# 20.E: Electrochemistry (Exercises)

These are homework exercises to accompany the Textmap created for "Chemistry: The Central Science" by Brown et al. Complementary General Chemistry question banks can be found for other Textmaps and can be accessed here. In addition to these publicly available questions, access to private problems bank for use in exams and homework is available to faculty only on an individual basis; please contact Delmar Larsen for an account with access permission.

## 20.1: Oxidation States

### Q20.1.1

Identify the oxidation state of the atoms in the following compounds:

1. $$PCl_3$$
2. $$CO_3^{2-}$$
3. $$H_2S$$
4. $$S_8$$
5. $$SCl_2$$
6. $$Na_2SO_3$$
7. $$SO_4^{2-}$$

### S20.1.1

1. The chlorine is more electronegative and so its oxidation number is set to -1. The overall molecule is neutral, so the oxidation number of P, in this case, is +3.
2. The oxygen is more electronegative and receives an oxidation number of -2. The overall molecule has a net charge of 2- (an overall oxidation number of ­2), therefore, the C must have an oxidation state of +4, i.e. (3*-2) + 'C' = -2.

3. Sulfur ($$\chi=2.5$$) is more electronegative than hydrogen ($$\chi=2.1$$), thus it has an oxidation number of -2. The hydrogen will have an oxidation number of +1.

4. This is an elemental form of sulfur, and thus would have an oxidation number of 0.

5. Chlorine (3.0) is more electronegative than sulfur (2.5), thus it has an oxidation number of -1. The sulfur thus has an oxidation number of +2.

6. Sodium (alkali metal) always has an oxidation number of +1. The oxygen (3.5) is more electronegative than sulfur (2.5), thus the oxygen would have an oxidation number of -2. The sulfur would therefore have an oxidation number of +4.

7. The oxygen is more electronegative and thus has an oxidation number of -2. The sulfur thus has an oxidation number of +6.

• Sulfur exhibits a variety of oxidation numbers (-2 to +6)
• In general the most negative oxidation number corresponds to the number of electrons which must be added to give an octet of valence electrons
• The most positive oxidation number corresponds to a loss of all valence electrons

## 20.2: Balanced Oxidation-Reduction Equations

### Q20.2.1

Which elements in the periodic table tend to be good oxidants? Which tend to be good reductants?

### Q20.2.2

If two compounds are mixed, one containing an element that is a poor oxidant and one with an element that is a poor reductant, do you expect a redox reaction to occur? Explain your answer. What do you predict if one is a strong oxidant and the other is a weak reductant? Why?

### Q20.2.3

In each redox reaction, determine which species is oxidized and which is reduced:

1. Zn(s) + H2SO4(aq) → ZnSO4(aq) + H2(g)
2. Cu(s) + 4HNO3(aq) → Cu(NO3)2(aq) + 2NO2(g) + 2H2O(l)
3. BrO3(aq) + 2MnO2(s) + H2O(l) → Br(aq) + 2MnO4(aq) + 2H+(aq)

### Q20.2.4

Single-displacement reactions are a subset of redox reactions. In this subset, what is oxidized and what is reduced? Give an example of a redox reaction that is not a single-displacement reaction.

### Q20.2.5

Of the following elements, which would you expect to have the greatest tendency to be oxidized: Zn, Li, or S? Explain your reasoning.

### S20.2.5

Li would have the greatest tendency to be oxidized because lithium has the lowest reduction potential in the electrochemical series (Eo=-3.05V) as opposed to zinc (Eo=-1.66V) and sulfur (Eo=0.14V). Therefore, lithium would be a better reducing agent and have the greatest tendency to be oxidized.

### Q20.2.6

Of these elements, which would you expect to be easiest to reduce: Se, Sr, or Ni? Explain your reasoning.

### Q20.2.7

Which of these metals produces H2 in acidic solution?

1. Ag
2. Cd
3. Ca
4. Cu

### Q20.2.8

Using the activity series, predict what happens in each situation. If a reaction occurs, write the net ionic equation.

1. Mg(s) + Cu2+(aq) →
2. Au(s) + Ag+(aq) →
3. Cr(s) + Pb2+(aq) →
4. K(s) + H2O(l) →
5. Hg(l) + Pb2+(aq) →

### Q20.2.9

Balance each redox reaction under the conditions indicated.

1. CuS(s) + NO3(aq) → Cu2+(aq) + SO42−(aq) + NO(g); acidic solution
2. Ag(s) + HS(aq) + CrO42−(aq) → Ag2S(s) + Cr(OH)3(s); basic solution
3. Zn(s) + H2O(l) → Zn2+(aq) + H2(g); acidic solution
4. O2(g) + Sb(s) → H2O2(aq) + SbO2(aq); basic solution
5. UO22+(aq) + Te(s) → U4+(aq) + TeO42−(aq); acidic solution

### Q20.2.10

Balance each redox reaction under the conditions indicated.

1. MnO4(aq) + S2O32−(aq) → Mn2+(aq) + SO42−(aq); acidic solution
2. Fe2+(aq) + Cr2O72−(aq) → Fe3+(aq) + Cr3+(aq); acidic solution
3. Fe(s) + CrO42−(aq) → Fe2O3(s) + Cr2O3(s); basic solution
4. Cl2(aq) → ClO3(aq) + Cl(aq); acidic solution
5. CO32−(aq) + N2H4(aq) → CO(g) + N2(g); basic solution

### Q20.2.11

Using the activity series, predict what happens in each situation. If a reaction occurs, write the net ionic equation; then write the complete ionic equation for the reaction.

