Electrochemistry: Chemical Change and Electrical Work

Comparing the standard electrode potentials ${\text{(E}}^{\text{o}}\text{)}$ of the Group $\text{1A(1)}$  metals $\text{Li, Na, and K}$with the negative of their first ionization energies reveals a discrepancy:

Ionization process reversed: ${\text{M}}^{\text{ + }}{\text{(g) + e}}^{\text{ - }}\rightleftharpoons \text{M(g) ( - IE)}$

Electrode reaction: ${\text{M}}^{\text{ + }}{\text{(aq) + e}}^{\text{ - }}\rightleftharpoons {\text{M(s) (E}}^{\text{o}}\text{)}$

Note that the electrode potentials do not decrease smoothly down the group, as 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 $\text{IE}$), then it would be less difficult to add an electron to an aqueous ion to form an atom (smaller ${\text{E}}^{\text{o}}$ ), yet  ${\text{Li}}^{\text{ + }}\text{(aq)}$is more difficult to reduce than ${\text{Na}}^{\text{ + }}\text{(aq)}$. Applying Hess’s law, use an approach similar to that for 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?

(a) How many minutes does it take to form 10.0 L of ${\text{O}}_{\text{2}}$ measured at  a$\text{99.8 kPa}$and  ${\text{28}}^{\text{o}}\text{C}$from water if a current of  1.3 A passes through the electrolytic cell? 

(b) What mass of ${\text{H}}_{\text{2}}$ forms?

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

(a) molten electrolysis and 

(b) aqueous electrolysis.

To improve conductivity in the electroplating of automobile bumpers, a thin coating of copper separates the steel from a heavy coating of chromium. 

1. What mass of $\text{Cu}$ is deposited on an automobile trim piece if plating continues for $\text{1.25 h}$at a current of $\text{5.0 A}$ ?
2. If the area of the trim piece is ${\text{50.0 cm}}^{\text{2}}$, what is the thickness of the $\text{Cu}$ coating ( d of ${\text{Cu = 8.95 g/cm}}^{\text{3}}$ )?

You are given the following three half-reactions:

 $$\begin{gathered} {\text{(1) Fe}}^{\text{3 + }}{\text{(aq) + e}}^{\text{ - }}\rightleftharpoons {\text{Fe}}^{\text{2 + }}\text{(aq)} \\ {\text{(2) Fe}}^{\text{2 + }}{\text{(aq) + 2e}}^{\text{ - }}\rightleftharpoons \text{Fe(s)} \\ {\text{(3) Fe}}^{\text{3 + }}{\text{(aq) + 3e}}^{\text{ - }}\rightleftharpoons \text{Fe(s)} \end{gathered}$$

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  g of Zn dissolves?

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 $\mathbf{\text{298}}$  K.

In an electric power plant, personnel monitor the ${\mathbf{\text{O}}}_{\mathbf{\text{2}}}$  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?

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

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

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:

$$\begin{gathered} {\mathbf{\text{U}}}^{\mathbf{\text{3 + }}}{\mathbf{\text{(aq) + Cr}}}^{\mathbf{\text{3 + }}}\mathbf{\text{(aq)}}\mathbf{\to }{\mathbf{\text{Cr}}}^{\mathbf{\text{2 + }}}{\mathbf{\text{(aq) + U}}}^{\mathbf{\text{4 + }}}\mathbf{\text{(aq)}} \\ {\mathbf{\text{Fe(s) + Sn}}}^{\mathbf{\text{2 + }}}\mathbf{\text{(aq)}}\mathbf{\to }{\mathbf{\text{Sn(s) + Fe}}}^{\mathbf{\text{2 + }}}\mathbf{\text{(aq)}} \\ {\mathbf{\text{Fe(s) + U}}}^{\mathbf{\text{4 + }}}\mathbf{\text{(aq)}}\mathbf{\to }\mathbf{\text{ no reaction }} \\ {\mathbf{\text{Cr}}}^{\mathbf{\text{3 + }}}\mathbf{\text{(aq) + Fe(s)}}\mathbf{\to }{\mathbf{\text{Cr}}}^{\mathbf{\text{2 + }}}{\mathbf{\text{(aq) + Fe}}}^{\mathbf{\text{2 + }}}\mathbf{\text{(aq)}} \\ {\mathbf{\text{Cr}}}^{\mathbf{\text{2 + }}}{\mathbf{\text{(aq) + Sn}}}^{\mathbf{\text{2 + }}}\mathbf{\text{(aq)}}\mathbf{\to }{\mathbf{\text{Sn(s) + Cr}}}^{\mathbf{\text{3 + }}}\mathbf{\text{(aq)}} \end{gathered}$$

