Question

Metal plating is done by passing a current through a metal solution. For example, an item can become gold plated by attaching the item to a power source and submerging it into an Au³⁺ solution. The item itself serves as the cathode, at which the Au³⁺ ions are reduced to Au(s). A piece of solid gold is used as the anode and is also connected to the power source, thus completing the circuit. What mass of gold is produced when 15.1 A of current are passed through a gold solution for 31.0 min?

Answer 1

A current of 15.1 A passed through a gold solution for 31.0 min will produce 70.45 grams of gold.

Step-by-step explanation:

In the given electroplating process, a current of 15.1 A is passed through a gold solution for 31.0 min.

Using the equation I = Q/t, where I is the current, Q is the charge, and t is the time, we can calculate the charge:

Q = I × t = 15.1 A × (31.0 min × 60 s/min) = 27,198 C

Next, we can use Faraday's law of electrolysis to determine the mass of gold deposited:

m = (Q ÷ n) × M, where m is the mass, Q is the charge, n is the number of moles of electrons transferred, and M is the molar mass of gold.

Since 1 mol of electrons is equivalent to 1 Faraday, and the molar mass of gold is 197 g/mol, we have:

m = (27,198 C ÷ 96,500 C/mol) × 197 g/mol = 70.45 g

Therefore, 70.45 grams of gold will be produced when 15.1 A of current is passed through the gold solution for 31.0 minutes.