Chemistry

Raymond Chang

Chapter 19

Electrochemistry - all with Video Answers

Educators

Chapter Questions

Problem 1

Balance the following redox equations by the ionelectron method:
(a) $\mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{Fe}^{2+} \longrightarrow \mathrm{Fe}^{3+}+\mathrm{H}_{2} \mathrm{O}$ (in acidic solution)
(b) $\mathrm{Cu}+\mathrm{HNO}_{3} \longrightarrow \mathrm{Cu}^{2+}+\mathrm{NO}+\mathrm{H}_{2} \mathrm{O}$ (in acidic solution)
(c) $\mathrm{CN}^{-}+\mathrm{MnO}_{4}^{-} \longrightarrow \mathrm{CNO}^{-}+\mathrm{MnO}_{2}$ (in
basic solution)
(d) $\mathrm{Br}_{2} \longrightarrow \mathrm{BrO}_{3}^{-}+\mathrm{Br}^{-}$ (in basic solution)
(e) $\mathrm{S}_{2} \mathrm{O}_{3}^{2-}+\mathrm{I}_{2} \longrightarrow \mathrm{I}^{-}+\mathrm{S}_{4} \mathrm{O}_{6}^{2-}$ (in acidic solution)

Shazia Naz

Shazia Naz

Numerade Educator

Problem 2

Balance the following redox equations by the ionelectron method:
(a) $\mathrm{Mn}^{2+}+\mathrm{H}_{2} \mathrm{O}_{2} \longrightarrow \mathrm{MnO}_{2}+\mathrm{H}_{2} \mathrm{O}$ (in basic
solution)
(b) $\mathrm{Bi}(\mathrm{OH})_{3}+\mathrm{SnO}_{2}^{2-} \longrightarrow \mathrm{SnO}_{3}^{2-}+\mathrm{Bi}(\mathrm{in}$
basic solution)
(c) $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+\mathrm{C}_{2} \mathrm{O}_{4}^{2-} \longrightarrow \mathrm{Cr}^{3+}+\mathrm{CO}_{2}(\mathrm{in}$
acidic solution)
(d) $\mathrm{ClO}_{3}^{-}+\mathrm{Cl}^{-} \longrightarrow \mathrm{Cl}_{2}+\mathrm{ClO}_{2}$ (in acidic
solution)

Shazia Naz

Numerade Educator

Problem 3

Define the following terms: anode, cathode, cell voltage, electromotive force, standard reduction potential.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 4

Describe the basic features of a galvanic cell. Why are the two components of the cell separated from each other?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 5

What is the function of a salt bridge? What kind of electrolyte should be used in a salt bridge?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 6

What is a cell diagram? Write the cell diagram for a galvanic cell consisting of an Al electrode placed in a $1 \mathrm{MAl}\left(\mathrm{NO}_{3}\right)_{3}$ solution and a Ag electrode placed in a $1 \mathrm{M} \mathrm{AgNO}_{3}$ solution.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 7

What is the difference between the half-reactions discussed in redox processes in Chapter 4 and the half-cell reactions discussed in Section $19.2 ?$

Shazia Naz

Numerade Educator

Problem 8

After operating a Daniell cell (see Figure 19.1) for a few minutes, a student notices that the cell emf begins to drop. Why?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 9

Use the information in Table $2.1$, and calculate the Faraday constant.

David Collins

Numerade Educator

Problem 10

Discuss the spontaneity of an electrochemical reaction in terms of its standard emf $\left(E_{\text {cell }}^{\circ}\right)$.

Vishal Sharma

Numerade Educator

Problem 10

Calculate the standard emf of a cell that uses the $\mathrm{Mg} / \mathrm{Mg}^{2+}$ and $\mathrm{Cu} / \mathrm{Cu}^{2+}$ half-cell reactions at $25^{\circ} \mathrm{C} .$ Write the equation for the cell reaction that occurs under standard-state conditions.

Ronald Prasad

Numerade Educator

Problem 11

Calculate the standard emf of a cell that uses the $\mathrm{Mg} / \mathrm{Mg}^{2+}$ and $\mathrm{Cu} / \mathrm{Cu}^{2+}$ half-cell reactions at $25^{\circ} \mathrm{C}$ Write the equation for the cell reaction that occurs under standard-state conditions.

Ronald Prasad

Numerade Educator

Problem 12

Calculate the standard emf of a cell that uses Ag/Ag and $\mathrm{Al} / \mathrm{Al}^{3+}$ half-cell reactions. Write the cell reaction that occurs under standard-state conditions.

Kevin Zaborsky

Numerade Educator

Problem 13

Predict whether $\mathrm{Fe}^{3+}$ can oxidize $\mathrm{I}^{-}$ to $\mathrm{I}_{2}$ under standard-state conditions.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 14

Which of the following reagents can oxidize $\mathrm{H}_{2} \mathrm{O}$ to $\mathrm{O}_{2}(g)$ under standard-state conditions? $\mathrm{H}^{+}(a q)$, $\mathrm{Cl}^{-}(a q), \mathrm{Cl}_{2}(g), \mathrm{Cu}^{2+}(a q), \mathrm{Pb}^{2+}(a q), \mathrm{MnO}_{4}^{-}(a q)$ (in
acid).