Use the half-reaction method to balance the equation for the conversion of ethanol to acetic acid in acid solution:

${\mathbf{\text{CH}}}_{\mathbf{\text{3}}}{\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{OH + Cr}}}_{\mathbf{\text{2}}}{{\mathbf{\text{O}}}_{\mathbf{\text{7}}}}^{\mathbf{\text{2 - }}}\mathbf{\to }{\mathbf{\text{CH}}}_{\mathbf{\text{3}}}{\mathbf{\text{COOH + Cr}}}^{\mathbf{\text{3 + }}}$

When zinc is refined by electrolysis, the desired half reaction at the cathode is:

 ${\mathbf{\text{Zn}}}^{\mathbf{\text{2 + }}}{\mathbf{\text{(aq) + 2e}}}^{\mathbf{\text{ - }}}\mathbf{\to }\mathbf{\text{Zn(s)}}$

A competing reaction, which lowers the yield, is the formation of hydrogen gas:

 ${\mathbf{\text{2H}}}^{\mathbf{\text{ + }}}{\mathbf{\text{(aq) + 2e}}}^{\mathbf{\text{ - }}}\mathbf{\to }{\mathbf{\text{H}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$

If   $\mathbf{\text{91.50\% }}$of the current flowing results in zinc being deposited, while $\mathbf{\text{8.50\% }}$  produces hydrogen gas, how many litres of ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}$ , measured at STP, form per kilogram of zinc?

A chemist designs an ion-specific probe for measuring [ ${\text{Ag}}^{\text{ + }}$] in an NaCl solution saturated with AgCl. One half-cell has an Ag-wire electrode immersed in the unknown AgCl saturated 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 calomel ( ${\mathbf{\text{Hg}}}_{\mathbf{\text{2}}}{\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}$)] in a saturated KCl solution. The measured ${\text{E}}_{\text{cell}}$  is  $\text{0.060}$ V. (a) Given the following standard half-reactions, calculate [${\text{Ag}}^{\text{ + }}$ ]. 

Calomel:  ${\text{Hg}}_{\text{2}}{\text{Cl}}_{\text{2}}{\text{(s) + 2e}}^{\text{ - }}\to {\text{2Hg + 2Cl}}^{\text{ - }}{\text{ E}}^{\text{o}}\text{ = 0.24 V}$

Silver:  ${\text{Ag}}^{+}{\text{(aq) + e}}^{\text{ - }}\to {\text{Ag(s) E}}^{\text{o}}\text{ = 0.80 V}$

(Hint: Assume [ ${\text{Cl}}^{\text{ - }}$] is so high that it is essentially constant.) (b) A mining engineer wants an ore sample analyzed with the ${\text{Ag}}^{\text{ + }}$ - selective probe. After pre-treating the ore sample, the chemist measures the cell voltage as   V. What is [ ${\text{Ag}}^{\text{ + }}$]?

