/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 9 Explain why cell potentials are ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 18: Problem 9

Explain why cell potentials are not multiplied by the coefficients in the balanced redox equation. (Use the relationship between \(\Delta G\) and cell potential to do this.)

Short Answer

Expert verified
Cell potentials are not multiplied by the coefficients in the balanced redox equation because reduction potentials are an intensive property, meaning they are independent of the extent of the reaction or the amount of the substance. As a result, doubling or tripling the reaction doesn't change the reduction potential. The cell potential is given by the difference between the reduction potentials of the half-reactions, and since coefficients don't affect this, they don't appear in the cell potential calculation. The number of moles of electrons transferred (n) impacts the calculation of Gibbs free energy (\(\Delta G\)) in the relationship \(\Delta G = -nFE_{cell}\), but not the cell potential itself.

Step by step solution

01

State the relationship between Gibbs free energy and cell potential

The relationship between Gibbs free energy (\(\Delta G\)) and cell potential (\(E_{cell}\)) is given by the equation: \[\Delta G = -nFE_{cell}\] where \(\Delta G\) is the Gibbs free energy, \(n\) is the number of moles of electrons transferred in the redox reaction, \(F\) is Faraday's constant (approximately 96485 C/mol), and \(E_{cell}\) is the cell potential.
02

Express cell potential as a difference of reduction potentials

Cell potential is equal to the difference between the standard reduction potentials of the half-reactions involved in the redox reaction: \[E_{cell} = E_{cathode} - E_{anode}\] Here, \(E_{cathode}\) is the reduction potential of the half-reaction occurring at the cathode, while \(E_{anode}\) is the reduction potential of the half-reaction occurring at the anode.
03

Explain why the balanced redox equation has no effect on the coefficient

In the balanced redox equation, each half-reaction is multiplied by a coefficient to ensure that the number of electrons transferred in each half-reaction is equal. However, when we look at the cell potential expression (difference between the reduction potentials), the coefficients do not appear. The reason is that the reduction potentials of half-reactions are an intensive property, meaning they are independent of the extent of the reaction or the amount of the substance. In other words, doubling or tripling the reaction (by multiplying the balanced half-reaction with a coefficient) doesn't change the reduction potential, so the coefficients will not appear when calculating the cell potential.
04

Conclude that the cell potential doesn't depend on the coefficients

Thus, we conclude that cell potentials are not multiplied by the coefficients in the balanced redox equation, since the coefficients don't affect the intensive property such as the reduction potentials. As a result, only the number of moles of electrons transferred (\(n\)) impacts the calculation of Gibbs free energy in the relationship between \(\Delta G\) and \(E_{cell}\), but not the cell potential itself.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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 the electrolysis of a molten salt of some metal. What information must you know to calculate the mass of metal plated out in the electrolytic cell?

Sketch a cell that forms iron metal from iron(II) while changing chromium metal to chromium(III). Calculate the voltage, show the electron flow, label the anode and cathode, and balance the overall cell equation.

Electrolysis of an alkaline earth metal chloride using a current of \(5.00 \mathrm{~A}\) for \(748 \mathrm{~s}\) deposits \(0.471 \mathrm{~g}\) of metal at the cathode. What is the identity of the alkaline earth metal chloride?

The ultimate electron acceptor in the respiration process is molecular oxygen. Electron transfer through the respiratory chain takes place through a complex series of oxidation-reduction reactions. Some of the electron transport steps use iron-containing proteins called cytochromes. All cytochromes transport electrons by converting the iron in the cytochromes from the \(+3\) to the \(+2\) oxidation state. Consider the following reduction potentials for three different cytochromes used in the transfer process of electrons to oxygen (the potentials have been corrected for \(\mathrm{pH}\) and for temperature): \(\begin{aligned} \text { cytochrome } \mathrm{a}\left(\mathrm{Fe}^{3+}\right)+\mathrm{e}^{-} \longrightarrow \text { cytochrome } \mathrm{a}\left(\mathrm{Fe}^{2+}\right) & \\ \mathscr{B} &=0.385 \mathrm{~V} \\ \text { cytochrome } \mathrm{b}\left(\mathrm{Fe}^{3+}\right)+\mathrm{e}^{-} \longrightarrow \text { cytochrome } \mathrm{b}\left(\mathrm{Fe}^{2+}\right) & \\ \mathscr{E} &=0.030 \mathrm{~V} \\ \text { cytochrome } \mathrm{c}\left(\mathrm{Fe}^{3+}\right)+\mathrm{e}^{-} \longrightarrow \text { cytochrome } \mathrm{c}\left(\mathrm{Fe}^{2+}\right) & \\ \mathscr{Z} &=0.254 \mathrm{~V} \end{aligned}\) In the electron transfer series, electrons are transferred from one cytochrome to another. Using this information, determine the cytochrome order necessary for spontaneous transport of electrons from one cytochrome to another, which eventually will lead to electron transfer to \(\mathrm{O}_{2}\).

Which of the following statements concerning corrosion is/are true? For the false statements, correct them. a. Corrosion is an example of an electrolytic process. b. Corrosion of steel involves the reduction of iron coupled with the oxidation of oxygen. c. Steel rusts more easily in the dry (arid) Southwest states than in the humid Midwest states. d. Salting roads in the winter has the added benefit of hindering the corrosion of steel. e. The key to cathodic protection is to connect via a wire a metal more easily oxidized than iron to the steel surface to be protected.
See all solutions

Recommended explanations on Chemistry Textbooks

Chemistry Branches

Read Explanation

Nuclear Chemistry

Read Explanation

Organic Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Kinetics

Read Explanation

Ionic and Molecular Compounds

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.