1. Platinum wire is dipped in hydrochloric acid.
2. Manganese metal is added to a solution of iron(II) chloride.
3. Tin is heated with steam.
4. Hydrogen gas is bubbled through a solution of lead(II) nitrate.

### Q20.2.12

Using the activity series, predict what happens in each situation. If a reaction occurs, write the net ionic equation; then write the complete ionic equation for the reaction.

1. A few drops of NiBr2 are dropped onto a piece of iron.
2. A strip of zinc is placed into a solution of HCl.
3. Copper is dipped into a solution of ZnCl2.
4. A solution of silver nitrate is dropped onto an aluminum plate.

### Q20.2.13

Dentists occasionally use metallic mixtures called amalgams for fillings. If an amalgam contains zinc, however, water can contaminate the amalgam as it is being manipulated, producing hydrogen gas under basic conditions. As the filling hardens, the gas can be released, causing pain and cracking the tooth. Write a balanced chemical equation for this reaction.

### Q20.2.14

Copper metal readily dissolves in dilute aqueous nitric acid to form blue Cu2+(aq) and nitric oxide gas.

1. What has been oxidized? What has been reduced?
2. Balance the chemical equation.

### Q20.2.15

Classify each reaction as an acid–base reaction, a precipitation reaction, or a redox reaction, or state if there is no reaction; then complete and balance the chemical equation:

1. Pt2+(aq) + Ag(s) →
2. HCN(aq) + NaOH(aq) →
3. Fe(NO3)3(aq) + NaOH(aq) →
4. CH4(g) + O2(g) →

### Q20.2.16

Classify each reaction as an acid–base reaction, a precipitation reaction, or a redox reaction, or state if there is no reaction; then complete and balance the chemical equation:

1. Zn(s) + HCl(aq) →
2. 3HNO3(aq) + AlCl3(aq) →
3. K2CrO4(aq) + Ba(NO3)2(aq) →
4. Zn(s) + Ni2+(aq) →

### A20.2.16

a) This is a precipitation reaction because Zinc Chloride (which would be a solid since zinc is insoluble according to solubility rules) is produced and Hydrogen gas.

Zn(s) + 2HCl(aq) → H2(g) + ZnCl2 (s)

b) There is no reaction because there is not an acid and base, so it is not an acid-base reaction, no precipitate is formed (HCl is aq and AlNO3 is always soluble- again, this is due to solubility rules) so it's not a precipitation reaction, and the oxidation numbers of the elements do not change in the equation, so it is not a redox reaction.

3HNO3(aq) + AlCl3(aq) → Al(NO3)(aq) + 3HCl (aq)

c) This is a precipitation reaction because chromates like BaCrOare insoluble. Again, not dealing with acids and bases and not with changing oxidation numbers.

K2CrO4(aq) + Ba(NO3)2(aq) → BaCrO4 (s) + 2KNO(aq)

d) This is a redox reaction because there is a change in the oxidation number of Zn and Ni.

To find the products, split the reaction into two half reactions:

Zn(s) → Zn2+(aq) + 2e-

Ni2+(aq) + 2e→ Ni(s)

Since there are 2ein the reactants side of the second half reaction and the same number of eat the products side of the first half reaction, they cancel out and you do not have to multiply the reactions by anything. So, you get:

Zn(s) + Ni2+(aq) → Zn2+(aq) + Ni(s)

## 20.3: Voltaic Cells

### Q20.3.1

Is $$2NaOH_{(aq)} + H_2SO_{4(aq)} \rightarrow Na_2SO_{4(aq)} + 2H_2O_{(l)}$$ an oxidation–reduction reaction? Why or why not?

### Q20.3.2

If two half-reactions are physically separated, how is it possible for a redox reaction to occur? What is the name of the apparatus in which two half-reactions are carried out simultaneously?

### S20.3.2

It's possible for a redox reaction to occur when two half-reactions are physically separated if there is a complete circuit made by an external electrical connection that helps the electrons flow from the oxidation reaction to the reduction reaction. The name of the apparatus in which two half-reactions are carried out simultaneously is called the electrochemical cell.

### Q20.3.3

What is the difference between a galvanic cell and an electrolytic cell? Which would you use to generate electricity?

### Q20.3.4

What is the purpose of a salt bridge in a galvanic cell? Is it always necessary to use a salt bridge in a galvanic cell?

### Q20.3.5

One criterion for a good salt bridge is that it contains ions that have similar rates of diffusion in aqueous solution, as K+ and Cl ions do. What would happen if the diffusion rates of the anions and cations differed significantly?

### Q20.3.6

It is often more accurate to measure the potential of a redox reaction by immersing two electrodes in a single beaker rather than in two beakers. Why?

### S20.3.6

A large difference in cation/anion diffusion rates would increase resistance in the salt bridge and limit electron flow through the circuit.

### Q20.3.7

Copper(II) sulfate forms a bright blue solution in water. If a piece of zinc metal is placed in a beaker of aqueous CuSO4 solution, the blue color fades with time, the zinc strip begins to erode, and a black solid forms around the zinc strip. What is happening? Write half-reactions to show the chemical changes that are occurring. What will happen if a piece of copper metal is placed in a colorless aqueous solution of $$ZnCl_2$$?

### Q20.3.8

Consider the following spontaneous redox reaction: NO3(aq) + H+(aq) + SO32−(aq) → SO42−(aq) + HNO2(aq).

1. Write the two half-reactions for this overall reaction.
2. If the reaction is carried out in a galvanic cell using an inert electrode in each compartment, which electrode corresponds to which half-reaction?
3. Which electrode is negatively charged, and which is positively charged?

