Chapter 19

What is a galvanic cell? What is a half-cell?

What is the function of a salt bridge?

In a copper-silver cell, why must the \(\mathrm{Cu}^{2+}\) and \(\mathrm{Ag}^{+}\) solutions be kept in separate containers?

What is the general name we give to reactions that take place at the anode and those that take place at the cathode in a galvanic cell? What is the sign of the electrical charges on the anode and cathode in a galvanic cell?

In a galvanic cell, do electrons travel from anode to cathode, or from cathode to anode? Explain.

Aluminum will displace tin from solution according to the equation $$ 2 \mathrm{Al}(s)+3 \mathrm{Sn}^{2+}(a q) \longrightarrow 2 \mathrm{Al}^{3+}(a q)+3 \operatorname{Sn}(s) $$ What would be the individual half-cell reactions if this were the cell reaction for a galvanic cell? Which metal would be the anode and which the cathode?

Make a sketch of a galvanic cell for which the cell notation is $$ \mathrm{Fe}(s)\left|\mathrm{Fe}^{3+}(a q) \| \mathrm{Ag}^{+}(a q)\right| \mathrm{Ag}(s) $$ (a) Label the anode and the cathode. (b) Indicate the charge on each electrode. (c) Indicate the direction of electron flow in the external circuit. (d) Write the equation for the net cell reaction.

What is the difference between a cell potential and a standard cell potential?

Galvanic cells are set up so that the cell potential always has a positive sign. What does this signify about the chemical reaction occurring in the cell?

Describe the hydrogen electrode. What is the value of its standard reduction potential?

What do the positive and negative signs of reduction potentials tell us?

Write the equation that relates the standard cell potential to the standard free energy change for a reaction.

What is the equation that relates the equilibrium constant to the cell potential?

What is the cell potential of a galvanic cell when the cell reaction has reached equilibrium?

What is a concentration cell? Why is the \(E_{\text {cell }}^{\circ}\) equal to zero for such a cell?

Describe what happens if a galvanic cell is short circuited by connecting the anode directly to the cathode.

What are the anode and cathode reactions during the discharge of a lead storage battery? How can a battery produce a potential of \(12 \mathrm{~V}\) if the cell reaction has a standard potential of only \(2 \mathrm{~V}\) ?

What are the anode and cathode reactions during the charging of a lead storage battery?

Give two reasons why lithium is such an attractive anode material for use in a battery. What are the problems associated with using lithium for this purpose?

What are the electrode materials in a typical lithium ion cell? Explain what happens when the cell is charged. Explain what happens when the cell is discharged.

Write the cathode, anode, and net cell reaction in a hydrogen-oxygen fuel cell.

What advantages do fuel cells offer over conventional means of obtaining electrical power by the combustion of fuels?

What electrical charges do the anode and the cathode carry in an electrolytic cell? What does the term inert electrode mean?

Why must electrolysis reactions occur at the electrodes in order for electrolytic conduction to continue?

Why must \(\mathrm{NaCl}\) be melted before it is electrolyzed to give \(\mathrm{Na}\) and \(\mathrm{Cl}_{2}\) ? Write the anode, cathode, and overall cell reactions for the electrolysis of molten \(\mathrm{NaCl}\).

Write half-reactions for the oxidation and the reduction of water.

Using the same current, which will require the greater length of time: depositing \(0.10 \mathrm{~mol}\) Cu from a \(\mathrm{Cu}^{2+}\) solution, or depositing \(0.10 \mathrm{~mol}\) of \(\mathrm{Cr}\) from a \(\mathrm{Cr}^{3+}\) solution? Explain your reasoning.

Describe the Hall-Héroult process for producing metallic aluminum. What half- reaction occurs at the anode? What half-reaction occurs at the cathode? What is the overall cell reaction?

In the Hall-Héroult process, why must the carbon anodes be replaced frequently?

Write the half-reactions and the balanced cell reaction for the following galvanic cells. $$ \begin{array}{l} \text { (a) } \mathrm{Zn}(s)\left|\mathrm{Zn}^{2+}(a q) \| \mathrm{Cr}^{3+}(a q)\right| \mathrm{Cr}(s) \\ \text { (b) } \mathrm{Pb}(s), \mathrm{PbSO}_{4}(s) \mid \mathrm{HSO}_{4}^{-}(a q) \| \\ \mathrm{H}^{+}(a q), \mathrm{HSO}_{4}^{2-}(a q) \mid \mathrm{PbO}_{2}(s), \mathrm{PbSO}_{4}(s) \\ \text { (c) } \mathrm{Mg}(s)\left|\mathrm{Mg}^{2+}(a q) \| \mathrm{Sn}^{2+}(a q)\right| \mathrm{Sn}(s) \end{array} $$

Write the half-reactions and the balanced cell reaction for the following galvanic cells. (a) \(\operatorname{Cd}(s)\left|\mathrm{Cd}^{2+}(a q) \| \mathrm{Au}^{3+}(a q)\right| \mathrm{Au}(s)\) (b) \(\mathrm{Fe}(s)\left|\mathrm{Fe}^{2+}(a q) \| \operatorname{Br}_{2}(a q), \operatorname{Br}^{-}(a q)\right| \operatorname{Pt}(s)\) (c) \(\operatorname{Cr}(s)\left|\mathrm{Cr}^{3+}(a q) \| \mathrm{Cu}^{2+}(a q)\right| \mathrm{Cu}(s)\)

