An inexpensive and accurate method of measuring the quantity of electricity flowing through a circuit is to pass the current through a solution of a metal ion and weigh the metal deposited. A silver electrode immersed in an Ag \(^{+}\) solution weighs \(1.7854 \mathrm{~g}\) before the current has passed and weighs \(1.8016 \mathrm{~g}\) after the current has passed. How many coulombs have passed?

Coulombs measure the quantity of electrical charge that flows in a circuit. In electrochemistry, understanding how many coulombs have passed through a solution helps us know how much electric current has been used.
To calculate the coulombs from a known mass of deposited material, the mass is first measured before and after the current flows.
This mass difference helps us find the number of moles of the substance deposited.
Once we know the number of moles, we multiply it by Faraday's constant (96485 C/mol) to find the total coulombs.
In this exercise, you found a silver electrode’s mass change, converting it to moles, then calculating the total charge in coulombs.

First, we must convert the mass of deposited material into moles. Moles are a key unit in chemistry that measures the amount of substance. This conversion is essential since it helps link mass to the number of atoms or molecules.
Here's a step-by-step to convert mass to moles:

• Measure the change in mass before and after the current passes.
• Use the molar mass (from the periodic table) of the substance. In this example, we used silver.
• Divide the mass of the substance by its molar mass.

For instance, the molar mass of silver is 107.87 g/mol. By dividing the mass change of silver by its molar mass, you get the number of moles deposited.
E.g., If 0.0162 g of silver was deposited, divide 0.0162 g by 107.87 g/mol (molar mass) to get around 1.502 x 10^-4 moles of silver.

Electrochemistry involves the study of the movement of electrons in chemical processes. Faraday's Law of Electrolysis plays a pivotal role.
This law states that the amount of any substance deposited or dissolved at an electrode during electrolysis is directly proportional to the amount of electricity passed through the electrolyte.
Using the law:

• First, convert the deposited mass into moles.
• Next, apply Faraday's constant (96485 C/mol). This constant links moles of electrons to electric charge.
• Multiply the moles of the substance by 96485 C/mol to get the total charge in coulombs.

For example, you've converted 0.0162 g of silver to moles of silver (about 1.502 x 10^-4 moles). Multiply this by 96485 C/mol to find out how many coulombs have passed through the solution, resulting in approximately 14.50 C.
Understanding these calculations is fundamental for interpreting results and solving complex electrochemical problems.