### Q20.3.9

The reaction $Pb(s) + 2VO^{2+}(aq) + 4H^+(aq) → Pb^{2+}(aq) + 2V^{3+}(aq) + 2H_2O(l)$ occurs spontaneously.

1. Write the two half-reactions for this redox reaction.
2. If the reaction is carried out in a galvanic cell using an inert electrode in each compartment, which reaction occurs at the cathode and which occurs at the anode?
3. Which electrode is positively charged, and which is negatively charged?

### Q20.3.10

Phenolphthalein is an indicator that turns pink under basic conditions. When an iron nail is placed in a gel that contains [Fe(CN)6]3−, the gel around the nail begins to turn pink. What is occurring? Write the half-reactions and then write the overall redox reaction.

Corrosion of a iron nail with a coiled copper wire, in agar-agar medium with ferroxyl indicator solution (potassium hexacyanoferrate(III), indicator of iron ions, and phenolphthalein, indicator of hydroxide ions). Image used with permission (CC BY-SA 3.0; Ricardo Maçãs).

### Q20.3.11

Sulfate is reduced to HS in the presence of glucose, which is oxidized to bicarbonate. Write the two half-reactions corresponding to this process. What is the equation for the overall reaction?

### S20.3.11

reduction: SO42−(aq) + 9H+(aq) + 8e → HS(aq) + 4H2O(l)

oxidation: C6H12O6(aq) + 12H2O(l) → 6HCO3(g) + 30H+(aq) + 24e

overall: C6H12O6(aq) + 3SO42−(aq) → 6HCO3(g) + 3H+(aq) + 3HS(aq)

### Q20.3.12

Write the spontaneous half-reactions and the overall reaction for each proposed cell diagram. State which half-reaction occurs at the anode and which occurs at the cathode.

1. Pb(s)∣PbSO4(s)∣SO42−(aq)∥Cu2+(aq)∣Cu(s)
2. Hg(l)∣Hg2Cl2(s)∣Cl(aq) ∥ Cd2+(aq)∣Cd(s)

### Q20.3.13

For each galvanic cell represented by these cell diagrams, determine the spontaneous half-reactions and the overall reaction. Indicate which reaction occurs at the anode and which occurs at the cathode.

1. Zn(s)∣Zn2+(aq) ∥ H+(aq)∣H2(g), Pt(s)
2. Ag(s)∣AgCl(s)∣Cl(aq) ∥ H+(aq)∣H2(g)∣Pt(s)
3. Pt(s)∣H2(g)∣H+(aq) ∥ Fe2+(aq), Fe3+(aq)∣Pt(s)

### S20.3.13

1. reduction: 2H+(aq) + 2e → H2(aq); cathode;

oxidation: Zn(s) → Zn2+(aq) + 2e; anode;

overall: Zn(s) + 2H+(aq) → Zn2+(aq) + H2(aq)

1. reduction: AgCl(s) + e → Ag(s) + Cl(aq); cathode;

oxidation: H2(g) → 2H+(aq) + 2e; anode;

overall: AgCl(s) + H2(g) → 2H+(aq) + Ag(s) + Cl(aq)

1. reduction: Fe3+(aq) + e → Fe2+(aq); cathode;

oxidation: H2(g) → 2H+(aq) + 2e; anode;

overall: 2Fe3+(aq) + H2(g) → 2H+(aq) + 2Fe2+(aq)

### Q20.3.14

For each redox reaction, write the half-reactions and draw the cell diagram for a galvanic cell in which the overall reaction occurs spontaneously. Identify each electrode as either positive or negative.

1. Ag(s) + Fe3+(aq) → Ag+(aq) + Fe2+(aq)
2. Fe3+(aq) + 1/2H2(g) → Fe2+(aq) + H+(aq)

### Q20.3.15

Write the half-reactions for each overall reaction, decide whether the reaction will occur spontaneously, and construct a cell diagram for a galvanic cell in which a spontaneous reaction will occur.

1. 2Cl(aq) + Br2(l) → Cl2(g) + 2Br(aq)
2. $$N_2O_4 (g) + H_2O → HNO_2 (aq) + H^+ (aq) + NO_3^- (aq)$$ (at pH=0)
3. 2H2O(l) + 2Cl(aq) → H2(g) + Cl2(g) + 2OH(aq)
4. C3H8(g) + 5O2(g) → 3CO2(g) + 4H2O(g)

### S20.3.15

Review Here for solutions: https://chem.libretexts.org/LibreTex...xtra_Credit_13

### Q20.3.16

Write the half-reactions for each overall reaction, decide whether the reaction will occur spontaneously, and construct a cell diagram for a galvanic cell in which a spontaneous reaction will occur.

1. Co(s) + Fe2+(aq) → Co2+(aq) + Fe(s)
2. O2(g) + 4H+(aq) + 4Fe2+(aq) → 2H2O(l) + 4Fe3+(aq)
3. 6Hg2+(aq) + 2NO3(aq) + 8H+ → 3Hg22+(aq) + 2NO(g) + 4H2O(l)
4. CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)

## 20.4: Cell Potential Under Standard Conditions

### Q20.4.1

Is a hydrogen electrode chemically inert? What is the major disadvantage to using a hydrogen electrode?

### Q20.4.2

List two factors that affect the measured potential of an electrochemical cell and explain their impact on the measurements.

### Q20.4.3

What is the relationship between electron flow and the potential energy of valence electrons? If the valence electrons of substance A have a higher potential energy than those of substance B, what is the direction of electron flow between them in a galvanic cell?