The following reactions are used in batteries:

 $\begin{array}{c}{\mathbf{\text{I 2H}}}_{\mathbf{\text{2}}}{\mathbf{\text{(g)+O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\to }{\mathbf{\text{2H}}}_{\mathbf{\text{2}}}{\mathbf{\text{O(l) E}}}_{\mathbf{\text{cell}}}\mathbf{\text{=1.23 V}}\\ {\mathbf{\text{II Pb(s)+PbO}}}_{\mathbf{\text{2}}}{\mathbf{\text{(s)+2H}}}_{\mathbf{\text{2}}}{\mathbf{\text{SO}}}_{\mathbf{\text{4}}}\mathbf{\text{(aq)}}\mathbf{\to }{\mathbf{\text{2PbSO}}}_{\mathbf{\text{4}}}{\mathbf{\text{(s)+2H}}}_{\mathbf{\text{2}}}{\mathbf{\text{O(l) E}}}_{\mathbf{\text{cell}}}\mathbf{\text{=2.04 V}}\\ {\mathbf{\text{III 2Na(l)+FeCl}}}_{\mathbf{\text{2}}}\mathbf{\text{(s)}}\mathbf{\to }{\mathbf{\text{2NaCl(s)+Fe(s) E}}}_{\mathbf{\text{cell}}}\mathbf{\text{=2.35 V}}\end{array}$

The 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 $∆\text{G}$ . (b) Calculate the ratio, in kJ/g, of ${\text{w}}_{\text{max}}$  to mass of reactants for each of the cells. Which has the highest ratio, which is 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.)

Calcium is obtained industrially by electrolysis of molten ${\mathbf{CaCl}}_{\mathbf{2}}$ and is used in aluminium alloys. How many coulombs are needed to produce 10.0 g of Ca metal? If a cell runs at 15 A, how many minutes will it take to produce 10.0 g of Ca(s)?

In addition to reacting with gold (see Problem ), aqua regia is used to bring other precious metals into the solution. Balance the skeleton equation for the reaction with Pt:

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

In Appendix D, standard electrode potentials range from about $\text{ + 3}$to $\text{- 3 V}$. 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 $\text{6 V}$ . However, most commercial aqueous voltaic cells have ${\text{E}}^{\text{o}}$ values of $\text{1.5}$ to $\text{2 V}$ . Why are there no aqueous cells with significantly higher potentials?

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$\text{12kg Mg}$ bar is attached to an iron pipe, and it takes  $\text{8.5 yr}$ for the Mg to be consumed. What is the average current flowing between the Mg and the Fe during this period?

Use Appendix D to calculate the  ${\mathbf{K}}_{\mathbf{sp}}$ of AgCl.

If the ${\mathbf{E}}_{\mathbf{cell}}$of the following cell is $\mathbf{0}\mathbf{.}\mathbf{915}\mathbf{ }\mathbf{V}$. what is the $\mathbf{pH}$ in the anode compartment? 

$\mathbf{Pt}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{\left|}{\mathbf{H}}_{\mathbf{2}}\mathbf{(}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{ }\mathbf{atm}\mathbf{)}\mathbf{\right|}{\mathbf{H}}^{\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}{\mathbf{Ag}}^{\mathbf{+}}\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{100}\mathbf{M}\mathbf{)}\mathbf{\mid }\mathbf{Ag}\mathbf{\left(}\mathbf{s}\mathbf{\right)}$

Gasoline is a mixture of hydrocarbons, but the heat released when it burns is close to that of octane, ${\mathbf{C}}_{\mathbf{8}}{\mathbf{H}}_{\mathbf{18}}\mathbf{\left(}\mathbf{l}\mathbf{\right)}\mathbf{,}\mathbf{ }\mathbf{ }\mathbf{∆}{\mathbf{H}}_{\mathbf{f}}^{\mathbf{o}}\mathbf{=}\mathbf{-}\mathbf{250}\mathbf{.}\mathbf{1}\mathbf{ }\mathbf{KJ}\mathbf{/}\mathbf{mol}$ As an alternative to gasoline, research is underway to use   from the electrolysis of water in fuel cells to power cars. 

(a) Calculate $\mathbf{∆}{\mathit{H}}^{\mathbf{o}}$when $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{gal}$ of gasoline $\mathbf{(}\mathbf{d}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{7028}\mathbf{ }\mathbf{g}\mathbf{/}\mathbf{mL}\mathbf{)}$ burns to produce carbon dioxide gas and water vapour.

