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Chapter 20: Problem 2

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.

Short Answer

Expert verified
While there is no specific numerical answer, because it will vary based on the materials used and the conditions of the experiment, the step-by-step guide provides detailed instructions on how to conduct the experiment and calculate the subsequent values of standard reduction potential for Indium. The accuracy of the experiment depends on several factors, including calibration of the voltmeter and overall temperature and nature of the competing reactions.

Step by step solution

01

Construct a Galvanic Cell

With the available metals and their ions, construct a galvanic cell using indium as one half-cell (\(\operatorname{In}^{3+}(\text { aq })/ \operatorname{In}(\mathrm{s})\)) and another metal from Table 20.1 as the second half-cell. The metal for the second half-cell should be chosen such that the electron flow is from indium to the second metal half-cell. This will generate a spontaneous reaction that can be measured.
02

Measure Reduction Potential

Measure the cell potential (\(E_{\text{cell}}\)). This potential difference recorded is the difference in standard reduction potentials between the half-cells.
03

Repeat With Different Metals

Repeat steps 1 and 2 with different metals from Table 20.1. This will give unique \(E_{\text{cell}}\) measurements that represent the difference in reduction potentials between indium and each metal.
04

Calculate Indium Reduction Potential

Calculate the standard reduction potential of the Indium half-cell. Using the equation \(E_{\text{cell}}^{°}=E_{\text{cathode}}^{°}-E_{\text{anode}}^{°}\), and by knowing the \(E_{\text{cell}}^{°}\) from your measurements and \(E_{\text{cathode}}^{°}\) from the tables (which is the metal you picked for your different half-cells), estimate the \(E_{\text{anode}}^{°}\), which in this case is for Indium (\(E_{\text{In}}^{°}\)). Here, \(E_{\text{cell}}^{°}\) is the standard cell potential, \(E_{\text{cathode}}^{°}\) is the standard reduction potential for the cathode, and \(E_{\text{anode}}^{°}\) is the standard reduction potential for the anode (which is what we're trying to estimate).
05

Taking Into Account the Accuracy

As this is an estimate, there will be some degree of error. The accuracy of the value depends on the quality and calibration of the voltmeter, and also on the concentration of the solutions, temperature, equation balance and any competing reactions. Usually, under ideal conditions, the result should be within the range of the known values.

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Most popular questions from this chapter

\(\mathrm{Ni}^{2+}\) has a more positive reduction potential than \(\mathrm{Cd}^{2+}\) (a) Which ion is more easily reduced to the metal? (b) Which metal, Ni or Cd, is more easily oxidized?

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.

Refer to standard reduction potentials, and predict which metal in each of the following pairs is the stronger reducing agent: (a) sodium or potassium (b) magnesium or barium

Construct a concept map illustrating the relationship between batteries and electrochemical ideas.

In the construction of the Statue of Liberty, a framework of iron ribs was covered with thin sheets of copper less than \(2.5 \mathrm{mm}\) thick. A layer of asbestos separated the copper skin and iron framework. Over time, the asbestos wore away and the iron ribs corroded. Some of the ribs lost more than half their mass in the 100 years before the statue was restored. At the same time, the copper skin lost only about \(4 \%\) of its thickness. Use electrochemical principles to explain these observations.
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