Exercises

Identify each half-reaction below as either oxidation or reduction.

(a) ${\text{Fe}}^{\mathrm{3+}}+{\text{3e}}^{\text{−}}⟶\text{Fe}$

(b) $\text{Cr}⟶{\text{Cr}}^{\mathrm{3+}}+{\text{3e}}^{\text{−}}$

(c) ${\text{MnO}}_4{}^{\mathrm{2-}}⟶{\text{MnO}}_4{}^{-}+{\text{e}}^{\text{−}}$

(d) ${\text{Li}}^{\text{+}}+{\text{e}}^{\text{−}}⟶\text{Li}$

Assuming each pair of half-reactions below takes place in an acidic solution, write a balanced equation for the overall reaction.

(a) $\text{Ca}⟶{\text{Ca}}^{\mathrm{2+}}+{\text{2e}}^{\text{−}},$ ${\text{F}}_2+{\text{2e}}^{\text{−}}⟶{\text{2F}}^{\text{−}}$

(b) $\text{Li}⟶{\text{Li}}^{\text{+}}+{\text{e}}^{\text{−}},$ ${\text{Cl}}_2+{\text{2e}}^{\text{−}}⟶{\text{2Cl}}^{\text{−}}$

(c) $\text{Fe}⟶{\text{Fe}}^{\mathrm{3+}}+{\text{3e}}^{\text{−}},$ ${\text{Br}}_2+{\text{2e}}^{-}⟶{\text{2Br}}^{-}$

(d) $\text{Ag}⟶{\text{Ag}}^{\text{+}}+{\text{e}}^{\text{−}},$ ${\text{MnO}}_4{}^{-}+{\text{4H}}^{\text{+}}+{\text{3e}}^{\text{−}}⟶{\text{MnO}}_2+{\text{2H}}_2\text{O}$

Identify the oxidant and reductant of each reaction of the previous exercise.

Identify the oxidant and reductant of each reaction of the previous exercise.

Why don’t hydrogen ions appear in equations for half-reactions occurring in basic solution?

Write cell schematics for the following cell reactions, using platinum as an inert electrode as needed.

(a) $\text{Mg}(s)+{\text{Ni}}^{\mathrm{2+}}(aq)⟶{\text{Mg}}^{\mathrm{2+}}(aq)+\text{Ni}(s)$

(b) $2{\text{Ag}}^{\text{+}}(aq)+\text{Cu}(s)⟶{\text{Cu}}^{\mathrm{2+}}(aq)+\text{2Ag}(s)$

(c) $\text{Mn}(s)+{\text{Sn(NO}}_3{)}_2(aq)⟶{\text{Mn(NO}}_3{)}_2(aq)+\text{Sn}(s)$

(d) $3{\text{CuNO}}_3(aq)+{\text{Au(NO}}_3{)}_3(aq)⟶{\text{3Cu(NO}}_3{)}_2(aq)+\text{Au}(s)$

Write a balanced equation for the cell reaction of each cell in the previous exercise.

Identify the oxidant and reductant in each reaction of the previous exercise.

Why is a salt bridge necessary in galvanic cells like the one in Figure 16.3?

An active (metal) electrode was found to lose mass as the oxidation-reduction reaction was allowed to proceed. Was the electrode an anode or a cathode? Explain.

Calculate the standard cell potential for each reaction below, and note whether the reaction is spontaneous under standard state conditions.

(a) $\text{Mg}(s)+{\text{Ni}}^{\mathrm{2+}}(aq)⟶{\text{Mg}}^{\mathrm{2+}}(aq)+\text{Ni}(s)$

(b) $2{\text{Ag}}^{\text{+}}(aq)+\text{Cu}(s)⟶{\text{Cu}}^{\mathrm{2+}}(aq)+\text{2Ag}(s)$

(c) $\text{Mn}(s)+{\text{Sn(NO}}_3{)}_2(aq)⟶{\text{Mn(NO}}_3{)}_2(aq)+\text{Sn}(s)$

(d) $3{\text{Fe(NO}}_3{)}_2(aq)+{\text{Au(NO}}_3{)}_3(aq)⟶{\text{3Fe(NO}}_3{)}_3(aq)+\text{Au}(s)$

Write the balanced cell reaction for the cell schematic below, calculate the standard cell potential, and note whether the reaction is spontaneous under standard state conditions.