### S20.4.3

In a galvanic cell, the difference in potential energy of valence electrons cause the electrons to flow through the circuit from anode to cathode. This in turns produce a current. If the valence electrons of substance A have a higher potential energy than those of substance B, the electrons will flow from A to B.

### Q20.4.4

If the components of a galvanic cell include aluminum and bromine, what is the predicted direction of electron flow? Why?

### Q20.4.5

Write a cell diagram representing a cell that contains the Ni/Ni2+ couple in one compartment and the SHE in the other compartment. What are the values of E°cathode, E°anode, and E°cell?

### S20.4.5

Ni(s)∣Ni2+(aq)∥H+(aq, 1 M)∣H2(g, 1 atm)∣Pt(s)

 $$E^\circ_{\textrm{anode}} \\ E^\circ_{\textrm{cathode}} \\ E^\circ_{\textrm{cell}}$$ $$\mathrm{Ni^{2+}(aq)}+\mathrm{2e^-}\rightarrow\mathrm{Ni(s)};\;-\textrm{0.257 V} \\ \mathrm{2H^+(aq)}+\mathrm{2e^-}\rightarrow\mathrm{H_2(g)};\textrm{ 0.000 V} \\ \mathrm{2H^+(aq)}+\mathrm{Ni(s)}\rightarrow\mathrm{H_2(g)}+\mathrm{Ni^{2+}(aq)};\textrm{ 0.257 V}$$

### Q20.4.6

Explain why E° values are independent of the stoichiometric coefficients in the corresponding half-reaction.

### Q20.4.7

Identify the oxidants and the reductants in each redox reaction.

1. Cr(s) + Ni2+(aq) → Cr2+(aq) + Ni(s)
2. Cl2(g) + Sn2+(aq) → 2Cl(aq) + Sn4+(aq)
3. H3AsO4(aq) + 8H+(aq) + 4Zn(s) → AsH3(g) + 4H2O(l) + 4Zn2+(aq)
4. 2NO2(g) + 2OH(aq) → NO2(aq) + NO3(aq) + H2O(l)

### S20.4.7

1. oxidant: Ni2+(aq); reductant: Cr(s)
2. oxidant: Cl2(g); reductant: Sn2+(aq)
3. oxidant: H3AsO4(aq); reductant: Zn(s)
4. oxidant: NO2(g); reductant: NO2(g)

### Q20.4.8

Identify the oxidants and the reductants in each redox reaction.

1. Br2(l) + 2I(aq) → 2Br(aq) + I2(s)
2. Cu2+(aq) + 2Ag(s) → Cu(s) + 2Ag+(aq)
3. H+(aq) + 2MnO4(aq) + 5H2SO3(aq) → 2Mn2+(aq) + 3H2O(l) + 5HSO4(aq)
4. IO3(aq) + 5I(aq) + 6H+(aq) → 3I2(s) + 3H2O(l)

### Q20.4.9

All reference electrodes must conform to certain requirements. List the requirements and explain their significance.

### Q20.4.10

For each application, describe the reference electrode you would use and explain why. In each case, how would the measured potential compare with the corresponding E°?

1. measuring the potential of a Cl/Cl2 couple
2. measuring the pH of a solution
3. measuring the potential of a MnO4/Mn2+ couple

### Q20.4.11

Draw the cell diagram for a galvanic cell with an SHE and a copper electrode that carries out this overall reaction:

$H_2(g) + Cu^{2+}(aq) → 2H^+(aq) + Cu(s)$

### S20.4.10

Pt(s)∣H2(g, 1 atm) | H+(aq, 1M)∥Cu2+(aq)∣Cu(s)

### Q20.4.12

Draw the cell diagram for a galvanic cell with an SHE and a zinc electrode that carries out this overall reaction: Zn(s) + 2H+(aq) → Zn2+(aq) + H2(g).

### Q20.4.13

Balance each reaction and calculate the standard electrode potential for each. Be sure to include the physical state of each product and reactant.

1. Cl2(g) + H2(g) → 2Cl(aq) + 2H+(aq)
2. Br2(aq) + Fe2+(aq) → 2Br(aq) + Fe3+(aq)
3. Fe3+(aq) + Cd(s) → Fe2+(aq) + Cd2+(aq)

### S20.4.13

1. Cl2(g) + H2(g) → 2Cl(aq) + 2H+(aq); E° = 1.358 V
2. Br2(l) + 2Fe2+(aq) → 2Br(aq) + 2Fe3+(aq); E° = 0.316 V
3. 2Fe3+(aq) + Cd(s) → 2Fe2+(aq) + Cd2+(aq); E° = 1.174 V

### Q20.4.14

Balance each reaction and calculate the standard reduction potential for each. Be sure to include the physical state of each product and reactant.

1. Cu+(aq) + Ag+(aq) → Cu2+(aq) + Ag(s)
2. Sn(s) + Fe3+(aq) → Sn2+(aq) + Fe2+(aq)
3. Mg(s) + Br2(l) → 2Br(aq) + Mg2+(aq)

### Q20.4.15

Write a balanced chemical equation for each redox reaction.

1. H2PO2(aq) + SbO2(aq) → HPO32−(aq) + Sb(s) in basic solution
2. HNO2(aq) + I(aq) → NO(g) + I2(s) in acidic solution
3. N2O(g) + ClO(aq) → Cl(aq) + NO2(aq) in basic solution
4. Br2(l) → Br(aq) + BrO3(aq) in basic solution
5. Cl(CH2)2OH(aq) + K2Cr2O7(aq) → ClCH2CO2H(aq) + Cr3+(aq) in acidic solution

### Q20.4.16

Write a balanced chemical equation for each redox reaction.

