Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 75

During a period of discharge of a lead-acid battery, \(402 \mathrm{~g}\) of \(\mathrm{Pb}\) from the anode is converted into \(\mathrm{PbSO}_{4}(s) .\) (a) What mass of \(\mathrm{PbO}_{2}(s)\) is reduced at the cathode during this same period? (b) How many coulombs of electrical charge are transferred from \(\mathrm{Pb}\) to \(\mathrm{PbO}_{2} ?\)

Short Answer

Expert verified
The mass of PbO₂ reduced at the cathode is 466.53 g. The electrical charge transferred from Pb to PbO₂ is 388,978 C.

Step by step solution

01

Convert mass of Pb to moles

We first need to convert the mass of Pb (402 g) to moles using the molar mass of Pb (207.2 g/mol). \[moles \text{ } \mathrm{Pb} = \frac{mass \text{ } \mathrm{Pb}}{molar \text{ } mass \text{ } \mathrm{Pb}}\]
02

Use stoichiometry to find moles of PbO2

In the lead-acid battery, the overall redox reaction occurring is: \[ \mathrm{Pb} + \mathrm{PbO}_2 + 2 \mathrm{H}_2 \mathrm{SO}_4 \rightarrow 2 \mathrm{PbSO}_4 + 2 \mathrm{H}_2 \mathrm{O} \] From the balanced equation, we see that the molar ratio of Pb to PbO2 is 1:1. Therefore, the number of moles of PbO2 reduced at the cathode will be equal to the number of moles of Pb converted.
03

Convert moles of PbO2 to mass

Now, we'll convert the number of moles of PbO2 to mass using the molar mass of PbO2 (239.2 g/mol): \[mass \text{ } \mathrm{PbO_2} = moles \text{ } \mathrm{PbO_2} \times molar \text{ } mass \text{ } \mathrm{PbO_2}\] This will give us the mass of PbO2 reduced at the cathode.
04

Calculate the charge transferred

Now we'll determine the number of coulombs of electrical charge transferred from Pb to PbO2. In the redox reaction, both Pb and PbO2 have two electrons involved. Since the number of moles of Pb and PbO2 are equal, we first need to determine the total moles of electrons involved in the reaction: \[moles \text{ } electrons = 2 \times moles \text{ } \mathrm{Pb}\] Next, use the Faraday's constant (96,485 C/mol) to determine the total charge transferred: \[charge = moles \text{ } electrons \times Faraday's \text{ } constant\] This will provide the number of coulombs of electrical charge transferred from Pb to PbO2.

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) Write the reactions for the discharge and charge of a nickelcadmium (nicad) rechargeable battery. (b) Given the following reduction potentials, calculate the standard emf of the cell: $$ \begin{array}{r} \mathrm{Cd}(\mathrm{OH})_{2}(s)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Cd}(s)+\begin{array}{c} 2 \mathrm{OH}^{-}(a q) \\ E_{\mathrm{red}}^{\circ}=-0.76 \mathrm{~V} \end{array} \\ \mathrm{NiO}(\mathrm{OH})(s)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{e}^{-} \longrightarrow \mathrm{Ni}(\mathrm{OH})_{2}(s)+\mathrm{OH}^{-}(a q) \\ E_{\mathrm{red}}^{\circ}=+0.49 \mathrm{~V} \end{array} $$ (c) A typical nicad voltaic cell generates an emf of \(+1.30 \mathrm{~V}\). Why is there a difference between this value and the one you calculated in part (b)? (d) Calculate the equilibrium constant for the overall nicad reaction based on this typical emf value.

(a) Why is it impossible to measure the standard reduction potential of a single half-reaction? (b) Describe how the standard reduction potential of a half-reaction can be determined.

(a) What is electrolysis? (b) Are electrolysis reactions thermodynamically spontaneous? Explain. (c) What process occurs at the anode in the electrolysis of molten NaCl? (d) Why is sodium metal not obtained when an aqueous solution of \(\mathrm{NaCl}\) undergoes electrolysis?

(a) What is meant by the term oxidation? (b) On which side of an oxidation half-reaction do the electrons appear? (c) What is meant by the term oxidant? (d) What is meant by the term oxidizing agent?

(a) Write the anode and cathode reactions that cause the corrosion of iron metal to aqueous iron(II). (b) Write the balanced half-reactions involved in the air oxidation of \(\mathrm{Fe}^{2+}(a q)\) to \(\mathrm{Fe}_{2} \mathrm{O}_{3} \cdot 3 \mathrm{H}_{2} \mathrm{O}\).
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Physical Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Nuclear Chemistry

Read Explanation

Chemistry Branches

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