### Video Transcript

Smelting of copper ore produces an impure material which can be converted to pure copper using the electrolysis apparatus illustrated in the diagram. An electrical current causes the immersed cathode to be coated with pure copper, while less reactive impurities fall to the bottom of the cell. What is the half equation of the reaction taking place at the anode?

Before we answer this question, let’s take a look at the diagram of the experimental apparatus. This diagram shows an electrolytic cell. In an electrolytic cell, we use a power source, in this case a battery to apply an electrical current to power reaction in the nonspontaneous direction. On the positive side of our cell, we have the anode which is where oxidation occurs. And on the negative side we have the cathode which is where reduction occurs.

As a reminder, when a chemical species is oxidized, it loses electrons. And when a chemical species is reduced, it gains electrons when we attach the battery to the cell, electrons will begin flowing from the positive terminal to the negative terminal powering the reaction. Copper from the impure copper anode will then be oxidized and go into the copper sulfate and sulfuric acid solution as a copper(II) plus ion leaving the impurities behind to fall to the bottom of the cell. The copper will then be plated onto the pure copper cathode as solid copper. Now that we’ve reviewed this diagram, let’s take a look at the question.

We want to know the half equation of the reaction taking place at the anode. We know that oxidation always occurs at the anode. And in this particular cell, solid copper from the impure copper is being oxidized and going into the solution as a copper(II) plus ion. The chemical equation that describes this process is copper solid forming copper(II) plus aqueous plus two electrons. We can confirm that this is the correct equation because copper is losing electrons. And its oxidation number is increasing from zero to plus two.

What is the half equation of the reaction taking place at the cathode?

We know the cathode is where reduction occurs. And in this cell, copper(II) plus is being reduced and deposited onto the pure copper cathode as solid copper. The chemical equation that describes this process is copper(II) plus aqueous plus two electrons forming copper solid. Again, we can confirm that this is the correct equation because copper is gaining electrons. And its oxidation number has been reduced from plus two to zero.

A 95.0 kilogram pure copper cathode has a surface area of 1.50 meters squared and a density of 9.00 grams per cubic centimeter. The cathode is electroplated with a layer of pure copper 2.00 millimeters in thickness. It is assumed that the cathode is coated evenly with copper and that the coating has a negligible effect on the surface area. What is the mass of the cathode after the coating is complete?

In this part of the question, we’ve electroplated copper onto the cathode by running the electrolytic cell. And now we want to know the final mass of the cathode after it’s been electroplated with more copper. Well, we’re not given the mass of copper that was plated onto the cathode. We do know the surface area of the cathode, the density of copper, and the thickness of the layer that was plated. When a layer of copper was electroplated onto the cathode, it increased the thickness of the cathode. And therefore, it also increased the volume of the cathode. So to solve this problem, we’re first going to find the volume of copper that is played at under the cathode. Then we’ll find the mass of copper that was plated onto the cathode. And finally, we’ll find the final mass of the cathode after it’s been electroplated with more copper.

We can find the volume of the copper that was plated onto the cathode by multiplying the surface area of the cathode by the thickness of the layer that was plated. The surface area of the cathode is 1.50 meter squared, and the thickness of the layer of copper that plated was two millimeters. We need both of these units to match to do this calculation. So let’s go ahead in converted into centimeters because the density of copper is given in units of grams per cubic centimeter. And we’ll be using that later. Since there are 100 centimeter in a meter, we can convert from meters to centimeters by multiplying by 100. However, the surface area is in meters squared. So we need to square this whole conversion in order to make the units cancel.

There are 10 millimeters in one centimeter, so we can convert from millimeters to centimeters by dividing by 10. We can now perform the calculation to find the volume of copper. And we’ll find that the volume of copper that was plated is 3000 cubic centimeters. Now, we can find the mass of copper that was plated onto the cathode. Since density is mass divided by volume, we can find the mass of copper that was plated by multiplying the density of copper by the volume of copper that was plated. The density of copper is nine grams per cubic centimeter. And the volume of copper that we just found is 3000 cubic centimeters. So the mass of copper that was plated is 27000 grams. Since our next step is to find the final mass of copper and the copper cathode was given in units of kilograms, let’s go ahead and convert this mass to kilograms.

Since there are 1000 grams in one kilograms, we can convert from grams to kilograms by dividing by 1000. So we plated 27 kilograms of copper. Now, we finally have everything we need to find the final mass of the copper cathode after it’s been electroplated. We can find the final mass of the copper cathode by adding the original mass of the copper cathode to the mass of copper that was plated onto the cathode. The original mass of the copper cathode is 95 kilograms. And the mass of copper that was plated onto the cathode is 27 kilograms. This gives us a mass of 122 kilograms. The original mass of the cathode, as well as the other data in the problem, was given to three significant figures. So our answer should be rounded to three significant figures, as well. So the final mass of the cathode after it’s been electroplated is 122 kilograms.