Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 18: Problem 67

The overall reaction in the lead storage battery is \(\mathrm{Pb}(s)+\mathrm{PbO}_{2}(s)+2 \mathrm{H}^{+}(a q)+2 \mathrm{HSO}_{4}^{-}(a q) \longrightarrow\) Calculate \(\mathscr{8}\) at \(25^{\circ} \mathrm{C}\) for this battery when \(\left[\mathrm{H}_{2} \mathrm{SO}_{4}\right]=4.5 M\), that is, \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{HSO}_{4}^{-}\right]=4.5 M .\) At \(25^{\circ} \mathrm{C}, \mathscr{b}^{\circ}=2.04 \mathrm{~V}\) for the lead storage battery.

Short Answer

Expert verified
The cell potential of the lead-acid battery at the given conditions, with [\(\text{H}^{+}\)] = [HSO₄⁻] = 4.5 M and T = 25°C (298 K), is approximately 2.0073 V.

Step by step solution

01

Write down the Nernst equation

The Nernst Equation relates the cell potential (E), the standard cell potential (E°), the number of electrons transferred (n), the gas constant (R), the temperature (T), and the concentrations of species involved in the reaction. The Nernst equation is given as follows: \[E = E° - \frac{RT}{nF} \ln Q\] where E° is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of electrons transferred, F is Faraday's constant, and Q is the reaction quotient.
02

Identify the given values and constants

From the question, we have E° = 2.04 V, concentration of H⁺ and HSO₄⁻ both equal to 4.5 M, and temperature T = 25°C = 298 K. The gas constant (R) is 8.314 J/(mol·K) and Faraday's constant (F) is 96485 C/mol. For the lead-acid battery, two electrons are transferred in the reaction, so n = 2.
03

Calculate the reaction quotient (Q)

For the given reaction, \[Pb(s) + PbO_2(s) + 2 H⁺(aq) + 2 HSO₄⁻(aq) \longrightarrow\] the reaction quotient Q is defined as follows: \[Q = \frac{[H⁺]^2[H_{2}SO_4]^2}{1}\] Since [H⁺] = [HSO₄⁻] = 4.5 M, Q simplifies to \[Q = (4.5)^2(4.5)^2 = 410.0625\]
04

Calculate the cell potential (E) using the Nernst Equation

By substituting the given values and constants into the Nernst Equation, we can solve for the cell potential E: \[E = E° - \frac{RT}{nF} \ln Q\] \[E = 2.04 - \frac{8.314×298}{2×96485} \ln 410.0625\] \[E \approx 2.04 - 0.0211 \ln 410.0625 \approx 2.0073\, V\] So, the cell potential of this battery at the given conditions is approximately 2.0073 V.

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 factory wants to produce \(1.00 \times 10^{3} \mathrm{~kg}\) barium from the electrolysis of molten barium chloride. What current must be applied for \(4.00 \mathrm{~h}\) to accomplish this?

. When jump-starting a car with a dead battery, the ground jumper should be attached to a remote part of the engine block. Why?

What is electrochemistry? What are redox reactions? Explain the difference between a galvanic and an electrolytic cell.

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 blood alcohol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) level can be determined by titrating a sample of blood plasma with an acidic potassium dichromate solution, resulting in the production of \(\mathrm{Cr}^{3+}(a q)\) and carbon dioxide. The reaction can be monitored because the dichromate ion \(\left(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\right)\) is orange in solution, and the \(\mathrm{Cr}^{3+}\) ion is green. The unbalanced redox equation is $$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q) \longrightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{CO}_{2}(g)$$ If \(31.05 \mathrm{~mL}\) of \(0.0600 M\) potassium dichromate solution is required to titrate \(30.0 \mathrm{~g}\) blood plasma, determine the mass percent of alcohol in the blood.
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

The Earths Atmosphere

Read Explanation

Inorganic Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Making Measurements

Read Explanation

Kinetics

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