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

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주요 개념

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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.

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.

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?