Fundamentals of Chemistry Concepts

Hey everybody, this is Mrs. Townsend and I'm here with Chemistry 1406 Chapter 1 notes. And I'll just give you a heads up, I've got three kids, three dogs, and three cats, so don't be surprised if any of them make an appearance at any point in time during any of my videos. So I just wanted to let you know about that. Chapter 1 starts off with some definitions about chemistry and then the different classifications of matter and so forth like that. And those are slides and notes that you'll be able to read through on your own. I'd use the videos to kind of hit some of the main points that may be a little bit harder to understand and then definitely to work through the examples that are in the notes as well. So I really want you to kind of skip ahead until you get to, it should be slides 23 and 24, which are the heating and cooling curves. This will be after the changes of state. So slides 23 and 24 should be your heating and then your cooling curve right after your changes of state. And sometimes these can be a little bit difficult to really understand what the curves are trying to show you. So I wanted to draw the curve out and then point out a few things on that curve. Okay, first off, and I'm going to show you the heating curve, but the same information can be found on the cooling curve. It's just a mirror image. And we have temperature increasing here and we have heat being added across here and then a heating curve we start down here at the bottom with a solid and we take that solid and we start heating it up And then it changes, change of state occurs, and it changes into a liquid. And then we have a liquid that we heat up. We have a liquid that we heat up, which then goes through another change of state and turns into a gas. So again, we start solid, which then changes into a liquid. which then changes into a gas. Okay, now from solid to liquid, from solid to liquid, that is what we commonly call the melting phase. So this plateau, this flat line right here, is the melting point. Okay, from liquid to gas, that's what we call the boiling point. And that's where vaporization occurs, okay? So if you have your piece of matter, and it is at a temperature that is below the melting point, if it's below the melting point, that means you have a solid. If your piece of matter is at a temperature that is above the boiling point, then that means you have a gas. And if your piece of matter is at a temperature in between melting and boiling, then that means that you have a liquid. Okay, so what if you're right on this line? Okay, what if you were right at that melting point? Well, when you're right on the line, when you're right at that plateau, you're going to have two states of matter. So right here at the melting point, you will have solid and liquid. And at the boiling point, you'll have liquid and gas. When you're right on that line, you're going to have two states of matter. Okay, now at what temperature? Does this happen? And at what temperature does this happen? Well, it completely depends on your substance, okay? It completely depends on your piece of matter. Everybody tends to use the temperatures of water just because, you know, it's really common. They're used to working with it, and they use those temperatures, but then they get those temperatures stuck in their head, and they compare everything, or they try to compare everything to the temperatures of water. Well, we are going to look at water, but then I also want to look at a different substance as well. So I'm going to start off with water. Okay, and I'm sure you know these temperatures, but I'm going to write them down anyway. The melting point, which is also at the same point as the freezing point. The only difference between melting point and freezing point is what direction you're going. From what state of matter to what state of matter. But both of those occur at the exact same temperature, which for H2O is 0 degrees Celsius. And then boiling point is at 100 degrees Celsius. Okay, so this heating curve right here, this melting point for H2O, this melting point is occurring at zero degrees Celsius, and this boiling point is occurring at 100 degrees Celsius. Okay, so let's look at a few temperatures. Let's look at a negative 125 degrees Celsius. Well, at a negative 125 degrees Celsius, that is definitely below zero degrees Celsius. That is below the melting point. That means H2O is a solid at that temperature. Okay, at a negative 114 degrees Celsius. Well, we are still below that melting point, so it is still a solid. At a negative 100. degrees Celsius, still below the melting point, still a solid. At zero degrees Celsius, now we're right on that line. Now we are right at that melting point. So for H2O, at zero degrees Celsius, it is both solid and liquid. You have some molecules that have not gained quite enough energy yet to make that change in state. And then you have some molecules that have gained enough energy and have made that change in state. So when you're right on that line, you've got both of those states of matter. Okay, at 50 degrees Celsius. Now, 50 degrees Celsius is above the melting point, but it is below the boiling point. It's right in here. So at 50 degrees Celsius, that means H2O is a liquid. Okay, 78.4 degrees Celsius. It's still above the melting point, but still below the boiling point, so we're still right in here in this range, which means it is still a liquid. Okay, at 100 degrees Celsius. Now, at 100 degrees Celsius, now we're right on this line up here, right on the boiling point line. Again, when you're right on a plateau, when you're right on the line, you're going to have two states of matter. So in this case, at 100 degrees Celsius, H2O is both liquid and gas. Again, you're going to have some molecules that have not gained enough energy to make that transition, to make that change in state yet, but then you do have some molecules that have gained enough energy and have made that transition. Okay, and then let's look at a positive 125 degrees Celsius. Well at a positive 125 degrees Celsius, now we are above this boiling point over here. And when you are above the boiling point, your state of matter is a gas. Now again, everybody knows these temperatures or are mostly comfortable with these temperatures for water. So everybody tends to get those temperatures of 0 and 100 stuck in their head. And they try to compare everything to 0 and 100. So they try to compare all of these states of matter using 0 at the melting point and 100 at the boiling point. And you can't do that because these temperatures right here completely depend on your matter, your piece of matter, your substance that you're dealing with. So the next piece of matter, the next substance that I want to take a look at is ethanol. And I'm going to try to use a different color pen here. We'll see if it shows up on the screen. Okay, not too bad. Alright, ethanol, and I don't expect y'all to know these temperatures, but melting point, freezing point of ethanol is at a negative 114 degrees Celsius, and its boiling point is at a positive 78.4 degrees Celsius, which means that for ethanol, this melting point right here. It's not occurring at zero. That zero was there for H2O. So now when we're looking at ethanol, this melting point here is occurring at a negative 114 degrees Celsius, and this boiling point is not at 100 degrees Celsius. That was for the H2O. For ethanol, this boiling point is occurring at a positive 78.4 degrees Celsius. So now what we're going to do is we're going to compare the same temperatures that we looked at for H2O. We're going to look at the same temperatures for ethanol. So a negative... 125 degrees Celsius. Well a negative 125 degrees Celsius is definitely below negative 114 so it's below the melting point so it is a solid. So at a negative 125 degrees Celsius both H2O and ethanol are solids. Okay. Add a negative 114 degrees Celsius. Well, now for ethanol, a negative 114 is right on that melting point line, right on that plateau. And remember, when you're right on the line, it has two states of matter. So for ethanol, at a negative 114, it is solid and liquid. Now again, I want you to compare. At a negative 114, H2O is just a solid. At a negative 114 degrees Celsius, ethanol is solid and liquid. How can they be different? Because of their properties. They have different melting points. Okay? They have different melting points. Don't get the temperatures of water stuck in your head. Make sure that you're applying the correct temperatures on your heating or cooling curve so then you can determine the correct state of matter. Okay? Negative 100 degrees Celsius. Well, for ethanol, a negative 100 is slightly above the melting point. It is slightly above that negative 114, still well below the boiling point. So we're in this range right here, which means it is a liquid. Zero degrees Celsius. Well, zero degrees Celsius is above the negative 114 degrees Celsius melting point. point but it is below the boiling point so we're still in this range here which means it is still a liquid 50 degrees Celsius is still above the melting point but below the boiling point so we're still in this range here of a liquid 78 Well, for ethanol, 78.4 degrees Celsius is right on this line right here, right on this boiling point line, which means it has two states of matter, which is liquid and gas. One hundred degrees Celsius is now above the boiling point. So when you're at one hundred degrees Celsius above the boiling point, that means you have a gas. And then 125 degrees Celsius is also above that boiling point, so that means it is also a gas. Okay, now again everybody