Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 39

The standard reduction potentials of the following half-reactions are given in Appendix E: $$ \begin{array}{l} \mathrm{Fe}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Fe}(s) \\ \mathrm{Cd}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \operatorname{Cd}(s) \\\ \mathrm{Sn}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \operatorname{Sn}(s) \\\ \mathrm{Ag}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \operatorname{Ag}(s) \end{array} $$ (a) Determine which combination of these half-cell reactions leads to the cell reaction with the largest positive cell potential and calculate the value. (b) Determine which combination of these half-cell reactions leads to the cell reaction with the smallest positive cell potential and calculate the value.

Short Answer

Expert verified
The combination of half-cell reactions that leads to the largest positive cell potential is Fe(s) with Ag(s), and the value can be calculated using \( E°_{Ag} - E°_{Fe} \). The combination with the smallest positive cell potential is Fe(s) with Cd(s), and the value can be calculated using \( E°_{Cd} - E°_{Fe} \).

Step by step solution

01

List all possible half-cell reaction combinations

To find the combination of half-cell reactions that produce the largest and smallest positive cell potentials, start by listing all the possible combinations. Ignore same element combinations as they result in no reaction. There are four different elements, and hence, six possible combinations: 1. Fe(s) with Cd(s) 2. Fe(s) with Sn(s) 3. Fe(s) with Ag(s) 4. Cd(s) with Sn(s) 5. Cd(s) with Ag(s) 6. Sn(s) with Ag(s)
02

Find the standard cell potentials for each combination

Using the standard reduction potentials from Appendix E, calculate the standard cell potential E° of each combination by subtracting the lower potential from the higher potential, ensuring that the resultant potential is positive. (Note: You can find the standard reduction potentials of these half-cell reactions in the AIME table). 1. Fe(s) with Cd(s): \( E°_{Cd} - E°_{Fe} \) 2. Fe(s) with Sn(s): \( E°_{Sn} - E°_{Fe} \) 3. Fe(s) with Ag(s): \( E°_{Ag} - E°_{Fe} \) 4. Cd(s) with Sn(s): \( E°_{Sn} - E°_{Cd} \) 5. Cd(s) with Ag(s): \( E°_{Ag} - E°_{Cd} \) 6. Sn(s) with Ag(s): \( E°_{Ag} - E°_{Sn} \)
03

Determine the combination with the largest positive cell potential

After calculating the standard cell potentials for each combination, you'll find that Fe(s) with Ag(s) has the largest positive cell potential. 3. Fe(s) with Ag(s)
04

Determine the combination with the smallest positive cell potential

Similar to step 3, you'll find that Fe(s) with Cd(s) has the smallest positive cell potential. 1. Fe(s) with Cd(s)
05

Calculate the values of the largest and smallest positive cell potentials

By comparing the calculated E° values, you'll be able to find the largest and smallest positive cell potentials: (a) The largest positive cell potential value occurs when Fe(s) and Ag(s) react together, and its E° value can be calculated as follows: \( E°_{Ag} - E°_{Fe} \) (b) The smallest positive cell potential value occurs when Fe(s) and Cd(s) react together, and its E° value can be calculated as follows: \( E°_{Cd} - E°_{Fe} \)

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

Mercuric oxide dry-cell batteries are often used where a flat discharge voltage and long life are required, such as in watches and cameras. The two half-cell reactions that occur in the battery are $$ \begin{array}{l} \mathrm{HgO}(s)+\mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Hg}(l)+2 \mathrm{OH}^{-}(a q) \\ \mathrm{Zn}(s)+2 \mathrm{OH}^{-}(a q) \longrightarrow \mathrm{ZnO}(s)+\mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{e}^{-} \end{array} $$ (a) Write the overall cell reaction. (b) The value of $E_{\text {red }}^{\circ}\( for the cathode reaction is \)+0.098 \mathrm{~V}$. The overall cell potential is \(+1.35 \mathrm{~V}\). Assuming that both half-cells operate under standard conditions, what is the standard reduction potential for the anode reaction? (c) Why is the potential of the anode reaction different than would be expected if the reaction occurred in an acidic medium?

Indicate whether each statement is true or false: (a) The cathode is the electrode at which oxidation takes place. (b) A galvanic cell is another name for a voltaic cell. (c) Electrons flow spontaneously from anode to cathode in a voltaic cell.

Indicate whether the following balanced equations involve oxidation-reduction. If they do, identify the elements that undergo changes in oxidation number. (a) $2 \mathrm{AgNO}_{3}(a q)+\mathrm{CoCl}_{2}(a q) \longrightarrow 2 \mathrm{AgCl}(s)+ \mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}(a q)$ (b) $2 \mathrm{PbO}_{2}(s) \longrightarrow 2 \mathrm{PbO}(s)+\mathrm{O}_{2}(g)$ (c) $2 \mathrm{H}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{NaBr}(s) \longrightarrow \mathrm{Br}_{2}(l)+\mathrm{SO}_{2}(g)+ \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)$

From each of the following pairs of substances, use data in Appendix \(\mathrm{E}\) to choose the one that is the stronger reducing agent: (a) \(\mathrm{Al}(s)\) or \(\mathrm{Mg}(s)\) (b) \(\mathrm{Fe}(s)\) or \(\mathrm{Ni}(s)\) (c) \(\mathrm{H}_{2}(g\), acidic solution) or \(\operatorname{Sn}(s)\) (d) \(\mathrm{I}^{-}(a q)\) or \(\mathrm{Br}^{-}(a q)\)

For a spontaneous reaction $\mathrm{A}(a q)+\mathrm{B}(a q) \longrightarrow \mathrm{A}^{-}(a q)+$ \(\mathrm{B}^{+}(a q),\) answer the following questions: (a) If you made a voltaic cell out of this reaction, what halfreaction would be occurring at the cathode, and what half reaction would be occurring at the anode? (b) Which half-reaction from (a) is higher in potential energy? (c) What is the sign of \(E_{\text {cell }}^{\circ}\) ?
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Inorganic Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Nuclear Chemistry

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