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?

Verified step by step guidance

1. insert step 1> Determine the molar mass of Zn (zinc) from the periodic table, which is approximately 65.38 g/mol.
2. insert step 2> Calculate the number of moles of Zn consumed using the formula: \( \text{moles of Zn} = \frac{\text{mass of Zn}}{\text{molar mass of Zn}} \).
3. insert step 3> Write the half-reaction for the oxidation of Zn at the anode: \( \text{Zn} \rightarrow \text{Zn}^{2+} + 2e^- \). This shows that each mole of Zn produces 2 moles of electrons.
4. insert step 4> Calculate the total moles of electrons transferred using the stoichiometry from the half-reaction: \( \text{moles of electrons} = 2 \times \text{moles of Zn} \).
5. insert step 5> Convert the moles of electrons to coulombs using Faraday's constant (\( F = 96485 \text{ C/mol} \)): \( \text{coulombs} = \text{moles of electrons} \times F \).

Key Concepts

Electrochemical Reactions

Electrochemical reactions involve the transfer of electrons between chemical species, typically occurring in galvanic cells like batteries. In an alkaline battery, zinc (Zn) is oxidized at the anode, releasing electrons that flow through the circuit to reduce manganese dioxide (MnO2) at the cathode. Understanding these reactions is crucial for calculating the charge transferred during the battery's operation.

Faraday's Law of Electrolysis

Faraday's Law states that the amount of substance transformed at an electrode during electrolysis is directly proportional to the quantity of electric charge passed through the system. This law allows us to calculate the total charge (in coulombs) based on the moles of electrons involved in the reaction, which is essential for determining how much charge is transferred when zinc is consumed in the battery.

Molar Mass and Moles

The molar mass of a substance is the mass of one mole of that substance, typically expressed in grams per mole. For zinc, the molar mass is approximately 65.38 g/mol. By converting the mass of zinc consumed (4.50 g) into moles, we can determine the number of electrons transferred during its oxidation, which is necessary for calculating the total charge using Faraday's Law.