tends to get these temperatures of water stuck in their head and they try to compare everything to 0, 100 and you can't do that. Because these temperatures, these plateaus, these change in states here completely depend on the properties of that substance, of that chemical. Okay? So when you're looking at different chemicals, you're looking at different properties. And these temperatures on these plateaus right here will change a little bit, which could potentially change your state of matter. So you just have to watch out for that and be really careful. Okay? I want you to think about it for a minute. Ethanol. Ethanol is a major component in a couple of things that I'm sure college students use. One would be the gasoline. Okay, well think about the gas in your tanks, in your car. Have you ever wondered why it doesn't freeze even though it's below freezing outside? It's not cold enough yet. Ethanol is not going to freeze until it's below a negative 114 degrees Celsius. Okay, another example is alcohol. Ethanol is a major component in alcohol. Ever wonder why you put alcohol in the freezer and you can get it cold, but it won't freeze? Again, it's not cold enough. Okay, it's not cold enough. Again, everybody tends to compare everything to the temperatures of water, but you can't do that. It has different properties, different melting points and boiling points, okay, which adjust their heating and cooling curves there. So I wanted to draw out that curve, and then I wanted to look at a couple of examples there so that you can see how you can figure out states of matter based off of melting points and boiling points. I recommend anytime you have questions like this on worksheets or the exam, draw the heating curve or you could draw the cooling curve. It's just a mirror image. Draw the curve, label it, put down your temperatures, and then that can help you see exactly where you are with your question. Okay, so the next topic that I want to go over with you deals with metric prefixes. And I believe those start, I think it's your slide 29 is where it starts talking about metric prefixes. And they're placed in front of a base unit, it gives the actual size of the measurement used. The next slide gives you the common prefixes that we work with. And then the next slide gives you a saying. King Henry died by drinking chocolate milk. Okay, King Henry died by drinking chocolate milk. All right, so I'm going to get that little saying written up here. King Henry died by, and I'm going to box in the by, and I'll explain why here in just a minute. Drinking chocolate. Okay, the first letter in each one of these represents a prefix, metric prefix, that we're going to be working with. The by that I boxed in a moment ago, that is your base unit. Okay, that is your base unit, which is your measurement of unit that you're working with. So that's your... meters, or it may be liters, or it may be grams, or seconds, or so forth. But that is your base unit. Now, one thing I want to point out about the base unit is that there's no prefix in front of that base unit. Okay? There is no prefix in front of that base unit. So anytime we're working with measurements, if there's no prefix, then you know that that's gonna be sitting at the base. Okay, that's representing the base right there. All right, king, let's start over here, represents kilo, and the symbol that we use for kilo is a lowercase k. Henry, this is a prefix that's not used just a whole lot. This is hecta, and the symbol for that is a lowercase h. Now we do have two D's here. We've got one that comes before the base unit and one that comes after the base unit. The one that comes before the base unit is deca with an A at the end and the one after is deci with an I at the end. Now obviously they both cannot be a single lowercase D or we'll never know which prefix we're talking about and using. Deca is our only two letter prefix. Deca is D-A and deci is just the single lowercase d. Chocolate represents centi and the symbol for that's a lowercase c. And then milk represents milly represented by a single lowercase m. Okay, now the way that the prefixes work together is in between each of these prefixes, as well as from deca to base, and base to deci. In between each of these prefixes, there's a power of 10. In between each prefix, there's a power of 10. Okay, now what that means... is that when you've got two prefixes that sit right next to each other, they're separated by only one power of 10. As an example, if we have one kilogram, okay, kilo, there are 10 hectograms. Kilo and hecta are right next to each other, separated by only one 10. So one kilogram has 10 hectograms. Okay, hecta and deca are right next to each other. So one hecta liter, hecta, has 10 deca liters. Hecta and deca are right next to each other, separated by only one 10. So hecta and deca are right next to each other, separated by only one 10 there. And of course we can keep on going. Deca and base are right next to each other. So one decameter, deca, has ten meters. Now remember, meters, there's no prefix here. That's your base. So deca and base are right next to each other, separated by only one ten there. Okay? We can keep going. One second. has 10 deciseconds. Seconds, there's no prefix on it. Well, when there's no prefix, that's base. Base and deci are right next to each other, separated by only one 10. One decigram has 10 centigrams. Deci and centi are right next to each other. Okay, one centiliter has 10 milliliters. Centi and milli right next to each other. Now again, these are prefixes that are right next to each other, so they're only separated by one power of 10. What if they're not right next to each other? What if they're separated by more than one 10? Okay, so if we have one. Kilogram, and we're looking at grams. Kilo, and grams, there's no prefix on it, so that is base. Okay, one kilo to base. All right, kilo to base. There are three tens from kilo to base. Okay, there are three tens in between kilo and base. Do not do 3 times 10 and give me 30. Okay, do not do that. Take the three 10s times each other. So 10 times 10 times 10, and you'll give me 1,000. Or if you are already familiar with scientific notation and you want to go ahead and start using that now, you're more than welcome to do so. This could be written as... 10 to the third. Another example, let's say that we have one deciliter and we're going to milliliters. Deci to milli. Deci to milli. Okay, here's deci, milli. In between those, there are two tens. Okay, again, do not do two times ten and give me twenty. Take the two tens times each other and give me one hundred. Or, if you want to do scientific notation, that'd be ten squared. Alright, now, one thing I want to point out is that when you're moving... with these prefixes here. Anytime you're moving to the right, okay? Anytime you're moving to the right, you are multiplying times 10, okay? You're multiplying times 10. Well, when you multiply times 10, all you really have to do is move a decimal to the right, okay? When you multiply times 10, that's really all you have to do is move your decimal to the right. As an example, now let's say we've got 3.75 meters. and we want to go to millimeters. 3.75 meters to millimeters. Okay. Well, meters, there's no prefix there. So that's going to be representing your base. And then we're going to milli. From base to milli, we're moving to the right. So again, we're multiplying times 10. And from base to milli, that is one, two, three places, or one, two, three tens. Okay. So we're going to take our decimal point here, and we're going to move that decimal point three places to the right. Now when we do that, we create this empty spot, or this open spot right here. And when you create an open spot, you always fill those in with zeros. You always fill those in with zeros. So that 3.75 became 3,750. Okay, or scientific notation, if you want to use that, leave it as 3.75 times 10 to the, and we moved our decimal three places because there's three tens in between base and milli. So 3.75 times 10 to the third could be your scientific notation answer. Okay, so let's look at another example like that. Let's say that we've got 10 point. eight, nine. And let's do deca liters into deci liters. Okay, deca into deci, deca into deci. It's going to the right and we'll go two places or there are two tens from deca to deci. So we're going to take our decimal point and we're going to move it. two places to the right and in this case we did not create any empty spots so we don't have to add any zeros or anything like that but that 10.89 becomes 1089. Scientific notation there are actually a couple of ways that you could write this one you can leave it as 10.89 and then times 10 squared since we moved that decimal over two places or 1.08 eight nine times ten to the third the difference between these is the placement of that decimal which then in turn accounts for the difference in the power of ten there when it comes to scientific notation these are both correct answers they both give you the correct answer but this one right here is actually the best way to write it in scientific notation because you want this number out front to be in between one and ten And since 10.89 is just outside of that range slightly, but outside of that range, we move the decimal over a spot, and then that adjusts and changes the power of 10. Okay? So just watch out for that if you're using scientific notation. Okay, now if you look at all of these examples that we looked at, whether the prefixes were right next to each other or separated out a little bit, in every single one of these examples, I was moving to the right. I started with one