# CHEMISTRY: The Molecular Nature of Matter and Change 2016

## Educators

### Problem 1

Define oxidation and reduction in terms of electron transfer
and change in oxidation number.

Ahmed A.

### Problem 2

Why must an electrochemical process involve a redox reaction?

Ahmed A.

### Problem 3

Can one half-reaction in a redox process take place independently of the other? Explain.

Ahmed A.

### Problem 4

Water is used to balance O atoms in the half-reaction method. Why can't $\mathrm{O}^{2-}$ ions be used instead?

Ahmed A.

### Problem 5

During the redox balancing process, what step is taken to ensure that $\mathrm{e}^{-}$ loss equals $\mathrm{e}^{-}$ gain?

Ahmed A.

### Problem 6

How are protons removed when balancing a redox reaction in basic solution?

Ahmed A.

### Problem 7

Are spectator ions used to balance the half-reactions of a redox reaction? At what stage might spectator ions enter the balancing process?

Ahmed A.

### Problem 8

Which type of electrochemical cell has $\Delta G_{\text { sys }}<0 ?$ Which type shows an increase in free energy?

Ahmed A.

### Problem 9

Which statements are true? Correct any that are false.
(a) In a voltaic cell, the anode is negative relative to the cathode.
(b) Oxidation occurs at the anode of a voltaic or electrolytic cell.
(c) Electrons flow into the cathode of an electrolytic cell.
(d) In a voltaic cell, the surroundings do work on the system.
(e) A metal that plates out of an electrolytic cell appears on the
cathode.
(f) In an electrochemical cell, the electrolyte provides a solution
of mobile electrons.

Ahmed A.

### Problem 10

Consider the following balanced redox reaction:
\begin{aligned} 16 \mathrm{H}^{+}(a q)+2 \mathrm{MnO}_{4}^{-}(a q)+& 10 \mathrm{Cl}^{-}(a q) \longrightarrow \\ & 2 \mathrm{Mn}^{2+}(a q)+5 \mathrm{Cl}_{2}(g)+8 \mathrm{H}_{2} \mathrm{O}(l) \end{aligned}
(a) Which species is being oxidized?
(b) Which species is being reduced?
(c) Which species is the oxidizing agent?
(d) Which species is the reducing agent?
(e) From which species to which does electron transfer occur?
(f) Write the balanced molecular equation, with $\mathrm{K}^{+}$ and $\mathrm{SO}_{4}^{2-}$
the spectator ions.

Ahmed A.

### Problem 11

Consider the following balanced redox reaction
\begin{aligned} 2 \mathrm{CrO}_{2}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)+& 6 \mathrm{ClO}^{-}(a q) \longrightarrow \\ & 2 \mathrm{CrO}_{4}^{2-}(a q)+3 \mathrm{Cl}_{2}(g)+4 \mathrm{OH}^{-}(a q) \end{aligned}
(a) Which species is being oxidized?
(b) Which species is being reduced?
(c) Which species is the oxidizing agent?
(d) Which species is the reducing agent?
(e) From which species to which does electron transfer occur?
(f) Write the balanced molecular equation, with Na' $^{2}$ the
spectator ion.

Ahmed A.

### Problem 12

Balance the following skeleton reactions and identify the oxidizing and reducing agents:
(a) $\mathrm{O}_{2}(g)+\mathrm{NO}(g) \longrightarrow \mathrm{NO}_{3}^{-(a q)}[\text { acidic }]$
(b) $\mathrm{CrO}_{4}^{2-}(a q)+\mathrm{Cu}(s) \longrightarrow \mathrm{Cr}(\mathrm{OH})_{3}(s)+\mathrm{Cu}(\mathrm{OH})_{2}(s)[\text { basic }]$
(c) $\mathrm{AsO}_{4}^{3-}(a q)+\mathrm{NO}_{2}^{-}(a q) \longrightarrow$ $\mathrm{AsO}_{2}^{-}(a q)+\mathrm{NO}_{3}^{-}(a q)[\mathrm{basic}]$

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### Problem 12

The overall cell reaction occurring in an alkaline battery is
$$\mathrm{Zn}(s)+\mathrm{MnO}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{ZnO}(s)+\mathrm{Mn}(\mathrm{OH})_{2}(s)$$
(a) How many moles of electrons flow per mole of reaction?
(b) If 4.50 $\mathrm{g}$ of zinc is oxidized, how many grams of manganese dioxide and of water are consumed?
(c) What is the total mass of reactants consumed in part (b)?
(d) How many coulombs are produced in part (b)?
(e) In practice, voltaic cells of a given capacity (coulombs) are heavier than the calculation in part(c) indicates. Explain.

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### Problem 13

Balance the following skeleton reactions and identify the oxidizing and reducing agents:
(a) $\mathrm{O}_{2}(g)+\mathrm{NO}(g) \longrightarrow \mathrm{NO}_{3}^{-}(a q)[\text { acidic }]$(b) $\mathrm{CrO}_{4}^{2-}(a q)+\mathrm{Cu}(s) \longrightarrow \mathrm{Cr}(\mathrm{OH})_{3}(b)+\mathrm{Cu}(\mathrm{OH})_{2}(s)[\text { basic }]$
(c) $\mathrm{AsO}_{4}^{3-}(a q)+\mathrm{NO}_{2}^{-(a q)} \longrightarrow_{\mathrm{AsO}_{2}^{-}(a q)+\mathrm{NO}_{3}^{-}(a q)[\text { basic }]}$

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### Problem 14

Balance the following skeleton reactions and identify the oxidizing and reducing agents:
(a) $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{Zn}(s) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{Cr}^{3+}(a q)$ [acidic]
(b) $\mathrm{Fe}(\mathrm{OH})_{2}(s)+\mathrm{ MnO}_{4}^{-}(a q) \longrightarrow$ $\mathrm{MnO}_{2}(s)+\mathrm{Fe}(\mathrm{OH})_{3}(s)[\mathrm{basic}]$
(c) $\operatorname{Zn}(s)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{N}_{2}(g)[\text { acidic }]$

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### Problem 15

Balance the following skeleton reactions and identify the oxidizing and reducing agents:
(a) $\mathrm{BH}_{4}^{-}(a q)+\mathrm{ClO}_{3}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{BO}_{3}^{-}(a q)+\mathrm{Cl}^{-}(a q)[\mathrm{basic}]$
(b) $\mathrm{CrO}_{4}^{2-}(a q)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{NO}(g)[\text { acidic }]$
(c) $\mathrm{Br}_{2}(l) \longrightarrow \mathrm{BrO}_{3}^{-}(a q)+\mathrm{Br}^{-}(a q)[\text { basic }]$

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### Problem 16

Balance the following skeleton reactions and identify the oxidizing and reducing agents:
(a) $\mathrm{Sb}(s)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{Sb}_{4} \mathrm{O}_{6}(s)+\mathrm{NO}(g)[\text { acidic }]$
(b) $\operatorname{Mn}^{2+}(a q)+\operatorname{Bi} \mathrm{O}_{3}^{-}(a q) \longrightarrow$ $\mathrm{MnO}_{4}^{-}(a q)+\mathrm{Bi}^{3+}(a q)[\text { acidic }]$
(c) $\mathrm{Fe}(\mathrm{OH})_{2}(s)+\mathrm{Pb}(\mathrm{OH})_{3}^{-}(a q) \longrightarrow$ $\mathrm{Fe}(\mathrm{OH})_{3}(s)+\mathrm{Pb}(s)[\text { basic }]$

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### Problem 17

Balance the following skeleton reactions and identify the oxidizing and reducing agents:
(a) $\mathrm{NO}_{2}(g) \longrightarrow \mathrm{NO}_{3}^{-}(a q)+\mathrm{NO}_{2}^{-}(a q)[\text { basic }]$
(b) $\mathrm{Zn}(s)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{Zn}(\mathrm{OH})_{4}^{2-}(a q)+\mathrm{NH}_{3}(g)[\text { basic }]$
(c) $\mathrm{H}_{2} \mathrm{S}(g)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{S}_{8}(s)+\mathrm{NO}(g)[\text { acidic }]$

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### Problem 18

Balance the following skeleton reactions and identify the oxidizing and reducing agents:
(a) $\mathrm{As}_{4} \mathrm{O}_{6}(s)+\mathrm{MnO}_{4}^{-}(a q) \longrightarrow$ $\mathrm{AsO}_{4}^{3-}(a q)+\mathrm{Mn}^{2+}(a q)[\text { acidic }]$
(b) $\mathrm{P}_{4}(s) \longrightarrow \mathrm{HPO}_{3}^{2-}(a q)+\mathrm{PH}_{3}(g)[\text { acidic }]$
(c) $\mathrm{MnO}_{4}^{-}(a q)+\mathrm{CN}^{-}(a q) \longrightarrow \mathrm{MnO}_{2}(s)+\mathrm{CNO}^{-}(a q)[\text { basic }]$

