Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 5

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 \(E_{\text {cell }}^{\circ}\) ?

Short Answer

Expert verified
The cathode half-reaction is \(\mathrm{B} + e^{-} \longrightarrow \mathrm{B}^{+}\), and the anode half-reaction is \(\mathrm{A} \longrightarrow \mathrm{A}^{-} + e^{-}\). We cannot determine which half-reaction has higher potential energy without the standard electrode potentials for A and B. However, since the reaction is spontaneous, the sign of \(E_{\text {cell}}^{\circ}\) is positive.

Step by step solution

01

Identify the redox process

First, let's write the given reaction: \(\mathrm{A}(aq)+\mathrm{B}(aq) \longrightarrow \mathrm{A}^{-}(aq)+\mathrm{B}^{+}(aq)\) In this reaction, A is losing an electron to become A⁻, and B is gaining an electron to become B⁺. So, A is being oxidized (loss of electron) and B is being reduced (gain of electron).
02

Identify the cathode and anode half-reactions

In a voltaic cell, the cathode is where the reduction occurs, and the anode is where oxidation occurs. So, we can identify the half-reactions: Cathode (reduction): \(\mathrm{B} + e^{-} \longrightarrow \mathrm{B}^{+}\) Anode (oxidation): \(\mathrm{A} \longrightarrow \mathrm{A}^{-} + e^{-}\)
03

Determine the half-reaction with higher potential energy

To determine which half-reaction has higher potential energy, we need to compare their standard electrode potentials, denoted as \(E^{\circ}\). However, we are not given the values for \(E_{\text {A}}^{\circ}\) and \(E_{\text {B}}^{\circ}\) in the problem. Since we don't have this information, we cannot definitively answer this part of the question.
04

Determine the sign of E_cell

The cell potential, \(E_{\text {cell}}^{\circ}\), is given by the difference between the cathode's potential and the anode's potential: \[E_{\text {cell}}^{\circ} = E_{\text {cathode}}^{\circ} - E_{\text {anode}}^{\circ}\] As we don't have the standard electrode potentials for A and B, we can't directly calculate the value of \(E_{\text {cell}}^{\circ}\). However, we are told that the reaction is spontaneous. For a spontaneous reaction, the cell potential must be positive: \[E_{\text {cell}}^{\circ} > 0\] So, without knowing the actual values of the electrode potentials, we can conclude that the sign of \(E_{\text {cell}}^{\circ}\) is positive.

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

(a) What is an electrolytic cell? (b) The negative terminal of a voltage source is connected to an electrode of an electrolytic cell. Is the electrode the anode or the cathode of the cell? Explain. (c) The electrolysis of water is often done with a small amount of sulfuric acid added to the water. What is the role of the sulfuric acid? (d) Why are active metals such as Al obtained by electrolysis using molten salts rather than aqueous solutions?

A voltaic cell is based on \(\mathrm{Cu}^{2+}(a q) / \mathrm{Cu}(s)\) and \(\mathrm{Br}_{2}(l) /\) \(\mathrm{Br}^{-}(a q)\) half-cells. (a) What is the standard emf of the cell? (b) Which reaction occurs at the cathode and which at the anode of the cell? (c) Use \(S^{\circ}\) values in Appendix \(\mathrm{C}\) and the relationship between cell potential and free-energy change to predict whether the standard cell potential increases or decreases when the temperature is raised above \(25^{\circ} \mathrm{C}\). (Thestandard entropy of \(\mathrm{Cu}^{2+}(a q)\) is $\left.S^{\circ}=-99.6 \mathrm{~J} / \mathrm{K}\right)$

Consider a redox reaction for which \(E^{\circ}\) is a negative number. (a) What is the sign of \(\Delta G^{\circ}\) for the reaction? (b) Will the equilibrium constant for the reaction be larger or smaller than \(1 ?\) (c) Can an electrochemical cell based on this reaction accomplish work on its surroundings?

In some applications nickel-cadmium batteries have been replaced by nickel- zinc batteries. The overall cell reaction for this relatively new battery is: $$ \begin{aligned} 2 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{NiO}(\mathrm{OH})(s) &+\mathrm{Zn}(s) \\\ & \longrightarrow 2 \mathrm{Ni}(\mathrm{OH})_{2}(s)+\mathrm{Zn}(\mathrm{OH})_{2}(s) \end{aligned} $$ (a)What is the cathode half-reaction? (b) What is the anode half-reaction? (c) A single nickel-cadmium cell has a voltage of \(1.30 \mathrm{~V}\). Based on the difference in the standard reduction potentials of \(\mathrm{Cd}^{2+}\) and \(\mathrm{Zn}^{2+}\), what voltage would you estimate a nickel-zinc battery will produce? (d) Would you expect the specific energy density of a nickel-zinc battery to be higher or lower than that of a nickel-cadmium battery?

(a) Based on standard reduction potentials, would you expect copper metal to oxidize under standard conditions in the presence of oxygen and hydrogen ions? (b) When the Statue of Liberty was refurbished, Teflon spacers were placed between the iron skeleton and the copper metal on the surface of the statue. What role do these spacers play?
See all solutions

Recommended explanations on Chemistry Textbooks

Nuclear Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Chemistry Branches

Read Explanation

Inorganic Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Chemical Analysis

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