prefix. and we moved to the right. And when you move to the right, you multiply times 10. And when you multiply times 10, that's where you can just move your decimal, okay? So what do you think's gonna happen if we change direction? And now we go to the left. As an example, if we have 11.75 centigrams, and we're headed into grams, okay? Well, centi. And then grams, there's no prefix there, so that's representing your base. Okay. Centi to base is now moving to the left. From centi to base is now going to the left. And to get there, it takes two places or two tens. So we're going to take that 11.75, and we're now going to take our decimal and move it to the left two places. Technically, what you're doing now when you move to the left is you're dividing by those tens. You're dividing by those tens. And when we divide by tens, you move to the left. Okay? So that 11.75 is now.1175. Scientific notation, there's a couple ways you can write this one. You can do 11.75 times 10 to the negative 2. Negative because now we're moving to the left, okay, and then 2 because that's how many places or how many tens we moved. Or 1.175 times 10 to the negative 1. Again, the difference between these is the placement of that decimal, which in turn affects the power of 10. This second one is actually the best option because, again, you want that number out front to be in between 1 and 10. And since 11.75 is outside of that range, we move the decimal over a spot, but then that adjusts and that changes your power of 10. Okay, one more example of that. Let's look at 4.2 grams into kilograms. Grams, there's no prefix, so again, that's base. To kilo. Okay, base tequila is moving to the left. Well, base tequila was 1, 2, 3 places, or 3 tens. So now we're going to take that decimal point, and we're going to move it. It's three places to the left. One, two, three. Now when we do that, that has created a couple of empty spots there. And remember when we create empty spots, we add in zeros there. So 4.2 becomes 0.0042. Scientific notation, 4.2 times 10 to the negative 3. Negative because again we're moving to the left and then three because it is three places, three tens that we moved. Now your slide number 30 has a few examples on it. I'm going to do a couple of them with you and then I'll let you do the other two on your own. I'm just going to flip this paper around. Let me get my King Henry and I'm not going to write out all of the words, just my symbols. Again, your slide number 30, first example is 24 milligrams into decigrams, milli to deci, okay, from milli to now deci. Remember we have two D's here. Deci is the one on the right side of the base unit, okay. Well, from milli to deci, that means we're moving to the left, and it's going to take us two places, or two tens, to get there. So when you have a whole number, even when that decimal is not written in, it naturally falls at the end of that number. And you're going to take that decimal, and we're going to move it two places to the left. So 24 becomes.24. The next example on your slide number 30, 10.59 meters into millimeters. Meters, there's no prefix there, so that's representing base. Meters, there's no prefix, so that's representing base. To millimeters. This time base to milli, we're going to the right. Okay, from base to milli, we're going to the right. And to get there, it'll be one, two, three places to the right, or three tens. So we're going to take our decimal point and move that decimal three places to the right. And when we do that, it will create an empty spot right there that we're going to fill in with a zero. So ten point. five nine becomes ten thousand five hundred and ninety and of course if you want to use scientific notation you're more than welcome to do so on your slide number 30 there are a couple of more examples i'm going to leave those for you to do on your own okay so slide number 31 There are actually a few more prefixes that we add onto our kilo, onto our King Henry saying. On our King Henry saying, there are some prefixes that come out on this side from kilo. That's where you get your mega, giga, tera prefixes. There is nothing mega, giga, tera about atoms and molecules. So we really don't work with the prefixes that come out on the left side past kilo. We do, however, work with prefixes that come out on the right side past millie and that's what your slide number 31 is adding so again we have king henry died by drinking chocolate milk okay and then your slide number 31 wants you to put down two dots the dots are important i'll explain why here in just a minute and then we have mac Now the symbol for micro is the Greek letter mu. Kinda sorta looks like a lowercase cursive u in a way. But it is the Greek letter mu. After micro we have two dots, nano. Symbol for nano is the Greek letter eta. Looks like a lowercase m which is kind of a long tail on it. After nano, put down two more dots, pico. The symbol for pico is the Greek letter rho, and it just looks like more of a rounded lowercase p. These dots are very important because they are placeholders, okay? They're representing prefixes that some of them don't even have names to them, but they're representing prefixes that we don't have to worry about, but they're placeholders to let us know that milli and micro are not right next to each other, separated by only one. 10, milli and micro are actually separated by three tens. Same thing from micro to nano, there are three tens there as well. And then again from nano to pico, there are three tens there as well. And you know, sometimes when you look at the prefixes, if you can look at them in chunks of three, Sometimes that can really help you count as you're having to move back and forth on this King Henry or move back and forth between prefixes. What do I mean by chunks of three? Well, from kilo to base, there are three tens there. From kilo to base, there are three tens. From base to milli, there are three tens there as well. From base to milli, there are three tens there as well. And we've already counted them, but again, from milli to micro. there are three tens there. From micro to nano, there are three tens there. And then again, from nano to pico, there are three tens there as well. Okay, now these three tens, again, what that means is that, let's look down here at milli and micro. If you have one milliliter, there are a thousand microliters. Milli and micro are three tens. away from each other. One microgram has a thousand nanograms. Micro and nano are three tens apart from each other. And one nanosecond has a thousand picoseconds. Nano and pico are three tens apart from each other. Okay, so again those dots are very very important because they're placeholders. Just trying to remind you, let you know that those prefixes are not right next to each other, separated by only one 10, they're actually separated by three 10s. Now, the whole process of if you move to the right, you're multiplying times 10, and your decimal moves to the right, or if you move to the left, you're dividing by those 10s, therefore your decimal moves to the left, all that stays the same, okay? All of that stays the same. So on your slide, I believe it's now slide number 32, you have some examples using these new prefixes here. And so I'm going to work those out. I'll work a couple of them out, and then I'll leave a couple of them for you to do on your own. So first we have 11.43 micrometers into millimeters, micro to milli. Okay, well, micro 2 milli is moving to the left. Okay, from a micro, 2 milli is moving to the left, and that's 1, 2, 3 places, or again, 3 tens. So you're going to take that decimal point, and we're going to move it 3 places to the left. Now, when we do that, we do create one empty spot there that we're going to fill in with zeros. So that 11.43 becomes.01143. The next example, 9.75 kilograms into picograms, kilo to pico. Okay, well this time going from kilo to pico, we're going from one end of our prefix spectrum here all the way down to the other end. From kilo all the way down to pico. Okay, well from kilo all the way down to pico is moving to the right. And here's where counting the prefixes and chunks of three is really going to help out. Okay, kilo to base is three. Base to milli is three more, making it a grand total of six. Millie to micro makes it 9. Micro to nano makes it 12. Nano to pico. Makes it a grand total of 15. 