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### Problem 19

Balance the following skeleton reactions and identify the oxidizing and reducing agents:
(a) $\mathrm{SO}_{3}^{2-}(a q)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SO}_{4}^{2-}(a q)+\mathrm{Cl}^{-}(a q)[\text { basic }]$
(b) $\mathrm{Fe}(\mathrm{CN})_{6}^{3-}(a q)+\operatorname{Re}(s) \longrightarrow$ $\mathrm{Fe}(\mathrm{CN})_{6}^{4-}(a q)+\mathrm{ReO}_{4}^{-}(a q)[\mathrm{basic}]$
(c) $\operatorname{Mn} \mathrm{O}_{4}^{-}(a q)+\mathrm{HCOOH}(a q) \longrightarrow$ $\mathrm{Mn}^{2+}(a q)+\mathrm{CO}_{2}(g)[\text { acidic }]$

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### Problem 20

In many residential water systems, the aqueous Fe $^{3+} \mathrm{concentration}$ is high enough to stain sinks and turn drinking water light brown. The iron content is analyzed by first reducing the
$\mathrm{Fe}^{3+}$ to $\mathrm{Fe}^{2+}$ and then titrating with MnO $_{4}-$ in acidic solution.
Balance the skeleton reaction of the titration step:
$$\mathrm{Fe}^{2+}(a q)+\mathrm{MnO}_{4}^{-}(a q) \longrightarrow \mathrm{Mn}^{2+}(a q)+\mathrm{Fe}^{3+}(a q)$$

Ahmed A.

### Problem 21

Aqua regia, a mixture of concentrated $\mathrm{HNO}_{2}$ and $\mathrm{HCl}$ , was developed by alchemists as a means to "dissolve" gold. The process is a redox reaction with this simplified skeleton reaction:
$$\mathrm{Au}(s)+\mathrm{NO}_{3}^{-}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{AuCl}_{4}^{-}(a q)+\mathrm{NO}_{2}(g)$$
(a) Balance the reaction by the half-reaction method.
(b) What are the oxidizing and reducing agents?
(c) What is the function of $\mathrm{HCl}$ in aqua regia?

Ahmed A.

### Problem 22

Consider the following general voltaic cell:
Identify the following:
(a) Anode
(b) Cathode
(c) Salt bridge
(d) Electrode from which e- leave the cell
(e) Electrode with a positive charge
(f) Electrode that gains mass as the cell operates (assuming that a
metal plates out)

Ahmed A.

### Problem 23

Why does a voltaic cell not operate unless the two compartments are connected through an external circuit?

Ahmed A.

### Problem 24

What purpose does the salt bridge serve in a voltaic cell, and how does it accomplish this purpose?

Ahmed A.

### Problem 25

What is the difference between an active and an inactive electrode? Why are inactive electrodes used? Name two substances commonly used for inactive electrodes.

Ahmed A.

### Problem 26

When a piece of metal A is placed in a solution containing
ions of metal B, metal B plates out on the piece of A.
(a) Which metal is being oxidized?
(b) Which metal is being displaced?
(c) Which metal would you use as the anode in a voltaic cell
incorporating these two metals?
(d) If bubbles of $\mathrm{H}_{2}$ form when $\mathrm{B}$ is placed in acid, will they form
if $\mathrm{A}$ is placed in acid? Explain.

Ahmed A.

### Problem 27

Consider the following voltaic cell:
(a) In which direction do electrons flow in the external circuit?
(b) In which half-cell does oxidation occur?
(c) In which half-cell do electrons enter the cell?
(d) At which electrode are electrons consumed?
(e) Which electrode is negatively charged?
(f) Which electrode decreases in mass during cell operation?
(g) Suggest a solution for the electrolyte in the cathode
compartment.
(h) Suggest a pair of ions for the salt bridge.
(i) For which electrode could you use an inactive material?
(j) In which direction do anions within the salt bridge move to
maintain charge neutrality?
(k) Write balanced half-reactions and the overall cell reaction.

Ahmed A.

### Problem 28

Consider the following voltaic cell:
(a) In which direction do electrons flow in the external circuit?
(b) In which half-cell does reduction occur?
(c) In which half-cell do electrons leave the cell?
(d) At which electrode are electrons generated?
(e) Which electrode is positively charged?
(f) Which electrode increases in mass during cell operation?
(g) Suggest a solution you can use as the electrolyte in the anode
compartment.
(h) Suggest a pair of ions for the salt bridge.
(i) For which electrode could you use an inactive material?
(j) In which direction do cations within the salt bridge move to
maintain charge neutrality?
(k) Write balanced half-reactions and the overall cell reaction.

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### Problem 29

A voltaic cell is constructed with an $\mathrm{Sn} / \mathrm{Sn}^{2+}$ half-cell and a Zn/Zn'+ half-cell. The zinc electrode is negative.
(a) Write balanced half-reactions and the overall cell reaction.
(b) Diagram the cell, labeling electrodes with their charges and showing the directions of electron flow in the circuit and of cation and anion flow in the salt bridge.

Ahmed A.

### Problem 30

A voltaic cell is constructed with an Ag/Ag $^{+}$ half-cell and a Pb/Pb ^{2+} half-cell. The silver electrode is positive.
(a) Write balanced half-reactions and the overall cell reaction.
(b) Diagram the cell, labeling electrodes with their charges and showing the directions of electron flow in the circuit and of cation and anion flow in the salt bridge.

Ahmed A.

### Problem 31

A voltaic cell is constructed with an Fe/Fe $^{2+}$ half-cell and an $\mathrm{Mn} / \mathrm{Mn}^{2+}$ half-cell. The iron electrode is positive.
(a) Write balanced half-reactions and the overall cell reaction.
(b) Diagram the cell, labeling electrodes with their charges and showing the directions of electron flow in the circuit and of cation and anion flow in the salt bridge.

Ahmed A.

### Problem 32

A voltaic cell is constructed with a $\mathrm{Cu} / \mathrm{Cu}^{2+}$ half-cell and an $\mathrm{Ni} / \mathrm{Ni}^{2+}$ half-cell. The nickel electrode is negative.
(a) Write balanced half-reactions and the overall cell reaction.
(b) Diagram the cell, labeling electrodes with their charges and
showing the directions of electron flow in the circuit and of cation
and anion flow in the salt bridge.

Ahmed A.

### Problem 33

Write the cell notation for the voltaic cell that incorporates
each of the following reactions:
(a) All(s) $+\mathrm{Cr}^{3+}(a q) \longrightarrow \mathrm{Al}^{3+}(a q)+\mathrm{Cr}(s)$
(b) $\mathrm{Cu}^{2+}(a q)+\mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow$

$$\mathrm{Cu}(s)+\mathrm{SO}_{4}^{2-}(a q)+4 \mathrm{H}^{+}(a q)$$

Ahmed A.

### Problem 34

Write a balanced equation from each cell notation:
(a) $\operatorname{Mn}(s)\left|\mathrm{Mn}^{2+}(a q) \| \mathrm{Cd}^{2+}(a q)\right| \mathrm{Cd}(s)$
(b) Fe(s) $\left|\mathrm{Fe}^{2+}(a q) \| \mathrm{NO}_{3}^{-}(a q)\right| \mathrm{NO}(g) | \mathrm{Pt}(s)$

Ahmed A.

### Problem 35

How is a standard reference electrode used to determine unknown $E_{\text { half-cell values? }}^{\circ}$ values?

Ahmed A.

### Problem 36

What does a negative $E_{\text { cell }}^{\circ}$ indicate about a redox reaction? What does it indicate about the reverse reaction?

Ahmed A.

### Problem 37

The standard cell potential is a thermodynamic state function. How are $E^{\circ}$ values treated similarly to $\Delta H^{\circ}, \Delta G^{\circ},$ and $S^{\circ}$ values? How are they treated differently?

Ahmed A.

