 Alright, the last math topic in this unit is percent concentration. Percent concentration is used commercially when describing solutions. For example, fruit juices. If a fruit juice says it contains 10% juice, that's a percent concentration. So if you buy a liter of the fruit juice, you can count on 0.1 liters of that being actual juice, the other 0.9 liters, but end up being water and sugar for the most part. So it gives you an idea of how much juice is in there, it gives you an idea of concentration. It's not really used as often in science as malaria and malality are, but because of its commercial aspect, its everyday aspect, it's worth us knowing. Now any percent, no matter what you're calculating, is some part divided by the whole times 100. That's why all percent work. So if you wanted to calculate your percent on a test, let's say you get 19 out of 30 questions. Well to find your percent on that test, you would take the part, the 19, divided by the whole, the total number of questions, times 100. So 19 divided by 30 equals times 100, you'll have gotten a 63%. And this is really no different except we're dealing with volumes or masses, the two major types of percent concentrations that we deal with. There's percent by mass where the grams or the kilograms of solute and solvent are measured out. And again we're going to use the same general equation, part divided by whole times 100. So it would be the mass of the solute divided by the mass of the solution times 100. That's going to give you the percent by mass. The equation is exactly the same for percent by volume, except where it says mass, you're going to put volume. So again it's solute over solution, it's part over whole, that's important. It's the total solution that goes on the bottom. So if they give you information about the solvent, you'll have to add the solute and the solvent together to get that total. So they said for example in a percent by volume problem that you had 50 milliliters of isopropyl alcohol and 300 milliliters of water, the 50 milliliters of isopropyl alcohol would be your solute, the one that you have the smaller amount of. But for your solution you would have to add the two together. Make sure it's the total that you put on the bottom. Masses can be measured in grams or kilograms, either you don't work just fine, they just have to both be the same. So if one of them is in grams and the other one is in kilograms, you have to choose one to convert and it does not matter which one you convert. For volume it'll be milliliters or liters, and again it can be either one, you just have to make sure they match. But if they give you milliliters of solute and liters of solution, you'd have to convert one or the other, it doesn't matter which one you convert, you will get the same answer either way. So let's take a look at what a sample problem might look like. A solution is made by mixing 15 milliliters of alcohol, like isopropyl alcohol, rubbing alcohol, maybe what we're making here, with 0.5 liters of water, what is the percent concentration? Alright, so this problem has everything that I told you might happen in it. It's got two different units, milliliters and liters, and we're going to have to convert one of them to make sure that they match and it wouldn't matter if we convert the milliliters into liters or the liters into milliliters as long as they're both the same or fine. The other thing that happens here is that we have solute and solvent, the one we have in the smaller amount that's the solute, the one we have in the larger amount that's the solvent. We have to add these together to get the total amount of solution. So let's go ahead and begin by doing a conversion. Again, it really doesn't matter. So what I'm going to do, just for fun, is I'm going to convert the 0.5 liters of water into milliliters. King Henry died by drinking chocolate milk. And if you practice this enough, if you learn this back in physical science, you already know the answer to that is 500 milliliters. Because you've learned in your head, you just got to move the decimal point three places to the right. If you haven't learned that yet, King Henry died by drinking chocolate milk, Kilo hectodeca base, Desi-Seni-Milli. Liters is a base unit, and we're going to convert it over to mille. One, two, three places to the right. So we take that decimal point and move it one, two, three places to the right, fill the empty place values with zeros. So it is 500 milliliters of water that our 15 milliliters of alcohol has been dissolved in. Now, again, that solvent, the one in the smaller amount when you're mixing two liquids together will be the solute, the one with the larger amount when you're mixing two liquids together will be the solvent. We do have to add these together. We have 515 milliliters of solution. So again, both the little tricks that I told you might happen here, making sure that the units match, having to do these metric conversions, and then making sure that what you're using on the bottom is the whole, is the solution. And whenever you're given solute and solvent, you will add the two together to get the solution. So now we're ready to do our calculation. The part is the 15 milliliters of the alcohol that we're dissolving, probably isopropyl alcohol here, divided by the total amount of solution times 100. So 15 divided by 515 times 100. This is a 2.9 or 3% alcohol solution. And I like to write that by volume after the answer there so we know that it was a percent by volume that we calculated. Percent by mass problems are exactly the same. The only difference is, instead of having liters in the problem, you might have grams or kilograms in there. But it's the same two things you have to worry about, making sure both your units match and have them do a little metric conversion from time to time. I mean, if they really wanted to be a pain and they want, I told you, they like to test multiple things in the same question. And they wanted to make sure you can convert using dimensional analysis that could give you an English unit for one, like gallons and a metric unit for the other one, like milliliters and expect you to be able to convert from gallons to milliliters. I mean, it's pretty much fair game on the final exam. The people that write these tests seem to go for the most awkward and challenging questions they can write. So you've got to be prepared for those kind of things. For me and my test, it's not going to be anything more than metric conversions that you'll have to do. No equivalences, no dimensional analysis required. If you're in my fifth period or eighth period class, hopefully this video will help you get through the practice set that you're going to be giving with the sub today. Eighth period, I will go over this with you tomorrow because you're really the only class I'm going to see because of the ready to work testing. We will meet at the end of the day. I will go over this with you to make sure you understand it. Fifth period, you're just going to have to count on this video to get you through.