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Chapter 20: Problem 66

An aqueous solution of \(\mathrm{K}_{2} \mathrm{SO}_{4}\) is electrolyzed by means of Pt electrodes. (a) Which of the following gases should form at the anode: \(\mathrm{O}_{2}, \mathrm{H}_{2}, \mathrm{SO}_{2}, \mathrm{SO}_{3} ?\) Explain. (b) What product should form at the cathode? Explain. (c) What is the minimum voltage required? Why is the actual voltage needed likely to be higher than this value?

Short Answer

Expert verified
a) Oxygen (\(\mathrm{O}_{2}\)) would form at the anode because the oxidation of water (\(\mathrm{H}_{2}\mathrm{O}\)) is more likely than the oxidation of sulfate (\(\mathrm{SO}_{4}^{2-}\)). b) Hydrogen (\(\mathrm{H}_{2}\)) would form at the cathode because the reduction of water (\(\mathrm{H}_{2}\mathrm{O}\)) is more thermodynamically favorable than the reduction of potassium ions (\(\mathrm{K}^{+}\)). c) The minimum voltage required for electrolysis to take place is 2.06 V. However, the actual voltage will likely be higher due to overpotential, which accounts for energy losses in the system.

Step by step solution

01

Identifying the Anodic Reaction

In electrolysis, the anode is where oxidation occurs. Here, either water (\(\mathrm{H}_{2}\mathrm{O}\)) or sulfate (\(\mathrm{SO}_{4}^{2-}\)) can be oxidized. The oxidation of water produces oxygen gas (\(\mathrm{O}_{2}\)) and hydrogen ions (\(\mathrm{H}^{+}\)) while the oxidation of sulfate would produce sulfur dioxide (\(\mathrm{SO}_{2}\)) or sulfur trioxide (\(\mathrm{SO}_{3}\)). However, the oxidation potential of \(\mathrm{SO}_{4}^{2-}\) is much higher than \(\mathrm{H}_{2}\mathrm{O}\). Therefore, it's more likely to have \(\mathrm{O}_{2}\) gas evolving at the anode.
02

Identifying the Cathodic Reaction

At the cathode, reduction takes place. Given that the electrolyte is in an aqueous solution, the possible ions that can be reduced are the potassium ions (\(\mathrm{K}^{+}\)) and the water molecules (\(\mathrm{H}_{2}\mathrm{O}\)). The reduction of \(\mathrm{K}^{+}\) is less likely due to its position on the electrochemical series which makes the reduction of water to form \(\mathrm{H}_{2}\) gas and \(\mathrm{OH}^{-}\) ions more thermodynamically favorable.
03

Calculating the Minimum Voltage Required

The minimum voltage required is determined by the difference in reduction potentials of the anode and cathode reactions, also known as the cell potential. The oxidation potential of \(\mathrm{H}_{2}\mathrm{O}\) to \(\mathrm{O}_{2}\) is 1.23 V and the reduction potential of \(\mathrm{H}_{2}\mathrm{O}\) to \(\mathrm{H}_{2}\) is -0.83 V. Hence, the minimum voltage required for the electrolysis to take place is 1.23 - (-0.83) = 2.06 V.
04

Discussing the Higher Voltage Required in Practice

The actual voltage will likely be higher due to what is known as overpotential. Overpotential denotes energy losses in an electrolytic system due to various factors such as ohmic resistance, mass transfer and kinetics of electrode reactions. Overpotential makes it necessary to use a higher voltage so that electrolysis can proceed at a practical rate.

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Most popular questions from this chapter

In your own words, define the following symbols or terms: (a) \(E^{\circ} ;\) (b) \(F ;\) (c) anode; (d) cathode.

A concentration cell is constructed of two hydrogen electrodes: one immersed in a solution with \(\left[\mathrm{H}^{+}\right]=1.0 \mathrm{M}\) and the other in \(0.65 \mathrm{M} \mathrm{KOH}\) (a) Determine \(E_{\text {cell for the reaction that occurs. }}\) (b) Compare this value of \(E_{\text {cell }}\) with \(E^{\circ}\) for the reduction of \(\mathrm{H}_{2} \mathrm{O}\) to \(\mathrm{H}_{2}(\mathrm{g})\) in basic solution, and explain the relationship between them.

The quantity of electric charge that will deposit \(4.5 \mathrm{g}\) Al at a cathode will also produce the following volume at STP of \(\mathrm{H}_{2}(\mathrm{g})\) from \(\mathrm{H}^{+}(\) aq) at a cathode: (a) \(44.8 \mathrm{L} ;\) (b) \(22.4 \mathrm{L} ;\) (c) \(11.2 \mathrm{L} ;\) (d) \(5.6 \mathrm{L}\).

Use the data in Appendix D to calculate the standard cell potential for each of the following reactions. Which reactions will occur spontaneously? (a) \(\mathrm{H}_{2}(\mathrm{g})+\mathrm{F}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{H}^{+}(\mathrm{aq})+2 \mathrm{F}^{-}(\mathrm{aq})\) (b) \(\mathrm{Cu}(\mathrm{s})+\mathrm{Ba}^{2+}(\mathrm{aq}) \longrightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{Ba}(\mathrm{s})\) (c) \(3 \mathrm{Fe}^{2+}(\mathrm{aq}) \longrightarrow \mathrm{Fe}(\mathrm{s})+2 \mathrm{Fe}^{3+}(\mathrm{aq})\) (d) \(\mathrm{Hg}(1)+\mathrm{HgCl}_{2}(\mathrm{aq}) \longrightarrow \mathrm{Hg}_{2} \mathrm{Cl}_{2}(\mathrm{s})\)

Describe a laboratory experiment that you could perform to evaluate the Faraday constant, \(F,\) and then show how you could use this value to determine the Avogadro constant.
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