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 15

Consider the following half-reactions:
$\mathrm{MnO}_{4}^{-}(a q)+8 \mathrm{H}^{+}(a q)+5 e^{-}$
$\mathrm{Mn}^{2+}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l)$
$\mathrm{NO}_{3}^{-}(a q)+4 \mathrm{H}^{+}(a q)+3 e^{-} \longrightarrow$
$\mathrm{NO}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$
Predict whether $\mathrm{NO}_{3}^{-}$ ions will oxidize $\mathrm{Mn}^{2+}$ to $\mathrm{MnO}_{4}^{-}$ under standard-state conditions.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 16

Predict whether the following reactions would occur spontaneously in aqueous solution at $25^{\circ} \mathrm{C}$. Assume that the initial concentrations of dissolved species are all $1.0 M$.
(a) $\mathrm{Ca}(s)+\mathrm{Cd}^{2+}(a q) \longrightarrow \mathrm{Ca}^{2+}(a q)+\mathrm{Cd}(s)$
(b) $2 \mathrm{Br}^{-}(a q)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Br}_{2}(l)+\operatorname{Sn}(s)$
(c) $2 \mathrm{Ag}(s)+\mathrm{Ni}^{2+}(a q) \longrightarrow 2 \mathrm{Ag}^{+}(a q)+\mathrm{Ni}(s)$
(d) $\mathrm{Cu}^{+}(a q)+\mathrm{Fe}^{3+}(a q) \longrightarrow{\mathrm{Cu}^{2+}}(a q)+\mathrm{Fe}^{2+}(a q)$

Kevin Zaborsky

Numerade Educator

Problem 17

Which species in each pair is a better oxidizing agent under standard-state conditions?
(a) $\mathrm{Br}_{2}$ or $\mathrm{Au}^{3+}$,
(b) $\mathrm{H}_{2}$ or $\mathrm{Ag}^{+}$,
(c) $\mathrm{Cd}^{2+}$ or $\mathrm{Cr}^{3+}$
(d) $\mathrm{O}_{2}$ in acidic media or $\mathrm{O}_{2}$ in basic media.

Shazia Naz

Numerade Educator

Problem 18

Which species in each pair is a better reducing agent under standard-state conditions? (a) Na or $\mathrm{Li}$, (b) $\mathrm{H}_{2}$ or $\mathrm{I}_{2},(\mathrm{c}) \mathrm{Fe}^{2+}$ or $\mathrm{Ag},(\mathrm{d}) \mathrm{Br}^{-}$ or $\mathrm{Co}^{2+}$.

Shazia Naz

Numerade Educator

Problem 19

Write the equations relating $\Delta G^{\circ}$ and $K$ to the standard emf of a cell. Define all the terms.

Kevin Zaborsky

Numerade Educator

Problem 20

The $E^{\circ}$ value of one cell reaction is positive and that of another cell reaction is negative. Which cell reaction will proceed toward the formation of more products at equilibrium?

Shazia Naz

Numerade Educator

Problem 21

What is the equilibrium constant for the following reaction at $25^{\circ} \mathrm{C} ?$
$$
\operatorname{Mg}(s)+\mathrm{Zn}^{2+}(a q) \rightleftharpoons \mathrm{Mg}^{2+}(a q)+\operatorname{Zn}(s)
$$

Dr. Satish Ingale

Dr. Satish Ingale

Numerade Educator

Problem 22

The equilibrium constant for the reaction
$$
\operatorname{Sr}(s)+\mathrm{Mg}^{2+}(a q) \rightleftharpoons \mathrm{Sr}^{2+}(a q)+\operatorname{Mg}(s)
$$
is $2.69 \times 10^{12}$ at $25^{\circ} \mathrm{C}$. Calculate $E^{\circ}$ for a cell made up of $\mathrm{Sr} / \mathrm{Sr}^{2+}$ and $\mathrm{Mg} / \mathrm{Mg}^{2+}$ half-cells.

Shazia Naz

Numerade Educator

Problem 23

Use the standard reduction potentials to find the equilibrium constant for each of the following reactions at $25^{\circ} \mathrm{C}$ :
(a) $\mathrm{Br}_{2}(l)+2 \mathrm{I}^{-}(a q) \rightleftharpoons 2 \mathrm{Br}^{-}(a q)+\mathrm{I}_{2}(s)$
(b) $2 \mathrm{Ce}^{4+}(a q)+2 \mathrm{Cl}^{-}(a q) \underset{\mathrm{Cl}_{2}(g)+2 \mathrm{Ce}^{3+}(a q)}{\rightleftharpoons}$
(c) $5 \mathrm{Fe}^{2+}(a q)+\mathrm{MnO}_{4}^{-}(a q)+8 \mathrm{H}^{+}(a q) \rightleftharpoons$
$\mathrm{Mn}^{2+}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l)+5 \mathrm{Fe}^{3+}(a q)$

Manik Pulyani

Numerade Educator

Problem 24

Calculate $\Delta G^{\circ}$ and $K_{\mathrm{c}}$ for the following reactions at $25^{\circ} \mathrm{C}:$
(a) $\mathrm{Mg}(s)+\mathrm{Pb}^{2+}(a q) \rightleftharpoons \mathrm{Mg}^{2+}(a q)+\mathrm{Pb}(s)$
(b) $\mathrm{Br}_{2}(l)+2 \mathrm{I}^{-}(a q) \rightleftharpoons 2 \mathrm{Br}^{-}(a q)+\mathrm{I}_{2}(s)$
(c) $\mathrm{O}_{2}(g)+4 \mathrm{H}^{+}(a q)+4 \mathrm{Fe}^{2+}(a q) \rightleftharpoons{2 \mathrm{H}_{2} \mathrm{O}(l)+4 \mathrm{Fe}^{3+}(a q)}$
(d) $2 \mathrm{Al}(s)+3 \mathrm{I}_{2}(s) \rightleftharpoons 2 \mathrm{Al}^{3+}(a q)+6 \mathrm{I}^{-}(a q)$

Manik Pulyani

Numerade Educator

Problem 25

Under standard-state conditions, what spontaneous reaction will occur in aqueous solution among the ions $\mathrm{Ce}^{4+}, \mathrm{Ce}^{3+}, \mathrm{Fe}^{3+}$, and $\mathrm{Fe}^{2+} ?$ Calculate $\Delta G^{\circ}$ and $K_{\mathrm{c}}$ for the reaction.

