An acidified solution was electrolyzed using copper...

An acidified solution was electrolyzed using copper electrodes. A constant current of 1.18 A caused the anode to lose $0.584 \mathrm{g}$ after $1.52 \times 10^{3} \mathrm{s}$. (a) What is the gas produced at the cathode and what is its volume at STP? (b) Given that the charge of an electron is $1.6022 \times 10^{-19} \mathrm{C},$ calculate Avogadro's number. Assume that copper is oxidized to $\mathrm{Cu}^{2+}$ ions.

Key Concepts

Standard Molar Volume at STP

The standard molar volume is the volume occupied by one mole of an ideal gas at standard temperature and pressure (STP), typically 22.4 liters. This concept is used to convert between the moles of gas produced in an electrochemical process and its corresponding volume, providing a bridge between microscopic reaction quantities and observable gas volumes.

Hydrogen Evolution Reaction

In the context of electrolysis in an acidic solution, the hydrogen evolution reaction refers to the reduction of hydrogen ions (H+) at the cathode to form hydrogen gas (H2). This reaction is important in electrochemistry when an inert or non-consumable electrode carries out a reduction process, resulting in observable gas production at the cathode.

Determination of Avogadro's Number from Electrochemical Data

This involves calculating Avogadro's number using experimental electrolysis data by combining measures of mass change, electron charge, and current. By determining the number of electrons and linking that to the moles of material oxidized or reduced, one can derive Avogadro’s number, which is fundamental in understanding the mole concept and the scale of atoms and molecules.

Faraday's Laws of Electrolysis

This concept relates the quantity of electric charge passed through an electrolyte to the amount of substance that undergoes oxidation or reduction at the electrodes. In practice, Faraday's laws allow one to calculate the moles of a substance produced or consumed during an electrochemical reaction when the current and time are known, connecting microscopic charge transfer to macroscopic mass changes.

Electrode Reaction Stoichiometry

Electrode reaction stoichiometry involves the balanced chemical equations at the anode and cathode, showing how electrons are transferred in a redox process. It highlights the molar relationships between the species involved (for instance, the two-electron transfer in copper oxidation or the reduction of hydrogen ions to produce hydrogen gas), which is essential for linking the observed current to the number of moles of products or reactants.

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