(b) How many litres of ${\mathbf{H}}_{\mathbf{2}}$ at $\mathbf{25}\mathbf{°}\mathbf{C}$and $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{atm}$must burn to produce this quantity of energy?

(c) How long would it take to produce this amount of ${\mathbf{H}}_{\mathbf{2}}$ by electrolysis with a current of $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{ }\mathbf{A}$ at $\mathbf{6}\mathbf{.}\mathbf{00}\mathbf{ }\mathbf{V}$.

(d) How much power in kilowatt hours $\mathbf{(}\mathbf{kW}\mathbf{\times }\mathbf{h}\mathbf{)}$ is required to generate this amount of ${\mathbf{H}}_{\mathbf{2}}$? $\mathbf{(}\mathbf{1}\mathbf{ }\mathbf{W}\mathbf{=}\mathbf{1}\mathbf{ }\mathbf{J}\mathbf{/}\mathbf{s}\mathbf{,}\mathbf{1}\mathbf{ }\mathbf{J}\mathbf{=}\mathbf{1}\mathbf{C}\mathbf{\times }\mathbf{V}\mathbf{,}\mathbf{and}\mathbf{1}\mathbf{ }\mathbf{kW}\mathbf{\times }\mathbf{h}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{ }\mathbf{J}\mathbf{.}\mathbf{)}$

(e) If the cell is $\mathbf{88}\mathbf{.}\mathbf{0}\mathbf{\%}$ efficient and electricity costs $\mathbf{0}\mathbf{.}\mathbf{950}\mathbf{C}$ per $\mathbf{kW}\mathbf{\times }\mathbf{h}$, what is the cost of producing the amount of ${\mathbf{H}}_{\mathbf{2}}$ equivalent to $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{gal}$ of gasoline?

A voltaic cell has one half-cell with a $\mathbf{Cu}$ bar in a $\mathbf{1}\mathbf{.}\mathbf{00}{\mathbf{MCu}}^{\mathbf{2}\mathbf{+}}$salt, and the other half-cell with a Cd bar in the same volume of a $\mathbf{1}\mathbf{.}\mathbf{00}{\mathbf{MCd}}^{\mathbf{2}\mathbf{+}}$ salt.

(a) Find ${\mathit{E}}_{\mathbf{c}\mathbf{e}\mathbf{l}\mathbf{l}}^{\mathbf{o}}$ , $\mathbf{∆}{\mathit{G}}^{\mathbf{o}}$ and $\mathit{K}$ 

(b) As the cell operates, $\left[{\mathrm{Cd}}^{2+}\right]$ increases; find ${\mathbf{E}}_{\mathbf{cell}}$ and $\mathit{\Delta }\mathit{G}$ when $\left[{\mathrm{Cd}}^{2+}\right]$ is $\mathbf{1}\mathbf{.}\mathbf{95}\mathbf{M}$.

(c) Find${\mathbf{E}}_{\mathbf{cell}}\mathbf{,}\mathbf{\Delta G}$ and $\left[{\mathrm{Cu}}^{2+}\right]$ at equilibrium.

Two concentration cells are prepared, both with   $\mathbf{90}\mathbf{.}\mathbf{0}$mL of $\mathbf{0}\mathbf{.}\mathbf{0100}$M  $\mathbf{Cu}\mathbf{(}\mathbf{N}{\mathbf{H}}_{\mathbf{3}}{\mathbf{)}}_{\mathbf{2}}$ and a Cu bar in each half-cell. 

(a) In the first concentration cell,   $\mathbf{10}\mathbf{.}\mathbf{0}$mL of  $\mathbf{0}\mathbf{.}\mathbf{500}$M  is added to one half-cell; the complex ion  $\mathbf{Cu}\mathbf{(}\mathbf{N}{\mathbf{H}}_{\mathbf{3}}{{\mathbf{)}}_{\mathbf{4}}}^{\mathbf{2}\mathbf{+}}$ forms, and ${\mathbf{E}}_{\mathbf{cell}}$  is   $\mathbf{0}\mathbf{.}\mathbf{129}$V. Calculate ${\mathbf{K}}_{\mathbf{f}}$  for the formation of the complex ion. 