Kevin Zaborsky

Numerade Educator

Problem 26

Given that $E^{\circ}=0.52 \mathrm{~V}$ for the reduction $\mathrm{Cu}^{+}(a q)+$ $e^{-} \rightarrow \operatorname{Cu}(s)$, calculate $E^{\circ}, \Delta G^{\circ}$, and $K$ for the following reaction at $25^{\circ} \mathrm{C}$ :
$$
2 \mathrm{Cu}^{+}(a q) \longrightarrow \mathrm{Cu}^{2+}(a q)+\operatorname{Cu}(s)
$$

Kevin Zaborsky

Numerade Educator

Problem 27

Write the Nernst equation and explain all the terms.

Kevin Zaborsky

Numerade Educator

Problem 28

Write the Nernst equation for the following processes at some temperature $T$ :
(a) $\mathrm{Mg}(s)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\operatorname{Sn}(s)$
(b) $2 \mathrm{Cr}(s)+3 \mathrm{~Pb}^{2+}(a q) \longrightarrow 2 \mathrm{Cr}^{3+}(a q)+3 \mathrm{~Pb}(s)$

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 29

What is the potential of a cell made up of $\mathrm{Zn} / \mathrm{Zn}^{2+}$ and $\mathrm{Cu} / \mathrm{Cu}^{2+}$ half-cells at $25^{\circ} \mathrm{C}$ if $\left[\mathrm{Zn}^{2+}\right]=0.25 \mathrm{M}$
and $\left[\mathrm{Cu}^{2+}\right]=0.15 M ?$

Kevin Zaborsky

Numerade Educator

Problem 30

Calculate $E^{\circ}, E$, and $\Delta G$ for the following cell reactions. (a) $\mathrm{Mg}(s)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Sn}(s)$
$\left[\mathrm{Mg}^{2+}\right]=0.045 M,\left[\mathrm{Sn}^{2+}\right]=0.035 M$
(b) $3 \mathrm{Zn}(s)+2 \mathrm{Cr}^{3+}(a q) \longrightarrow 3 \mathrm{Zn}^{2+}(a q)+2 \operatorname{Cr}(s)$
$\left[\mathrm{Cr}^{3+}\right]=0.010 M,\left[\mathrm{Zn}^{2+}\right]=0.0085 M$

Kevin Zaborsky

Numerade Educator

Problem 31

Calculate the standard potential of the cell consisting of the $\mathrm{Zn} / \mathrm{Zn}^{2+}$ half-cell and the SHE. What will the emf of the cell be if $\left[\mathrm{Zn}^{2+}\right]=0.45 M, P_{\mathrm{H}_{2}}=2.0 \mathrm{~atm}$, and $\left[\mathrm{H}^{+}\right]=1.8 M ?$

Shazia Naz

Numerade Educator

Problem 32

What is the emf of a cell consisting of a $\mathrm{Pb}^{2+} / \mathrm{Pb}$ half-cell and a $\mathrm{Pt} / \mathrm{H}^{+} / \mathrm{H}_{2}$ half-cell if $\left[\mathrm{Pb}^{2+}\right]=0.10 \mathrm{M}$,
$\left[\mathrm{H}^{+}\right]=0.050 M$, and $P_{\mathrm{H}_{2}}=1.0 \mathrm{~atm} ?$

Shazia Naz

Numerade Educator

Problem 33

Referring to the arrangement in Figure $19.1$, calculate the $\left[\mathrm{Cu}^{2+}\right] /\left[\mathrm{Zn}^{2+}\right]$ ratio at which the following reaction is spontaneous at $25^{\circ} \mathrm{C}$ :
$$
\mathrm{Cu}(s)+\mathrm{Zn}^{2+}(a q) \longrightarrow \mathrm{Cu}^{2+}(a q)+\mathrm{Zn}(s)
$$

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 34

Calculate the emf of the following concentration cell:
$$
\operatorname{Mg}(s)\left|\mathrm{Mg}^{2+}(0.24 M) \| \mathrm{Mg}^{2+}(0.53 M)\right| \operatorname{Mg}(s)
$$

Kevin Zaborsky

Numerade Educator

Problem 35

Explain the differences between a primary galvanic cell-one that is not rechargeable-and a storage cell (for example, the lead storage battery), which is rechargeable.

Shazia Naz

Numerade Educator

Problem 36

Discuss the advantages and disadvantages of fuel cells over conventional power plants in producing electricity.

Shazia Naz

Numerade Educator

Problem 37

The hydrogen-oxygen fuel cell is described in Section 19.6. (a) What volume of $\mathrm{H}_{2}(\mathrm{~g})$, stored at $25^{\circ} \mathrm{C}$ at a pressure of $155 \mathrm{~atm}$, would be needed to run an electric motor drawing a current of $8.5 \mathrm{~A}$ for $3.0 \mathrm{~h}$ ? (b) What volume (liters) of air at $25^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}$ will have to pass into the cell per minute to run the motor? Assume that air is 20 percent $\mathrm{O}_{2}$ by volume and that all the $\mathrm{O}_{2}$ is consumed in the cell. The other components of air do not affect the fuel-cell reactions. Assume ideal gas behavior.

Manik Pulyani

Numerade Educator

Problem 38

Calculate the standard emf of the propane fuel cell discussed on p. 862 at $25^{\circ} \mathrm{C}$, given that $\Delta G_{\mathrm{f}}^{\circ}$ for propane is $-23.5 \mathrm{~kJ} / \mathrm{mol}$.

Manik Pulyani

Numerade Educator

Problem 39

Steel hardware, including nuts and bolts, is often coated with a thin plating of cadmium. Explain the function of the cadmium layer.

Shazia Naz

Numerade Educator

Problem 40

"Galvanized iron" is steel sheet that has been coated with zinc; "tin" cans are made of steel sheet coated with tin. Discuss the functions of these coatings and the electrochemistry of the corrosion reactions that occur if an electrolyte contacts the scratched surface of a galvanized iron sheet or a tin can.

