Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 107

Describe in words how you would calculate the standard potential of the \(\mathrm{Fe}^{2+} / \mathrm{Fe}(\mathrm{s})\) couple from those of \(\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+} / \mathrm{Fe}(\mathrm{s})\).

Short Answer

Expert verified
To calculate the standard potential of the Fe2+/Fe(s) couple from those of the Fe3+/Fe2+ and Fe3+/Fe(s) couples, one must first write out the half-reactions for the given couples. Then, by using the Nernst equation, and considering that both reactions involve the Fe3+ ion, the standard potential for the Fe2+/Fe(s) couple can be found. This shows the link between the standard potential for different redox couples involving the same element, in this case iron.

Step by step solution

01

Expression of Redox Couples

Begin by expressing each of the two given redox couples as half-reactions. The first one is \(\mathrm{Fe}^{3+} + e^- \rightarrow \mathrm{Fe}^{2+}\) and the second is \(\mathrm{Fe}^{3+} + 3e^- \rightarrow \mathrm{Fe}(\mathrm{s})\).
02

Design the Required Half-Reaction

We want to obtain the half-reaction for the \(\mathrm{Fe}^{2+}/\mathrm{Fe}(s)\) couple, which is \(\mathrm{Fe}^{2+} + 2e^- \rightarrow \mathrm{Fe}(\mathrm{s})\). To obtain this, we can subtract the first half-reaction from the second, as they have the same oxidation state Fe3+ in common.
03

Apply the Nernst Equation

Use the Nernst equation to calculate the potential. In this situation, it's expressed as \(E = E_{\mathrm{Fe}^{3+}/\mathrm{Fe}(\mathrm{s})} - E_{\mathrm{Fe}^{3+}/\mathrm{Fe}^{2+}}\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Consider two cells involving two metals \(X\) and \(Y\) $$\begin{aligned} \mathrm{X}(\mathrm{s})\left|\mathrm{X}^{+}(\mathrm{aq})\right|\left|\mathrm{H}^{+}(\mathrm{aq}), \mathrm{H}_{2}(\mathrm{g}, 1 \mathrm{bar})\right| \mathrm{Pt}(\mathrm{s}) & \\\ \mathrm{X}(\mathrm{s})\left|\mathrm{X}^{+}(\mathrm{aq}) \| \mathrm{Y}^{2+}(\mathrm{aq})\right| \mathrm{Y}(\mathrm{s}) \end{aligned}$$ In the first cell electrons flow from the metal \(X\) to the standard hydrogen electrode. In the second cell electrons flow from metal \(X\) to metal Y. Is \(E_{x^{+} / x}^{\circ_{+}}\) greater orless than zero? Is \(E_{x^{+} / x}^{\circ}>E_{\mathrm{Y}^{2+}},_{\mathrm{Y}} ?\) Explain.

Write an equation to represent the oxidation of \(\mathrm{Cl}^{-}(\mathrm{aq})\) to \(\mathrm{Cl}_{2}(\mathrm{g})\) by \(\mathrm{PbO}_{2}(\mathrm{s})\) in an acidic solution. Will this reaction occur spontaneously in the forward direction if all other reactants and products are in their standard states and (a) \(\left[\mathrm{H}^{+}\right]=6.0 \mathrm{M} ;\) (b) \(\left[\mathrm{H}^{+}\right]=1.2 \mathrm{M}\) (c) \(\mathrm{pH}=4.25 ?\) Explain.

Briefly describe each of the following ideas, methods, or devices: (a) salt bridge; (b) standard hydrogen electrode (SHE); (c) cathodic protection; (d) fuel cell.

Consider the following electrochemical cell: $$ \operatorname{Pt}(\mathrm{s})\left|\mathrm{H}_{2}(\mathrm{g}, 1 \mathrm{atm})\right| \mathrm{H}^{+}(1 \mathrm{M}) \| \mathrm{Ag}^{+}(x \mathrm{M}) | \mathrm{Ag}(\mathrm{s}) $$ (a) What is \(E_{\text {cell }}^{\circ}-\) that is, the cell potential when \(\left[\mathrm{Ag}^{+}\right]=1 \mathrm{M} ?\) (b) Use the Nernst equation to write an equation for \(E_{\text {cell }}\) when \(\left[\mathrm{Ag}^{+}\right]=x\) (c) Now imagine titrating \(50.0 \mathrm{mL}\) of \(0.0100 \mathrm{M}\) \(\mathrm{AgNO}_{3}\) in the cathode half-cell compartment with 0.0100 M KI. The titration reaction is $$\mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{I}^{-}(\mathrm{aq}) \longrightarrow \mathrm{AgI}(\mathrm{s})$$ Calculate \(\left[\mathrm{Ag}^{+}\right]\) and then \(E_{\text {cell }}\) after addition of the following volumes of \(0.0100 \mathrm{M} \mathrm{KI}:(\mathrm{i}) 0.0 \mathrm{mL} ;(\mathrm{ii}) 20.0 \mathrm{mL}\) (iii) \(49.0 \mathrm{mL} ;(\text { iv }) 50.0 \mathrm{mL} ;(\mathrm{v}) 51.0 \mathrm{mL} ;(\mathrm{vi}) 60.0 \mathrm{mL}\) (d) Use the results of part (c) to sketch the titration curve of \(E_{\text {cell }}\) versus volume of titrant.

For the reaction \(\mathrm{Zn}(\mathrm{s})+\mathrm{H}^{+}(\mathrm{aq})+\mathrm{NO}_{3}^{-}(\mathrm{aq}) \longrightarrow\) \(\mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(1)+\mathrm{NO}(\mathrm{g}),\) describe the voltaic cell in which it occurs, label the anode and cathode,use a table of standard electrode potentials to evaluate \(E_{\text {cell }}^{\circ},\) and balance the equation for the cell reaction.
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Inorganic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemistry Branches

Read Explanation

Making Measurements

Read Explanation

Chemical Reactions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free