1. I(aq) + HClO2(aq) → IO3(aq) + Cl2(g) in acidic solution
2. Cr2+(aq) + O2(g) → Cr3+(aq) + H2O(l) in acidic solution
3. CrO2(aq) + ClO(aq) → CrO42−(aq) + Cl(aq) in basic solution
4. S(s) + HNO2(aq) → H2SO3(aq) + N2O(g) in acidic solution
5. F(CH2)2OH(aq) + K2Cr2O7(aq) → FCH2CO2H(aq) + Cr3+(aq) in acidic solution

### Q20.4.17

The standard cell potential for the oxidation of Pb to Pb2+ with the concomitant reduction of Cu+ to Cu is 0.39 V. You know that E° for the Pb2+/Pb couple is −0.13 V. What is E° for the Cu+/Cu couple?

### S20.4.17

(1) Standard Cell Potential is measured by:

EoCell = EoCathode - EoAnode

(2) Cathode is where reduction occurs. Thus, Cu+/Cu is located at the cathode.

Anode is where the oxidation occurs. Thus, Pb2+/Pb is located at the anode.

(3) You are given the EoCell and EoAnode . After substituting all know values, we solve for EoCathode:

0.39V  =  EoCathode - (-0.13V)

EoCathode = +0.26V

The E° for the Cu+/Cu couple is +0.26V

### Q20.4.18

You have built a galvanic cell using an iron nail, a solution of FeCl2, and an SHE. When the cell is connected, you notice that the iron nail begins to corrode. What else do you observe? Under standard conditions, what is Ecell?

### Q20.4.19

Carbon is used to reduce iron ore to metallic iron. The overall reaction is as follows:

$2Fe_2O_3 \cdot xH_2O(s) + 3C(s) → 4Fe(l) + 3CO_2(g) + 2xH_2O(g)$

Write the two half-reactions for this overall reaction.

### Q20.4.20

Will each reaction occur spontaneously under standard conditions?

1. Cu(s) + 2H+(aq) → Cu2+(aq) + H2(g)
2. Zn2+(aq) + Pb(s) → Zn(s) + Pb2+(aq)

### Q20.4.21

Each reaction takes place in acidic solution. Balance each reaction and then determine whether it occurs spontaneously as written under standard conditions.

1. Se(s) + Br2(l) → H2SeO3(aq) + Br(aq)
2. NO3(aq) + S(s) → HNO2(aq) + H2SO3(aq)
3. Fe3+(aq) + Cr3+(aq) → Fe2+(aq) + Cr2O72−(aq)

### Q20.4.22

Calculate E°cell and ΔG° for the redox reaction represented by the cell diagram Pt(s)∣Cl2(g, 1 atm)∥ZnCl2(aq, 1 M)∣Zn(s). Will this reaction occur spontaneously?

### Q20.4.23

If you place Zn-coated (galvanized) tacks in a glass and add an aqueous solution of iodine, the brown color of the iodine solution fades to a pale yellow. What has happened? Write the two half-reactions and the overall balanced chemical equation for this reaction. What is E°cell?

### Q20.4.24

Your lab partner wants to recover solid silver from silver chloride by using a 1.0 M solution of HCl and 1 atm H2 under standard conditions. Will this plan work?

### S20.4.24

Oxidation reaction: Ag+(aq) + e--> Ag(s)    Eo=+0.800V

AgCl(s) --> Ag+(aq) + e-

HCl

## 20.5: Free Energy and Redox Reactions

### Q20.5.1

State whether you agree or disagree with this reasoning and explain your answer: Standard electrode potentials arise from the number of electrons transferred. The greater the number of electrons transferred, the greater the measured potential difference. If 1 mol of a substance produces 0.76 V when 2 mol of electrons are transferred—as in Zn(s) → Zn2+(aq) + 2e—then 0.5 mol of the substance will produce 0.76/2 V because only 1 mol of electrons is transferred.

### Q20.5.2

What is the relationship between the measured cell potential and the total charge that passes through a cell? Which of these is dependent on concentration? Which is dependent on the identity of the oxidant or the reductant? Which is dependent on the number of electrons transferred?

### Q20.5.3

In the equation wmax = −nFE°cell, which quantities are extensive properties and which are intensive properties?

### S20.5.3

extensive: wmax and n; intensive: E°cell

### Q20.5.4

For any spontaneous redox reaction, E is positive. Use thermodynamic arguments to explain why this is true.

### Q20.5.5

State whether you agree or disagree with this statement and explain your answer: Electrochemical methods are especially useful in determining the reversibility or irreversibility of reactions that take place in a cell.

### Q20.5.6

Although the sum of two half-reactions gives another half-reaction, the sum of the potentials of the two half-reactions cannot be used to obtain the potential of the net half-reaction. Why? When does the sum of two half-reactions correspond to the overall reaction? Why?

### Q20.5.7

Occasionally, you will find high-quality electronic equipment that has its electronic components plated in gold. What is the advantage of this?

### S20.5.7

Gold is highly resistant to corrosion because of its very positive reduction potential.

### Q20.5.8

Blood analyzers, which measure pH, $$P_\mathrm{CO_2}$$ , and $$P_\mathrm{O_2}$$ , are frequently used in clinical emergencies. For example, blood $$P_\mathrm{CO_2}$$ is measured with a pH electrode covered with a plastic membrane that is permeable to CO2. Based on your knowledge of how electrodes function, explain how such an electrode might work. Hint: CO2(g) + H2O(l) → HCO3(aq) + H+(aq).

