The electrolysis of an aqueous solution of NaCl has the...

The electrolysis of an aqueous solution of 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?

The electrolysis of an aqueous solution of 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?

Key Concepts

Coulomb’s Constant and Charge Conversion

The coulomb is the SI unit of electric charge. In electrolysis, the relationship between moles of electrons and coulombs of charge is established using Faraday’s constant, approximately 96485 coulombs per mole of electrons. This conversion is key in linking the electrical input (in coulombs) to the chemical changes observed in the reaction.

Electrolysis

Electrolysis is the process by which electrical energy is used to drive a non-spontaneous chemical reaction. During electrolysis, electrons are transferred from one species to another, causing oxidation at the anode and reduction at the cathode. This process is fundamental in converting electrical energy into chemical change, and in aqueous solutions, it can produce gases, ions, or other chemical species at the electrodes.

Faraday’s Laws of Electrolysis

Faraday’s laws provide a quantitative relationship between the amount of electrical charge passed through an electrolyte and the amount of chemical change that occurs at the electrodes. The first law states that the mass of a substance altered at an electrode is proportional to the quantity of electricity (charge) passed through the cell. The second law indicates that the amounts of different substances liberated by the same quantity of charge are in proportion to their chemical equivalent weights.

Mole and Avogadro’s Number

A mole is a standard unit in chemistry used to count particles, defined as exactly 6.022×10^23 entities (atoms, molecules, electrons, etc.). This allows chemists to bridge the gap between the microscopic world of atoms and molecules and the macroscopic quantities observed in the laboratory, providing a common language for expressing amounts of substances in chemical reactions.

Stoichiometry in Electrochemical Reactions

Stoichiometry in electrochemical reactions involves using balanced chemical equations to relate the quantities of reactants and products with the electrons transferred during the reaction. It allows for the calculation of the amounts of various chemical species produced or consumed by taking into account the electron exchange, helping to determine yields and convert between quantities such as moles, mass, and charge.

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