Let’s do some electrochemistry. A process for electroplating an object with gold is as follows. The object to be electroplated is immersed in a bath of gold chloride (AuCl₄-) and connected to the negative terminal of a battery. A gold electrode is also placed in the solution and is connected to the positive terminal of the battery. At the gold electrode (which is the positive electrode the anode) the reaction:

Au(sol.) +4Cl- ---> AuCl₄- +3e-

takes place.

The electrons produced are taken up by the electrode and pass through the battery to the other electrode (the object being electroplated). On the object being electroplated (which is negative, so it is the cathode) there is a steady supply of electrons arriving from the anode via the battery. As a result, the reverse reaction

AuCl₄- +3e- ---> Au(sol.) +4Cl-

takes place, resulting in gold being deposited on the surface.

(a) For each gold atom that is deposited on the surface, how many electrons flow through the battery?

(b) Electrons are flowing from the anode, through the battery, to the cathode. For the current to be sustained we cannot have a buildup of charge anywhere. So there must be a current through the solution as well. What is the charge carrier in the solution (there might be more than one kind of charge carrier...)? Which way do they flow in the solution (from anode to cathode or vice versa)? For each electron that flows through the battery, how many charge carriers flow through the solution?

(c) An ammeter connected to the battery detects a current of 0.5 A. At what rate are gold atoms being deposited on the object?

(d) The electroplating cell (the container containing the solution) is a trough 10 cm long, 3 cm wide and filled to a depth of 4 cm with the solution. Given the current measured in c) what is the current density in the electroplating cell?