### Q20.5.9

Concentration cells contain the same species in solution in two different compartments. Explain what produces a voltage in a concentration cell. When does V = 0 in such a cell?

### Q20.5.10

Describe how an electrochemical cell can be used to measure the solubility of a sparingly soluble salt.

### Q20.5.11

The chemical equation for the combustion of butane is as follows:

$$\mathrm{C_4H_{10}(g)+\frac{13}{2}O_2(g)\rightarrow4CO_2(g)+5H_2O(g)}$$

This reaction has ΔH° = −2877 kJ/mol. Calculate E°cell and then determine ΔG°. Is this a spontaneous process? What is the change in entropy that accompanies this process at 298 K?

### A20.5.11

Since there is a circle next to delta H, E cell, etc., it means "standard," in that you have to find these values at standard conditions.

K (which is used to find ΔG° with the equation ΔG°=-RT*ln Keq) is 1 at standard conditions (since gas pressures = 1 bar and K= concentrations/gas pressures of products/ concentrations/gas pressures of reactants).

Plugging in K=1 into the equation ΔG°=-RT*ln Keq, we find that ΔG°=0. This means that the reaction is at equilibrium and is neither spontaneous nor non-spontaneous.

To calculate E°cell, use the equation: ΔG°=-nFE°cell, where n is the number of electrons and F is Faraday's constant. Since ΔG°=0, E°cell=0.

To find the change in entropy, or ΔS°, use the equation: ΔG°= ΔH° - TΔS°, where T is temperature in kelvin.

So, the equation (after plugging in given ΔH°, ΔG°, and T values) would be 0 = −2877 kJ/mol - 298*ΔS°. Solving for ΔS°, we get that the change in entropy= -9.65 kJ/mol, which is equivalent to about -9650 J/mol (technically -9654 but sig figs). ΔS° is usually written as J/mol rather than kJ/mol.

### Q20.5.12

How many electrons are transferred during the reaction Pb(s) + Hg2Cl2(s) → PbCl2(aq) + 2Hg(l)? What is the standard cell potential? Is the oxidation of Pb by Hg2Cl2 spontaneous? Calculate ΔG° for this reaction.

### Q20.5.13

For the cell represented as Al(s)∣Al3+(aq)∥Sn2+(aq), Sn4+(aq)∣Pt(s), how many electrons are transferred in the redox reaction? What is the standard cell potential? Is this a spontaneous process? What is ΔG°?

### S20.5.13

6e; E°cell = 1.813 V; the reaction is spontaneous; ΔG° = −525 kJ/mol Al.

### Q20.5.14

Calculate the pH of this cell constructed with the following half reactions when the potential is 0 at 25 °C

$MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O$

$Au^{3+} + 3e^- \rightarrow Au(s)$

Under this condition, the concentrations of other species in the cell are:

• 0.36 M: $$MnO_4^-$$
• 0.004 M: $$Au^{3+}$$
• 0.001 M: $$Mn^{2+}$$

### Q20.5.15

Based on Table 19.2 and Table P2, do you agree with the proposed potentials for the following half-reactions? Why or why not?

1. Cu2+(aq) + 2e → Cu(s), E° = 0.68 V
2. Ce4+(aq) + 4e → Ce(s), E° = −0.62 V

### Q20.5.16

For each reaction, calculate E°cell and then determine ΔG°. Indicate whether each reaction is spontaneous.

1. 2Na(s) + 2H2O(l) → 2NaOH(aq) + H2(g)
2. K2S2O6(aq) + I2(s) → 2KI(aq) + 2K2SO4(aq)
3. Sn(s) + CuSO4(aq) → Cu(s) + SnSO4(aq)

### Q20.5.17

What is the standard change in free energy for the reaction between Ca2+ and Na(s) to give Ca(s) and Na+? Do the sign and magnitude of ΔG° agree with what you would expect based on the positions of these elements in the periodic table? Why or why not?

### Q20.5.18

In acidic solution, permanganate (MnO4) oxidizes Cl to chlorine gas, and MnO4 is reduced to Mn2+(aq).

1. Write the balanced chemical equation for this reaction.
2. Determine E°cell.
3. Calculate the equilibrium constant.

### Q20.5.19

Potentiometric titrations are an efficient method for determining the endpoint of a redox titration. In such a titration, the potential of the solution is monitored as measured volumes of an oxidant or a reductant are added. Data for a typical titration, the potentiometric titration of Fe(II) with a 0.1 M solution of Ce(IV), are given in the following table. The starting potential has been arbitrarily set equal to zero because it is the change in potential with the addition of the oxidant that is important.

Titrant (mL) E (mV)
2.00 50
6.00 100
9.00 255
10.00 960
11.00 1325
12.00 1625
14.00 1875
1. Write the balanced chemical equation for the oxidation of Fe2+ by Ce4+.
2. Plot the data and then locate the endpoint.
3. How many millimoles of Fe2+ did the solution being titrated originally contain?

### Q20.5.20

The standard electrode potential (E°) for the half-reaction Ni2+(aq) + 2e → Ni(s) is −0.257 V. What pH is needed for this reaction to take place in the presence of 1.00 atm H2(g) as the reductant if [Ni2+] is 1.00 M?

