Weighing a copper atom in an electrolysis experiment. A...

Weighing a copper atom in an electrolysis experiment. A standard experiment involves passing a current of several amperes through a copper sulfate solution $\left(\mathrm{CuSO}_{4}\right)$ for a period of time and determining the mass of copper plated onto the cathode. If it is found that a current of 1.00 A flowing for 3600 s deposits 1.185 g of copper, find $($ a) the number of copper atoms deposited, (b) the weight of a copper atom, and (c) the molar mass of copper.

Weighing a copper atom in an electrolysis experiment. A standard experiment involves passing a current of several amperes through a copper sulfate solution $\left(\mathrm{CuSO}_{4}\right)$ for a period of time and determining the mass of copper plated onto the cathode. If it is found that a current of 1.00 A flowing for 3600 s deposits 1.185 g of copper, find $($ a) the number of copper atoms deposited,
(b) the weight of a copper atom, and (c) the molar mass of copper.

Key Concepts

Faraday's Law of Electrolysis

This concept explains that the amount of substance deposited at an electrode during electrolysis is directly proportional to the total electric charge passed through the electrolyte. The law links the microscopic world of electrons to the macroscopic quantities measured in grams, using the Faraday constant, which represents the charge per mole of electrons exchanged.

Electric Charge, Current, and Time Relationship

This fundamental concept involves the relation Q = I × t, where Q is the total electric charge in coulombs, I is the current in amperes, and t is the time in seconds during which the current flows. This calculation is essential for determining how many electrons are transferred in the electrolytic process.

Electrochemical Reaction Stoichiometry

This principle deals with the balanced chemical equations for the electrode processes. In electrolysis, the stoichiometry tells you how many electrons are required to deposit one atom of a substance (for example, the reduction of Cu2+ to copper metal requires 2 electrons), which is critical for connecting the charge passed to the amount of substance deposited.

Avogadro's Number

Avogadro’s number is the number of atoms, ions, or molecules in one mole of a substance, typically 6.022 × 10^23. It serves as a bridge between atomic-scale measurements and macroscopic quantities, allowing conversion between moles and the actual number of atoms or molecules present.

Molar Mass and Atomic Weight

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol), and is numerically equivalent to the atomic or molecular weight in atomic mass units. Understanding this concept is key for converting between the mass of a deposited element and the number of moles, and consequently the number of individual atoms.

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