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Chapter 20: Problem 30

(a) Which electrode of a voltaic cell, the cathode or the anode, corresponds to the higher potential energy for the electrons? (b) What are the units for electrical potential? How does this unit relate to energy expressed in joules? (c) What is special about a standard cell potential?

Short Answer

Expert verified
In a voltaic cell, the anode has a higher potential energy for electrons. Electrical potential units are volts (V), and one volt corresponds to one joule per coulomb (\(1V = 1\frac{J}{C}\)). A standard cell potential (\(E^{\circ}\)) represents the potential energy difference between the cathode and the anode under standard conditions, which helps compare the relative strengths and spontaneity of redox reactions.

Step by step solution

01

(a) Cathode or Anode: Higher Potential Energy for Electrons

In a voltaic cell, the anode is the electrode where oxidation occurs, and the cathode is the electrode where reduction occurs. Electrons are released during oxidation, causing them to have higher potential energy at the anode. Therefore, the anode corresponds to the higher potential energy for electrons in a voltaic cell.
02

(b) Units for Electrical Potential and Relation to Joules

The unit of electrical potential is the volt (V). One volt is equivalent to one joule of energy per coulomb of charge (\(1V = 1\frac{J}{C}\)). This unit reflects the amount of energy needed (or provided) to move a unit of charge (1 coulomb) between two points in an electric field, such as the electrodes in a voltaic cell.
03

(c) Special Features of a Standard Cell Potential

A standard cell potential, denoted as \(E^{\circ}\), represents the difference in potential energy between the cathode and the anode when all the components of the cell are in their standard states. Standard states are typically defined as having concentrations of 1 mol/L for all dissolved species, a pressure of 1 atm for gases, and pure solid or liquid forms of the substances involved. The standard cell potential is a measure of the ability of a redox reaction to provide electrical energy under these defined conditions, and it can be used to compare the relative strengths and spontaneity of different redox reactions.

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Most popular questions from this chapter

A voltaic cell is constructed that uses the following half-cell reactions: $$ \begin{aligned} \mathrm{Cu}^{+}(a q)+\mathrm{e}^{-} & \longrightarrow \mathrm{Cu}(s) \\ \mathrm{I}_{2}(s)+2 \mathrm{e}^{-} \longrightarrow & 2 \mathrm{I}^{-}(a q) \end{aligned} $$ The cell is operated at \(298 \mathrm{~K}\) with \(\left[\mathrm{Cu}^{+}\right]=0.25 \mathrm{M}\) and \(\left[\mathrm{I}^{-}\right]=3.5 \mathrm{M} .\) (a) Determine \(E\) for the cell at these concentrations. (b) Which electrode is the anode of the cell? (c) Is the answer to part (b) the same as it would be if the cell were operated under standard conditions? (d) If \(\left[\mathrm{Cu}^{+}\right]\) was equal to \(0.15 \mathrm{M},\) at what concentration of \(\mathrm{I}^{-}\) would the cell have zero potential?

A common shorthand way to represent a voltaic cell is anode|anode solution \(\|\) cathode solution \(\mid\) cathode A double vertical line represents a salt bridge or a porous barrier. A single vertical line represents a change in phase, such as from solid to solution. (a) Write the half-reactions and overall cell reaction represented by \(\mathrm{Fe}\left|\mathrm{Fe}^{2+} \| \mathrm{Ag}^{+}\right| \mathrm{Ag} ;\) sketch the cell. (b) Write the half-reactions and overall cell reaction represented by \(\mathrm{Zn}\left|\mathrm{Zn}^{2+} \| \mathrm{H}^{+}\right| \mathrm{H}_{2}\); sketch the cell. (c) Using the notation just described, represent a cell based on the following reaction: $$ \begin{aligned} \mathrm{ClO}_{3}^{-}(a q)+3 \mathrm{Cu}(s)+6 \mathrm{H}^{+}(a q) & \mathrm{Cl}^{-}(a q)+3 \mathrm{Cu}^{2+}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) \end{aligned} $$ \(\mathrm{Pt}\) is used as an inert electrode in contact with the \(\mathrm{ClO}_{3}^{-}\) and \(\mathrm{Cl}^{-}\). Sketch the cell.

If you were going to apply a small potential to a steel ship resting in the water as a means of inhibiting corrosion, would you apply a negative or a positive charge? Explain.

During a period of discharge of a lead-acid battery, \(402 \mathrm{~g}\) of \(\mathrm{Pb}\) from the anode is converted into \(\mathrm{PbSO}_{4}(s) .\) (a) What mass of \(\mathrm{PbO}_{2}(s)\) is reduced at the cathode during this same period? (b) How many coulombs of electrical charge are transferred from \(\mathrm{Pb}\) to \(\mathrm{PbO}_{2} ?\)

(a) What is electrolysis? (b) Are electrolysis reactions thermodynamically spontaneous? Explain. (c) What process occurs at the anode in the electrolysis of molten NaCl? (d) Why is sodium metal not obtained when an aqueous solution of \(\mathrm{NaCl}\) undergoes electrolysis?
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