, yielding $\mathrm{Mn}^{2+}$ and $\mathrm{CO}_{2}$ gas, is widely used to determine the concentration of permanganate solutions:
(a) Write a balanced net ionic equation for the reaction.
(b) Use the data in Appendix D to calculate $E^{\circ}$ for the reaction.
(c) Show that the reaction goes to completion by calculating the values of $\Delta G^{\circ}$ and $K$ at $25^{\circ} \mathrm{C} .$
(d) A 1.200 g sample of sodium oxalate (Na_ $\mathrm{C}_{2} \mathrm{O}_{4} )$ is dissolved in dilute $\mathrm{H}_{2} \mathrm{SO}_{4}$ and then titrated with a $\mathrm{KMnO}_{4}$solution. If
32.50 $\mathrm{mL}$ of the KMnO $_{4}$ solution is required to reach the equivalence point, what is the molarity of the KMnO_ solution?

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Problem 132

Calculate the standard reduction potential for $\mathrm{Ba}^{2+}(a q)+2 \mathrm{e}^{-} \rightarrow \mathrm{Ba}(s)$ given that $\Delta G^{\circ}=16.7 \mathrm{kJ}$ for the reaction $\mathrm{Ba}^{2+}(a q)+2 \mathrm{Cl}^{-}(a q) \rightarrow \mathrm{BaCl}_{2}(s) .$ Use any data needed from Appendixes B and D.

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Problem 133

A concentration cell has the same half-reactions at the anode and cathode, but a voltage results from different concentrations in the two electrode compartments.
(a) What is $x$ in the concentration cell $\mathrm{Cu}(s) | \mathrm{Cu}^{2+}(x \mathrm{M}) \|$ $\mathrm{Cu}^{2+}(0.10 \mathrm{M}) \mathrm{Cu}(s)$ if the measured cell potential is 0.0965 $\mathrm{V}$ ?
(b) A similar cell has 0.10 $\mathrm{M} \mathrm{Cu}^{2+}$ in both compartments. When a stoichiometric amount of ethylenediamine $\left(\mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)$ is added to one compartment, the measured cell potential is 0.179 V. Calculate the formation constant $K_{\mathrm{f}}$ for the complex ion $\mathrm{Cu}\left(\mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)_{2}^{2+}$ . Assume there is no volume change.

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Problem 134

Consider the redox titration (Section 4.10$)$ of 120.0 $\mathrm{mL}$ of 0.100 $\mathrm{M} \mathrm{FeSO}_{4}$ with 0.120 $\mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$ at $25^{\circ} \mathrm{C},$ assuming that the pH of the solution is maintained at 2.00 with a suit- - able buffer. The solution is in contact with a platinum electrode and constitutes one half-cell of an electrochemical cell. The other half-cell is a standard hydrogen electrode. The two half-cells are connected with a wire and a salt bridge, and the progress of the titration is monitored by measuring the cell potential with a voltmeter.
(a) Write a balanced net ionic equation for the titration reaction, assuming that the products are $\mathrm{Fe}^{3+}$ and $\mathrm{Cr}^{3+}$
(b) What is the cell potential at the equivalence point?

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Problem 135

Consider the reaction that occurs in the hydrogen–oxygen fuel cell:
$$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)$$
(a) Use the thermodynamic data in Appendix $\mathrm{B}$ to calcu- late the values of $\Delta G^{\circ}$ and $E^{\circ}$ at $95^{\circ} \mathrm{C},$ assuming that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are independent of temperature.
(b) Calculate the cell voltage at $95^{\circ} \mathrm{C}$ when the partial pressures of $\mathrm{H}_{2}$ and $\mathrm{O}_{2}$ are 25 $\mathrm{atm} .$

