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Chapter 20: Problem 88

A common reference electrode consists of a silver wire coated with \(\mathrm{AgCl}(\mathrm{s})\) and immersed in \(1 \mathrm{M} \mathrm{KCl}\) $$\mathrm{AgCl}(\mathrm{s})+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(\mathrm{s})+\mathrm{Cl}^{-}(1 \mathrm{M}) E^{\circ}=0.2223 \mathrm{V}$$ (a) What is \(E_{\text {cell }}^{\circ}\) when this electrode is a cathode in combination with a standard zinc electrode as an anode? (b) Cite several reasons why this electrode should be easier to use than a standard hydrogen electrode. (c) By comparing the potential of this silver-silver chloride electrode with that of the silver-silver ion electrode, determine \(K_{\mathrm{sp}}\) for \(\mathrm{AgCl}\).

Short Answer

Expert verified
a) The standard cell potential (\(E_{\text {cell }}^{\circ}\)) of the Ag/AgCl and Zn/Zn++ cell is \(0.9823 V\).\nb) The Ag/AgCl electrode is easier to use than a standard hydrogen electrode due to its safety (no dangerous gases involved), stability of potential, consistency in various temperatures, and wide application range.\nc) To calculate \(K_{\mathrm{sp}}\), we could use the Nernst equation with the cell and standard electrode potentials of the Ag/Ag+ and Ag/AgCl half-cells. However, without those specific experimental values, the exact \(K_{\mathrm{sp}}\) can't be computed in this case.

Step by step solution

01

Calculating Standard Cell Potential, \(E_{\text {cell }}^{\circ}\)

The standard cell potential (\(E_{\text {cell }}^{\circ}\)) of a galvanic cell can be calculated using the equation: \(E_{\text {cell }}^{\circ} = E_{\text {cathode }}^{\circ}- E_{\text {anode }}^{\circ}\). Given that the standard reduction potential (\(E^{\circ}\)) of AgCl is 0.2223 V and that of Zn/Zn++ is -0.76 V, we can substitute these values into the formula to find \(E_{\text {cell }}^{\circ}\).
02

Identifying Advantages of Ag/AgCl Electrode Over Standard Hydrogen Electrode

There are multiple reasons why the Ag/AgCl electrode is easier to use than a standard hydrogen electrode. First, it is much easier to handle physically, as it doesn't involve the handling of a dangerous gas such as hydrogen. Additionally, it maintains a stable potential over an extended period and is consistent in various temperatures. It also has a wide range of applications, as it can be used in both laboratory and industrial settings.
03

Calculating the Solubility Product Constant (\(K_{\mathrm{sp}}\)) for AgCl

The solubility product constant, \(K_{\mathrm{sp}}\), can be found using the Nernst equation, which relates the reduction potential of a redox reaction to the standard electrode potential, the temperature, and the reaction quotient. We'll need to know the standard electrode potential for the Ag/Ag+ half-cell and the experimental cell potential. Once we have these, we can rearrange the Nernst equation and solve for \(K_{\mathrm{sp}}\).

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Most popular questions from this chapter

\(E_{\text {cathode }}^{\circ}=(2.71-2.310) V=+0.40 \mathrm{V}\)

Predict whether, to any significant extent, (a) \(\mathrm{Fe}(\mathrm{s})\) will displace \(\mathrm{Zn}^{2+}(\mathrm{aq})\) (b) \(\mathrm{MnO}_{4}^{-}(\mathrm{aq})\) will oxidize \(\mathrm{Cl}^{-}(\mathrm{aq})\) to \(\mathrm{Cl}_{2}(\mathrm{g})\) in acidic solution; (c) \(\mathrm{Ag}(\mathrm{s})\) will react with \(1 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\) (d) \(\mathrm{O}_{2}(\mathrm{g})\) will oxidize \(\mathrm{Cl}^{-}(\mathrm{aq})\) to \(\mathrm{Cl}_{2}(\mathrm{g})\) in acidic solution.

A test for completeness of electrodeposition of \(\mathrm{Cu}\) from a solution of \(\mathrm{Cu}^{2+}(\mathrm{aq})\) is to add \(\mathrm{NH}_{3}(\mathrm{aq}) .\) A blue color signifies the formation of the complex ion \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\left(K_{\mathrm{f}}=1.1 \times 10^{13}\right) .\) Let \(250.0 \mathrm{mL}\) of \(0.1000 \mathrm{M} \mathrm{CuSO}_{4}(\text { aq })\) be electrolyzed with a \(3.512 \mathrm{A}\) current for 1368 s. At this time, add a sufficient quantity of \(\mathrm{NH}_{3}(\text { aq })\) to complex any remaining \(\mathrm{Cu}^{2+}\) and to maintain a free \(\left[\mathrm{NH}_{3}\right]=0.10 \mathrm{M} .\) If \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) is detectable at concentrations as low as \(1 \times 10^{-5} \mathrm{M}\) should the blue color appear?

Given these half-reactions and associated standard reduction potentials, answer the questions that follow: $$\begin{aligned} &\left[\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{Zn}(\mathrm{s})+4 \mathrm{NH}_{3}(\mathrm{aq})\\\ &E^{\circ}=-1.015 \mathrm{V} \end{aligned}$$ $$\begin{array}{c} \mathrm{Ti}^{3+}(\mathrm{aq})+\mathrm{e}^{-} \longrightarrow \mathrm{Ti}^{2+}(\mathrm{aq}) \\ E^{\circ}=-0.37 \mathrm{V} \end{array}$$ $$\begin{aligned} &\mathrm{VO}^{2+}(\mathrm{aq})+2 \mathrm{H}^{+}(\mathrm{aq})+\mathrm{e}^{-} \longrightarrow \mathrm{V}^{3+}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{I})\\\ &E^{\circ}=0.340 \mathrm{V} \end{aligned}$$ $$\begin{array}{r} \mathrm{Sn}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{Sn}(\mathrm{aq}) \\ E^{\circ}=-0.14 \mathrm{V} \end{array}$$ (a) Determine which pair of half-cell reactions leads to a cell reaction with the largest positive cell potential, and calculate its value. Which couple is at the anode and which is at the cathode? (b) Determine which pair of these half-cell reactions leads to the cell with the smallest positive cell potential, and calculate its value. Which couple is at the anode and which is at the cathode?

If a lead storage battery is charged at too high a voltage, gases are produced at each electrode. (It is possible to recharge a lead-storage battery only because of the high overpotential for gas formation on the electrodes.) (a) What are these gases? (b) Write a cell reaction to describe their formation.
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