After use, a nickel-cadmium (Nicad) battery has 0.129 g of Cd(OH)2 deposited on the anode. The b

step 1 Okay, so we've got some cadmium hydroxide, which is going to get converted back to cadmium. Cadm

After use, a nickel-cadmium (Nicad) battery has 0.129 g of...

After use, a nickel-cadmium (Nicad) battery has 0.129 g of $\mathrm{Cd}(\mathrm{OH})_2$ deposited on the anode. The battery is inserted into a recharger, which supplies 0.175 A . How many hours does the Nicad battery need for recharging so that all the $\mathrm{Cd}(\mathrm{OH})_2$ is converted back to Cd ? Assume that the recharger is $100 \%$ efficient. (See Problem 76 for a description of the Nicad battery.)

Key Concepts

Unit Conversions in Electrochemistry

Unit conversion is a critical skill in electrochemistry, ensuring that calculated quantities are expressed in appropriate and meaningful units. This typically includes converting time from seconds to hours or mass from grams to moles, facilitating the practical application of theoretical calculations in real-world problems.

Molar Mass and Mole Conversion

Molar mass serves as a conversion factor between the mass of a substance and the number of moles present. By converting g to moles, one can use the stoichiometric coefficients from the balanced chemical equation to determine the quantity of electrons involved in the reaction, linking mass measurements with electrochemical calculations.

Electrochemical Stoichiometry

Electrochemical stoichiometry involves using the balanced chemical equation for a redox reaction to relate the number of electrons transferred to the number of moles of reactant or product. This concept is crucial for determining how much charge, in terms of electrons, is required to complete a specific electrochemical conversion.

Faraday's Laws of Electrolysis

Faraday's laws state that the amount of chemical change produced by an electric current is proportional to the quantity of electricity that passes through the electrolyte. This fundamental principle allows one to calculate the mass of material transformed at an electrode based on the total charge delivered during the reaction.

Electric Current and Charge Relationship

The relationship between electric current and charge is given by the equation Q = I × t, where Q is the total charge in coulombs, I is the current in amperes, and t is the time in seconds. Understanding this relationship is essential for converting a given current and time into the total electrical charge used during an electrochemical process.

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