### Problem 38

In basic solution, $\mathrm{Se}^{2-}$ and $\mathrm{SO}_{3}^{2-}$ ions react spontaneously:
$$\begin{array}{l}{2 \mathrm{Se}^{2-}(a q)+2 \mathrm{SO}_{3}^{2-}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow} \\ {2 \mathrm{Se}(s)+6 \mathrm{OH}^{-}(a q)+\mathrm{S}_{2} \mathrm{O}_{3}^{2-}(a q) \quad E_{\mathrm{cell}}^{\circ}=0.35 \mathrm{V}}\end{array}$$
(a) Write balanced half-reactions for the process.
(b) If $E_{\text { sulfite }}^{\circ}$ is $-0.57 \mathrm{V},$ calculate $E_{\text { selenium }}^{\circ} .$

Ahmed A.

### Problem 39

In acidic solution, $\mathrm{O}_{3}$ and $\mathrm{Mn}^{2+}$ ions react spontaneously:
$$\begin{array}{c}{\mathrm{O}_{3}(g)+\mathrm{Mn}^{2+}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow} \\ {\qquad \mathrm{O}_{2}(g)+\mathrm{MnO}_{2}(s)+2 \mathrm{H}^{+}(a q)} & {E_{\mathrm{cell}}^{\circ}=0.84 \mathrm{V}}\end{array}$$
(a) Write the balanced half-reactions.
(b) Using Appendix D to find $E_{\text { ozone }}^{\circ}$ calculate $E_{\text { manganese }}^{\circ}$

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### Problem 40

Use the emf series (Appendix D) to arrange the species.
(a) In order of decreasing strength as oxidizing agents: $\mathrm{Fe}^{3+}, \mathrm{Br}_{2}$
$\mathrm{Cu}^{2+}$
(b) In order of increasing strength as oxidizing agents: $\mathrm{Ca}^{2+}$ ,
$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}, \mathrm{Ag}^{+}$

Ahmed A.

### Problem 41

Use the emf series (Appendix D) to arrange the species.
(a) In order of decreasing strength as reducing agents: $\mathrm{SO}_{2}$
PbSO, $\mathrm{MnO}_{2}$
(b) In order of increasing strength as reducing agents: Hg, Fe, Sn

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### Problem 42

Balance each skeleton reaction, use Appendix D to calculate $E_{\text { cell }}^{\circ}$ and state whether the reaction is spontaneous:
(a) $\mathrm{Co}(s)+\mathrm{H}^{+}(a q) \longrightarrow \mathrm{Co}^{2+}(a q)+\mathrm{H}_{2}(g)$
(b) $\mathrm{Hg}_{2}^{2+}(a q) \longrightarrow \mathrm{Hg}^{2+}(a q)+\mathrm{Hg}(l)$

Ahmed A.

### Problem 43

Balance each skeleton reaction, use Appendix $D$ to calculate $E_{\text { cll }}^{\circ}$ and state whether the reaction is spontaneous:
(a) $\operatorname{Mn}^{2+}(a q)+\mathrm{Co}^{3+}(a q) \longrightarrow \mathrm{MnO}_{2}(s)+\mathrm{Co}^{2+}(a q)[\text { acidic }]$
(b) $\mathrm{AgCl}(s)+\mathrm{NO}(g) \longrightarrow$
$\mathrm{Ag}(s)+\mathrm{Cl}^{-}(a q)+\mathrm{NO}_{3}^{-}(a q)[\text { acidic }]$

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### Problem 44

Balance each skeleton reaction, use Appendix D to calcu-
late $E_{\text { cell }}^{\circ}$ and state whether the reaction is spontaneous:
(a) $\mathrm{Cd}(s)+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q) \longrightarrow \mathrm{Cd}^{2+}(a q)+\mathrm{Cr}^{3+}(a q)$
(b) $\mathrm{Ni}^{2+}(a q)+\mathrm{Pb}(s) \longrightarrow \mathrm{Ni}(s)+\mathrm{Pb}^{2+}(a q)$

Ahmed A.

### Problem 45

Balance each skeleton reaction, use Appendix D to calculate $E_{\mathrm{cel}}^{\circ}$ and state whether the reaction is spontaneous:
(a) $\mathrm{Cu}^{+}(a q)+\mathrm{PbO}_{2}(s)+\mathrm{SO}_{4}^{2-}(a q) \longrightarrow$
(b) $\mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{Ni}^{2+}(a q) \longrightarrow \mathrm{O}_{2}(g)+\mathrm{Ni}(s)[\text { acidic }]$

Ahmed A.

### Problem 46

Use the following half-reactions to write three spontaneous reactions, calculate $E_{\text { cell }}^{\circ}$ for each reaction, and rank the strengths of the oxidizing and reducing agents:
(1) $\mathrm{Al}^{3+}(a q)+3 \mathrm{e}^{-} \longrightarrow \mathrm{Al}(s) \quad E^{\circ}=-1.66 \mathrm{V}$
(2) $\mathrm{N}_{2} \mathrm{O}_{4}(g)+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{NO}_{2}^{-}(a q) \qquad E^{\circ}=0.867 \mathrm{V}$
(3) $\mathrm{SO}_{4}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{e}^{-} \longrightarrow \mathrm{SO}_{3}^{2-}(a q)+2 \mathrm{OH}^{-}(a q)$
$E^{\circ}=0.93 \mathrm{V}$

Ahmed A.

### Problem 47

Use the following half-reactions to write three spontaneous reactions, calculate $E_{\mathrm{cell}}^{\circ}$ for each reaction, and rank the strengths of the oxidizing and reducing agents:
(1) $\mathrm{Au}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Au}(s) \quad E^{\circ}=1.69 \mathrm{V}$
(2) $\mathrm{N}_{2} \mathrm{O}(g)+2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)$
$(3) \mathrm{Cr}^{3+}(a q)+3 \mathrm{e}^{-} \longrightarrow \mathrm{Cr}(s) \qquad E^{\circ}=-0.74 \mathrm{V}$

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### Problem 48

Use the following half-reactions to write three spontaneous reactions, calculate $E_{\text { cell }}^{\circ}$ for each reaction, and rank the strengths of the oxidizing and reducing agents:
(1) $2 \mathrm{HClO}(a q)+2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Cl}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$
(2) $\mathrm{Pt}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Pt}(s) \quad E^{\circ}=1.20 \mathrm{V}$
(3) $\mathrm{PbSO}_{4}(s)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Pb}(s)+\mathrm{SO}_{4}^{2-}(a q) \quad E^{\circ}=-0.31 \mathrm{V}$

Ahmed A.

### Problem 49

Use the following half-reactions to write three spontaneous reactions, calculate $E_{\mathrm{cell}}^{\circ}$ for each reaction, and rank the strengths of the oxidizing and reducing agents:
(1) $\mathrm{I}_{2}(s)+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{I}^{-}(a q) \quad E^{\circ}=0.53 \mathrm{V}$
(2) $\mathrm{S}_{2} \mathrm{O}_{8}^{2-}(a q)+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{SO}_{4}^{2-}(a q) \qquad E^{\circ}=2.01 \mathrm{V}$
(3) $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+14 \mathrm{H}^{+}(a q)+6 \mathrm{e}^{-} \longrightarrow$
$$2 \mathrm{Cr}^{3+}(a q)+7 \mathrm{H}_{2} \mathrm{O}(l) \quad E^{\circ}=1.33 \mathrm{V}$$

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### Problem 50

When metal A is placed in a solution of a salt of metal B, the surface of metal A changes color. When metal B is placed in acid solution, gas bubbles form on the surface of the metal. When
metal A is placed in a solution of a salt of metal C, no change is observed in the solution or on the surface of metal A.
(a) Will metal C cause formation of H2 when placed in acid solution?
(b) Rank metals A, B, and C in order of decreasing reducing strength.

Ahmed A.

### Problem 51

When a clean iron nail is placed in an aqueous solution of copper(II) sulfate, the nail becomes coated with a brownish black material.
(a) What is the material coating the iron?
(b) What are the oxidizing and reducing agents?
(c) Can this reaction be made into a voltaic cell?
(d) Write the balanced equation for the reaction.
(e) Calculate $E_{\text { cell }}^{\circ}$ for the process.

Ahmed A.

### Problem 52

(a) How do the relative magnitudes of $Q$ and $K$ relate to the
signs of $\Delta G$ and $E_{\text { cell }} ?$ Explain.
(b) Can a cell do work when $Q / K>1$ or $Q / K<1 ?$ Explain.

Ahmed A.

