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Chapter 20: Problem 22

In each of the following examples, sketch a voltaic cell that uses the given reaction. Label the anode and cathode; indicate the direction of electron flow; write a balanced equation for the cell reaction; and calculate \(E_{\mathrm{cell}}^{\circ}\). (a) \(\mathrm{Cu}(\mathrm{s})+\mathrm{Fe}^{3+}(\mathrm{aq}) \longrightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{Fe}^{2+}(\mathrm{aq})\) (b) \(\mathrm{Pb}^{2+}(\mathrm{aq})\) is displaced from solution by \(\mathrm{Al}(\mathrm{s})\) (c) \(\mathrm{Cl}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow \mathrm{Cl}^{-}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{g})+\mathrm{H}^{+}(\mathrm{aq})\) (d) \(\mathrm{Zn}(\mathrm{s})+\mathrm{H}^{+}+\mathrm{NO}_{3}^{-} \longrightarrow \mathrm{Zn}^{2+}+\) \(\mathrm{H}_{2} \mathrm{O}(1)+\mathrm{NO}(\mathrm{g})\)

Short Answer

Expert verified
In the reaction, the copper electrode acts as the anode and is being oxidized whereas the iron ion is the cathode and is being reduced. Electrons flow from the copper electrode to the iron ions. The balanced equation for the cell reaction is \(\mathrm{Cu(s) + Fe^{3+}(aq) \rightarrow Cu^{2+}(aq) + Fe^{2+}(aq)}\). The standard electromotive force for the cell reaction is +1.11V.

Step by step solution

01

Identify the Half-Reactions

For the provided reaction, the half-reactions that lay the groundwork for the voltaic cell are: (1) Oxidation - \(\mathrm{Cu(s)} \rightarrow \mathrm{Cu^{2+}}(\mathrm{aq}) + 2e^-\) and (2) Reduction - \(\mathrm{Fe^{3+}}(\mathrm{aq}) + e^- \rightarrow \mathrm{Fe^{2+}}(\mathrm{aq})\).
02

Determine the Anode and Cathode

The anode is where oxidation occurs. Therefore, in this case, the copper electrode is the anode. The cathode is where the reduction takes place, so the iron ion is being reduced at the cathode.
03

Indicate the Direction of Electron Flow

In a voltaic cell, electrons always flow from anode to cathode. Therefore, in this case, electrons would be flowing from the copper electrode to the iron ions.
04

Write a Balanced Equation for the Cell Reaction

The balanced equation for the cell reaction is given in the problem as: \(\mathrm{Cu(s) + Fe^{3+}(aq) \rightarrow Cu^{2+}(aq) + Fe^{2+}(aq)}\).
05

Calculate \(E_{\mathrm{cell}}^{\circ}\)

To calculate \(E_{\mathrm{cell}}^{\circ}\), the standard reduction potentials of the half-reactions are needed. The standard reduction potentials are as follows: for Fe3+ to Fe2+, \(E^{\circ}_{cathode}=+0.77 V\) and for Cu to Cu2+, \(E^{\circ}_{anode}=+0.34 V\). However, as Cu to Cu2+ is acting as an anode (oxidation), its \(E^{\circ}\) will change the sign, thus \(E^{\circ}_{anode}=-0.34 V\). The standard electromotive force \(E_{\mathrm{cell}}^{\circ}\) for the reaction is calculated by: \(E^{\circ}_{cell} = E^{\circ}_{cathode} - E^{\circ}_{anode} = +0.77 V - (-0.34 V) = +1.11 V\).

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Most popular questions from this chapter