Write the cell notation for the following galvanic cells. For half-reactions in which all the reactants are in solution or are gases, assume the use of inert platinum electrodes. $$ \begin{array}{l} \text { (a) } \mathrm{NO}_{3}^{-}(a q)+4 \mathrm{H}^{+}(a q)+3 \mathrm{Fe}^{2+}(a q) \longrightarrow \\ 3 \mathrm{Fe}^{3+}(a q)+\mathrm{NO}(g)+2 \mathrm{H}_{2} \mathrm{O} \\ \text { (b) } \mathrm{Cl}_{2}(g)+2 \mathrm{Br}^{-}(a q) \longrightarrow \mathrm{Br}_{2}(a q)+2 \mathrm{Cl}^{-}(a q) \\ \text { (c) } \mathrm{Au}^{3+}(a q)+3 \mathrm{Ag}(s) \longrightarrow \mathrm{Au}(s)+3 \mathrm{Ag}^{+}(a q) \end{array} $$

Write the cell notation for the following galvanic cells. For half-reactions in which all the reactants are in solution or are gases, assume the use of inert platinum electrodes. $$ \text { (a) } \mathrm{Cd}^{2+}(a q)+\mathrm{Fe}(s) \longrightarrow \mathrm{Cd}(s)+\mathrm{Fe}^{2+}(a q) $$ (b) \(\mathrm{NiO}_{2}(s)+4 \mathrm{H}^{+}(a q)+2 \mathrm{Ag}(s) \longrightarrow\) $$ \begin{array}{l} \mathrm{Ni}^{2+}(a q)+2 \mathrm{H}_{2} \mathrm{O}+2 \mathrm{Ag}^{+}(a q) \\ \text { (c) } \mathrm{Mg}(s)+\mathrm{Cd}^{2+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Cd}(s) \end{array} $$

Erom the half-reactions below, determine the cell reaction and standard cell potential. $$ \begin{aligned} \mathrm{BrO}_{3}^{-}+6 \mathrm{H}^{+}+6 e^{-} \rightleftharpoons \mathrm{Br}^{-}+3 \mathrm{H}_{2} \mathrm{O} & \\ & E_{\mathrm{BrO}^{-}}^{\circ}=1.44 \mathrm{~V} \\ \mathrm{I}_{2}+2 e^{-} \rightleftharpoons 2 \mathrm{I}^{-} & E_{\mathrm{l}_{2}}^{\circ}=0.54 \mathrm{~V} \end{aligned} $$

What is the standard cell potential and the net reaction in a galvanic cell that has the following half reactions? $$ \begin{aligned} \mathrm{MnO}_{2}+4 \mathrm{H}^{+}+2 e^{-} \rightleftharpoons \mathrm{Mn}^{2+} &+2 \mathrm{H}_{2} \mathrm{O} \\ & E_{\mathrm{MnO}_{2}}^{\circ}=1.23 \mathrm{~V} \\ \mathrm{PbCl}_{2}+2 e^{-} \rightleftharpoons \mathrm{Pb}+2 \mathrm{Cl}^{-} & E_{\mathrm{PbCl}}^{\mathrm{o}}=-0.27 \mathrm{~V} \end{aligned} $$

Determine whether the reaction: $$ \begin{aligned} \mathrm{S}_{2} \mathrm{O}_{8}^{2-}+\mathrm{Ni}(\mathrm{OH})_{2}+2 \mathrm{OH}^{-} & \longrightarrow \\ 2 \mathrm{SO}_{4}^{2-}+\mathrm{NiO}_{2}+2 \mathrm{H}_{2} \mathrm{O} \end{aligned} $$ will occur spontaneously under standard state conditions. Use \(E_{\text {cell }}^{\circ}\) calculated from the data below to answer the question. $$ \begin{aligned} \mathrm{NiO}_{2}+2 \mathrm{H}_{2} \mathrm{O}+2 e^{-} \rightleftharpoons \mathrm{Ni}(\mathrm{OH})_{2}+2 \mathrm{OH}^{-} \\ E_{\mathrm{NiO}_{2}}^{\circ}=0.49 \mathrm{~V} \\ \mathrm{~S}_{2} \mathrm{O}_{8}^{2-}+2 e^{-} \rightleftharpoons 2 \mathrm{SO}_{4}^{2-} & E_{\mathrm{SO}_{4}^{2-}}^{\circ}=2.01 \mathrm{~V} \end{aligned} $$

A cell was set up having the following reaction. $$ \begin{aligned} \mathrm{Mg}(s)+\mathrm{Cd}^{2+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Cd}(s) & \\ E_{\mathrm{cdl}}^{\circ} &=1.97 \mathrm{~V} \end{aligned} $$ The magnesium electrode was dipped into a \(1.00 \mathrm{M}\) solution of \(\mathrm{MgSO}_{4}\) and the cadmium electrode was dipped into a solution of unknown \(\mathrm{Cd}^{2+}\) concentration. The potential of the cell was measured to be \(1.54 \mathrm{~V}\). What was the unknown \(\mathrm{Cd}^{2+}\) concentration?