15 places. Now, if you just want to move your decimal over and add in a whole bunch of zeros, you're more than welcome to do that if you'd like to. But this is one of those that I'm definitely going to write in scientific notation. So 9.75 times 10 to the, and we counted a total of 15 places. And we're moving to the right, so that'll be a positive 15. Now again, if you want to move the decimal and add in zeros, you're more than welcome to do so. On this example, you would have 9, 7, 5, and then 13 zeros following that. Again, slide number 32 has a couple of more examples. I'm going to leave those for you to do on your own. Okay, now the next example that I want to take a look at with you starts our dimensional analysis, which is just a fancy phrase or a fancy saying for conversion problems. And this is where everybody tends to freak out. Don't freak out. When it comes to dimensional analysis, conversion problems, the key is you just have to take it slow and take it one step at a time. Okay, now the first example I'm going to look at with you is 62 inches into centimeters. Now we know that we cannot use King Henry here because we're dealing with completely different units. You can only use King Henry as long as your base unit stays the same. So as long as you're staying in meters or in liters or in grams or in seconds. But the moment your base unit changes completely, King Henry cannot help you. Okay, King Henry cannot help you there. Alright, so instead we have to do what's called dimensional analysis or conversion problem. There is a very important piece of information that we have to know in order to be able to do this conversion problem. And that piece of information is that 1 inch equals 2.54 centimeters. Now that piece of information right there is called a numerical relationship. And on slide number 33, numerical relationship. Your slide number 33 in your notes gives you a list of some common numerical relationships. Now that is just kind of a starting list to get us started in the notes and with our problems. As we continue on through the rest of the semester, you'll have some more numerical relationships that you can add to that list. So again, that's just kind of a starting list, but that gives you several of our common. numerical relationships that we're using in our notes right now. But it's a very important piece of information that you need to have, otherwise you cannot go from inches into centimeters. Now to carry out this problem, always, always start with what you've been given to convert. So in this case, we've been given the 62 inches to convert. You always start with that times the numerical relationship. Now, the numerical relationship, we are going to set it up like a fraction. So, I'm going to go ahead and draw my dividing line there, so I can clearly see that I will have a numerator and I will have a denominator. Now, how we set this up completely depends on the units, okay? How you set this numerical relationship up completely depends on the units. Since we are starting in inches, we need inches to cancel. In order for them to cancel, they're going to have to be opposite. So since these inches are in the numerator, they're up top. In order to cancel them, over here in our numerical relationship, they're going to have to be on bottom. Again, in order for them to cancel, they always have to be opposite. Okay, then we're going to cancel out inches and we're going to go into centimeters. The numbers stick to the unit. So when you look at your numerical relationship over here, we have one inch, okay, so one inch is 2.54 centimeters. So 2.54 goes with the centimeters on top. Then you always, always want to double check and make sure that the units you want to cancel out does in fact cancel out. And the units you want to end up with is what you will actually end up with. And then you can carry out the math and when we do 62 times a 2.54 you get 157.48. We cancelled out the inches and that leaves us in centimeters. So again, there's a list of numerical relationships on slide 33, but that's just kind of a starting list. As we continue throughout the rest of the semester, we'll be learning more numerical relationships that you can add to that list. That gives you a good starting point there. So on your next slide, so it should be slide number 34. slide oh i'm sorry 34 35 let me have my numbers off a little bit you've been given some examples to work out we just did this first one together the 62 inches into centimeters we canceled out inches converted that into centimeters and then we do the math 62 times the 2.54 and we ended up with 157.48 centimeters My general rule of thumb is to go two places past the decimal. I am not picky about significant figures. For most of our calculations, most of the things that we do, two places past the decimal is enough. And we don't have to worry about that. Sometimes if we have some tiny numbers that are less than one, we may take those out a little bit further. But generally just two places past the decimal is good for us. Okay, let's go ahead and do the next example. 110 pounds and 2 kilograms. 110 pounds into kilograms. Okay. Always, always start with what you've been given to convert. So we've been given the 110 pounds times numerical relationship. Okay. When we go to our list of numerical relationships on our list, we have that one kilogram. is 2.2 pounds. So that gives us a direct relationship between kilograms and pounds there. Because we're starting out with pounds, we want pounds to cancel. So that will go on bottom. We're trying to get it into kilograms. So the kilograms will go on top. To fill in the numbers, remember the numbers are attached to the units in your numerical relationship. So one kilogram, so wherever kilograms is, that's one kilogram. And the pounds are 2.2 pounds. Double check, make sure the units you want to cancel will in fact cancel out. Unit you want to end up with is what you'll actually end up with. And then you can carry out the math, which in this case will be 110 times 1, divide by 2.2. In this case, that should come out to be exactly 50 kilograms. Next example, 50 kilograms. Next example, 1,244 grams into pounds. 1,244 grams into pounds. When you look at your list of numerical relationships, we have one that gives us the direct relationship between grams and pounds, and that is that one pound is 454 grams. Take this 1,244 grams, since that's what we've been given to convert. Start with it. Times numerical relationship. We want grams to cancel, so that has to go opposite. So that means they'll go on bottom. Trying to get those into pounds. So pounds will go on top. One pound is 454 grams. Unit of grams will cancel out and we'll turn that into pounds for us. When you put this into the calculator, again, you'll have 1,244 times 1. Divide by 454 and I have 2.74 pounds. seven four okay that's the last example we've got 6.34 yards going into inches Okay, this one you can do it a couple of ways. And so I'd like to show you both ways and then you stick to whichever method you're most comfortable with. Alright, we have two numerical relationships that will be needed here. Yards to feet and then feet to inches. And they're both on your list on slide 33. One yard has three feet and one foot has... 12 inches okay now you can do this conversion in two steps or you can combine numerical relationships and then do it into or do it in one step i'm going to show you both okay the two-step process so we still start off with our 6.34 yards that we're trying to cancel out or convert times first conversion factor We want to cancel out yards so that goes on bottom and then this first one we're going to take it from yards to feet. Okay this first one we're going to go from yards to feet and one yard has three feet. That will cancel out our units of yards and get us into feet but we're not staying there because remember we're trying to ultimately get to inches so we're just pausing for a moment at feet. Okay times the next Numerical relationship, next conversion factor, we want to cancel out feet, so those have to be opposite of each other, and take that into inches, and one foot has 12 inches, and it'll cancel out the unit of feet and get us into the inches, which is what we ultimately are trying to end up with. And then when you do the math, I always recommend go all the way across the numerator and all the way across the denominator and then divide. So we have 6.34 times 3 times 12 all over and we just have 1s down here in the denominator. So divide by 1 and I have 228.24 inches. So that's an example of a multi-step problem. And what I recommend is you get all those numerical relationships in there and get those conversion factors in there and then do all the math at the very, very end. The other way that you could do this is you can combine these numerical relationships right here into one and then do this conversion problem in one step. So we still have our 6.34 yards that we are. starting with that we've been asked to convert, but we're going to combine a couple of numerical relationships into one here, okay? Now to combine them, you're basically just going to carry out the math problem that I've got in brackets here, okay? So 3 times 12 gives us 36 on top. 1 times 1 gives us 1 on bottom. The unit of feet have canceled and we have our inches up here on top we had yards on bottom so one yard is 36 inches that will cancel out the unit of yards get our answer into inches which again is what we're looking for take your 6.34 times 36 and you should still end up with your 228.24 So if you want to do a problem like this in multi-steps or if you would rather can combine a couple of numerical relationships and do the conversion in one step that's completely up to you that's just your personal preference whatever you want to do there okay it doesn't matter to me. So that was that last example there. Alright, now sometimes, sometimes the numerical relationship that we need, you're not going to find it on a list. Or you're not going to find it in any kind of textbook or reference book. Because sometimes the numerical relationship that you need is in a word problem. And you have to pull that information out in order to be able to use it. Example I've got on number 36 here. Okay, the example I've got on slide number 36. We have a patient who needs 0.024 grams of a sulfa drug. There are eight... milligram tablets in stock, how many tablets do we give him? So our patient needs 0.024 grams of a sulfa medication, but what the question is asking us to find is how many tablets do we give him? Okay, we're told how much of the medication our patient needs, but we're being asked, okay, how many tablets do we give him? That relationship there between the medication and the tablets, that is something that you're going to have to pull out of this work problem because you're not going to find it just in any book or any reference chart or on any list. You're going to have to pull it out of the