(b) Calculate  ${\mathbf{E}}_{\mathbf{cell}}$ when an additional   $\mathbf{10}\mathbf{.}\mathbf{0}$mL of  $\mathbf{0}\mathbf{.}\mathbf{500}$M ${\mathbf{NH}}_{\mathbf{3}}$ is added. 

(c) In the second concentration cell,   $\mathbf{10}\mathbf{.}\mathbf{0}$mL of  $\mathbf{0}\mathbf{.}\mathbf{500}$M NaOH is added to one half-cell; the precipitate $\mathbf{Cu}\mathbf{(}\mathbf{OH}{\mathbf{)}}_{\mathbf{2}}$ forms (${\mathbf{K}}_{\mathbf{sp}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{20}}$ ). Calculate ${{\mathbf{E}}^{\mathbf{o}}}_{\mathbf{cell}}$ . 

(d) What would the molarity of NaOH have to be for the addition of $\mathbf{10}\mathbf{.}\mathbf{0}$ mL to result in an ${{\mathbf{E}}^{\mathbf{o}}}_{\mathbf{cell}}$  of  $\mathbf{0}\mathbf{.}\mathbf{340}$ V?

For the reaction:

${\mathbf{S}}_{\mathbf{4}}{{\mathbf{O}}_{\mathbf{6}}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{I}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{\to }{\mathbf{I}}_{\mathbf{2}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{S}}_{\mathbf{2}}{{\mathbf{O}}_{\mathbf{3}}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{\Delta }{\mathbf{G}}^{\mathbf{o}}\mathbf{=}\mathbf{87}\mathbf{.}\mathbf{8}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

(a) Identify the oxidizing and reducing agents.

(b) Calculate ${{\mathbf{E}}^{\mathbf{o}}}_{\mathbf{cell}}$.

(c) For the reduction half-reaction, write a balanced equation, give the oxidation number of each element, and calculate ${{\mathbf{E}}^{\mathbf{o}}}_{\mathbf{half}\mathbf{-}\mathbf{cell}}$

Both Ti and V are reactive enough to displace ${\mathbf{H}}_{\mathbf{2}}$  from water. The difference in their  ${{\mathbf{E}}^{\mathbf{o}}}_{\mathbf{half}\mathbf{-}\mathbf{cell}}$ values is  $\mathbf{0}\mathbf{.}\mathbf{42}$ V.

Given:

$\mathbf{V}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{C}{\mathbf{u}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{\to }{\mathbf{V}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{Cu}\mathbf{\left(}\mathbf{s}\mathbf{\right)}$ ${\mathbf{\Delta G}}^{\mathbf{o}}\mathbf{=}\mathbf{-}\mathbf{298}$kJ/mol 

use Appendix D to calculate the ${{\mathbf{E}}^{\mathbf{o}}}_{\mathbf{half}\mathbf{-}\mathbf{cell}}$  values for V and Ti.

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 ${\mathbf{H}}_{\mathbf{2}}$  from water, those that displace ${\mathbf{H}}_{\mathbf{2}}$  from acid, and those that cannot displace ${\mathbf{H}}_{\mathbf{2}}$ .

The zinc-air battery is a less expensive alternative for silver batteries in hearing aids. The cell reaction is

$\mathbf{2}\mathbf{Zn}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}{\mathbf{O}}_{\mathbf{2}}\mathbf{\to }\mathbf{2}\mathbf{ZnO}\mathbf{\left(}\mathbf{s}\mathbf{\right)}$

A new battery weighs  $\mathbf{0}\mathbf{.}\mathbf{275}$ g. The zinc accounts for exactly  $\frac{\mathbf{1}}{\mathbf{10}}$ of the mass, and the oxygen does not contribute to the mass because it is supplied by the air.

(a) How much electricity (in C) can the battery deliver?

(b) How much free energy (in J) is released if ${\mathbf{E}}_{\mathbf{cell}}$  is  $\mathbf{1}\mathbf{.}\mathbf{3}$ V?