### Problem 53

A voltaic cell consists of $\mathrm{A} / \mathrm{A}^{+}$ and $\mathrm{B} / \mathrm{B}^{+}$ half-cells, where
$\mathrm{A}$ and $\mathrm{B}$ are metals and the A electrode is negative. The initial
$\left[\mathrm{A}^{+}\right] /\left[\mathrm{B}^{+}\right]$ is such that $E_{\mathrm{cell}}>E_{\mathrm{cell}}^{\circ}$
(a) How do $\left[\mathrm{A}^{+}\right]$ and $\left[\mathrm{B}^{+}\right]$ change as the cell operates?
(b) How does $E_{\text { cell }}$ change as the cell operates?
(c) What is $\left[\mathrm{A}^{+}\right] /\left[\mathrm{B}^{+}\right]$ when $E_{\text { cell }}=E_{\text { cell }}^{\circ}$ ? Explain.
(d) Is it possible for $E_{\text { cell }}$ to be less than $E_{\text { cell }}^{\circ}$ ? Explain.

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### Problem 54

Explain whether $E_{\text { cell }}$ of a voltaic cell will increase or decrease with each of the following changes:
(a) Decrease in cell temperature
(b) Increase in [active ion] in the anode compartment
(c) Increase in [active ion] in the cathode compartment
(d) Increase in pressure of a gaseous reactant in the cathode
compartment

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### Problem 55

In a concentration cell, is the more concentrated electrolyte in the cathode or the anode compartment? Explain.

Ahmed A.

### Problem 56

What is the value of the equilibrium constant for the reaction between each pair at $25^{\circ} \mathrm{C} ?$
$\begin{array}{llll}{\text { (a) } \mathrm{Ni}(s) \text { and } \mathrm{Ag}^{+}(a q)} & {{ } & {\text { (b) Fe }(s) \text { and } \mathrm{Cr}^{3+}(a q)} & {{ }\end{array}$

Ahmed A.

### Problem 57

What is the value of the equilibrium constant for the reaction between each pair at $25^{\circ} \mathrm{C} ?$
(a) $\mathrm{Al}(s)$ and $\mathrm{Cd}^{2+}(a q) \quad$ (b) $\mathrm{I}_{2}(s)$ and $\mathrm{Br}^{-}(a q)$

Ahmed A.

### Problem 58

What is the value of the equilibrium constant for the reaction between each pair at $25^{\circ} \mathrm{C} ?$
$\begin{array}{llll}{\text { (a) } \mathrm{Ag}(s) \text { and } \mathrm{Mn}^{2+}(a q)} & {{ } & {\text { (b) } \mathrm{Cl}_{2}(g) \text { and } \mathrm{Br}^{-}(a q)} & {{ }\end{array}$

Ahmed A.

### Problem 59

What is the value of the equilibrium constant for the reaction between each pair at $25^{\circ} \mathrm{C} ?$
$\begin{array}{ll}{\text { (a) } \mathrm{Cr}(s) \text { and } \mathrm{Cu}^{2+}(a q)} & {\text { (b) } \mathrm{Sn}(s) \text { and } \mathrm{Pb}^{2+}(a q)}\end{array}$

Ahmed A.

### Problem 60

Calculate $\Delta G^{\circ}$ for each of the reactions in Problem 21.56

Ahmed A.

### Problem 61

Calculate $\Delta G^{\circ}$ for each of the reactions in Problem 21.57

Ahmed A.

### Problem 62

Calculate $\Delta G^{\circ}$ for each of the reactions in Problem 21.58

Ahmed A.

### Problem 63

Calculate $\Delta G^{\circ}$ for each of the reactions in Problem 21.59

Ahmed A.

### Problem 64

What are $E_{\text { cell }}^{\circ}$ and $\Delta G^{\circ}$ of a redox reaction at $25^{\circ} \mathrm{C}$ forwhich $n=1$ and $K=5.0 \times 10^{4} ?$

Ahmed A.

### Problem 65

What are $E_{\text { cell }}^{\circ}$ and $\Delta G^{\circ}$ of a redox reaction at $25^{\circ} \mathrm{C}$ for which $n=1$ and $K=5.0 \times 10^{-6} ?$

Ahmed A.

### Problem 66

What are $E_{\text { cell }}^{\circ}$ and $\Delta G^{\circ}$ of a redox reaction at $25^{\circ} \mathrm{C}$ for which $n=2$ and $K=65 ?$

Ahmed A.

### Problem 67

What are $E_{\text { cel }}^{\circ}$ and $\Delta G^{\circ}$ of a redox reaction at $25^{\circ} \mathrm{C}$ for which $n=2$ and $K=0.065 ?$

Ahmed A.

### Problem 68

A voltaic cell consists of a standard reference half-cell and a $\mathrm{Cu} / \mathrm{Cu}^{2+}$ half-cell. Calculate $\left[\mathrm{Cu}^{2+}\right]$ when $E_{\text { cell }}$ is 0.22 $\mathrm{V} .$

Ahmed A.

### Problem 69

$\mathrm{A}$ voltaic cell consists of an $\mathrm{Mn} / \mathrm{Mn}^{2+}$ half-cell and a
$\mathrm{Pb} / \mathrm{Pb}^{2+}$ half-cell. Calculate $\left[\mathrm{Pb}^{2+}\right]$ when $\left[\mathrm{Mn}^{2+}\right]$ is 1.4$M$ and $E_{\text { cell }}$ is 0.44 $\mathrm{V} .$

Ahmed A.

### Problem 70

A voltaic cell with $\mathrm{Ni} / \mathrm{Ni}^{2+}$ and $\mathrm{Co} / \mathrm{Co}^{2+}$ half-cells has the following initial concentrations: $\left[\mathrm{Ni}^{2+}\right]=0.80 M ;\left[\mathrm{Co}^{2+}\right]=$ 0.20$M .$
(a) What is the initial $E_{\text { cell }} ?$
(b) What is $\left[\mathrm{Ni}^{2+}\right]$ when $E_{\text { cell reaches } 0.03 \mathrm{V} ?}$
(c) What are the equilibrium concentrations of the ions?

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### Problem 71

A voltaic cell with $\mathrm{Mn} / \mathrm{Mn}^{2+}$ and $\mathrm{Cd} / \mathrm{Cd}^{2+}$ half-cells has the following initial concentrations: $\left[\mathrm{Mn}^{2+}\right]=0.090 M ;\left[\mathrm{Cd}^{2+}\right]=$ 0.060 $\mathrm{M} .$
(a) What is the initial $E_{\text { cell }} ?$
(b) What is $E_{\text { cell }}$ when $\left[\mathrm{Cd}^{2+}\right]$ reaches 0.050$M ?$
(c) What is $\left[\mathrm{Mn}^{2+}\right]$ when $E_{\text { cell }}$ reaches 0.055 $\mathrm{V}$ ?
(d) What are the equilibrium concentrations of the ions?

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### Problem 72

A voltaic cell consists of two $\mathrm{H}_{2} / \mathrm{H}^{+}$ half-cells. Half-cell $\mathrm{A}$ has $\mathrm{H}_{2}$ at 0.95 atm bubbling into 0.10 $\mathrm{M}$ HCl. Half-cell $\mathrm{B}$ has $\mathrm{H}_{2}$ at 0.60 $\mathrm{atm}$ bubbling into 2.0 $\mathrm{M}$ HCl. Which half-cell houses the anode? What is the voltage of the cell?

Ahmed A.

### Problem 73

A voltaic cell consists of two $\mathrm{Sn} / \mathrm{Sn}^{2+}$ half-cells, A and B. The electrolyte in $\mathrm{A}$ is 0.13$M \mathrm{Sn}\left(\mathrm{NO}_{3}\right)_{2} .$ The electrolyte in $\mathrm{B}$ is 0.87$M \mathrm{Sn}\left(\mathrm{NO}_{3}\right)_{2}$ . Which half-cell houses the cathode? What is the voltage of the cell?

Ahmed A.

### Problem 74

What is the direction of electron flow with respect to the anode and the cathode in a battery? Explain.

Ahmed A.

### Problem 75

In the everyday batteries used in flashlights, toys, and so forth, no salt bridge is evident. What is used in these cells to separate the anode and cathode compartments?

Ahmed A.

### Problem 76

Both a D-sized and an AAA-sized alkaline battery have an output of 1.5 $\mathrm{V}$ . What property of the cell potential allows this to occur? What is different about these two batteries?

Ahmed A.

### Problem 77

Many common electrical devices require the use of more than one battery
(a) How many alkaline batteries must be placed in series to light a flashlight with a 6.0 -V bulb?
(b) What is the voltage requirement of a camera that uses six silver batteries?
(c) How many volts can a car battery deliver if two of its anodel cathode cells are shorted?

Ahmed A.