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Problem 136

Consider a galvanic cell that utilizes the following half-reactions:
$\begin{array}{ll}{\text { Anode: }} & {\mathrm{Zn}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{ZnO}(s)+2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-}} \\ {\text { Cathode: }} & {\mathrm{Ag}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(s)}\end{array}$
(a) Write a balanced equation for the cell reaction, and use the thermodynamic data in Appendix $\mathrm{B}$ to calculate the values of $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ for the reaction.
(b) What are the values of $E^{\circ}$ and the equilibrium constant $K$ for the cell reaction at $25^{\circ} \mathrm{C} ?$
(c) What happens to the cell voltage if aqueous ammonia is added to the cathode compartment? Calculate the cell voltage assuming that the solution in the cathode compartment was prepared by mixing 50.0 $\mathrm{mL}$ of 0.100 $\mathrm{M} \mathrm{AgNO}_{3}$ and 50.0 $\mathrm{mL}$ of 4.00 $\mathrm{M} \mathrm{NH}_{3}$
(d) Will AgCl precipitate if 10.0 $\mathrm{mL}$ of 0.200 $\mathrm{M} \mathrm{NaCl}$ is added to the solution in part (c)? Will AgBr precipitate if 10.0 $\mathrm{mL}$ of 0.200 $\mathrm{M} \mathrm{KBr}$ is added to the resulting solution?

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Problem 137

The nickel-iron battery has an iron anode, an NiO(OH) cathode, and a KOH electrolyte. This battery uses the following half-reactions and has an $E^{\circ}$ value of 1.37 $\mathrm{V}$ at $25^{\circ} \mathrm{C} :$
(a) Write a balanced equation for the cell reaction.
(b) Calculate $\Delta G^{\circ}$ (in kilojoules) and the equilibrium constant $K$ for the cell reaction at $25^{\circ} \mathrm{C} .$
(c) What is the cell voltage at $25^{\circ} \mathrm{C}$ when the concentration of $\mathrm{KOH}$ in the electrolyte is 5.0 $\mathrm{M}$ ?
(d) How many grams of Fe(OH) 2 are formed at the anode when the battery produces a constant current of 0.250 $\mathrm{A}$ for 40.0 $\mathrm{min}$ ? How many water molecules are consumed in the process?

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Problem 138

Experimental solid-oxide fuel cells that use butane $\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)$ as the fuel have been reported recently. These cells contain composite metal/metal oxide electrodes and a solid metal oxide electrolyte. The cell half-reactions are
Anode: $\mathrm{C}_{4} \mathrm{H}_{10}(g)+13 \mathrm{O}^{2-}(s) \longrightarrow 4 \mathrm{CO}_{2}(g)+5 \mathrm{H}_{2} \mathrm{O}(l)+26 \mathrm{e}^{-}$
Cathode: $\quad \mathrm{O}_{2}(g)+4 \mathrm{e}^{-} \longrightarrow 2 \mathrm{O}^{2-}(s)$
(a) Write a balanced equation for the cell reaction.
(b) Use the thermodynamic data in Appendix $\mathrm{B}$ to calculate the values of $E^{\circ}$ and the equilibrium constant $K$ for the cell reaction at $25^{\circ} \mathrm{C} .$ Will $E^{\circ}$ and $K$ increase, decrease, or remain the same on raising the temperature?
(c) How many grams of butane are required to produce a constant current of 10.5 $\mathrm{A}$ for 8.00 $\mathrm{h} ?$ How many liters of gaseous butane at $20^{\circ} \mathrm{C}$ and 815 $\mathrm{mm}$ Hg pressure are required?

