Final answer:
To find the mass of gold produced, calculate the total electrical charge passed through the solution and then apply Faraday's laws of electrolysis to relate charge to mass of gold deposited.
Step-by-step explanation:
The student's question involves calculating the mass of gold produced through electroplating by passing a certain amount of electric current through a gold solution for a specified period of time.
To determine the mass of gold, we can use Faraday's laws of electrolysis, which relate electric charge to the amount of a substance that is deposited or dissolved during the process.
First, we must calculate the total charge Q in coulombs using the formula Q = It, where I is the current in amperes and t is the time in seconds.
The mass of gold can then be calculated using the formula m = (M * Q) / (n * F), where M is the molar mass of gold, Q is the total charge, n is the number of moles of electrons required to reduce one mole of gold ions, and F is Faraday's constant.
For gold, we know that one mole of Au3+ ions requires 3 moles of electrons to be reduced to gold metal. Given the molar mass of gold (197 g/mol) and Faraday's constant (96485 C/mol), we can calculate the mass of gold deposited.