### Problem 78

During reconstruction of the Statue of Liberty, Teflon spacers were placed between the iron skeleton and the copper plates that cover the statue. What purpose do these spacers serve?

Ahmed A.

### Problem 79

Why do steel bridge-supports rust at the waterline but not above or below it?

Ahmed A.

### Problem 80

After the 1930s, chromium replaced nickel for corrosion resistance and appearance on car bumpers and trim. How does chromium protect steel from corrosion?

Ahmed A.

### Problem 81

Which of the following metals are suitable for use as sacrificial anodes to protect against corrosion of underground iron pipes? If any are not suitable, explain why:
(a) Aluminum $\quad$ (b) Magnesium $\quad(\mathrm{c})$ Sodium $\quad$ (d) Lead
(e) Nickel (f) Zinc (g) Chromium

Ahmed A.

### Problem 82

Consider the following general electrolytic cell:
(a) At which electrode does oxidation occur?
(b) At which electrode does elemental M form?
(c) At which electrode are electrons being released by ions?
(d) At which electrode are electrons entering the cell?

Ahmed A.

### Problem 83

A voltaic cell consists of $\mathrm{Cr} / \mathrm{Cr}^{3+}$ and $\mathrm{Cd} / \mathrm{Cd}^{2+}$ half-cells with all components in their standard states. After 10 minutes of operation, a thin coating of cadmium metal has plated out on the cathode. Describe what will happen if you attach the negative terminal of a dry cell (1.5 V) to the cell cathode and the positive terminal to the cell anode.

Ahmed A.

### Problem 84

Why are $E_{\text { half-cell values for the oxidation and reduction of }}$ water different from $E_{\text { half-cell }}^{\circ}$ values for the same processes?

Ahmed A.

### Problem 85

In an aqueous electrolytic cell, nitrate ions never react at the anode, but nitrite ions do. Explain.

Ahmed A.

### Problem 86

How does overvoltage influence the products in the electrolysis of aqueous salts?

Ahmed A.

### Problem 87

In the electrolysis of molten NaBr,
(a) What product forms at the anode?
(b) What product forms at the cathode?

Ahmed A.

### Problem 88

In the electrolysis of molten BaI_
(a) What product forms at the negative electrode?
(b) What product forms at the positive electrode?

Ahmed A.

### Problem 89

In the electrolysis of a molten mixture of $\mathrm{KI}$ and $\mathrm{MgF}_{2}$ identify the product that forms at the anode and at the cathode.

Ahmed A.

### Problem 90

In the electrolysis of a molten mixture of $\mathrm{CsBr}$ and $\mathrm{SrCl}_{2}$ , identify the product that forms at the negative electrode and at the positive electrode.

Ahmed A.

### Problem 91

1 In the electrolysis of a molten mixture of $\mathrm{NaCl}$ and $\mathrm{CaBr}_{2}$ , identify the product that forms at the anode and at the cathode.

Ahmed A.

### Problem 92

In the electrolysis of a molten mixture of RbF and $\mathrm{CaCl}_{2}$ , identify the product that forms at the negative electrode and at the positive electrode.

Ahmed A.

### Problem 93

Which of the following elements can be prepared by electrolysis of their aqueous salts: copper, barium, aluminum, bromine?

Ahmed A.

### Problem 94

Which of the following elements can be prepared by electrolysis of their aqueous salts: strontium, gold, tin, chlorine?

Ahmed A.

### Problem 95

Which of the following elements can be prepared by electrolysis of their aqueous salts: lithium, iodine, zinc, silver?

Ahmed A.

### Problem 95

Write a balanced half-reaction for the product that forms at each electrode in the aqueous electrolysis of the following salts: (a) $\operatorname{ZnBr}_{2} ;(\mathrm{b}) \mathrm{Cu}\left(\mathrm{HCO}_{3}\right)_{2}$

Ahmed A.

### Problem 96

Which of the following elements can be prepared by electrolysis of their aqueous salts: fluorine, manganese, iron, cadmium?

Ahmed A.

### Problem 97

Write a balanced half-reaction for the product that forms at each electrode in the aqueous electrolysis of the following salts:
(a) LiF; (b) SnSO.

Ahmed A.

### Problem 99

Write a balanced half-reaction for the product that forms at each electrode in the aqueous electrolysis of the following salts:
(a) $\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} ;(\mathrm{b}) \mathrm{MnCl}_{2}$

Ahmed A.

### Problem 100

Write a balanced half-reaction for the product that forms at each electrode in the aqueous electrolysis of the following salts:
(a) $\mathrm{FeI}_{2} ;(\mathrm{b}) \mathrm{K}_{3} \mathrm{PO}_{4}$

Ahmed A.

### Problem 101

Electrolysis of molten $\mathrm{MgCl}_{2}$ is the final production step in the isolation of magnesium from seawater by the Dow process
(Section 22.4$) .$ Assuming that 45.6 $\mathrm{g}$ of Mg metal forms,
(a) How many moles of electrons are required?
(b) How many coulombs are required?
(c) How many amps will produce this amount in 3.50 $\mathrm{h}$ ?

Ahmed A.

### Problem 102

Electrolysis of molten NaCl in a Downs cell is the major isolation step in the production of sodium metal (Section 22.4$)$ Assuming that 215 g of Na metal forms,
(a) How many moles of electrons are required?
(b) How many coulombs are required?
(c) How many amps will produce this amount in 9.50 $\mathrm{h}$ ?

Ahmed A.

### Problem 103

How many grams of radium can form by passing 235 C through an electrolytic cell containing a molten radium salt?

Ahmed A.

### Problem 104

How many grams of aluminum can form by passing 305 C through an electrolytic cell containing a molten aluminum salt?

Ahmed A.

### Problem 105

How many seconds does it take to deposit 65.5 $\mathrm{g}$ of $\mathrm{Zn}$ on a steel gate when 21.0 $\mathrm{A}$ is passed through a $\mathrm{ZnSO}_{4}$ solution?

Ahmed A.

### Problem 106

How many seconds does it take to deposit 1.63 $\mathrm{g}$ of $\mathrm{Ni}$ on a decorative drawer handle when 13.7 $\mathrm{A}$ is passed through a $\mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}$ solution?

Ahmed A.

### Problem 107

A professor adds $\mathrm{Na}_{2} \mathrm{SO}_{4}$ to water to facilitate its electrolysis in a lecture demonstration. (a) What is the purpose of the $\mathrm{Na}_{2} \mathrm{SO}_{4} ?(\mathrm{b})$ Why is the water electrolyzed instead of the salt?

Ahmed A.

### Problem 108

Subterranean brines in parts of the United States are rich in iodides and bromides and serve as an industrial source of these elements. In one recovery method, the brines are evaporated to dryness and then melted and electrolyzed. Which halogen is more likely to form from this treatment? Why?

Ahmed A.

### Problem 109

Zinc plating (galvanizing) is an important means of corrosion protection. Although the process is done customarily by dipping the object into molten zinc, the metal can also be electroplated from aqueous solutions. How many grams of zinc can be deposited on a steel tank from a $\mathrm{ZnSO}_{4}$ solution when a $0.855-\mathrm{A}$ current flows for 2.50 days?

Ahmed A.

### Problem 110

The $\mathrm{MnO}_{2}$ used in alkaline batteries can be produced by an electrochemical process of which one half-reaction is
$$\mathrm{Mn}^{2+}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{MnO}_{2}(s)+4 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-}$$
If a current of 25.0 $\mathrm{A}$ is used, how many hours are needed to produce 1.00 $\mathrm{kg}$ of $\mathrm{MnO}_{2} ?$ At which electrode is the MnO $_{2}$ formed?

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### Problem 111

Car manufacturers are developing engines that use $\mathrm{H}_{2}$ as fuel. In Iceland, Sweden, and other parts of Scandinavia, where hydroelectric plants produce inexpensive electric power, the $\mathrm{H}_{2}$ can be made industrially by the electrolysis of water.
(a) How many coulombs are needed to produce $3.5 \times 10^{6} \mathrm{L}$ of $\mathrm{H}_{2}$
gas at 12.0 $\mathrm{atm}$ and $25^{\circ} \mathrm{C} ?$ (Assume that the ideal gas law applies.)
(b) If the coulombs are supplied at $1.44 \mathrm{V},$ how many joules are produced?
(c) If the combustion of oil yields $4.0 \times 10^{4} \mathrm{kJ} / \mathrm{kg}$ , what mass of oil
must be burned to yield the number of joules in part (b)?