Shazia Naz

Numerade Educator

Problem 41

Tarnished silver contains $\mathrm{Ag}_{2} \mathrm{~S}$. The tarnish can be removed by placing silverware in an aluminum pan containing an inert electrolyte solution, such as $\mathrm{NaCl}$. Explain the electrochemical principle for this procedure. [The standard reduction potential for the half-cell reaction $\mathrm{Ag}_{2} \mathrm{~S}(s)+2 e^{-} \rightarrow 2 \mathrm{Ag}(s)+\mathrm{S}^{2-}(a q)$
is $-0.71 \mathrm{~V} .]$

Shazia Naz

Numerade Educator

Problem 42

How does the tendency of iron to rust depend on the pH of solution?

Shazia Naz

Numerade Educator

Problem 43

What is the difference between a galvanic cell (such as a Daniell cell) and an electrolytic cell?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 44

Describe the electrolysis of an aqueous solution of $\mathrm{KNO}_{3}$

Shazia Naz

Numerade Educator

Problem 45

The half-reaction at an electrode is
$$
\mathrm{Mg}^{2+}(\text { molten })+2 e^{-} \longrightarrow \operatorname{Mg}(s)
$$
Calculate the number of grams of magnesium that can be produced by supplying $1.00 F$ to the electrode.

Kevin Zaborsky

Numerade Educator

Problem 46

Consider the electrolysis of molten barium chloride, $\mathrm{BaCl}_{2}$. (a) Write the half-reactions. (b) How many grams of barium metal can be produced by supplying $0.50 \mathrm{~A}$ for $30 \mathrm{~min} ?$

Shazia Naz

Numerade Educator

Problem 47

Considering only the cost of electricity, would it be cheaper to produce a ton of sodium or a ton of aluminum by electrolysis?

Shazia Naz

Numerade Educator

Problem 48

If the cost of electricity to produce magnesium by the electrolysis of molten magnesium chloride is $\$ 155$ per ton of metal, what is the cost (in dollars) of the electricity necessary to produce (a) $10.0$ tons of aluminum, (b) $30.0$ tons of sodium, (c) $50.0$ tons of calcium?

Shazia Naz

Numerade Educator

Problem 49

One of the half-reactions for the electrolysis of water is
$$
2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{O}_{2}(g)+4 \mathrm{H}^{+}(a q)+4 e^{-}
$$
If $0.076 \mathrm{~L}$ of $\mathrm{O}_{2}$ is collected at $25^{\circ} \mathrm{C}$ and $755 \mathrm{mmHg}$, how many moles of electrons had to pass through the solution?

Rashmi Sinha

Numerade Educator

Problem 50

How many moles of electrons are required to produce (a) $0.84 \mathrm{~L}$ of $\mathrm{O}_{2}$ at exactly $1 \mathrm{~atm}$ and $25^{\circ} \mathrm{C}$ from aqueous $\mathrm{H}_{2} \mathrm{SO}_{4}$ solution; (b) $1.50 \mathrm{~L}$ of $\mathrm{Cl}_{2}$ at $750 \mathrm{mmHg}$ and $20^{\circ} \mathrm{C}$ from molten $\mathrm{NaCl} ;$ (c) $6.0 \mathrm{~g}$ of Sn from molten $\mathrm{SnCl}_{2}$ ?

Rashmi Sinha

Numerade Educator

Problem 51

Calculate the amounts of $\mathrm{Cu}$ and $\mathrm{Br}_{2}$ produced in $1.0 \mathrm{~h}$ at inert electrodes in a solution of $\mathrm{CuBr}_{2}$ by a current of $4.50 \mathrm{~A}$.

Shazia Naz

Numerade Educator

Problem 52

In the electrolysis of an aqueous $\mathrm{AgNO}_{3}$ solution. $0.67 \mathrm{~g}$ of $\mathrm{Ag}$ is deposited after a certain period of time. (a) Write the half-reaction for the reduction of $\mathrm{Ag}^{+}$. (b) What is the probable oxidation halfreaction? (c) Calculate the quantity of electricity used, in coulombs.

Manik Pulyani

Numerade Educator

Problem 53

A steady current was passed through molten $\operatorname{CoSO}_{4}$ until $2.35 \mathrm{~g}$ of metallic cobalt was produced. Calculate the number of coulombs of electricity used.

Ronald Prasad

Numerade Educator

Problem 54

A constant electric current flows for $3.75 \mathrm{~h}$ through two electrolytic cells connected in series. One contains a solution of $\mathrm{AgNO}_{3}$ and the second a solution of $\mathrm{CuCl}_{2}$. During this time $2.00 \mathrm{~g}$ of silver are deposited in the first cell. (a) How many grams of copper are deposited in the second cell? (b) What is the current flowing, in amperes?

Shazia Naz

Numerade Educator

Problem 55

What is the hourly production rate of chlorine gas (in kg) from an electrolytic cell using aqueous $\mathrm{NaCl}$ electrolyte and carrying a current of $1.500 \times 10^{3} \mathrm{~A}$ ?
The anode efficiency for the oxidation of $\mathrm{Cl}^{-}$ is $93.0$ percent.

Kevin Zaborsky

Numerade Educator

Problem 56

Chromium plating is applied by electrolysis to objects suspended in a dichromate solution, according to the following (unbalanced) half-reaction:
$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+e^{-}+\mathrm{H}^{+}(a q) \longrightarrow \mathrm{Cr}(s)+\mathrm{H}_{2} \mathrm{O}(l)$
How long (in hours) would it take to apply a chromium plating $1.0 \times 10^{-2} \mathrm{~mm}$ thick to a car bumper with a surface area of $0.25 \mathrm{~m}^{2}$ in an electrolytic cell carrying a current of $25.0 \mathrm{~A} ?$ (The density of chromium is $7.19 \mathrm{~g} / \mathrm{cm}^{3} .$ )

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 57

The passage of a current of $0.750 \mathrm{~A}$ for $25.0 \mathrm{~min} \mathrm{de}-$ posited $0.369 \mathrm{~g}$ of copper from a $\mathrm{CuSO}_{4}$ solution. From this information, calculate the molar mass of copper.