work problem. And what this tells us here is that there are 8 mg tablets in stock, meaning that one tablet contains 8 mg of our sulfa medication. Alright, now there's something we need to address here. The amount of medication our patient needs has been measured in grams, but our tablets have the medication in milligrams. So we're going to have to convert one of those. Really, ultimately, it doesn't matter which one, but we've got to convert one of them so that they match up. Now, grams, milligrams, those are the same base unit of grams. We've got base unit over here because there's no prefix. And then we've got milli is what our tablets are measured in. So what I'm going to do is I'm going to take that 0.024 grams, and I'm going to get that converted into milligrams using King Henry. Okay, using King Henry. So I'm going to come out to the side to work this one out. King Henry. Died by drinking chocolate milk. Again, our grams right here, there's no prefix, so that's at base. We need to get that into milli. Okay, well, base to milli is moving to the right. Going to the right, that's one, two, three places to the right. So we're going to take that decimal and move it one, two, three places to the right. Point 024 becomes 20. Again, the.024, we moved our decimal three places to the right, and we end up with 24 milligrams. Now, we don't stop there, because that's not what the question asked. The question didn't ask how many milligrams of medication does our patient need. The question wants to know tablets. How many tablets do we give him? So the conversion problem comes in next. Where we need to cancel out the amount of medication, so in this case we need to cancel out milligrams of sulfa, and turn that into the number of tablets that we should give our patient. And this information comes from the numerical relationship that we had to pull out of the word problem. And one tablet, so one tablet, contains eight. milligrams of the medication. The amount of medication is going to cancel out and leave us with tablets, which is perfect because that's exactly what we're trying to determine. And when you do the math you have 24 times 1 divided by 8. That leaves you with 3 tablets. We're going to give our patient 3 tablets. Next slide, next example. We have the daily dose of ampicillin for the treatment of an ear infection is 115 milligrams per kilogram of body weight. What is the daily dose for a 34-pound toddler? So we have a 34-pound toddler. Toddler, that 34 pounds, that's how much he weighs. So that's 34 pounds of body weight. I'm doing a little bit of abbreviating here, okay? 34 pounds of body weight. And we're trying to calculate how much of the medicine, ampicillin, I'm going to abbreviate that as well, amp, do we give him? How much of the medication do we give him? Well, the medication tells us, give him 115 milligrams of ampicillin for every kilogram, so for every 1 kilogram of body weight. Give him 115 milligrams of ampicillin for every 1 kilogram of body weight. Okay, a little detail we're going to have to work with here. We weighed our toddler in pounds. The medication has body weight measured in kilograms. We're going to have to convert one of those to match the other. Again, ultimately, it really doesn't matter which one, because in the end, the math will take care of everything, but we've got to convert them so that they match. Okay, for the extra practice, we're going to take our 34 pounds, and we're going to get that into kilograms of body weight. Now, in order to do that, pounds and kilograms, those are definitely not the same base unit, okay? So King Henry is not going to be able to help us here. So we're going to have to do a conversion to get that from pounds to kilograms first. before we can then continue to get to the medication. Okay, so I'm going to come out here to the side and do this in a different color. 34 pounds of body weight, and we need to get that into kilograms. So we want to cancel out the pounds and get that into our kilograms. Okay, going back to your list of numerical relationships, one kilogram has 2.2 pounds. Pounds will cancel out and leave us with kilograms, which is good because that's where we're headed. That's what we need. You'll take your 34 times 1, divide by 2.2, and I have 50. 15.45 kilograms of body weight. Okay, now we don't stop there because that's not what the question asked for. The question did not ask how much does our toddler weigh in kilograms. The question is asking us all about how much medication do we give him. Okay, so our next conversion, now we want to cancel out the whole body weight completely. kilograms of body weight and this time we want to convert it into the medication of ampicillin. Now again the problem told us give him 115 milligrams of ampicillin for every one kilogram of body weight. Okay kilograms of body weight will cancel out completely. And we'll be left with milligrams of the medication ampicillin. Now this is going to look like a huge number because you are taking 15.45 times 115. Okay. But remember this is a daily dose. It would be split up over three or four doses in a 24-hour period. But you're taking 15.45 times 115. 1,777.27, and that comes out in milligrams of ampicillin. So again, sometimes that numerical relationship that you need to do the conversion problem is not going to be on any list. Okay, sometimes you have to be able to pull that out of the word problem in order to be able to use it. Okay, all right, the next slide I've got it is number 38. Okay, we're going to be dealing with conversion of units in numerator and denominator. So here we have the speed of sound and error. It's about 343 meters per second. What is this speed in miles per hour? So we're going to have to go from meters to miles. And then we're also going to have to take our seconds to hours. And I went ahead and listed those numerical relationships. So this one mile is 1609 meters. That's one you can add to your list that previous slide. And then the minutes to seconds, hour to minutes, I figure you know those, but I went ahead and wrote them down anyway. Okay, so we are taking 343 meters per second. And we ultimately want to get that into miles per hour. So I always take care of the unit that's in the numerator first. It really doesn't matter which one you work with first as long as they all get taken care of. Just out of habit, I take care of the numerator first. So my first conversion, I want to cancel out the meters and get that into miles. Okay, and the relationship that's given to us, one mile is 1609 meters. That will cancel out meters and get us into miles there. I'm going to go ahead with my next conversion factors and then do all the math at the end. So next conversion. Now we're going to try to get seconds to hours and we're going to do this one in two steps. We're going to go seconds to minutes and then minutes to hours. So seconds we want to cancel out. Now pay attention here. The seconds that we're given are starting out in the bottom. They're starting out in the denominator. So in order for them to cancel, they have to go on top. And again, we're going to go from seconds to minutes first. And one minute has 60 seconds in it. That'll cancel out our seconds and get us to minutes. But we're not staying there. So I'm not going to circle it. I just underlined it because we're just pausing there for a moment. Because then the very next conversion factor, we're going to cancel out minutes. Now again, minutes here is in the bottom in the denominator. So to cancel it out, it has to go on top. We're going to get those to hours. An hour, that's 60 minutes. So now those unit of minutes will cancel and get us into hours. Take a look at your units. all the way across the top all the way across the numerator so we canceled out meters we got that into miles seconds have canceled minutes have canceled so all the way across the top the only unit we still have are these miles and then all the way across the bottom all the way across the denominator the only unit we have left are the hours over here miles per hour that's perfect that's exactly what we need that's exactly what we want So again, when you do the math, I always recommend go all the way across the top, all the way across the denominator, and then divide last. So we have 343 times 1 times 60 times 60. Divide by, we've got 1609 down here at the bottom. So I have 767.43. 767.43 miles per hour. Okay, so again, units that we're dealing with in the numerator and units in the denominator, just take it a step at a time. Okay, you can do the math all at the same time at the end, but do each conversion factor just a step at a time. And then remember, wherever your unit is that you want to cancel, it must go opposite. So if it starts out in the denominator to get it to cancel in your numerical relationship conversion factor, it's got to go on top in the numerator. Now one thing that I want to talk to you about before we do the next example are dealing with units that are squared or units that are cubed. First of all, how do we even get units that are squared or cubed? okay all right we've got a box here it is not a perfect box okay not a perfect cube but if we want to solve for area okay if we want to solve for area that formula is two measurements length times width well if we take both of those measurements let's say in centimeters we would have centimeters times centimeters Or what we more commonly write down would be centimeters squared. My point here is that units that are squared, that means you're really dealing with two of those units. So when you're doing a conversion with units that are squared, you're going to have to be very, very careful because you'll have to do that conversion two times to take care of each one of those units. Okay, volume. For calculating volume, that's three measurements. Length, width, and height. And if we're taking those in centimeters, we'll have centimeters times centimeters times centimeters. which we more commonly write down as centimeters cubed. My point here is that when units are cubed, that means you're really dealing with three of those units. So when you're converting units that are cubed, you're gonna have to do that conversion three times to take care of each one of those units. Okay, as an example, let's take a look at 9.8. inches squared into centimeters squared. 