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### Problem 113

An inexpensive and accurate method of measuring the quantity of electricity flowing through a circuit is to pass the current through a solution of a metal ion and weigh the metal deposited. A silver electrode immersed in an Ag' solution weighs 1.7854 g before the current has passed and weighs 1.8016 $\mathrm{g}$ after the current has passed. How many coulombs have passed?

Ahmed A.

### Problem 114

Brass, an alloy of copper and zinc, can be produced by simultaneously electroplating the two metals from a solution con- ctaining their $2+$ ions. If 65.0$\%$ of the total current is used to plate
copper, while 35.0$\%$ goes to plating zinc, what is the mass percent of copper in the brass?

Ahmed A.

### Problem 115

A thin circular disk earring 4.00 $\mathrm{cm}$ in diameter is plated with a coating of gold 0.25 $\mathrm{mm}$ thick from an Au $^{3+}$ bath.
(a) How many days does it take to deposit the gold on one side of one earring if the current is 0.013 $\mathrm{A}\left(d \text { of gold }=19.3 \mathrm{g} / \mathrm{cm}^{3}\right) ?$
(b) How many days does it take to deposit the gold on both sides of the pair of earrings?

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### Problem 119

Like any piece of apparatus, an electrolytic cell operates at less than 100$\%$ efficiency. A cell depositing Cu from a Cu't bath operates for 10 $\mathrm{h}$ with an average current of 5.8 $\mathrm{A} .$ If 53.4 $\mathrm{g}$ of copper is deposited, at what efficiency is the cell operating?

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### Problem 120

Commercial electrolysis is performed on both molten NaCl and aqueous NaCl solutions. Identify the anode product, cathode product, species reduced, and species oxidized for the (a) molten electrolysis and (b) aqueous electrolysis.

Ahmed A.

### Problem 121

To examine the effect of ion removal on cell voltage, a chemist constructs two voltaic cells, each with a standard hydrogen electrode in one compartment. One cell also contains a $\mathrm{Pb} / \mathrm{Pb}^{2+}$ half-cell; the other contains a $\mathrm{Cu} / \mathrm{Cu}^{2+}$ half-cell.
(a) What is $E^{\circ}$ of each cell at 298 $\mathrm{K}$ ?
(b) Which electrode in each cell is negative?
(c) When $\mathrm{Na}_{2}$ S solution is added to the Pb $^{2+}$ electrolyte, solid PbS
forms. What happens to the cell voltage?
(d) When sufficient $\mathrm{Na}_{2} \mathrm{S}$ is added to the $\mathrm{Cu}^{2+}$ electrolyte, CuS
forms and $\left[\mathrm{Cu}^{2+}\right]$ drops to $1 \times 10^{-16} \mathrm{M} .$ Find the cell voltage.

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### Problem 122

Electrodes used in electrocardiography are disposable, and many of them incorporate silver. The metal is deposited in a thin layer on a small plastic "button," and then some is converted to
AgCl:
$$\mathrm{Ag}(s)+\mathrm{Cl}^{-}(a q) \rightleftharpoons \mathrm{AgCl}(s)+\mathrm{e}^{-}$$
(a) If the surface area of the button is 2.0 $\mathrm{cm}^{2}$ and the thickness of
the silver layer is $7.5 \times 10^{-6} \mathrm{m}$ , calculate the volume (in $\mathrm{cm}^{3} )$ of
Ag used in one electrode.
(b) The density of silver metal is 10.5 $\mathrm{g} / \mathrm{cm}^{3} .$ How many grams of
silver are used per electrode?
(c) If Ag is plated on the button from an Ag^{+} solution with a
current of 12.0 $\mathrm{mA}$ , how many minutes does the plating take?
(d) If bulk silver costs $\$ 28.93$per troy ounce$(31.10 \mathrm{g}),$what is the cost (in cents) of the silver in one disposable electrode? Check back soon! ### Problem 123 Commercial aluminum production is done by electrolysis of a bath containing$\mathrm{Al}_{2} \mathrm{O}_{3}$dissolved in molten$\mathrm{Na}_{3} \mathrm{AlF}_{6} .$Why isn't it done by electrolysis of an aqueous AlCl_ solution? Ahmed A. Numerade Educator ### Problem 124 Comparing the standard electrode potentials$\left(E^{\circ}\right)$of the Group 1$\mathrm{A}(1)$metals Li, Na, and$\mathrm{K}$with the negative of their first ionization energies reveals a discrepancy: Ionization process reversed:$\mathrm{M}^{+}(g)+\mathrm{e}^{-} \rightleftharpoons \mathrm{M}(g) \quad(-\mathrm{IE})$Electrode reaction:$\quad \quad \mathrm{M}^{+}(a q)+\mathrm{e}^{-} \rightleftharpoons \mathrm{M}(s) \quad\left(E^{\circ}\right)$Note that the electrode potentials do not decrease smoothly down the group, while the ionization energies do. You might expect that if it is more difficult to remove an electron from an atom to form a gaseous ion (larger IE), then it would be less difficult to add an electron to an aqueous ion to form an atom (smaller$E^{\circ} ),$yet Lit$(a q)$is more difficult to reduce than$\mathrm{Na}^{+}(a q) .$Applying Hess's law, use an approach similar to a Born-Haber cycle to break down the process occurring at the electrode into three steps and label the energy involved in each step. How can you account for the discrepancy? Check back soon! ### Problem 125 In Appendix$D,$standard electrode potentials range from about$+3 \mathrm{V}$to$-3 \mathrm{V}$. Thus, it might seem possible to use a half- cell from each end of this range to construct a cell with a voltage of approximately 6$\mathrm{V}$. However, most commercial aqueous voltaic cells have$E^{\circ}$values of$1.5-2 \mathrm{V} .$Why are there no aqueous cells with significantly higher potentials? Ahmed A. Numerade Educator ### Problem 126 Tin is used to coat "tin" cans used food storage. If the tin is scratched and the iron of the can exposed, will the iron corrode more or less rapidly than if the tin were not present? Inside the can, the tin itself is coated with a clear varnish. Explain. Ahmed A. Numerade Educator ### Problem 127 Commercial electrolytic cells for producing aluminum operate at 5.0$\mathrm{V}$and$100,000 \mathrm{A}$. (a) How long does it take to produce exactly 1 metric ton$(1000 \mathrm{kg})$of aluminum? (b) How much electrical power (in kilowatt-hours, kW h) is used$\left(1 \mathrm{W}=1 \mathrm{J} / \mathrm{s} ; 1 \mathrm{kW} \cdot \mathrm{h}=3.6 \times 10^{3} \mathrm{kJ}\right) ?$(c) If electricity costs$\$0.123$ per kW h and cell efficiency is $90 . \%$ ,
what is the cost of electricity to produce exactly 1 lb of aluminum?

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### Problem 128

Magnesium bars are connected electrically to underground iron pipes to serve as sacrificial anodes.
(a) Do electrons flow from the bar to the pipe or the reverse?
(b) A 12 -kg Mg bar is attached to an iron pipe, and it takes 8.5 yr for the Mg to be consumed. What is the average current flowing between the Mg and the Fe during this period?

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### Problem 129

Bubbles of $\mathrm{H}_{2}$ form when metal $\mathrm{D}$ is placed in hot $\mathrm{H}_{2} \mathrm{O}$ . No reaction occurs when $\mathrm{D}$ is placed in a solution of a salt of
metal $\mathrm{E}$ , but $\mathrm{D}$ is discolored and coated immediately when placed in a solution of a salt of metal F. What happens if $\mathrm{E}$ is placed in a solution of a salt of metal $\mathrm{F}$ ? Rank metals $\mathrm{D}, \mathrm{E},$ and $\mathrm{F}$ in order of increasing reducing strength.

Ahmed A.

### Problem 130

In addition to reacting with gold (see Problem 21.21$)$ , aqua regia is used to bring other precious metals into solution. Balance the skeleton equation for the reaction with Pt:
$$\mathrm{Pt}(s)+\mathrm{NO}_{3}^{-}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{PtCl}_{6}^{2-}(a q)+\mathrm{NO}(g)$$

Ahmed A.

