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.

Faraday's laws of electrolysis are crucial in understanding the principles behind the electrolytic process, like the one involving copper electrodes in an acidified solution. There are two laws that Michael Faraday formulated: the first law states that the mass of a substance altered at an electrode during electrolysis is directly proportional to the quantity of electricity that passes through the electrolyte. The second law says that, for the same quantity of electricity passing through different electrolytes, the mass of substances altered at the electrodes is proportional to their equivalent weights.

In the context of calculating the volume of hydrogen gas at STP, Faraday's second law is applied particularly well. Since hydrogen gas (\(H_2\)) has a molar mass of approximately 2 grams, we can use Faraday's constant of 96,485 coulombs per mole to calculate how much charge is needed to produce a mole of hydrogen gas. Remember that hydrogen gas is diatomic, meaning that two atoms make up one molecule, thus two moles of electrons are needed to produce one mole of hydrogen gas.

Avogadro's number is a fundamental constant in chemistry, representing the number of constituent particles (usually atoms or molecules) in one mole of a substance. The number is approximately 6.022 x 10²³ particles/mol. When calculating Avogadro's number from electrolysis data, as exemplified in the given exercise, we combine our understanding of Faraday's laws of electrolysis with the electron charge to estimate the number of atoms. By dividing the total charge by the charge per copper atom, the calculated Avogadro's number should be close to the accepted value. This approach assumes each copper ion (\(Cu^{2+}\)) releases two electrons, linking the charge to the number of atoms—ultimately drawing a connection between macroscopic measurements and atomic scale units.

Students should pay close attention to ensuring that they use the correct mass of the substance and its molar mass, which allows them to find the number of moles and from there calculate the number of atoms. The exercise weaves together the concept of molar mass with the charge per ion to arrive at a calculation of Avogadro's number, a brilliant example of quantitative analysis in chemistry.

The electrochemical series is a list that ranks elements and molecules based on their standard electrode potentials. This series determines the tendency of a chemical species to be reduced or oxidized during an electrochemical reaction. In other words, it predicts which substances will be oxidized or reduced in an electrolytic cell.

In the given exercise, the electrochemical series helps us identify that in an acidified solution with copper electrodes, hydrogen ions will be reduced before copper ions. This is because hydrogen has a higher position in the series compared to copper. Hydrogen gas being produced at the cathode during electrolysis is in part predicted by the electrochemical series. A solid understanding of this series is therefore invaluable for anticipating the outcomes of electrolysis, as well as for understanding redox reactions––a fundamental aspect of chemistry.

Standard Temperature and Pressure, abbreviated as STP, refers to a set of conditions commonly used for measuring gases. At STP, the temperature is set at 0 degrees Celsius (273.15 Kelvins), and the pressure is 1 atmosphere (atm). Under these conditions, one mole of any ideal gas occupies 22.4 liters.

This concept is important when it comes to the electrolysis problem tackled here. Calculating the volume of hydrogen gas at STP after electrolysis allows for a standardized comparison with other reactions and conditions. When the exercise states that the volume of hydrogen gas at STP is needed, applying the ideal gas law under STP conditions simplifies calculations and helps in reaching a valuable conclusion. Understanding how volumes of gases vary with temperature and pressure is foundational in chemistry and particularly crucial in calculations involving gaseous products in electrochemical reactions.