### Q20.5.21

The reduction of Mn(VII) to Mn(s) by H2(g) proceeds in five steps that can be readily followed by changes in the color of the solution. Here is the redox chemistry:

1. MnO4−(aq) + e → MnO42−(aq); E° = +0.56 V (purple → dark green)
2. MnO42−(aq) + 2e + 4H+(aq) → MnO2(s); E° = +2.26 V (dark green → dark brown solid)
3. MnO2(s) + e + 4H+(aq) → Mn3+(aq); E° = +0.95 V (dark brown solid → red-violet)
4. Mn3+(aq) + e → Mn2+(aq); E° = +1.51 V (red-violet → pale pink)
5. Mn2+(aq) + 2e → Mn(s); E° = −1.18 V (pale pink → colorless)

1. Is the reduction of MnO4 to Mn3+(aq) by H2(g) spontaneous under standard conditions? What is E°cell?
2. Is the reduction of Mn3+(aq) to Mn(s) by H2(g) spontaneous under standard conditions? What is E°cell?

### Q20.5.22

Mn(III) can disproportionate (both oxidize and reduce itself) by means of the following half-reactions:

Mn3+(aq) + e → Mn2+(aq)    E°=1.51 V
Mn3+(aq) + 2H2O(l) → MnO2(s) + 4H+(aq) + e    E°=0.95 V
1. What is E° for the disproportionation reaction?
2. Is disproportionation more or less thermodynamically favored at low pH than at pH 7.0? Explain your answer.
3. How could you prevent the disproportionation reaction from occurring?

### Q20.5.23

For the reduction of oxygen to water, E° = 1.23 V. What is the potential for this half-reaction at pH 7.00? What is the potential in a 0.85 M solution of NaOH?

yes; E° = 0.40 V

### Q20.5.24

The biological molecule abbreviated as NADH (reduced nicotinamide adenine dinucleotide) can be formed by reduction of NAD+ (nicotinamide adenine dinucleotide) via the half-reaction NAD+ + H+ + 2e → NADH; E° = −0.32 V.

1. Would NADH be able to reduce acetate to pyruvate?
2. Would NADH be able to reduce pyruvate to lactate?
3. What potential is needed to convert acetate to lactate?
acetate + CO2 + 2H+ +2e → pyruvate +H2O    E° = −0.70 V
pyruvate + 2H+ + 2e → lactate E° = −0.185 V

### Q20.5.25

Given the following biologically relevant half-reactions, will FAD (flavin adenine dinucleotide), a molecule used to transfer electrons whose reduced form is FADH2, be an effective oxidant for the conversion of acetaldehyde to acetate at pH 4.00?

acetate + 2H+ +2e → acetaldehyde + H2O    E° = −0.58 V

### Q20.5.26

Ideally, any half-reaction with E° > 1.23 V will oxidize water as a result of the following half-reaction:

$O_2(g) + 4H^+(aq) + 4e^− → 2H_2O(l)$

1. Will $$FeO_4^{2−}$$ oxidize water if the half-reaction for the reduction of Fe(VI) → Fe(III) is FeO42−(aq) + 8H+(aq) + 3e → Fe3+(aq) + 4H2O; E° = 1.9 V?
2. What is the highest pH at which this reaction will proceed spontaneously if [Fe3+] = [FeO42−] = 1.0 M and $$P_\mathrm{O_2}$$= 1.0 atm?

### Q20.5.27

Under acidic conditions, ideally any half-reaction with E° > 1.23 V will oxidize water via the reaction

$2H_2O(l) → O_2(g) + 4H^+(aq) + 4e^−.$

• Will aqueous acidic KMnO4 evolve oxygen with the formation of MnO2?
• At pH 14.00, what is E° for the oxidation of water by aqueous KMnO4 (1 M) with the formation of MnO2?
• At pH 14.00, will water be oxidized if you are trying to form MnO2 from MnO42− via the reaction 2MnO42−(aq) + 2H2O(l) → 2MnO2(s) + O2(g) + 4OH(aq)?

### Q20.5.28

Complexing agents can bind to metals and result in the net stabilization of the complexed species. What is the net thermodynamic stabilization energy that results from using CN as a complexing agent for Mn3+/Mn2+?

Mn3+(aq) + e → Mn2+(aq)    E° = 1.51 V
Mn(CN)63−(aq) + e → Mn(CN)64−    E° = −0.24 V

### Q20.5.29

You have constructed a cell with zinc and lead amalgam electrodes described by the cell diagram Zn(Hg)(s)∣Zn(NO3)2(aq)∥Pb(NO3)2(aq)∣Pb(Hg)(s). If you vary the concentration of Zn(NO3)2 and measure the potential at different concentrations, you obtain the following data:

Zn(NO3)2 (M) Ecell (V)
0.0005 0.7398
0.002 0.7221
0.01 0.7014
1. Write the half-reactions that occur in this cell.
2. What is the overall redox reaction?
3. What is E°cell? What is ΔG° for the overall reaction?
4. What is the equilibrium constant for this redox reaction?

### Q20.5.30

Hydrogen gas reduces Ni2+ according to the following reaction: Ni2+(aq) + H2(g) → Ni(s) + 2H+(aq); E°cell = −0.25 V; ΔH = 54 kJ/mol.

1. What is K for this redox reaction?
2. Is this reaction likely to occur?
3. What conditions can be changed to increase the likelihood that the reaction will occur as written?
4. Is the reaction more likely to occur at higher or lower pH?

### Q20.5.31

The silver–silver bromide electrode has a standard potential of 0.07133 V. What is Ksp of AgBr?

## 20.6: Cell EMF Under Nonstandard Conditions

Problems folded into 20.5. Must tease out

## 20.7: Batteries and Fuel Cells

### Q20.7.1

What advantage is there to using an alkaline battery rather than a Leclanché dry cell?

