Textbook Question
During a period of discharge of a lead–acid battery, 402 g of Pb from the anode is converted into PbSO4(s). (b) How many coulombs of electrical charge are transferred from Pb to PbO2?
Ch.20 - Electrochemistry
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970
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Table of contents
- Ch.1 - Introduction: Matter, Energy, and Measurement146
- Ch.2 - Atoms, Molecules, and Ions200
- Ch.3 - Chemical Reactions and Reaction Stoichiometry176
- Ch.4 - Reactions in Aqueous Solution155
- Ch.5 - Thermochemistry126
- Ch.6 - Electronic Structure of Atoms131
- Ch.7 - Periodic Properties of the Elements126
- Ch.8 - Basic Concepts of Chemical Bonding123
- Ch.9 - Molecular Geometry and Bonding Theories143
- Ch.10 - Gases147
- Ch.11 - Liquids and Intermolecular Forces91
- Ch.12 - Solids and Modern Materials122
- Ch.13 - Properties of Solutions126
- Ch.14 - Chemical Kinetics174
- Ch.15 - Chemical Equilibrium101
- Ch.16 - Acid-Base Equilibria139
- Ch.17 - Additional Aspects of Aqueous Equilibria146
- Ch.18 - Chemistry of the Environment72
- Ch.19 - Chemical Thermodynamics129
- Ch.20 - Electrochemistry142
- Ch.21 - Nuclear Chemistry101
- Ch.22 - Chemistry of the Nonmetals68
- Ch.23 - Transition Metals and Coordination Chemistry66
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry10
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
Chapter 20, Problem 77a
During a period of discharge of a lead–acid battery, 402 g of Pb from the anode is converted into PbSO4(s). (a) What mass of PbO2(s) is reduced at the cathode during this same period?
Verified step by step guidance1
Identify the balanced chemical reaction for the discharge of a lead-acid battery: \[ \text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4 \rightarrow 2\text{PbSO}_4 + 2\text{H}_2\text{O} \]
Determine the molar mass of Pb and PbSO_4 using the periodic table: \[ \text{Molar mass of Pb} = 207.2 \, \text{g/mol} \] and \[ \text{Molar mass of PbSO}_4 = 303.3 \, \text{g/mol} \]
Calculate the moles of Pb converted to PbSO_4 using the given mass: \[ \text{Moles of Pb} = \frac{402 \, \text{g}}{207.2 \, \text{g/mol}} \]
Use stoichiometry from the balanced equation to find the moles of PbO_2 reduced. The reaction shows a 1:1 mole ratio between Pb and PbO_2.
Calculate the mass of PbO_2 reduced using its molar mass: \[ \text{Molar mass of PbO}_2 = 239.2 \, \text{g/mol} \] and \[ \text{Mass of PbO}_2 = \text{Moles of PbO}_2 \times 239.2 \, \text{g/mol} \]
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Redox Reactions
Redox reactions involve the transfer of electrons between two species, where one species is oxidized (loses electrons) and the other is reduced (gains electrons). In the context of a lead-acid battery, lead (Pb) at the anode is oxidized to lead sulfate (PbSO4), while lead oxide (PbO2) at the cathode is reduced during discharge. Understanding this electron transfer is crucial for calculating the mass changes in the battery components.
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Stoichiometry
Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the relationships between the amounts of substances involved. In this case, knowing the mass of Pb oxidized helps us use stoichiometric ratios to find the mass of PbO2 reduced at the cathode, as both processes are linked through the overall reaction of the battery.
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Molar Mass
Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essential for converting between mass and moles in chemical calculations. For this problem, knowing the molar masses of lead (Pb) and lead oxide (PbO2) allows us to calculate the mass of PbO2 reduced based on the mass of Pb oxidized, facilitating the stoichiometric calculations needed to answer the question.
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Related Practice
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During the discharge of an alkaline battery, 4.50 g of Zn is consumed at the anode of the battery. (b) How many coulombs of electrical charge are transferred from Zn to MnO2?
Textbook Question
A voltaic cell is constructed that is based on the following reaction: Sn2+(aq) + Pb(s) → Sn(s) + Pb2+(aq) (a) If the concentration of Sn2+ in the cathode half-cell is 1.00 M and the cell generates an emf of +0.22 V, what is the concentration of Pb2+ in the anode half-cell?
Textbook Question
A voltaic cell utilizes the following reaction: (b) What is the emf for this cell when 3Fe3+4 = 3.50 M, PH2= 0.95 atm, 3Fe2+4 = 0.0010 M, and the pH in both half-cells is 4.00?
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Textbook Question
Heart pacemakers are often powered by lithium–silver chromate 'button' batteries. The overall cell reaction is 2 Li(s) + Ag2CrO4(s) → Li2CrO4(s) + 2 Ag(s) (a) Lithium metal is the reactant at one of the electrodes of the battery. Is it the anode or the cathode?