The electrolytic cell represented in Figure \(16.17\) can be used to plate silver onto other metal surfaces. The plating reaction is: \(\mathrm{Ag}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(s)\). Notice from the reaction that \(1 \mathrm{~mol} \mathrm{e}^{-}\)plates out \(1 \mathrm{~mol} \mathrm{Ag}(\mathrm{s})\). Use this stoichiometric relationship to determine how much time is required with an electrical current \(0.100\) amp to plate out \(1.0 \mathrm{~g}\) Ag. The amp is a unit of electrical current equivalent to \(1 \mathrm{C} / \mathrm{s}\). (Hint: Recall that the charge of an electron is 1.60 \(\times 10^{-19} \mathrm{C}\) )

Stoichiometry is a branch of chemistry that involves the calculation of reactants and products in chemical reactions. In the context of electrochemistry, stoichiometry deals with the relationships between the electrons transferred in a redox reaction and the substances oxidised or reduced.

Understanding stoichiometry is essential when dealing with electrolytic cells, where electrical energy causes non-spontaneous chemical reactions. For example, in the plating reaction \(\mathrm{Ag}^{+}(aq)+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(s)\), stoichiometry tells us that one mole of electrons (\(\mathrm{e}^{-}\)) is required to reduce one mole of silver ions (\(\mathrm{Ag}^{+}\)) to solid silver (\(\mathrm{Ag}(s)\)). This one-to-one ratio simplifies the calculation of the amount of substance deposited or dissolved in an electrolytic process.

When performing stoichiometric calculations in an electrolytic cell, one must consider the charge of each electron and how many electrons are involved per ion in the reaction. For reactions where the stoichiometry is not a simple one-to-one ratio, the calculations would involve determining the proportion of electrons to ions.

Electrochemistry is the study of the chemical processes that cause electrons to move. This movement of electrons, or electricity, can be used to bring about a chemical change. Electrolytic cells are a typical application of electrochemistry, used for processes such as electroplating, in which a metal coating is applied to a surface.

An electrochemical reaction involves the transfer of electrons from one substance to another. When an electric current is passed through an electrolytic cell, a chemical reaction is induced at the electrodes. The electrons needed for these reactions come from the external power source connected to the cell. The amount of electricity used directly relates to the amount of chemical change according to Faraday's laws of electrolysis. This is where stoichiometry becomes invaluable in predicting and calculating the outcomes of electrochemical processes.

Using the principles of electrochemistry, we can calculate the amount of time required to deposit a certain mass of a substance onto an electrode, based on the current applied and the stoichiometry of the reaction.

Faraday's constant is a fundamental value in electrochemistry that represents the charge carried by one mole of electrons, approximately equal to \(96485\) coulombs (C). It bridges the gap between the macroscopic world of chemical reactions and the microscopic world of electron transfer.

In our electrodeposition example, Faraday's constant is used to determine the total charge required to deposit the desired amount of silver. Since the reaction stoichiometry implies a one mole to one mole relationship between silver ions and electrons, the number of moles of silver to be plated can be directly converted into the charge needed by multiplying by Faraday's constant. Knowing the total charge and the current (\(0.100\) amp, equivalent to \(0.100\) C/s), we can calculate the amount of time required to complete the plating process.

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It serves as a conversion factor between the weight of a substance and the number of moles. The molar mass of silver, \(107.87\) g/mol, allows us to translate the mass of silver we aim to plate (1.0 g) into moles, which is pivotal for stoichiometric calculations in electrochemistry.

Once we know the number of moles of silver to be plated, we can use stoichiometry to calculate the total number of moles of electrons needed and then convert this to the total charge using Faraday's constant. Molar mass thus links the actual mass of silver being deposited to the electrical charge required to deposit it, highlighting the importance of molar mass in understanding the quantitative aspects of electrochemical reactions.