### Problem 131

The following reactions are used in batteries:
$\mathrm{I} \quad 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \quad E_{\mathrm{cell}}=1.23 \mathrm{V}$
\begin{aligned} \text { II } \quad \mathrm{Pb}(s)+\mathrm{PbO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{SO}_{4}(a q) & \longrightarrow \\ 2 \mathrm{PbSO}_{4}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) & E_{\mathrm{cell}}=2.04 \mathrm{V} \end{aligned}
III $2 \mathrm{Na}(l)+\mathrm{FeCl}_{2}(s) \longrightarrow 2 \mathrm{NaCl}(s)+\mathrm{Fe}(s) \quad E_{\mathrm{cell}}=2.35 \mathrm{V}$
Reaction I is used in fuel cells, II in the automobile lead-acid battery, and III in an experimental high-temperature battery for powering electric vehicles. The aim is to obtain as much work as possible from a cell, while keeping its weight to a minimum.
(a) In each cell, find the moles of electrons transferred and $\Delta G .$
(b) Calculate the ratio, in $\mathrm{kJ} / \mathrm{g},$ of $w_{\text { max }}$ to mass of reactants for each of the cells. Which has the highest ratio, which the lowest, and why? (Note: For simplicity, ignore the masses of cell components that do not appear in the cell as reactants, including electrode
materials, electrolytes, separators, cell casing, wiring, etc.)

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### Problem 132

A current is applied to two electrolytic cells in series. In the first, silver is deposited; in the second, a zinc electrode is consumed. How much Ag is plated out if 1.2 $\mathrm{g}$ of Zn dissolves?

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### Problem 133

You are investigating a particular chemical reaction. State all the types of data available in standard tables that enable you to calculate the equilibrium constant for the reaction at 298 $\mathrm{K}$ .

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### Problem 134

In an electric power plant, personnel monitor the $\mathrm{O}_{2}$ content of boiler feed water to prevent corrosion of the boiler tubes. Why does Fe corrode faster in steam and hot water than in cold
water?

Ahmed A.

### Problem 135

A voltaic cell using $\mathrm{Cu} / \mathrm{Cu}^{2+}$ and $\mathrm{Sn} / \mathrm{Sn}^{2+}$ half-cells is set up at standard conditions, and each compartment has a volume of
345 $\mathrm{mL}$ . The cell delivers 0.17 $\mathrm{A}$ for 48.0 $\mathrm{h}$ . (a) How many grams
of $\mathrm{Cu}(s)$ are deposited? (b) What is the $\left[\mathrm{Cu}^{2+}\right]$ remaining?

Ahmed A.

### Problem 136

If the $E_{\text { cell }}$ of the following cell is $0.915 \mathrm{V},$ what is the $\mathrm{pH}$ in the anode compartment?
$$\mathrm{Pt}(s)\left|\mathrm{H}_{2}(1.00 \mathrm{atm})\right| \mathrm{H}^{+}(a q) \| \mathrm{Ag}^{+}(0.100 M) | \mathrm{Ag}(s)$$

Ahmed A.

### Problem 137

From the skeleton equations below, create a list of balanced half-reactions in which the strongest oxidizing agent is on top and the weakest is on the bottom:
$$\begin{array}{c}{\mathrm{U}^{3+}(a q)+\mathrm{Cr}^{3+}(a q) \longrightarrow \mathrm{Cr}^{2+}(a q)+\mathrm{U}^{4+}(a q)} \\ {\mathrm{Fe}(s)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Sn}(s)+\mathrm{Fe}^{2+}(a q)} \\ {\mathrm{Fe}(s)+\mathrm{U}^{4+}(a q) \longrightarrow \text { no reaction }} \\ {\mathrm{Cr}^{3+}(a q)+\mathrm{Fe}(s) \longrightarrow \mathrm{Cr}^{2+}(a q)+\mathrm{Fe}^{2+}(a q)} \\ {\mathrm{Cr}^{2+}(a q)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Sn}(s)+\mathrm{Cr}^{3+}(a q)}\end{array}$$

Ahmed A.

### Problem 138

You are given the following three half-reactions:
(1) $\mathrm{Fe}^{3+}(a q)+\mathrm{e}^{-} \Longrightarrow \mathrm{Fe}^{2+}(a q)$
(2) $\mathrm{Fe}^{2+}(a q)+2 \mathrm{e}^{-} \rightleftharpoons \mathrm{Fe}(s)$
(3) $\mathrm{Fe}^{3+}(a q)+3 \mathrm{e}^{-} \Longrightarrow \mathrm{Fe}(s)$
(a) Use $E_{\text { half-cell }}^{\circ}$ values for $(1)$ and $(2)$ to find $E_{\text { half-cell }}^{\circ}$ for $(3)$
(b) Calculate $\Delta G^{\circ}$ for $(1)$ and $(2)$ from their $E_{\text { half-cell values. }}^{\text { olues. }}$
(c) Calculate $\Delta G^{\circ}$ for $(3)$ from $(1)$ and $(2)$
(d) Calculate $E_{\text { half-cell }}^{\circ}$ for $(3)$ from its $\Delta G^{\circ} .$
(e) What is the relationship between the $E_{\text { half-cell }}^{\circ}$ values for $(1)$ and
(2) and the $E_{\text { half-cell }}^{\circ}$ value for $(3) ?$

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### Problem 139

Use the half-reaction method to balance the equation for the conversion of ethanol to acetic acid in acid solution:
$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \longrightarrow \mathrm{CH}_{3} \mathrm{COOH}+\mathrm{Cr}^{3+}$$

Ahmed A.

### Problem 140

When zinc is refined by electrolysis, the desired half- reaction at the cathode is
$$\mathrm{Zn}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Zn}(s)$$
A competing reaction, which lowers the yield, is the formation of hydrogen gas:
$$2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}(g)$$
If 91.50$\%$ of the current flowing results in zinc being deposited, while 8.50$\%$ produces hydrogen gas, how many liters of $\mathrm{H}_{2}$ , measured at STP, form per kilogram of zinc?

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### Problem 141

21.141 $\mathrm{A}$ chemist designs an ion-specific probe for measur-
ing [Ag'l in an NaCl solution saturated with AgCl. One half-
cell has an Ag-wire electrode immersed in the unknown
AgCl-saturated $\mathrm{NaCl}$ solution. It is connected through a salt
bridge to the other half-cell, which has a calomel reference electrode [a platinum wire immersed in a paste of mercury and calo-
mel $\left(\mathrm{Hg}_{2} \mathrm{Cl}_{2}\right) ]$ in a saturated $\mathrm{KCl}$ solution. The measured $E_{\mathrm{cell}}$ is
0.060 $\mathrm{V} .$
$\begin{array}{l}{\text { (a) Given the following standard half-reactions, calculate }\left[\mathrm{Ag}^{+}\right] .} \\ {\text { Calomel: } \mathrm{Hg}_{2} \mathrm{Cl}_{2}(s)+2 \mathrm{e}^{-} \longrightarrow} \\ {\text { Silver: } \mathrm{Ag}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(s)} & {E^{\circ}=0.80 \mathrm{V}}\end{array}$
(Hint: Assume that $\left[\mathrm{Cl}^{-}\right]$ is so high that it is essentially constant.)
(b) A mining engineer wants an ore sample analyzed with the
Ag'-selective probe. After pretreating the ore sample, the chemist
measures the cell voltage as 0.53 $\mathrm{V} .$ What is $\left[\mathrm{Ag}^{+}\right] ?$

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### Problem 142

Use Appendix D to calculate the $K_{\mathrm{sp}}$ of $\mathrm{AgCl}$

Ahmed A.

### Problem 143

21.143 Black-and-white photographic film is coated with silver halides. Because silver is expensive, the manufacturer monitors the Ag' content of the waste stream, [Ag $^{+} ]_{\text { waste }}$ from the plant with an Ag'-selective electrode at $25^{\circ} \mathrm{C}$ . A stream of known Ag^{+} concentration, $\left[\mathrm{Ag}^{+}\right]_{\text { standard }},$ is passed over the electrode in turn with the waste stream and the data recorded by a computer.
(a) Write the equations relating the nonstandard cell potential to the standard cell potential and [Ag' ] for each solution.
(b) Combine these into a single equation to find $\left[\mathrm{Ag}^{+}\right]_{\text { waste }}$
(c) Rewrite the equation from part (b) to find $\left[\mathrm{Ag}^{+}\right]_{\text { waste }}$ in $\mathrm{ng} / \mathrm{L}$ .
(d) If $E_{\text { waste }}$ is 0.003 V higher than $E_{\text { standard }},$ and the standard
solution contains 1000 . ng/L, what is $\left[\mathrm{Ag}^{+}\right]_{\text { waste }} ?$
(e) Rewrite the equation from part (b) to find $\left[\mathrm{Ag}^{+}\right]_{\text { waste for a }}$
system in which $T$ changes and $T_{\text { waste }}$ and $T_{\text { standard }}$ may be different.

