Textbook Question
Consider the following half-reactions and E° values: (c) Write the cell reaction for part (b), and calculate the values of E°, ∆G° (in kilojoules), and K for this reaction at 25 °C
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Ch.19 - Electrochemistry
McMurry8th EditionChemistryISBN: 9781292336145
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Table of contents
- Ch.1 - Chemical Tools: Experimentation & Measurement143
- Ch.2 - Atoms, Molecules & Ions134
- Ch.3 - Mass Relationships in Chemical Reactions149
- Ch.4 - Reactions in Aqueous Solution157
- Ch.5 - Periodicity & Electronic Structure of Atoms92
- Ch.6 - Ionic Compounds: Periodic Trends and Bonding Theory73
- Ch.7 - Covalent Bonding and Electron-Dot Structures47
- Ch.8 - Covalent Compounds: Bonding Theories and Molecular Structure51
- Ch.9 - Thermochemistry: Chemical Energy104
- Ch.10 - Gases: Their Properties & Behavior138
- Ch.11 - Liquids & Phase Changes43
- Ch.12 - Solids and Solid-State Materials56
- Ch.13 - Solutions & Their Properties98
- Ch.14 - Chemical Kinetics79
- Ch.15 - Chemical Equilibrium107
- Ch.16 - Aqueous Equilibria: Acids & Bases94
- Ch.17 - Applications of Aqueous Equilibria125
- Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium66
- Ch.19 - Electrochemistry130
- Ch.20 - Nuclear Chemistry73
- Ch.21 - Transition Elements and Coordination Chemistry122
- Ch.22 - The Main Group Elements155
- Ch.23 - Organic and Biological Chemistry43
Chapter 19, Problem 146c
In order to charge a lead storage battery (Section 19.10) 500.0 g of PbSO4(s) must be converted into PbO2(s) and Pb(s). (c) If a current of 500 A is used, how long will it take?
Verified step by step guidance1
First, write the balanced chemical equation for the conversion of PbSO4(s) to PbO2(s) and Pb(s). The overall reaction involves the reduction of PbSO4 to Pb and the oxidation of PbSO4 to PbO2.
Calculate the molar mass of PbSO4 using the atomic masses of lead (Pb), sulfur (S), and oxygen (O). This will help in determining the number of moles of PbSO4 present in 500.0 g.
Determine the number of moles of electrons required for the conversion. For each mole of PbSO4, two moles of electrons are needed: one for the reduction to Pb and one for the oxidation to PbO2.
Use Faraday's law of electrolysis, which states that the amount of substance transformed in an electrochemical reaction is directly proportional to the quantity of electricity (in coulombs) passed through the substance. The formula is: \( Q = n \times F \), where \( Q \) is the total charge in coulombs, \( n \) is the number of moles of electrons, and \( F \) is Faraday's constant (approximately 96485 C/mol).
Finally, calculate the time required using the formula \( t = \frac{Q}{I} \), where \( t \) is the time in seconds, \( Q \) is the total charge calculated in the previous step, and \( I \) is the current in amperes (500 A in this case).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Electrochemical Reactions
Electrochemical reactions involve the transfer of electrons between chemical species, typically occurring in an electrochemical cell. In the context of a lead storage battery, the conversion of PbSO4 to PbO2 and Pb involves oxidation and reduction processes, where lead ions undergo changes in oxidation states. Understanding these reactions is crucial for calculating the amount of charge transferred during the charging process.
Faraday's Laws of Electrolysis
Faraday's laws of electrolysis relate the amount of substance transformed at an electrode to the quantity of electric charge passed through the cell. The first law states that the mass of a substance altered at an electrode is proportional to the total electric charge. This principle is essential for determining how long it will take to convert a specific mass of PbSO4 into PbO2 and Pb, given a constant current.
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Current and Time Relationship
The relationship between current (I), charge (Q), and time (t) is described by the equation Q = I × t. This relationship allows us to calculate the time required for a specific charge to flow through the circuit. In this scenario, knowing the current (500 A) and the total charge needed to convert the lead sulfate is necessary to determine how long the charging process will take.
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Related Practice
Textbook Question
When the nickel–zinc battery, used in digital cameras, is recharged, the following cell reaction occurs: (a) How many grams of zinc are formed when 3.35 x 10-2 g of Ni(OH)2 are consumed?
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Textbook Question
In order to charge a lead storage battery (Section 19.10) 500.0 g of PbSO4(s) must be converted into PbO2(s) and Pb(s). (a) Does the reaction represent an electrolytic or galvanic cell?
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Textbook Question
Chlorine can be prepared in the laboratory by the reaction of hydrochloric acid and potassium permanganate.(b) Calculate E° and ∆G° for the reaction
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Textbook Question
Electrolysis of a metal nitrate solution M(NO3)2(aq) for 325 min with a constant current of 20.0 A gives 111 g of the metal. Identify the metal ion M2+.
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Textbook Question
In order to charge a lead storage battery (Section 19.10) 500.0 g of PbSO4(s) must be converted into PbO2(s) and Pb(s). (b) How many coulombs of electrical charge are needed?
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