Only a tiny fraction of the diffusible ions move across a cell membrane in establishing a Nernst potential (see Focus On 20: Membrane Potentials), so there is no detectable concentration change. Consider a typical cell with a volume of \(10^{-8} \mathrm{cm}^{3},\) a surface area \((A)\) of \(10^{-6} \mathrm{cm}^{2},\) and a membrane thickness \((l)\) of \(10^{-6} \mathrm{cm}\) Suppose that \(\left[\mathrm{K}^{+}\right]=155 \mathrm{mM}\) inside the cell and \(\left[\mathrm{K}^{+}\right]=4 \mathrm{mM}\) outside the cell and that the observed Nernst potential across the cell wall is \(0.085 \mathrm{V}\). The membrane acts as a charge-storing device called a capacitor, with a capacitance, \(C,\) given by $$C=\frac{\varepsilon_{0} \varepsilon A}{l}$$ where \(\varepsilon_{0}\) is the dielectric constant of a vacuum and the product \(\varepsilon_{0} \varepsilon\) is the dielectric constant of the membrane, having a typical value of \(3 \times 8.854 \times 10^{-12}\) \(\mathrm{C}^{2} \mathrm{N}^{-1} \mathrm{m}^{-2}\) for a biological membrane. The SI unit of capacitance is the firad, \(1 \mathrm{F}=1\) coulomb per volt \(=1 \mathrm{CV}^{-1}=1 \times \mathrm{C}^{2} \mathrm{N}^{-1} \mathrm{m}^{-1}\) (a) Determine the capacitance of the membrane for the typical cell described. (b) What is the net charge required to maintain the observed membrane potential? (c) How many \(\mathrm{K}^{+}\) ions must flow through the cell membrane to produce the membrane potential? (d) How many \(\mathrm{K}^{+}\) ions are in the typical cell? (e) Show that the fraction of the intracellular \(K^{+}\) ions transferred through the cell membrane to produce the membrane potential is so small that it does not change \(\left[\mathrm{K}^{+}\right]\) within the cell.

For the reaction \(2 \mathrm{Cu}^{+}(\mathrm{aq})+\mathrm{Sn}^{4+}(\mathrm{aq}) \longrightarrow\) \(2 \mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{Sn}^{2+}(\mathrm{aq}), E_{\mathrm{cell}}^{\circ}=-0.0050 \mathrm{V}\) (a) can a solution be prepared at \(298 \mathrm{K}\) that is \(0.500 \mathrm{M}\) in each of the four ions? (b) If not, in which direction will a reaction occur?

You must estimate \(E^{\circ}\) for the half-reaction \(\operatorname{In}^{3+}(\mathrm{aq})+\) \(3 \mathrm{e}^{-} \longrightarrow \operatorname{In}(\mathrm{s}) .\) You have no electrical equipment, but you do have all of the metals listed in Table 20.1 and aqueous solutions of their ions, as well as \(\operatorname{In}(\mathrm{s})\) and \(\operatorname{In}^{3+}(\text { aq })\). Describe the experiments you would perform and the accuracy you would expect in your result.

When deciding whether a particular reaction corresponds to a cell with a positive standard cell potential, which of the following thermodynamic properties would you use to get your answer without performing any calculations? Which would you not use? Explain. (a) \(\Delta G^{\circ} ;\) (b) \(\Delta S^{\circ} ;\) (c) \(\Delta H^{\circ} ;\) (d) \(\Delta U^{\circ} ;\) (e) \(K\).

Derive a balanced equation for the reaction occurring in the cell: $$\mathrm{Fe}(\mathrm{s})\left|\mathrm{Fe}^{2+}(\mathrm{aq}) \| \mathrm{Fe}^{3+}(\mathrm{aq}), \mathrm{Fe}^{2+}(\mathrm{aq})\right| \mathrm{Pt}(\mathrm{s})$$ (a) If \(E_{\text {cell }}^{\circ}=1.21 \mathrm{V},\) calculate \(\Delta G^{\circ}\) and the equilibrium constant for the reaction. (b) Use the Nernst equation to determine the potential for the cell: $$\begin{array}{r} \mathrm{Fe}(\mathrm{s}) | \mathrm{Fe}^{2+}\left(\mathrm{aq}, 1.0 \times 10^{-3} \mathrm{M}\right) \| \mathrm{Fe}^{3+}\left(\mathrm{aq}, 1.0 \times 10^{-3} \mathrm{M}\right) \\ \mathrm{Fe}^{2+}(\mathrm{aq}, 0.10 \mathrm{M}) | \mathrm{Pt}(\mathrm{s}) \end{array}$$ (c) In light of (a) and (b), what is the likelihood of being able to observe the disproportionation of \(\mathrm{Fe}^{2+}\) into \(\mathrm{Fe}^{3+}\) and Fe under standard conditions?
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