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### Problem 144

Calculate the $K_{\mathrm{f}}$ of $\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}$ from
$\mathrm{Ag}^{+}(a q)+\mathrm{e}^{-} \rightleftharpoons \mathrm{Ag}(s) \quad E^{\circ}=0.80 \mathrm{V}$
$\operatorname{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}(a q)+\mathrm{e}^{-} \rightleftharpoons \mathrm{Ag}(s)+2 \mathrm{NH}_{3}(a q) \qquad E^{\circ}=0.37 \mathrm{V}$

Ahmed A.

### Problem 145

Even though the toxicity of cadmium has become a concern, nickel-cadmium (nicad) batteries are still used commonly in many devices. The overall cell reaction is
$$\mathrm{Cd}(s)+2 \mathrm{NiO}(\mathrm{OH})(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow$$
$$2 \mathrm{Ni}(\mathrm{OH})(s)+\mathrm{Cd}(\mathrm{OH})_{2}(s)$$
A certain nicad battery weighs 18.3 $\mathrm{g}$ and has a capacity of
$300 . \mathrm{mA} \cdot \mathrm{h}$ (that is, the cell can store charge equivalent to a current
of $300 .$ mA flowing for 1 $\mathrm{h}$ ).
(a) What is the capacity of this cell in coulombs?
(b) What mass of reactants is needed to deliver $300 . \mathrm{mA}$ - h?
(c) What percentage of the cell mass consists of reactants?

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### Problem 146

The zinc-air battery is a less expensive alternative to silver batteries for use in hearing aids. The cell reaction is
$$2 \mathrm{Zn}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{ZnO}(s)$$
A new battery weighs 0.275 g. The zinc accounts for exactly $\frac{1}{10}$ of the mass, and the oxygen does not contribute to the mass because it is supplied by the air.
(a) How much electricity (in $\mathrm{C} )$ can the battery deliver?
(b) How much free energy (in $\mathrm{J} )$ is released if $E_{\text { cell }}$ is 1.3 $\mathrm{V}$ ?

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### Problem 147

Use Appendix $D$ to create an activity series of Mn, Fe, Ag, Sn, Cr, Cu, Ba, Al, Na, Hg, Ni, Li, Au, Zn, and Pb. Rank these metals in order of decreasing reducing strength, and divide them into three groups: those that displace $\mathrm{H}_{2}$ from water, those that displace $\mathrm{H}_{2}$ from acid, and those that cannot displace $\mathrm{H}_{2} .$

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### Problem 148

Both Ti and $V$ are reactive enough to displace $\mathrm{H}_{2}$ from water. The difference in their $E_{\text { half-cell values is } 0.43}$ V.\mathrm Given
$$\mathrm{V}(s)+\mathrm{Cu}^{2+}(a q) \longrightarrow \mathrm{V}^{2+}(a q)+\mathrm{Cu}(s) \quad \Delta G^{\circ}=-298 \mathrm{kJ} / \mathrm{mol}$$
use Appendix D to calculate the $E_{\text { half-cell }}^{\circ}$ values for $\mathrm{V}$ and Ti.

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### Problem 149

For the reaction
$$\mathrm{S}_{4} \mathrm{O}_{6}^{2-}(a q)+2 \mathrm{I}^{-}(a q) \longrightarrow \mathrm{I}_{2}(s)+\mathrm{S}_{2} \mathrm{O}_{3}^{2-}(a q)$$
$$\Delta G^{\circ}=87.8 \mathrm{kJ} / \mathrm{mol}$$
(a) Identify the oxidizing and reducing agents. (b) Calculate $E_{\text { cell. }}^{\circ}$
(c) For the reduction half-reaction, write a balanced equation, give
the oxidation number of each element, and calculate $E_{\text { half cell. }}^{\circ}$

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### Problem 150

Two concentration cells are prepared, both with 90.0 $\mathrm{mL}$ of 0.0100$M \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}$ and a Cu bar in each half-cell.
(a) In the first concentration cell, 10.0 $\mathrm{mL}$ of 0.500 $\mathrm{MNH}_{3}$ is added
to one half-cell; the complex ion $\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}$ forms, and $E_{\mathrm{cell}}$ is 0.129 $\mathrm{V} .$ Calculate $K_{\mathrm{f}}$ for the formation of the complex ion.
(b) Calculate $E_{\text { cell }}$ when an additional 10.0 $\mathrm{mL}$ of 0.500 $\mathrm{M} \mathrm{NH}_{3}$ is added.
(c) In the second concentration cell, 10.0 $\mathrm{mL}$ of 0.500 $\mathrm{M}$ NaOH is added to one half-cell; the precipitate $\mathrm{Cu}(\mathrm{OH})_{2}$ forms $\left(K_{\mathrm{sp}}=\right.$ $2.2 \times 10^{-20} ) .$ Calculate $E_{\mathrm{cell}}^{\circ}$
(d) What would the molarity of NaOH have to be for the addition of 10.0 $\mathrm{mL}$ to result in an $E_{\mathrm{cell}}^{\mathrm{o}}$ of 0.340 $\mathrm{V} ?$

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### Problem 151

Two voltaic cells are to be joined so that one will run the other as an electrolytic cell. In the first cell, one half-cell has Au foil in $1.00 M \mathrm{Au}\left(\mathrm{NO}_{3}\right)_{3},$ and the other half-cell has a Cr bar in 1.00$M \mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} .$ In the second cell, one half-cell has a Co bar in $1.00 M \mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2},$ and the other half-cell has a $\mathrm{Zn}$ bar in 1.00 $\mathrm{M}$$\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}$
(a) Calculate $E_{\text { cell }}^{\circ}$ for each cell.
(b) Calculate the total potential if the two cells are connected as voltaic cells in series.
(c) When the electrode wires are switched in one of the cells, which cell will run as the voltaic cell and which as the electrolytic cell?
(d) Which metal ion is being reduced in each cell?
(e) If 2.00 g of metal plates out in the voltaic cell, how much metal ion plates out in the electrolytic cell?

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### Problem 152

A voltaic cell has one half-cell with a Cu bar in a 1.00$M$ $\mathrm{Cu}^{2+}$ salt, and the other half-cell with a Cd bar in the same volume of a 1.00 $\mathrm{M} \mathrm{Cd}^{2+}$ salt.
(a) Find $E_{\text { cell }}^{\circ}, \Delta G^{\circ},$ and $K$
(b) As the cell operates, $\left[\mathrm{Cd}^{2+}\right]$ increases ; find $E_{\text { cell }}$ and $\Delta G$ when $\left[\mathrm{Cd}^{2+}\right]$ is 1.95 $\mathrm{M} .$
(c) Find $E_{\text { cell }}, \Delta G,$ and $\left[\mathrm{Cu}^{2+}\right]$ at equilibrium.

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### Problem 153

Gasoline is a mixture of hydrocarbons, but the heat released when it burns is close to that of octane, $\mathrm{C}_{8} \mathrm{H}_{18}(l)\left(\Delta H_{\mathrm{f}}^{\circ}=\right.$ $-250.1 \mathrm{kJ} / \mathrm{mol} ) .$ Research is underway to use $\mathrm{H}_{2}$ from the electrolysis of water in fuel cells to power cars instead of gasoline.
(a) Calculate $\Delta H^{\circ}$ when 1.00 gal of gasoline $(d=0.7028 \mathrm{g} / \mathrm{mL})$
burns to produce carbon dioxide gas and water vapor.
(b) How many liters of $\mathrm{H}_{2}$ at $25^{\mathrm{C}} \mathrm{C}$ and 1.00 atm must burn to
produce this quantity of energy?
(c) How long would it take to produce this amount of $\mathrm{H}_{2}$ by electrolysis with a current of $1.00 \times 10^{3} \mathrm{A}$ at 6.00 $\mathrm{V}$ ?
(d) How much power in kilowatt-hours (kW. h) is required to generate this amount of $\mathrm{H}_{2} ?(1 \mathrm{W}=1 \mathrm{J} / \mathrm{s}, 1 \mathrm{J}=1 \mathrm{C} \cdot \mathrm{V}, \text { and }$ $1 \mathrm{kW} \cdot \mathrm{h}=3.6 \times 10^{6} \mathrm{J} . )$
(e) If the cell is 88.0$\%$ efficient and electricity costs $\$ 0.123$per$\mathrm{kW} \cdot \mathrm{h},$what is the cost of producing the amount of$\mathrm{H}_{2}\$ equivalent to 1.00 gal of gasoline?

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