A silver wire coated with \(\mathrm{AgCl}\) is sensitive to the presence of chloride ion because of the half-cell reaction \(\mathrm{AgCl}(s)+e^{-} \rightleftharpoons \mathrm{Ag}(s)+\mathrm{Cl}^{-} \quad E_{\mathrm{AgC}}^{\circ}=0.2223 \mathrm{~V}\) A student, wishing to measure the chloride ion concentration in a number of water samples, constructed a galvanic cell using the \(\mathrm{AgCl}\) electrode as one half-cell and a copper wire dipping into \(1.00 \mathrm{M} \mathrm{CuSO}_{4}\) solution as the other half-cell. In one analysis, the potential of the cell was measured to be \(0.0895 \mathrm{~V}\) with the copper half-cell serving as the cathode. What was the chloride ion concentration in the water? (Take \(E_{\mathrm{Cu}^{2+}}^{\circ}=0.3419 \mathrm{~V}\).)

Suppose a galvanic cell was constructed at \(25^{\circ} \mathrm{C}\) using a \(\mathrm{Cu} / \mathrm{Cu}^{2+}\) half-cell (in which the molar concentration of \(\mathrm{Cu}^{2+}\) was \(1.00 \mathrm{M}\) ) and a hydrogen electrode having a partial pressure of \(\mathrm{H}_{2}\) equal to 1 atm. The hydrogen electrode dips into a solution of unknown hydrogen ionconcentration, and the two half- cells are connected by a salt bridge. The precise value of \(E_{\mathrm{cell}}^{\circ}\) is \(+0.3419 \mathrm{~V}\). (a) Derive an equation for the \(\mathrm{pH}\) of the solution with the unknown hydrogen ion concentration, expressed in terms of \(E_{\text {cell }}\) and \(E_{\text {cell }}^{\circ}\) (b) If the \(\mathrm{pH}\) of the solution were \(5.15,\) what would be the observed potential of the cell? (c) If the potential of the cell were \(0.645 \mathrm{~V}\), what would be the \(\mathrm{pH}\) of the solution?

If electrolysis is carried out on an aqueous solution of cadmium iodide, what products are expected at the electrodes? Write the equation for the net cell reaction.

The value of \(K_{\mathrm{g}}\) for \(\mathrm{AgBr}\) is \(5.4 \times 10^{-13}\). What will be the potential of a cell constructed of a standard hydrogen electrode as one half-cell and a silver wire coated with AgBr dipping into \(0.10 M \mathrm{HBr}\) as the other halfcell. For the \(\mathrm{Ag} / \mathrm{AgBr}\) electrode, $$ \begin{aligned} \mathrm{AgBr}(s)+e^{-} \rightleftharpoons \mathrm{Ag}(s)+\mathrm{Br}^{-}(a q) & \\ E_{\mathrm{AgBr}}^{\circ} &=+0.070 \mathrm{~V} \end{aligned} $$

An \(\mathrm{Ag} / \mathrm{AgCl}\) electrode dipping into \(1.00 \mathrm{M} \mathrm{HCl}\) has a standard reduction potential of \(+0.2223 \mathrm{~V}\). The half reaction is $$ \mathrm{AgCl}(s)+e^{-} \rightleftharpoons \mathrm{Ag}(s)+\mathrm{Cl}^{-}(a q) $$ A second \(\mathrm{Ag} / \mathrm{AgCl}\) electrode is dipped into a solution containing \(\mathrm{Cl}\) at an unknown concentration. The cell generates a potential of \(0.0478 \mathrm{~V}\), with the electrode in the solution of unknown concentration having a negative charge. What is the molar concentration of \(\mathrm{Cl}\) in the unknown solution?

A galvanic cell was constructed with a nickel electrode that was dipped into \(1.20 \mathrm{M} \mathrm{NiSO}_{4}\) solution and a chromium electrode that was immersed into a solution containing \(\mathrm{Cr}^{3+}\) at an unknown concentration. The potential of the cell was measured to be \(0.552 \mathrm{~V}\), with the chromium serving as the anode. The standard cell potential for this system was determined to be \(0.487 \mathrm{~V}\). What was the concentration of \(\mathrm{Cr}^{3+}\) in the solution of unknown concentration?

There are a variety of methods available for generating electricity. List as many methods as you can. Rank each of these methods based on your knowledge of (a) the efficiency of the method and (b) the environmental pollution caused by each method.

Most flashlights use two or more batteries in series. Use the concepts of galvanic cells in this chapter to explain why a flashlight with two new batteries and one "dead" battery will give only a dim light if any light is obtained at all.

If two electrolytic cells are placed in series, the same number of electrons must pass through both cells. One student argues that you can get twice as much product if two cells are placed in series compared to a single cell and therefore the cost of production (i.e., the cost of electricity) will decrease greatly and profits will increase. Is the student correct? Explain your reasoning based on the principles of electrochemistry.