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:

$\mathbf{Cd}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathbf{NiO}\mathbf{\left(}\mathbf{OH}\mathbf{\right)}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{l}\mathbf{\right)}\mathbf{\to }\mathbf{2}\mathbf{Ni}\mathbf{\left(}\mathbf{OH}\mathbf{\right)}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{Cd}\mathbf{(}\mathbf{OH}{\mathbf{)}}_{\mathbf{2}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}$

A certain nicad battery weighs  $\mathbf{18}\mathbf{.}\mathbf{3}$g and has a capacity of $\mathbf{300}$mAh (that is, the cell can store charge equivalent to a current of  $\mathbf{300}$mA flowing for 1 h). (a) What is the capacity of this cell in coulombs? (b) What mass of reactants is needed to deliver  $\mathbf{300}$mAh? (c) What percentage of the cell mass consists of reactants?

Calculate the ${\mathbf{K}}_{\mathbf{f}}$ of $\mathbf{Ag}\mathbf{(}\mathbf{N}{\mathbf{H}}_{\mathbf{3}}{{\mathbf{)}}_{\mathbf{2}}}^{\mathbf{+}}$ from:

$$\begin{gathered} {\mathbf{Ag}}^{\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{e}}^{\mathbf{-}}\mathbf{\rightleftharpoons }\mathbf{Ag}{\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{,}\mathbf{ }\mathbf{ }{\mathbf{E}}^{\mathbf{o}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{80}\mathbf{V} \\ }^{\mathbf{+}} \\ \mathbf{Ag}\mathbf{(}\mathbf{N}{\mathbf{H}}_{\mathbf{3}}{\mathbf{)}}_{\mathbf{2}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{e}}^{\mathbf{-}}\mathbf{\rightleftharpoons }\mathbf{Ag}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathbf{N}{\mathbf{H}}_{\mathbf{3}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{,}\mathbf{ }{\mathbf{E}}^{\mathbf{o}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{37}\mathbf{V} \end{gathered}$$

Black-and-white photographic film is coated with silver halides. Because silver is expensive, the manufacturer monitors the ${\mathbf{Ag}}^{\mathbf{+}}$content of the waste stream, $\mathbf{[}\mathbf{A}{\mathbf{g}}^{\mathbf{+}}{\mathbf{]}}_{\mathbf{waste}}$, from the plant with an ${\mathbf{Ag}}^{\mathbf{+}}$selective electrode at ${\mathbf{25}}^{\mathbf{o}}\mathbf{C}$. A stream of known ${\mathbf{Ag}}^{\mathbf{+}}$ concentration, $\mathbf{[}\mathbf{A}{\mathbf{g}}^{\mathbf{+}}{\mathbf{]}}_{\mathbf{standard}}$, 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 [${\mathbf{Ag}}^{\mathbf{+}}$] for each solution. (b) Combine these into a single equation to find $\mathbf{[}\mathbf{A}{\mathbf{g}}^{\mathbf{+}}{\mathbf{]}}_{\mathbf{waste}}$. (c) Rewrite the equation from part (b) to find $\mathbf{[}\mathbf{A}{\mathbf{g}}^{\mathbf{+}}{\mathbf{]}}_{\mathbf{waste}}$ in ng/L.  (d) If ${\mathbf{E}}_{\mathbf{waste}}$ is  $0.003$V higher than , and the standard solution contains $\mathbf{1000}$ng/L, what is $\mathbf{[}\mathbf{A}{\mathbf{g}}^{\mathbf{+}}{\mathbf{]}}_{\mathbf{waste}}$? (e) Rewrite the equation in part (b) to find $\mathbf{[}\mathbf{A}{\mathbf{g}}^{\mathbf{+}}{\mathbf{]}}_{\mathbf{waste}}$ for a system in which T changes and ${\mathbf{T}}_{\mathbf{waste}}$ and  ${\mathbf{T}}_{\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{d}\mathbf{a}\mathbf{r}\mathbf{d}}$ may be different.

Balance the following redox reactions: