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Ch.20 - Electrochemistry
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.20 - ElectrochemistryProblem 73a
Chapter 20, Problem 73a

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?

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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 \[ \text{Mass of PbO}_2 = \text{Moles of PbO}_2 \times 239.2 \, \text{g/mol} \]

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.

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
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?

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Textbook Question

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?

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Textbook Question

During the discharge of an alkaline battery, 4.50 g of Zn is consumed at the anode of the battery. (a) What mass of MnO2 is reduced at the cathode during this discharge?

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?

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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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