Manik Pulyani

Numerade Educator

Problem 58

A quantity of $0.300 \mathrm{~g}$ of copper was deposited from a $\mathrm{CuSO}_{4}$ solution by passing a current of $3.00 \mathrm{~A}$ through the solution for $304 \mathrm{~s}$. Calculate the value of the Faraday constant.

Ronald Prasad

Numerade Educator

Problem 59

In a certain electrolysis experiment, $1.44 \mathrm{~g}$ of $\mathrm{Ag}$ were deposited in one cell (containing an aqueous $\mathrm{AgNO}_{3}$ solution), while $0.120 \mathrm{~g}$ of an unknown metal $\mathrm{X}$ was deposited in another cell (containing an aqueous $\mathrm{XCl}_{3}$ solution) in series with the $\mathrm{AgNO}_{3}$ cell. Calculate the molar mass of $X$.

Rashmi Sinha

Numerade Educator

Problem 60

One of the half-reactions for the electrolysis of water is
$$
2 \mathrm{H}^{+}(a q)+2 e^{-} \longrightarrow \mathrm{H}_{2}(g)
$$
If $0.845 \mathrm{~L}$ of $\mathrm{H}_{2}$ is collected at $25^{\circ} \mathrm{C}$ and $782 \mathrm{mmHg}$, how many moles of electrons had to pass through the solution?

Rashmi Sinha

Numerade Educator

Problem 61

For each of the following redox reactions, (i) write the half-reactions; (ii) write a balanced equation for the whole reaction, (iii) determine in which direction the reaction will proceed spontaneously under standard-state conditions:
(a) $\mathrm{H}_{2}(g)+\mathrm{Ni}^{2+}(a q) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{Ni}(s)$
(b) $\mathrm{MnO}_{4}^{-}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow$
$\mathrm{Mn}^{2+}(a q)+\mathrm{Cl}_{2}(g)$ (in acid solution)
(c) $\mathrm{Cr}(s)+\mathrm{Zn}^{2+}(a q) \longrightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{Zn}(s)$

Rashmi Sinha

Numerade Educator

Problem 62

The oxidation of $25.0 \mathrm{~mL}$ of a solution containing $\mathrm{Fe}^{2+}$ requires $26.0 \mathrm{~mL}$ of $0.0250 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$ in
acidic solution. Balance the following equation and calculate the molar concentration of $\mathrm{Fe}^{2+}:$
$$
\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+\mathrm{Fe}^{2+}+\mathrm{H}^{+} \longrightarrow \mathrm{Cr}^{3+}+\mathrm{Fe}^{3+}
$$

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 63

The $\mathrm{SO}_{2}$ present in air is mainly responsible for the phenomenon of acid rain. The concentration of $\mathrm{SO}_{2}$ can be determined by titrating against a standard permanganate solution as follows:
Calculate the number of grams of $\mathrm{SO}_{2}$ in a sample of air if $7.37 \mathrm{~mL}$ of $0.00800 \mathrm{M} \mathrm{KMnO}_{4}$ solution are required for the titration.

Manik Pulyani

Numerade Educator

Problem 64

A sample of iron ore weighing $0.2792 \mathrm{~g}$ was dissolved in an excess of a dilute acid solution. All the iron was first converted to Fe(II) ions. The solution then required $23.30 \mathrm{~mL}$ of $0.0194 \mathrm{M} \mathrm{KMnO}_{4}$ for oxidation to Fe(III) ions. Calculate the percent by mass of iron in the ore

Shazia Naz

Numerade Educator

Problem 65

The concentration of a hydrogen peroxide solution can be conveniently determined by titration against a standardized potassium permanganate solution in an acidic medium according to the following unbalanced equation:
$$
\mathrm{MnO}_{4}^{-}+\mathrm{H}_{2} \mathrm{O}_{2} \longrightarrow \mathrm{O}_{2}+\mathrm{Mn}^{2+}
$$
(a) Balance the above equation. (b) If $36.44 \mathrm{~mL}$ of a $0.01652 \mathrm{M} \mathrm{KMnO}_{4}$ solution are required to completely oxidize $25.00 \mathrm{~mL}$ of a $\mathrm{H}_{2} \mathrm{O}_{2}$ solution, calculate the molarity of the $\mathrm{H}_{2} \mathrm{O}_{2}$ solution.

Kevin Zaborsky

Numerade Educator

Problem 66

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

Manik Pulyani

Numerade Educator

Problem 67

Complete the following table. State whether the cell reaction is spontaneous, nonspontaneous, or at equilibrium.
$$
\begin{array}{c|c|c}
\hline \boldsymbol{E} & \boldsymbol{\Delta} \boldsymbol{G} & \text { Cell Reaction } \\
\hline>0 & & \\
\hline & >0 & \\
\hline=0 & & \\
\hline
\end{array}
$$

Manik Pulyani

Numerade Educator

Problem 68

Calcium oxalate $\left(\mathrm{CaC}_{2} \mathrm{O}_{4}\right)$ is insoluble in water. This property has been used to determine the amount of $\mathrm{Ca}^{2+}$ ions in blood. The calcium oxalate isolated from blood is dissolved in acid and titrated against a standardized $\mathrm{KMnO}_{4}$ solution as described in Problem $19.66 .$ In one test it is found that the calcium oxalate isolated from a 10.0-mL sample of blood requires $24.2 \mathrm{~mL}$ of $9.56 \times 10^{-4} \mathrm{M} \mathrm{KMnO}_{4}$ for titration. Calculate the number of milligrams of calcium per milliliter of blood.

