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?

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Identify the balanced chemical reaction for the discharge of an alkaline battery. The typical reaction involves zinc (Zn) being oxidized at the anode and manganese dioxide (MnO2) being reduced at the cathode.

Write the half-reactions for the anode and cathode. The anode reaction is: Zn → Zn²⁺ + 2e⁻. The cathode reaction is: MnO2 + H2O + e⁻ → MnO(OH) + OH⁻.

Determine the molar mass of Zn. The molar mass of Zn is approximately 65.38 g/mol.

Calculate the moles of Zn consumed using the formula: moles of Zn = mass of Zn / molar mass of Zn. Substitute the given mass of Zn (4.50 g) and its molar mass.

Use the stoichiometry of the balanced chemical equation to find the moles of MnO2 reduced. The stoichiometry from the half-reactions shows that 1 mole of Zn corresponds to 1 mole of MnO2. Calculate the mass of MnO2 reduced using its molar mass (approximately 86.94 g/mol) and the moles of MnO2 obtained from the stoichiometry.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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 the alkaline battery, zinc (Zn) is oxidized at the anode, while manganese dioxide (MnO2) is reduced at the cathode. Understanding the stoichiometry of these reactions is essential for calculating the mass of reactants and products.

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 consumed and produced. In this case, knowing the molar masses of Zn and MnO2 and the balanced equation will enable us to find the mass of MnO2 reduced when a specific mass of Zn is oxidized.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is crucial for converting between the mass of a substance and the number of moles, which is necessary for stoichiometric calculations. For this problem, the molar masses of Zn and MnO2 will be used to relate the mass of Zn consumed to the mass of MnO2 reduced during the battery's discharge.

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?