Question

You must estimate $E^{\circ }$ for the half-reaction ${\mathrm{In}}^{3+}(\mathrm{aq})+$ $3{\mathrm{e}}^{-}⟶\mathrm{In}(\mathrm{s}).$ 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 $\mathrm{In}(\mathrm{s})$ and ${\mathrm{In}}^{3+}(\text{ aq })$. Describe the experiments you would perform and the accuracy you would expect in your result.

Short answer

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

Construct a Galvanic Cell

With the available metals and their ions, construct a galvanic cell using indium as one half-cell (${\mathrm{In}}^{3+}(\text{ aq })/\mathrm{In}(\mathrm{s})$) 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.

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.

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.

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).

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.

Key concepts

Understanding a Galvanic Cell

A galvanic cell, also known as a voltaic cell, is an electrochemical cell that derives energy from spontaneous redox reactions occurring within the cell. Here's how it works:

• Two different metals are placed into solutions containing their respective ions.
• Each metal acts as an electrode: one as the anode, where oxidation occurs, and the other as the cathode, where reduction happens.
• The cell allows electrons to flow from the anode to the cathode through an external circuit, generating an electrical current.
• A salt bridge connects the two half-cells, maintaining electrical neutrality by allowing the ions to move between solutions.

This setup is fundamental for comparing different metals and their ability to conduct electrons through chemical reactions.

Deciphering Standard Reduction Potential

The standard reduction potential, denoted as $E^{ext°}$, is a measure of the tendency of a chemical species to gain electrons and be reduced. Here’s why it matters:

• It's measured in volts (V), with more positive values indicating a greater likelihood of gaining electrons.
• Standard conditions are defined as 25°C, 1 M concentration for solutions, and 1 atm pressure for gases.
• Reduction potentials are essential when predicting the direction of redox reactions in a galvanic cell.

Understanding these potentials allows scientists to predict which metal will act as the anode or cathode when paired with other metals in electrochemical cells.

Exploring the Indium Half-Reaction

In the context of electrochemical cells, the indium half-reaction is represented as:

$${\mathrm{In}}^{3+}(extaq)+3{\mathrm{e}}^{-}\to \mathrm{In}(exts)$$

• This reaction involves the reduction of indium ions to solid indium by gaining three electrons.
• By setting up a half-cell with indium, it's possible to compare its reduction potential against other metals.
• This particular reaction's potential is critical in predicting how indium would behave as either the anode or cathode in a galvanic cell setup.

Students appreciate seeing this reaction in real scenarios, like estimating how indium competes with other metals.

Mastering Reduction Potential Measurement

Reduction potential measurement is crucial when working with electrochemical cells. Here's a simplified approach:

• Use a voltmeter to measure the electrochemical potential between two half-cells.
• This potential difference reflects the difference between the reduction potentials of the two metals used.
• To estimate indium's reduction potential, one would set indium metal against various other metals and record the cell potentials.
• Then, using known values from standard tables, the unknown potential of the indium half-cell can be isolated and calculated.

Accuracy in these measurements depends on factors like solution concentration and instrument calibration, so care must be taken to ensure reliable results.