9.8 inches squared into centimeters squared. Okay, so we've been given this 9.8 inches squared in order to convert. And one thing that I do that may just kind of help you remember how many times to do this conversion, when units are squared like that, separate them out. Okay, expand that. So we've got inches times inches. That way you can clearly see each one of those units that you're going to have to convert. Times conversion factor. We want to cancel out inches so that goes on bottom. Trying to get that into centimeters so that goes on top. Looking back at your numerical relationships, 1 inch is 2.54 centimeters. But this one conversion here is only going to take care of one of those units. Okay? It only cancels out one of those unit of inches and only gets us into one unit of centimeters. The units were squared, which meant that we had two of them, which means we have to do that conversion two times. So we're going to have to do this again. in order to take care of that second inches unit. Okay, so in the second conversion, it'll take care of that second inches unit and get us into that second centimeters unit. So now both of our inches have canceled. We have centimeters times centimeters, which we more commonly write down as centimeter squared. Math-wise, what that means, you have to do 9.8 times 2.54 times another 2.54. Okay, so again, 9.8 times 2.54 times 2.54, and I have 63.23 centimeters squared. Okay, another example. We're going to look at is 11.8 centimeters squared into meters squared. There's a couple ways you can do this one. I'll show you both ways and then you stick to whichever method you're most comfortable with. But 11.8 centimeters squared into meters squared. Okay. Alright, 11.8 centimeters squared, I'm going to expand that, so centimeters times centimeters, times conversion factor. We want centimeters to cancel, and we want to get that into meters. Okay, now let's talk about this relationship here. Centimeters, meters, those are the same base unit. So to find their relationship, We'll be able to use King Henry. So I'm going to come up here. King Henry died by drinking chocolate. Meters. There's no prefix there, so that's your base. And then centi. There's more than one way that you can look at this relationship. Here's what I recommend. Alright, so again meters, that's your base because there's no prefix, and then centi. Now look at these two measurements here, base and centi. The one that is further to the left, the one that is further to the left is the larger measurement. In this case, that would be our base. Our base is to the left, it's the larger measurement. Set that as 1. The measurement further to the left is your larger measurement. Set that as one. So we would have one meter. Okay. To find that relationship, to get to centi, we're going to the right. two places. So when we go to the right, we move the decimal to the right and for a whole number that means that decimals at the end. We're going to move it to the right two places. Fill in empty spots with zeros. So that means one meter has a hundred centimeters. Okay, again, the measurement that's further to the left is your larger measurement. Set that as 1, and then move your decimal over however many places you need to go to find that relationship to that second measurement. So in this case, 1 meter is 100 centimeters. The reason I do it that way is to avoid having a decimal in a conversion fraction like this. Okay, that'll give us nice pretty numbers, and we don't have to mess with a decimal in a fraction. Okay, but there's more than one way that you could find that relationship. Again, now, this one conversion factor here is only going to take care of one of those units. This one conversion factor only takes care of one of those centimeter to meter units. Because it was squared, that means there's two of them. That means we've got to do this again. Because it was squared. When there's two of those units, we've got to do that conversion a second time. That'll cancel out that second unit of centimeters and get us in the meters there. So now we have 11.8 times 1 times 1. Divide by 100. Divide by another 100. Be very careful about that. 11.8 times 1 times 1. Divide by 100, divide by another 100, and this should come out to be.00118 meters squared. The other way that you could do this one is because centimeters and meters are in the same base unit, and we can use King Henry, you can just move the decimal point around. You just have to be very careful about... how many times to move the decimal point around, okay? 11.8 centimeters squared to meters squared, okay? So we're going from centi to base, and from centi to base is moving to the left two places. Okay, from Senti to base is moving to the left two places, so we can move that decimal two places to the left, but that only takes care of one of those conversions. That only takes care of one of those conversions. In order to take care of the second unit, the second conversion, we've got to move that decimal two more times. And then, of course, fill in those empty spots with zeros. You still end up with the same answer. To be on the safe side, I always recommend when you're dealing with units that are squared or cubed, write out that conversion long version. Okay, write out that conversion factor long version so that you can see those relationships, even if it's King Henry, but then that way you can see each one of those relationships there. So on the next slide, I have it labeled as slide number 39. Okay, we're dealing with units that are in the numerator and denominator. And we're dealing with units that are cubed as well. So we've got several things going on here. Okay, all right, we've got 10. grams per, and it's centimeters cubed, and I'm going to expand that out so we can see each one. Trying to get it into grams per meters cubed. Now notice the numerator stays the same, grams and grams. So we're not going to have to convert the numerator at all. It's perfect, it's great the way that it is, okay? What we are having to convert is from centimeters cubed into meters cubed. So first conversion factor. We want to cancel out centimeters. Now again, pay attention. They're in the denominator to begin with. So to get them to cancel, they have to go opposite. You're going to have to go in the numerator over here. And we're trying to go from centimeters to meters. But that one conversion there is only going to take care of one of those units. Because it's cubed and there are three of them, we're going to have to do this conversion three times. Now to find that relationship with centimeters and meters, they are dealing with the same base unit, so we can use King Henry to help us out here. Centi and meters, there's no prefix there, so that would be base. To find their relationship, again we're comparing those two, centi and base. That base is the one that's to the left, so it's the larger measurement, so we're going to set that one as 1, so 1 meter. And if we have 1 at the base, then to get to centi, that is 2 places, which would be 2 zeros or 100 centimeters. You still want to make sure that units cancel. So the first unit of centimeters is canceled out in that first conversion and gives us meters there. Second unit of centimeters canceled out in that second conversion and give us meters there. Last unit of centimeters canceled out in last conversion and give us meters there. And remember the grams in the numerator, we didn't touch it, we didn't change it, so it stays the same. So as you look at your units all the way across the numerator, everything's been canceled out except those grams. So we still have those grams. And in the denominator, we have meters times meters times meters, which we more commonly write down as meters cubed. And in math, we've got 10.9 times 100 times 100 times 100. Okay, again, you've got 10.9. times 100 times 100 times 100, 10,900,000. Or if you'd rather write that in scientific notation, that can be 10.9 times 10 to the sixth, or 1.09 times 10 to the seventh is the better scientific notation. Again, all of those are expressing the same number. They're all expressing the correct answer. Just in scientific notation, one format is a little bit better than the other because you want that number to be in between 1 and 10. Okay, there's another example on this slide here dealing with units in the numerator and denominator and then units that are cubed as well. I'm going to leave that one for you to do on your own, but I am going to give you the answer so you can check yourself. This one should come out to be 3,750 kilograms per meters cubed. 3,750 kilograms per meters cubed on that last example there. Okay, now we do still have a few problems left in chapter one dealing with density, specific gravity, and then our temperature. conversions. I'm going to do that in a second video. So this first video was all about conversions, measurements and conversions, and then that second video will take care of the density, specific gravity, and temperature.