Kevin Zaborsky

Numerade Educator

Problem 69

From the following information, calculate the solubility product of $\operatorname{AgBr}$ :
$$
\begin{array}{ll}
\mathrm{Ag}^{+}(a q)+e^{-} \longrightarrow \operatorname{Ag}(s) & E^{\circ}=0.80 \mathrm{~V} \\
\mathrm{AgBr}(s)+e^{-} \longrightarrow \mathrm{Ag}(s)+\mathrm{Br}^{-}(a q) & E^{\circ}=0.07 \mathrm{~V}
\end{array}
$$

Kevin Zaborsky

Numerade Educator

Problem 70

Consider a galvanic cell composed of the SHE and a half-cell using the reaction $\mathrm{Ag}^{+}(a q)+e^{-} \rightarrow \operatorname{Ag}(s)$. (a) Calculate the standard cell potential. (b) What is the spontaneous cell reaction under standard-state conditions? (c) Calculate the cell potential when $\left[\mathrm{H}^{+}\right]$ in the hydrogen electrode is changed to (i) $1.0 \times 10^{-2} M$ and (ii) $1.0 \times 10^{-5} M$, all other reagents being held at standard-state conditions. (d) Based on this cell arrangement, suggest a design for a pH meter.

Rashmi Sinha

Numerade Educator

Problem 71

A galvanic cell consists of a silver electrode in contact with $346 \mathrm{~mL}$ of $0.100 \mathrm{M} \mathrm{AgNO}_{3}$ solution and a magnesium electrode in contact with $288 \mathrm{~mL}$ of $0.100 M$ $\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}$ solution. (a) Calculate $E$ for the cell at $25^{\circ} \mathrm{C}$. (b) A current is drawn from the cell until $1.20 \mathrm{~g}$ of silver have been deposited at the silver electrode. Calculate $E$ for the cell at this stage of operation.

Manik Pulyani

Numerade Educator

Problem 72

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

Shazia Naz

Numerade Educator

Problem 73

Calculate the emf of the following concentration cell at $25^{\circ} \mathrm{C}$ :
$$
\operatorname{Cu}(s)\left|\mathrm{Cu}^{2+}(0.080 M) \| \mathrm{Cu}^{2+}(1.2 M)\right| \operatorname{Cu}(s)
$$

Kevin Zaborsky

Numerade Educator

Problem 74

The cathode reaction in the Leclanché cell is given by
$$
2 \mathrm{MnO}_{2}(s)+\mathrm{Zn}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{ZnMn}_{2} \mathrm{O}_{4}(s)
$$
If a Leclanché cell produces a current of $0.0050 \mathrm{~A}$, calculate how many hours this current supply will last if there are initially $4.0 \mathrm{~g}$ of $\mathrm{MnO}_{2}$ present in the cell. Assume that there is an excess of $\mathrm{Zn}^{2+}$ ions.

Rashmi Sinha

Numerade Educator

Problem 75

Suppose you are asked to verify experimentally the electrode reactions shown in Example 19.8. In addition to the apparatus and the solution, you are also given two pieces of litmus paper, one blue and the other red. Describe what steps you would take in this experiment.

Rashmi Sinha

Numerade Educator

Problem 76

For a number of years it was not clear whether mercury(I) ions existed in solution as $\mathrm{Hg}^{+}$ or as $\mathrm{Hg}_{2}^{2+}$. To distinguish between these two possibilities, we could set up the following system:
$$
\operatorname{Hg}(l)|\operatorname{soln} \mathrm{A} \| \operatorname{soln} \mathrm{B}| \operatorname{Hg}(l)
$$
where soln A contained $0.263$ g mercury(I) nitrate per liter and soln $\mathrm{B}$ contained $2.63 \mathrm{~g}$ mercury $(\mathrm{I})$ nitrate per liter. If the measured emf of such a cell is $0.0289 \mathrm{~V}$ at $18^{\circ} \mathrm{C}$, what can you deduce about the nature of the mercury(I) ions?

Rashmi Sinha

Numerade Educator

Problem 77

An aqueous KI solution to which a few drops of phenolphthalein have been added is electrolyzed using an apparatus like the one shown here:
Describe what you would observe at the anode and the cathode. (Hint: Molecular iodine is only slightly soluble in water, but in the presence of $\mathrm{I}^{-}$ ions, it forms the brown color of $\mathrm{I}_{3}^{-}$ ions. See Problem 12.98.)

Rashmi Sinha

Numerade Educator

Problem 78

A piece of magnesium metal weighing $1.56 \mathrm{~g}$ is placed in $100.0 \mathrm{~mL}$ of $0.100 \mathrm{M} \mathrm{AgNO}_{3}$ at $25^{\circ} \mathrm{C}$. Calculate $\left[\mathrm{Mg}^{2+}\right]$ and $\left[\mathrm{Ag}^{+}\right]$ in solution at equilibrium. What is the mass of the magnesium left? The volume remains constant.

Manik Pulyani

Numerade Educator

Problem 79

Describe an experiment that would enable you to determine which is the cathode and which is the anode in a galvanic cell using copper and zinc electrodes.

Shazia Naz

Numerade Educator

Problem 80

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

Rashmi Sinha

Numerade Educator

Problem 81

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

Shazia Naz

Numerade Educator

Problem 82

Consider the oxidation of ammonia:
$$
4 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)
$$
(a) Calculate the $\Delta G^{\circ}$ for the reaction. (b) If this reaction were used in a fuel cell, what would the standard cell potential be?

Rashmi Sinha

Numerade Educator

Problem 83

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

Nicole Smina

Numerade Educator

Problem 84

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

Rashmi Sinha

Numerade Educator

Problem 85

People living in cold-climate countries where there is plenty of snow are advised not to heat their garages in the winter. What is the electrochemical basis for this recommendation?