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Problem 139

The half-reactions that occur in ordinary alkaline batteries can be written as
$\begin{array}{ll}{\text { Cathode: }} & {\mathrm{MnO}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{e}^{-} \longrightarrow \mathrm{MnO}(\mathrm{OH})(\mathrm{s})+\mathrm{OH}^{-}(a q)} \\ {\text { Anode: }} & {\mathrm{Zn}(\mathrm{s})+2 \mathrm{OH}^{-(a q)} \longrightarrow \mathrm{Zn}(\mathrm{OH})_{2}(s)+2 \mathrm{e}^{-}}\end{array}$
In 1999 , researchers in Israel reported a new type of alka- line battery, called a "super-iron" battery. This battery uses the same anode reaction as an ordinary alkaline battery but involves the reduction of FeO $_{4}^{2-}$ ion (from $\mathrm{K}_{2} \mathrm{FeO}_{4} )$ to solid $\mathrm{Fe}(\mathrm{OH})_{3}$ at the cathode.
(a) Use the following standard reduction potential and any data from Appendixes $\mathrm{C}$ and $D$ to calculate the standard cell potential expected for an ordinary alkaline battery:
$\mathrm{MnO}(\mathrm{OH})(s)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{e}^{-} \longrightarrow \mathrm{Mn}(\mathrm{OH})_{2}(s)+\mathrm{OH}^{-}(a q)$
$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad E^{\circ}=-0.380 \mathrm{V}$
(b) Write a balanced equation for the cathode half-reaction in a super-iron battery. The half-reaction occurs in a basic environment.
(c) A super-iron battery should last longer than an ordi- nary alkaline battery of the same size and weight because its cattery can provide more charge per unit mass. Quantitatively compare the number of coulombs of charge released by the reduction of 10.0 $\mathrm{g}$ of $\mathrm{K}_{2} \mathrm{FeO}_{4}$ to $\mathrm{Fe}(\mathrm{OH})_{3}$ with the number of coulombs of $\mathrm{MnO}_{2}$ to $\mathrm{MnO}(\mathrm{OH})$

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Problem 140

Gold metal is extracted from its ore by treating the crushed rock with an aerated cyanide solution. The unbalanced equation for the reaction is
$$\mathrm{Au}(s)+\mathrm{CN}^{-}(a q)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{Au}(\mathrm{CN})_{2}^{-}(a q)$$
(a) Balance the equation for this reaction in basic solution.
(b) Use any of the following data at $25^{\circ} \mathrm{C}$ to calculate $\Delta G^{\circ}$ for this reaction at $25^{\circ} \mathrm{C} : K_{\mathrm{f}}$ for $\mathrm{Au}(\mathrm{CN})_{2}=6.2 \times 10^{38}$ $K_{\mathrm{a}}$ for $\mathrm{HCN}=4.9 \times 10^{-10},$ and standard reduction potentials are
$$\begin{aligned} \mathrm{O}_{2}(g)+4 \mathrm{H}^{+}(a q)+4 \mathrm{e}^{-} \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) & E^{\circ}=1.229 \mathrm{V} \\ \mathrm{Au}^{3+}(a q)+3 \mathrm{e}^{-} \longrightarrow \mathrm{Au}(s) & E^{\circ}=1.498 \mathrm{V} \\ \mathrm{Au}^{3+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Au}^{+}(a q) & E^{\circ}=1.401 \mathrm{V} \end{aligned}$$

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Problem 141

Consider the redox titration of 100.0 $\mathrm{mL}$ of a solution of 0.010 $\mathrm{M} \mathrm{Fe}^{2+}$ in 1.50 $\mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}$ with a 0.010 $\mathrm{M}$ solution of $\mathrm{KMnO}_{4}$ yielding $\mathrm{Fe}^{3+}$ and $\mathrm{Mn}^{2+} .$ The titration is carried out in an electrochemical cell equipped with a platinum electrode and a calomel reference electrode consisting of an $\mathrm{Hg}_{2} \mathrm{Cl}_{2} / \mathrm{Hg}$ electrode in contact with a saturated $\mathrm{KCl}$ solution having $[\mathrm{Cl}]=2.9 \mathrm{M} .$ Using any data in Appendixes $\mathrm{C}$ and $\mathrm{D},$ calculate the cell potential after addition of (a) $5.0 \mathrm{mL},$ (b) 10.0 $\mathrm{mL}$ (c) 19.0 $\mathrm{mL}$ , and (d) 21.0 $\mathrm{mL}$ of the $\mathrm{KMnO}_{4}$ solution.

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