The electrolysis of an aqueous solution of \(\mathrm{NaCl}\) has the overall equation $$ 2 \mathrm{H}_{2} \mathrm{O}+2 \mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g)+2 \mathrm{OH}^{-}(a q) $$ During the electrolysis, \(0.228\) mol of electrons passes through the cell. (a) How many electrons does this represent? (b) How many coulombs does this represent? (c) Assuming \(100 \%\) yield, what masses of \(\mathrm{H}_{2}\) and \(\mathrm{Cl}_{2}\) are produced?

When discussing the fascinating process of electrolysis, specifically the electrolysis of an aqueous solution of NaCl, the magic of stoichiometry becomes apparent. Stoichiometry is the section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. In our scenario, stoichiometry plays an integral role because it allows us to predict the amounts of hydrogen (\text{H}\(_2\)) and chlorine (\text{Cl}\(_2\)) gases produced from a given amount of NaCl solution during electrolysis.

Applying stoichiometry starts with a balanced chemical equation, where the coefficients represent the mole ratio of each substance involved. For this NaCl aqueous solution, the electrolysis reaction is \(2 \text{H}_2\text{O} + 2 \text{Cl}^- \rightarrow \text{H}_2 + \text{Cl}_2 + 2 \text{OH}^-\). Here, we see that two moles of electrons produce one mole of hydrogen gas and half a mole of chlorine gas. With these ratios in mind, the stoichiometric calculations can determine the expected mass of gases released using the molar mass and the initial amount of electrons or moles of NaCl.

Using stoichiometry, if 0.228 mol of electrons pass through the cell, we can deduce that we will end up with 0.114 mol of hydrogen and 0.057 mol of chlorine. By converting these mole amounts into mass via the molar mass of each gas, you confidently reach the answer to the 'how much' of your chemical reaction yield, which is essential in both educational and industrial applications.

Diving deeper into the elements critical to the electrolysis of NaCl aqueous solution, Faraday's constant remains a keystone in understanding the process. Representing the total electric charge carried by one mole of electrons, this constant, approximately \(96485 \text{C/mol}\), bridges the gap between moles and electricity, which is fundamental in electrochemistry.

To compute the charge in coulombs that passed through your electrolysis cell, multiply the moles of electrons by Faraday's constant. This relationship is pivotal as it translates chemical quantities to electrical quantities; hence, it enables the measurement of the electrolytic effects based on the current passed through the solution. In the given problem, \(0.228\) mol of electrons holding a charge of approximately \(22006 \text{C}\) is a direct result of this constant's application, highlighting its practicality.

Faraday's constant not only aids in calculation but also reinforces the concept of electron charge quantization, implying that charge can only be an integral multiple of the elementary charge. For educators and students alike, grasping Faraday's constant is an empowering step in deciphering electrochemical processes and linking chemistry to physics.

Avogadro's constant is a fundamental figure in chemistry, especially when it comes to the study of substances at the microscopic level. It denotes the number of constituent particles, typically atoms or molecules, that are contained in one mole, which is approximately \(6.022 \times 10^{23}\) entities per mole. This incredible number is named after the scientist Amedeo Avogadro and is crucial for cracking the nitty-gritty of chemical reactions on an atomic scale.

In the context of our NaCl electrolysis problem, Avogadro's constant enables us to seamlessly switch from moles to the actual number of electrons involved in the reaction. For example, with \(0.228\) mol of electrons, by employing Avogadro's constant, we get a staggering figure of around \(1.37 \times 10^{23}\) electrons. This conversion is vital when you're dealing with the exact number of electrons transferring during electrolysis, which directly impacts the amounts of \text{H}\(_2\) and \text{Cl}\(_2\) produced.

Understanding Avogadro's constant is like having a translator between the world of the little (atoms and molecules) and the world we measure in the lab (grams and liters). It's an indispensable tool for students learning about the subtleties of chemical reactions, helping them gain a bird's-eye view of the molecular level happenings in a way that's quantifiable and relatable to their studies.