When an electric current is passed through acidulated water, \(112 \mathrm{~mL}\) of hydrogen gas at NTP collects at the cathode in 965 seconds. The current passed, in ampere is: (a) \(0.1\) (b) \(0.5\) (c) \(1.0\) (d) \(2.0\)

Electrolysis is a process by which electrical energy is used to drive a chemical reaction that would otherwise not be spontaneous. It involves passing an electric current through a substance to effect a chemical change. The substance can be either in a molten state or in an aqueous solution that contains ions.

For example, when acidulated water (water with a small amount of an acid added to increase conductivity) is subjected to electrolysis, hydrogen gas is released at the cathode (negative electrode) and oxygen at the anode (positive electrode). The amount of gas produced is directly related to the charge passed through the electrolyte, which can be determined by using Faraday's laws of electrolysis.

In the context of the original exercise, the hydrogen gas produced at the cathode can be measured to determine the amount of electricity, specifically current, that was used during the electrolysis. By understanding the relationship between the volume of hydrogen gas produced and the charge passing through the substance, precise chemical calculations can be performed to evaluate the current applied during the experiment.

The ideal gas law is an equation of state that gives us a simple relationship between the pressure, volume, temperature, and amount (in moles) of an ideal gas. Represented by the formula \( PV = nRT \), where \( P \) is the pressure, \( V \) the volume, \( n \) the number of moles of gas, \( R \) the ideal gas constant, and \( T \) the temperature in Kelvin.

The ideal gas law is crucial when dealing with gas-phase reactions and processes like electrolysis, where gases are produced or consumed. In the electrolysis of acidulated water, the volume of hydrogen produced can be plugged into the ideal gas law equation to determine the number of moles of gas produced at a known temperature and pressure. This key step links the physical measurement of gas volume to the moles needed for chemical calculations and further application in Faraday's laws of electrolysis, as shown in the exercise solution.

Chemical calculations are an essential part of understanding and executing reactions and processes in chemistry. They involve using stoichiometry, gas laws, and other principles to quantify the reactants and products in a chemical equation.

In electrolysis, for instance, it's important to calculate the number of moles of gas produced, as the volume alone does not provide enough information. Through chemical calculations, intertwined with the ideal gas law and the concepts underpinning Faraday's laws, we can relate the volume of hydrogen gas produced to the number of moles, then further estimate the charge involved, and finally the current that was passed during electrolysis. These steps are crucial for a comprehensive understanding of the process and are necessary to complete exercises like the one provided.

Chemical calculations involve conversion factors such as the ideal gas constant and Faraday's constant. These provide a bridge between the macroscopic measurements that can be directly observed (like volume and pressure) and the microscopic properties of molecules and atoms (like moles and charges). With a solid grasp on these calculations, students can confidently solve a broad range of chemistry problems, including those involving electrolysis and gas laws.