$\text{Cu}(s)│{\text{Cu}}^{\mathrm{2+}}(aq)║{\text{Au}}^{\mathrm{3+}}(aq)│\text{Au}(s)$

Determine the cell reaction and standard cell potential at 25 °C for a cell made from an anode half-cell containing a cadmium electrode in 1 M cadmium nitrate and a cathode half-cell consisting of an aluminum electrode in 1 M aluminum nitrate solution. Is the reaction spontaneous at standard conditions?

For each pair of standard cell potential and electron stoichiometry values below, calculate a corresponding standard free energy change (kJ).

(a) 0.000 V, n = 2

(b) +0.434 V, n = 2

(c) −2.439 V, n = 1

Determine the standard cell potential and the cell potential under the stated conditions for the electrochemical reactions described here. State whether each is spontaneous or nonspontaneous under each set of conditions at 298.15 K.

(a) $\text{Hg}(l)+{\text{S}}^{\mathrm{2-}}(aq\text{, 0.10}M)+2{\text{Ag}}^{\text{+}}(aq\text{, 0.25}M)⟶2\text{Ag}(s)+\text{HgS}(s)$

(b) The cell made from an anode half-cell consisting of an aluminum electrode in 0.015 M aluminum nitrate solution and a cathode half-cell consisting of a nickel electrode in 0.25 M nickel(II) nitrate solution.

(c) The cell comprised of a half-cell in which aqueous bromide ion (1.0 M) is being oxidized to aqueous bromine (0.11 M) and a half-cell in which Al³⁺ (0.023 M) is being reduced to aluminum metal.

Use the data in Appendix L to calculate equilibrium constants for the following reactions. Assume 298.15 K if no temperature is given.

(a) $\text{AgCl}(s)\rightleftharpoons {\text{Ag}}^{\text{+}}(aq)+{\text{Cl}}^{\text{−}}(aq)$

(b) $\text{CdS}(s)\rightleftharpoons {\text{Cd}}^{\mathrm{2+}}(aq)+{\text{S}}^{\mathrm{2-}}(aq)\text{at 377 K}$

(c) ${\text{Hg}}^{\mathrm{2+}}(aq)+4{\text{Br}}^{\text{−}}(aq)\rightleftharpoons {[{\text{HgBr}}_4]}^{\mathrm{2-}}(aq)$

(d) ${\text{H}}_2\text{O}(l)\rightleftharpoons {\text{H}}^{\text{+}}(aq)+{\text{OH}}^{\text{−}}(aq)\text{at 25}°C$

Consider a battery with the overall reaction: $\text{Cu}(s)+2{\text{Ag}}^{\text{+}}(aq)⟶\text{2Ag}(s)+{\text{Cu}}^{\mathrm{2+}}(aq).$

(a) What is the reaction at the anode and cathode?

(b) A battery is “dead” when its cell potential is zero. What is the value of Q when this battery is dead?

(c) If a particular dead battery was found to have [Cu²⁺] = 0.11 M, what was the concentration of silver ion?

Why do batteries go dead, but fuel cells do not?

Automobile batteries are often rated with regard to “cold-cranking amps,” a measure of the ability of the battery to perform in low-temperature weather. Suggest a reason to explain why a battery’s ability to deliver current is diminished at low temperatures. (Hint: Consider the kinetics of chemical reactions.)

Consider the following metals: Ag, Au, Mg, Ni, and Zn. Which of these metals could be used as a sacrificial anode in the cathodic protection of an underground steel storage tank? Steel is an alloy composed mostly of iron, so use −0.447 V as the standard reduction potential for steel.

If a sample of iron and a sample of zinc come into contact, the zinc corrodes but the iron does not. If a sample of iron comes into contact with a sample of copper, the iron corrodes but the copper does not. Explain this phenomenon.

Why would a sacrificial anode made of lithium metal be a bad choice

What mass of each product is produced in each of the electrolytic cells of the previous problem if a total charge of 3.33 $\times$ 10⁵ C passes through each cell?

A current of 2.345 A passes through the cell shown in Figure 16.19 for 45 minutes. What is the volume of the hydrogen collected at room temperature if the pressure is exactly 1 atm? (Hint: Is hydrogen the only gas present above the water?)