Static Electricity Legacy Problem #2 Guided Solution

An effective problem solver proceeds through the solution of a problem in a succession of steps, with the earliest steps including reading the problem carefully, developing a mental picture of what's going on, identifying known and unknown quantities. Applied to this problem, we read of a solution that contains dissolved ions of copper. And what this scientist wishes to do is to change the dissolved ions of copper into solid copper ions. And in order to do that, the copper ions have to gain two electrons. We're given much information, some of which is not important, about the solution of copper ions. One of the things that is important is the fact that we have 1.12 grams of copper ions. I'm going to write that down, 1.12 grams of Cu ions. I also know that each gram of copper ions contains 9.48 times 10 to the 21st atoms. And I'm going to write that down, and I'm going to write it down like this, 9.48 e to the 21st atoms per, divided by 1 gram of copper. And finally, the other pertinent information is that in order for these copper ions to be changed into copper atoms, each ion must gain two electrons. Now what I'm asked to determine is the total quantity of charge that must be supplied to turn these ions into solid copper atoms. Now this involves knowing that each electron has a charge of 1.6 times 10 to the negative 19th Coulombs. Now the next step in the solution process involves plotting a strategy for getting from known information to the unknown information. This includes making mental connections between the known quantities. What I know is I have 1.12 grams of copper, and for every 1 gram, there are 9.48 times 10 to the 21st atoms. So if I multiply these two numbers together, that's going to give me the number of atoms of copper ions, the number of ions of copper that I have to change into atoms. Now the next step of the process is to recognize that in order to change these ions to atoms, I have to gain two electrons. So I'm going to take the product of my two numbers, 1.12 grams and 9.48 times 10 to the 21st, and I'm going to multiply that by two, because for each one of these ions I have, I need to get two electrons added to them in order to become atoms. The final step of the process, I need to convert from the number of electrons to the Coulombs of charge, knowing that there's 1.60 times 10 to the negative 19th Coulombs for every one electron. Multiplying these two numbers together now gives me the number of Coulombs of charge. And that's the answer.