Shazia Naz

Numerade Educator

Problem 86

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

Rashmi Sinha

Numerade Educator

Problem 87

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

Rashmi Sinha

Numerade Educator

Problem 88

A 300 -mL solution of $\mathrm{NaCl}$ was electrolyzed for $6.00$ min. If the $\mathrm{pH}$ of the final solution was $12.24$ calculate the average current used.

Shazia Naz

Numerade Educator

Problem 89

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

Prashant Bana

Numerade Educator

Problem 90

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

Rashmi Sinha

Numerade Educator

Problem 91

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

Rashmi Sinha

Numerade Educator

Problem 92

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

Rashmi Sinha

Numerade Educator

Problem 93

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

Rashmi Sinha

Numerade Educator

Problem 94

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

Shazia Naz

Numerade Educator

Problem 95

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

Rashmi Sinha

Numerade Educator

Problem 96

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

Rashmi Sinha

Numerade Educator

Problem 97

Use the data in Table $19.1$ to determine whether or not hydrogen peroxide will undergo disproportionation in an acid medium: $2 \mathrm{H}_{2} \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}$.

Manik Pulyani

Numerade Educator

Problem 98

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

Rashmi Sinha

Numerade Educator

Problem 99

A galvanic cell is constructed as follows. One halfcell consists of a platinum wire immersed in a solution containing $1.0 \mathrm{MSn}^{2+}$ and $1.0 \mathrm{MSn}^{4+}$; the other half-cell has a thallium rod immersed in a solution of $1.0 M \mathrm{Tl}^{+}$. (a) Write the half-cell reactions and the overall reaction. (b) What is the equilibrium constant at $25^{\circ} \mathrm{C} ?(\mathrm{c})$ What is the cell voltage if the $\mathrm{T} 1^{+}$ concentration is increased tenfold? $\left(E_{\mathrm{Tl}^{+} / \mathrm{Tl}}^{\circ}=-0.34 \mathrm{~V} .\right)$

Manik Pulyani

Numerade Educator

Problem 100

Given the standard reduction potential for $\mathrm{Au}^{3+}$ in Table $19.1$ and
$$
\mathrm{Au}^{+}(a q)+e^{-} \longrightarrow \mathrm{Au}(s) \quad E^{\circ}=1.69 \mathrm{~V}
$$
answer the following questions. (a) Why does gold not tarnish in air? (b) Will the following disproportionation occur spontaneously?
$$
3 \mathrm{Au}^{+}(a q) \longrightarrow \mathrm{Au}^{3+}(a q)+2 \mathrm{Au}(s)
$$
(c) Predict the reaction between gold and fluorine gas.

Manik Pulyani

Numerade Educator

Problem 101

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

Shazia Naz

Numerade Educator

Problem 102

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

Manik Pulyani

Numerade Educator

Problem 103

Consider the Daniell cell in Figure 19.1. When viewed externally, the anode appears negative and the cathode positive (electrons are flowing from the anode to the cathode). Yet in solution anions are moving toward the anode, which means that it must appear positive to the anions. Because the anode cannot simultaneously be negative and positive, give an explanation for this apparently contradictory situation.

Shazia Naz

Numerade Educator

Problem 104

Use the data in Table $19.1$ to show that the decomposition of $\mathrm{H}_{2} \mathrm{O}_{2}$ (a disproportionation reaction) is spontaneous at $25^{\circ} \mathrm{C}$ :
$$
2 \mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)
$$

Shazia Naz

Numerade Educator

Problem 105

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

Rashmi Sinha

Numerade Educator

Problem 106

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

Shazia Naz

Numerade Educator

Problem 107

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

Manik Pulyani

Numerade Educator

Problem 108

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

Shazia Naz

Numerade Educator

Problem 109

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

Shazia Naz

Numerade Educator

Problem 110

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

Manik Pulyani

Numerade Educator

Problem 111

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

Manik Pulyani

Numerade Educator

Problem 112

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

Shazia Naz

Numerade Educator

Problem 113

Calculate $E^{\circ}$ for the reactions of mercury with (a) $1 M$ $\mathrm{HCl}$ and (b) $1 \mathrm{M} \mathrm{HNO}_{3}$. Which acid will oxidize $\mathrm{Hg}$ to $\mathrm{Hg}_{2}^{2+}$ under standard-state conditions? Can you identify which test tube below contains $\mathrm{HNO}_{3}$ and $\mathrm{Hg}$ and which contains $\mathrm{HCl}$ and $\mathrm{Hg}$ ?

Manik Pulyani

Numerade Educator

Problem 114

Because all alkali metals react with water, it is not possible to measure the standard reduction potentials of these metals directly as in the case of, say, zinc. An indirect method is to consider the following hypothetical reaction
$$
\mathrm{Li}^{+}(a q)+\frac{1}{2} \mathrm{H}_{2}(g) \longrightarrow \operatorname{Li}(s)+\mathrm{H}^{+}(a q)
$$
Use the appropriate equation presented in this chapter and the thermodynamic data in Appendix 3, calculate $E^{\circ}$ for $\mathrm{Li}^{+}(a q)+e^{-} \rightarrow \operatorname{Li}(s)$ at $298 \mathrm{~K}$.
Compare your result with that listed in Table $19.1$. (See back endpaper for the Faraday constant.)