And those are slides and notes that you'll be able to read through on your own. I'd use the videos to kind of hit some of the main points that may be a little bit harder to understand and then definitely to work through the examples that are in the notes as well. So I really want you to kind of skip ahead until you get to, it should be slides 23 and 24, which are the heating and cooling curves. This will be after the changes of state.

So slides 23 and 24 should be your heating and then your cooling curve right after your changes of state. And sometimes these can be a little bit difficult to really understand what the curves are trying to show you. So I wanted to draw the curve out and then point out a few things on that curve. Okay, first off, and I'm going to show you the heating curve, but the same information can be found on the cooling curve. It's just a mirror image.

And we have temperature increasing here and we have heat being added across here and then a heating curve we start down here at the bottom with a solid and we take that solid and we start heating it up And then it changes, change of state occurs, and it changes into a liquid. And then we have a liquid that we heat up. We have a liquid that we heat up, which then goes through another change of state and turns into a gas. So again, we start solid, which then changes into a liquid. which then changes into a gas.

Okay, now from solid to liquid, from solid to liquid, that is what we commonly call the melting phase. So this plateau, this flat line right here, is the melting point. Okay, from liquid to gas, that's what we call the boiling point. And that's where vaporization occurs, okay? So if you have your piece of matter, and it is at a temperature that is below the melting point, if it's below the melting point, that means you have a solid.

If your piece of matter is at a temperature that is above the boiling point, then that means you have a gas. And if your piece of matter is at a temperature in between melting and boiling, then that means that you have a liquid. Okay, so what if you're right on this line? Okay, what if you were right at that melting point? Well, when you're right on the line, when you're right at that plateau, you're going to have two states of matter.

So right here at the melting point, you will have solid and liquid. And at the boiling point, you'll have liquid and gas. When you're right on that line, you're going to have two states of matter.

Okay, now at what temperature? Does this happen? And at what temperature does this happen? Well, it completely depends on your substance, okay? It completely depends on your piece of matter.

Everybody tends to use the temperatures of water just because, you know, it's really common. They're used to working with it, and they use those temperatures, but then they get those temperatures stuck in their head, and they compare everything, or they try to compare everything to the temperatures of water. Well, we are going to look at water, but then I also want to look at a different substance as well.

So I'm going to start off with water. Okay, and I'm sure you know these temperatures, but I'm going to write them down anyway. The melting point, which is also at the same point as the freezing point. The only difference between melting point and freezing point is what direction you're going.

From what state of matter to what state of matter. But both of those occur at the exact same temperature, which for H2O is 0 degrees Celsius. And then boiling point is at 100 degrees Celsius. Okay, so this heating curve right here, this melting point for H2O, this melting point is occurring at zero degrees Celsius, and this boiling point is occurring at 100 degrees Celsius. Okay, so let's look at a few temperatures.

