How much chlorine will be liberated on passing one ampere current for 30 minutes through \(\mathrm{NaCl}\) solution? (a) \(0.66 \mathrm{~mol}\) (b) \(0.33 \mathrm{~mol}\) (c) \(0.66 \mathrm{~g}\) (d) \(0.33 \mathrm{~g}\)

Faraday's laws of electrolysis are seminal in understanding the quantitative aspects of electrochemistry, particularly during the process of electrolysis. The first law states that the amount of chemical change (or the mass of substance deposited) during the electrolysis process is directly proportional to the quantity of electricity that passes through the electrolyte. This can be mathematically represented as \( m = ZQ \), where \( m \) is the mass of the substance altered at an electrode, \( Z \) is the electrochemical equivalent, and \( Q \) is the total charge passed through the electrolyte.

The second law, on the other hand, indicates that if the same quantity of electricity passes through several electrolytes, the mass of substances altered at the electrodes is directly proportional to their equivalent weights. This law can be further simplified to the relationship between the number of moles of electrons and the number of moles of substance deposited. Knowing these laws allows students to correctly compute the amount of a substance produced during an electrochemical reaction, which is exactly what was done in the step-by-step solution presented.

The mole concept is a cornerstone of chemistry that enables scientists and students alike to quantify the amount of substance in a given chemical reaction. One mole of any substance contains Avogadro's number, approximately \(6.022 \times 10^{23}\), of units (atoms, molecules, ions, or electrons).

The application of the mole concept in electrochemistry is crucial when we are dealing with processes like electrolysis. In the example given, the calculation of the amount of chlorine gas liberated is based on the relationship between the moles of electrons and the moles of chlorine. Understanding the interconversion between moles, mass, and the number of particles forms the bedrock for solving stoichiometry problems within electrochemistry, as illustrated in the original solution provided.

Relevance in Electrolysis

During electrolysis, electrons are transferred, which means counting the number of moles of electrons is equivalent to measuring the charge passed. This concept was used to calculate the moles of chlorine gas by first determining the number of moles of electrons from the total charge.

Stoichiometry is the area of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is a powerful tool that helps predict the outcomes of reactions and can guide the scaling up of chemical processes from lab-scale to industrial-scale.

In the context of the given problem, stoichiometry was utilized to connect the moles of electrons involved in the reduction of chloride ions to the moles of chlorine gas produced. This relationship hinges on the balanced chemical equation for the chloride ion's reduction: \(2Cl^- \rightarrow Cl_2 + 2e^-\). It implies that two moles of electrons produce one mole of chlorine gas, which is an essential aspect to solve the question posed. The step-by-step solution correctly uses this stoichiometric principle to arrive at the final answer, highlighting the key role stoichiometry plays in solving electrolysis chemistry problems.

Electrochemistry is a branch of chemistry that deals with the interactions between electrical energy and chemical reactions. It encompasses a range of phenomena including battery technology, corrosion, and, most notably for our textbook problem, electrolysis — the process by which ionic substances are decomposed into simpler substances when an electric current is passed through them.

In the example problem, we delve into the electrochemistry behind the production of chlorine gas from a solution of sodium chloride (NaCl). Understanding the redox reactions that occur at the cathode and anode, and how electricity influences these reactions, is key to solving electrolysis problems. Practical applications of electrochemistry are extensive in our daily life, ranging from the batteries that power our mobile devices to the production of chemicals like chlorine. Therefore, a solid grasp of electrochemical principles not only aids in academic success but also provides insights into much of the technology that powers modern society.