### S20.7.1

An alkaline battery is a Leclanché cell that can operate under alkaline conditions. The Alkaline cell has twice the energy density of a Leclanché cell, which allows it to produce the same voltage while having a longer shelf life and better performance. Although the Leclanché cell is inexpensive to manufacture, it corrodes easier as opposed to the Alkaline cell, which, unused, could last up to seven years and does not run out of power easily. The Alkaline cell also works well at low temperature compared to the Leclanché cell. The Alkaline battery may be heavier than other batteries but it is better for the environment and does not post serious health complications.

### Q20.7.2

Why does the density of the fluid in lead–acid batteries drop when the battery is discharged?

### Q20.7.3

What type of battery would you use for each application and why?

1. powering an electric motor scooter
2. a backup battery for a smartphone
3. powering an iPod

### Q20.7.3

2. lithium–iodine battery
3. NiCad, NiMH, or lithium ion battery (rechargeable)

### Q20.7.4

Why are galvanic cells used as batteries and fuel cells? What is the difference between a battery and a fuel cell? What is the advantage to using highly concentrated or solid reactants in a battery?

### Q20.7.5

This reaction is characteristic of a lead storage battery:

Pb(s) + PbO2(s) + 2H2SO4(aq) → 2PbSO4(s) + 2H2O(l)

If you have a battery with an electrolyte that has a density of 1.15 g/cm3 and contains 30.0% sulfuric acid by mass, is the potential greater than or less than that of the standard cell?

### S20.7.5

1. [H2SO4] = 3.52 M; E > E°

## 20.8: Corrosion

### Q20.8.1

Do you expect a bent nail to corrode more or less rapidly than a straight nail? Why?

### Q20.8.2

What does it mean when a metal is described as being coated with a sacrificial layer? Is this different from galvanic protection?

### Q20.8.3

Why is it important for automobile manufacturers to apply paint to the metal surface of a car? Why is this process particularly important for vehicles in northern climates, where salt is used on icy roads?

### S20.8.3

Paint keeps oxygen and water from coming into direct contact with the metal, which prevents corrosion. Corrosion is a naturally occurring process, and paint creates a boundary layer for the metal, in order to keep oxygen from corroding the metal. Water freezes at 0^o, which creates ice. In northern climates that will make the roads very icy if temperatures drop below 0^o, but adding salt lowers the freezing point of the water, so the water will need a lower temperature in order to turn to ice.

## 20.9: Electrolysis

### Q20.9.1

Why might an electrochemical reaction that is thermodynamically favored require an overvoltage to occur?

### Q20.9.2

How could you use an electrolytic cell to make quantitative comparisons of the strengths of various oxidants and reductants?

### S20.9.2

If we know the stoichiometry of an electrolysis or electrochemical reaction, the amount of current passed, and the length of time, we can calculate the amount of material consumed or produced in a reaction, or in other words, we can calculate the quantity of material that is oxidized or reduced at an electrode. We can determine strength of oxidants and reductants by calculating the number of moles of electrons transferred when a known current is passed through a cell. We can also use the stoichiometry of the reaction and the total charge transferred to calculate the amount of product formed or the amount of metal deposited in an electroplating process.

### Q20.9.3

Why are mixtures of molten salts, rather than a pure salt, generally used during electrolysis?

### Q20.9.4

Two solutions, one containing Fe(NO3)2·6H2O and the other containing the same molar concentration of Fe(NO3)3·6H2O, were electrolyzed under identical conditions. Which solution produced the most metal? Justify your answer.

### Q20.9.5

The electrolysis of molten salts is frequently used in industry to obtain pure metals. How many grams of metal are deposited from these salts for each mole of electrons?

1. AlCl3
2. MgCl2
3. FeCl3

### Q20.9.6

Electrolysis is the most direct way of recovering a metal from its ores. However, the Na+(aq)/Na(s), Mg2+(aq)/Mg(s), and Al3+(aq)/Al(s) couples all have standard electrode potentials (E°) more negative than the reduction potential of water at pH 7.0 (−0.42 V), indicating that these metals can never be obtained by electrolysis of aqueous solutions of their salts. Why? What reaction would occur instead?

### Q20.9.7

What volume of chlorine gas at standard temperature and pressure is evolved when a solution of MgCl2 is electrolyzed using a current of 12.4 A for 1.0 h?

5.2 L

### Q20.9.8

What mass of copper metal is deposited if a 5.12 A current is passed through a Cu(NO3)2 solution for 1.5 h.

### Q20.9.9

What mass of PbO2 is reduced when a current of 5.0 A is withdrawn over a period of 2.0 h from a lead storage battery?

### S20.9.9

Pb+2(aq) + 2e= Pb(s)        E= -0.13V

This means that 2 moles of e- transferred is 1 mol of Pb reduced.

n = It/F

n= ((5.0A)(2.0h x 60min/hr x 60sec/min))/9.65x104c/mol

n= 0.373 mol e- transferred

0.373 mol e- transferred x 1mol Pb/2mol e= 0.187 mol Pb

0.187 mol Pb x 207.2 g/mol = 38.65 g Pb reduced

### Q20.9.10

Electrolysis of Cr3+(aq) produces Cr2+(aq). If you had 500 mL of a 0.15 M solution of Cr3+(aq), how long would it take to reduce the Cr3+ to Cr2+ using a 0.158 A current?

### Q20.9.11

Predict the products obtained at each electrode when aqueous solutions of the following are electrolyzed.

1. AgNO3
2. RbI

### S20.9.7

1. cathode: Ag(s); anode: O2(g);
2. cathode: H2(g); anode: I2(s)

### Q20.9.12

Predict the products obtained at each electrode when aqueous solutions of the following are electrolyzed.

1. MgBr2
2. Hg(CH3CO2)2
3. Al2(SO4)3