Manik Pulyani

Numerade Educator

Problem 115

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

Manik Pulyani

Numerade Educator

Problem 116

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

Manik Pulyani

Numerade Educator

Problem 117

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

Shazia Naz

Numerade Educator

Problem 118

Lead storage batteries are rated by ampere hours. that is, the number of amperes they can deliver in an hour. (a) Show that $1 \mathrm{~A} \cdot \mathrm{h}=3600 \mathrm{C}$. (b) The lead anodes of a certain lead-storage battery have a total mass of $406 \mathrm{~g}$. Calculate the maximum theoretical capacity of the battery in ampere hours. Explain why in practice we can never extract this much energy from the battery. (Hint: Assume all of the lead will be used up in the electrochemical reaction and refer to the electrode reactions on p. $858 .$ )
(c) Calculate $E_{\text {cell }}^{\circ}$ and $\Delta G^{\circ}$ for the battery.

Manik Pulyani

Numerade Educator

Problem 119

Use Equations (18.10) and (19.3) to calculate the emf values of the Daniell cell at $25^{\circ} \mathrm{C}$ and $80^{\circ} \mathrm{C}$. Comment on your results. What assumptions are used in the derivation? (Hint: You need the thermodynamic data in Appendix 3.)

Manik Pulyani

Numerade Educator

Problem 120

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

Manik Pulyani

Numerade Educator

Problem 121

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

Manik Pulyani

Numerade Educator

Problem 122

Based on the following standard reduction potentials:
$$
\begin{array}{cc}
\mathrm{Fe}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{Fe}(s) & E_{1}^{\circ}=-0.44 \mathrm{~V} \\
\mathrm{Fe}^{3+}(a q)+e^{-} \longrightarrow \mathrm{Fe}^{2+}(a q) & E_{2}^{\circ}=0.77 \mathrm{~V}
\end{array}
$$
calculate the standard reduction potential for the half-reaction
$$
\mathrm{Fe}^{3+}(a q)+3 e^{-} \longrightarrow \mathrm{Fe}(s) \quad E_{3}^{\circ}=?
$$

Rashmi Sinha

Numerade Educator

Problem 123

A galvanic cell is constructed by immersing a piece of copper wire in $25.0 \mathrm{~mL}$ of a $0.20 \mathrm{M} \mathrm{CuSO}_{4}$ solution and a zinc strip in $25.0 \mathrm{~mL}$ of a $0.20 \mathrm{M} \mathrm{ZnSO}_{4}$ solution. (a) Calculate the emf of the cell at $25^{\circ} \mathrm{C}$ and predict what would happen if a small amount of concentrated $\mathrm{NH}_{3}$ solution were added to (i) the $\mathrm{CuSO}_{4}$ solution and (ii) the $\mathrm{ZnSO}_{4}$ solution. Assume that the volume in each compartment remains constant at $25.0 \mathrm{~mL}$. (b) In a separate experiment, $25.0 \mathrm{~mL}$ of $3.00 \mathrm{M} \mathrm{NH}_{3}$ are added to the $\mathrm{CuSO}_{4}$ so-
lution. If the emf of the cell is $0.68 \mathrm{~V}$, calculate the formation constant $\left(K_{\mathrm{f}}\right)$ of $\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}$.

Manik Pulyani

Numerade Educator

Problem 124

Calculate the equilibrium constant for the following reaction at $298 \mathrm{~K}$ :
$$
\mathrm{Zn}(s)+\mathrm{Cu}^{2+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{Cu}(s)
$$

Shazia Naz

Numerade Educator

Problem 125

To remove the tarnish $\left(\mathrm{Ag}_{2} \mathrm{~S}\right)$ on a silver spoon, a student carried out the following steps. First, she placed the spoon in a large pan filled with water so the spoon was totally immersed. Next, she added a few tablespoonful of baking soda (sodium bicarbonate), which readily dissolved. Finally, she placed some aluminum foil at the bottom of the pan in contact with the spoon and then heated the solution to about $80^{\circ} \mathrm{C}$. After a few minutes, the spoon was removed and rinsed with cold water. The tarnish was gone and the spoon regained its original shiny appearance. (a) Describe with equations the electrochemical basis for the procedure. (b) Adding $\mathrm{NaCl}$ instead of $\mathrm{NaHCO}_{3}$ would also work because both compounds are strong electrolytes. What is the added advantage of using $\mathrm{NaHCO}_{3} ?$ (Hint: Consider the $\mathrm{pH}$ of the solution.) (c) What is the purpose of heating the solution? (d) Some commercial tarnish removers containing a fluid (or paste) that is a dilute HCl solution. Rubbing the spoon with the fluid will also remove the tarnish. Name two disadvantages of using this procedure compared to the one described above.

Manik Pulyani

Numerade Educator

Problem 126

The nitrite ion $\left(\mathrm{NO}_{2}^{-}\right)$ in soil is oxidized to nitrate ion $\left(\mathrm{NO}_{3}^{-}\right)$ by the bacteria Nitrobacter agilis in the presence of oxygen. The half-reduction reactions are
$$
\begin{aligned}
\mathrm{NO}_{3}^{-}+2 \mathrm{H}^{+}+2 e^{-} \longrightarrow \mathrm{NO}_{2}^{-}+\mathrm{H}_{2} \mathrm{O} & E^{\circ}=0.42 \mathrm{~V} \\
\mathrm{O}_{2}+4 \mathrm{H}^{+}+4 e^{-} \longrightarrow 2 \mathrm{H}_{2} \mathrm{O} & E^{\circ}=1.23 \mathrm{~V}
\end{aligned}
$$
Calculate the yield of ATP synthesis per mole of nitrite oxidized. (Hint: See Section 18.7.)

Manik Pulyani

Numerade Educator

Problem 127

Fluorine is a highly reactive gas that attacks water to form HF and other products. Follow the procedure in Problem $19.114$ to show how you can determine indirectly the standard reduction for fluorine as shown in Table $19.1$.

Manik Pulyani

Numerade Educator

Problem 128

As mentioned on p. 856 , a concentration cell ceases to operate when the concentrations of the two cell compartments are equal. At this stage, is it possible to generate an emf from the cell by adjusting another parameter without changing the concentrations? Explain.

Manik Pulyani

Numerade Educator