A metal forms the fluoride MF3. Electrolysis of the molten fluoride by a current of 3.86 A for 16.2 minutes deposits 1.25 g of the metal. Calculate the molar mass of the metal.

Electrolysis is a process that involves passing an electric current through a substance to cause a chemical change. This substance can be either in a molten state or dissolved in a suitable solvent - typically water. This process is crucial when a compound needs to be broken down into its elements, such as extracting aluminum from its ore or decomposing water into hydrogen and oxygen.

During electrolysis, the substance that undergoes the chemical change is called the electrolyte. Electrodes are submerged in the electrolyte and connected to a power supply, creating a circuit. When the electric current passes through, the electrolyte's ions move towards the electrodes where they gain or lose electrons, thus being reduced or oxidized.

The Role of Ions in Electrolysis

Positive ions, called cations, move towards the negative electrode (cathode) where they gain electrons (reduction). Negative ions, called anions, move toward the positive electrode (anode) where they lose electrons (oxidation). The substance deposited on the cathode or the gas evolved at the anode can be collected and weighed, providing quantitative insights about the reaction - as seen in the original exercise in determining the metal's mass.

Faraday's laws of electrolysis comprise two scientific statements that quantify the effect of an electric current passed through an electrolyte. These laws connect the amount of chemical change at an electrode to the quantity of electricity used in the electrolysis process.

Faraday's First Law

Faraday's first law states that the mass of a substance altered at an electrode during electrolysis is directly proportional to the amount of electricity that passes through the circuit. This law highlights that more extended periods of electrolysis or higher currents will lead to more significant chemical changes.

Faraday's Second Law

The second law posits that the amount of different substances altered by the same quantity of electricity passing through the electrolyte is directly proportional to their equivalent weights. This law serves as the principle behind calculating the moles of electrons and linking them to the moles of substance deposited, as expressed in the step-by-step solution of the exercise.

These laws were used in the original problem to convert the total charge passed into the moles of electrons and then relate this quantity to the amount of metal deposited.

The mole concept is a pivotal bridge between the microscopic world of atoms and molecules and the macroscopic world we observe. A mole is defined as the amount of substance that contains the same number of entities - such as atoms, ions, or molecules - as there are atoms in 12 grams of carbon-12.

This concept allows us to quantify substances based on a common unit, the Avogadro constant (\(6.022 \times 10^{23}\) entities per mole), helping us to relate mass to the number of atoms or molecules present. In the context of the exercise, once the moles of electrons are known, we employ the mole concept to find the corresponding moles of metal deposited through electrolysis.

From Moles to Molar Mass

The final step is to determine the substance's molar mass - the mass of one mole of substance, usually expressed in grams per mole (g/mol). By dividing the mass of metal deposited by the number of moles of metal, we obtain the molar mass of the metal. This calculation is essential in chemistry, as it helps convert between mass and moles, providing a necessary quantitative dimension to chemical reactions and processes.