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Chapter 20: Problem 32

(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?

Short Answer

Expert verified
(a) In a voltaic cell, the anode has higher potential energy for electrons as oxidation occurs at the anode and electrons flow towards the cathode. (b) The unit for electrical potential is the volt (V). The relationship between electrical potential and energy (in joules) can be expressed as: \(1\,V = 1\,J/C\), where V represents volts, J represents joules, and C represents charge in coulombs.

Step by step solution

01

Identify the electrode with higher potential energy for electrons

In a voltaic cell, oxidation occurs at the anode, resulting in the generation of positive ions and the release of electrons. These electrons move through the external circuit towards the cathode, where reduction occurs. Due to the flow of electrons from the anode to cathode, the anode is considered to have more potential energy for the electrons.
02

Determine the unit for electrical potential

The unit for electrical potential is the volt (V), named after Alessandro Volta.
03

Relate electrical potential unit to energy expressed in joules

The potential energy of the electrons is converted into electrical potential energy when they move through the voltaic cell. Electrical potential can be expressed in energy terms since it is the work done per unit charge. The relationship between electrical potential (measured in volts) and energy (measured in joules) can be expressed as: \(1\,V = 1\,J/C\) Where V represents electrical potential in volts, J represents energy in joules, and C represents charge in coulombs. In other words, an electrical potential of 1 volt is equal to 1 joule of energy per coulomb of charge.

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Most popular questions from this chapter

Li-ion batteries used in automobiles typically use a LiMn_ \(_{2} \mathrm{O}_{4}\) cathode in place of the LiCoO \(_{2}\) cathode found in most Li- ion batteries. (a) Calculate the mass percent lithium in each electrode material. (b) Which material has a higher percentage of lithium? Does this help to explain why batteries made with \(\mathrm{LiMn}_{2} \mathrm{O}_{4}\) cathodes deliver less power on discharging? (c) In a battery that uses a LiCoO\(_{2}\) cathode, approximately 50\(\%\) of the lithium migrates from the cathode to the anode on charging. In a battery that uses a LiMn_ \(_{2} \mathrm{O}_{4}\) cathode, what fraction of the lithium in LiMn_ \(_{2} \mathrm{O}_{4}\) would need to migrate out of the cathode to deliver the same amount of lithium to the graphite anode?

A voltaic cell similar to that shown in Figure 20.5 is constructed. One electrode half-cell consists of a silver strip placed in a solution of \(\mathrm{AgNO}_{3},\) and the other has an iron strip placed in a solution of \(\mathrm{FeCl}_{2}\) . The overall cell reaction is $$ \mathrm{Fe}(s)+2 \mathrm{Ag}^{+}(a q) \longrightarrow \mathrm{Fe}^{2+}(a q)+2 \mathrm{Ag}(s) $$ (a) What is being oxidized, and what is being reduced? (b) Write the half-reactions that occur in the two half-cells. (c) Which electrode is the anode, and which is the cathode? (d) Indicate the signs of the electrodes. (e) Do electrons flow from the silver electrode to the iron electrode or from the iron to the silver? (f) In which directions do the cations and anions migrate through the solution?

In a galvanic cell the cathode is an \(\mathrm{Ag}^{+}(1.00 \mathrm{M}) / \mathrm{Ag}(s)\) half-cell. The anode is a standard hydrogen electrode immersed in a buffer solution containing 0.10\(M\) benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\) and 0.050 \(\mathrm{M}\) sodium benzoate \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-} \mathrm{Na}^{+}\right) .\) The measured cell voltage is 1.030 \(\mathrm{V}\) . What is the \(\mathrm{p} K_{\mathrm{a}}\) of benzoic acid?

(a) Assuming standard conditions, arrange the following in order of increasing strength as oxidizing agents in acidic solution: \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}, \mathrm{H}_{2} \mathrm{O}_{2}, \mathrm{Cu}^{2+}, \mathrm{Cl}_{2}, \mathrm{O}_{2} .\) (b) Arrange the following in order of increasing strength as reducing agents in acidic solution: \(\text {Zn,}\) \(\mathrm{I}^{-}, \mathrm{Sn}^{2+}, \mathrm{H}_{2} \mathrm{O}_{2}, \mathrm{Al} .\)

Hydrazine \(\left(\mathrm{N}_{2} \mathrm{H}_{4}\right)\) and dinitrogen tetroxide \(\left(\mathrm{N}_{2} \mathrm{O}_{4}\right)\) form a self-igniting mixture that has been used as a rocket propellant. The reaction products are \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) . (a) Write a balanced chemical equation for this reaction. (b) What is being oxidized, and what is being reduced? (c) Which substance serves as the reducing agent and which as the oxidizing agent?
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