Let's look at a negative 125 degrees Celsius. Well, at a negative 125 degrees Celsius, that is definitely below zero degrees Celsius. That is below the melting point. That means H2O is a solid at that temperature.

Okay, at a negative 114 degrees Celsius. Well, we are still below that melting point, so it is still a solid. At a negative 100. degrees Celsius, still below the melting point, still a solid.

At zero degrees Celsius, now we're right on that line. Now we are right at that melting point. So for H2O, at zero degrees Celsius, it is both solid and liquid.

You have some molecules that have not gained quite enough energy yet to make that change in state. And then you have some molecules that have gained enough energy and have made that change in state. So when you're right on that line, you've got both of those states of matter. Okay, at 50 degrees Celsius. Now, 50 degrees Celsius is above the melting point, but it is below the boiling point.

It's right in here. So at 50 degrees Celsius, that means H2O is a liquid. Okay, 78.4 degrees Celsius.

It's still above the melting point, but still below the boiling point, so we're still right in here in this range, which means it is still a liquid. Okay, at 100 degrees Celsius. Now, at 100 degrees Celsius, now we're right on this line up here, right on the boiling point line. Again, when you're right on a plateau, when you're right on the line, you're going to have two states of matter.

So in this case, at 100 degrees Celsius, H2O is both liquid and gas. Again, you're going to have some molecules that have not gained enough energy to make that transition, to make that change in state yet, but then you do have some molecules that have gained enough energy and have made that transition. Okay, and then let's look at a positive 125 degrees Celsius. Well at a positive 125 degrees Celsius, now we are above this boiling point over here. And when you are above the boiling point, your state of matter is a gas.

Now again, everybody knows these temperatures or are mostly comfortable with these temperatures for water. So everybody tends to get those temperatures of 0 and 100 stuck in their head. And they try to compare everything to 0 and 100. So they try to compare all of these states of matter using 0 at the melting point and 100 at the boiling point. And you can't do that because these temperatures right here completely depend on your matter, your piece of matter, your substance that you're dealing with.

So the next piece of matter, the next substance that I want to take a look at is ethanol. And I'm going to try to use a different color pen here. We'll see if it shows up on the screen. Okay, not too bad. Alright, ethanol, and I don't expect y'all to know these temperatures, but melting point, freezing point of ethanol is at a negative 114 degrees Celsius, and its boiling point is at a positive 78.4 degrees Celsius, which means that for ethanol, this melting point right here.

It's not occurring at zero. That zero was there for H2O. So now when we're looking at ethanol, this melting point here is occurring at a negative 114 degrees Celsius, and this boiling point is not at 100 degrees Celsius.

That was for the H2O. For ethanol, this boiling point is occurring at a positive 78.4 degrees Celsius. So now what we're going to do is we're going to compare the same temperatures that we looked at for H2O. We're going to look at the same temperatures for ethanol. So a negative...

125 degrees Celsius. Well a negative 125 degrees Celsius is definitely below negative 114 so it's below the melting point so it is a solid. So at a negative 125 degrees Celsius both H2O and ethanol are solids. Okay. Add a negative 114 degrees Celsius.

Well, now for ethanol, a negative 114 is right on that melting point line, right on that plateau. And remember, when you're right on the line, it has two states of matter. So for ethanol, at a negative 114, it is solid and liquid.

Now again, I want you to compare. At a negative 114, H2O is just a solid. At a negative 114 degrees Celsius, ethanol is solid and liquid. How can they be different?

Because of their properties. They have different melting points. Okay? They have different melting points. Don't get the temperatures of water stuck in your head.

Make sure that you're applying the correct temperatures on your heating or cooling curve so then you can determine the correct state of matter. Okay? Negative 100 degrees Celsius. Well, for ethanol, a negative 100 is slightly above the melting point. It is slightly above that negative 114, still well below the boiling point.

So we're in this range right here, which means it is a liquid. Zero degrees Celsius. Well, zero degrees Celsius is above the negative 114 degrees Celsius melting point. point but it is below the boiling point so we're still in this range here which means it is still a liquid 50 degrees Celsius is still above the melting point but below the boiling point so we're still in this range here of a liquid 78 Well, for ethanol, 78.4 degrees Celsius is right on this line right here, right on this boiling point line, which means it has two states of matter, which is liquid and gas. One hundred degrees Celsius is now above the boiling point.

So when you're at one hundred degrees Celsius above the boiling point, that means you have a gas. And then 125 degrees Celsius is also above that boiling point, so that means it is also a gas. Okay, now again everybody tends to get these temperatures of water stuck in their head and they try to compare everything to 0, 100 and you can't do that. Because these temperatures, these plateaus, these change in states here completely depend on the properties of that substance, of that chemical. Okay?

So when you're looking at different chemicals, you're looking at different properties. And these temperatures on these plateaus right here will change a little bit, which could potentially change your state of matter. So you just have to watch out for that and be really careful.

Okay? I want you to think about it for a minute. Ethanol. Ethanol is a major component in a couple of things that I'm sure college students use. One would be the gasoline.

Okay, well think about the gas in your tanks, in your car. Have you ever wondered why it doesn't freeze even though it's below freezing outside? It's not cold enough yet.

Ethanol is not going to freeze until it's below a negative 114 degrees Celsius. Okay, another example is alcohol. Ethanol is a major component in alcohol. Ever wonder why you put alcohol in the freezer and you can get it cold, but it won't freeze? Again, it's not cold enough.

Okay, it's not cold enough. Again, everybody tends to compare everything to the temperatures of water, but you can't do that. It has different properties, different melting points and boiling points, okay, which adjust their heating and cooling curves there.

So I wanted to draw out that curve, and then I wanted to look at a couple of examples there so that you can see how you can figure out states of matter based off of melting points and boiling points. I recommend anytime you have questions like this on worksheets or the exam, draw the heating curve or you could draw the cooling curve. It's just a mirror image.

Draw the curve, label it, put down your temperatures, and then that can help you see exactly where you are with your question. Okay, so the next topic that I want to go over with you deals with metric prefixes. And I believe those start, I think it's your slide 29 is where it starts talking about metric prefixes.

And they're placed in front of a base unit, it gives the actual size of the measurement used. The next slide gives you the common prefixes that we work with. And then the next slide gives you a saying.

King Henry died by drinking chocolate milk. Okay, King Henry died by drinking chocolate milk. All right, so I'm going to get that little saying written up here.

King Henry died by, and I'm going to box in the by, and I'll explain why here in just a minute. Drinking chocolate. Okay, the first letter in each one of these represents a prefix, metric prefix, that we're going to be working with. The by that I boxed in a moment ago, that is your base unit.

Okay, that is your base unit, which is your measurement of unit that you're working with. So that's your... meters, or it may be liters, or it may be grams, or seconds, or so forth.

But that is your base unit. Now, one thing I want to point out about the base unit is that there's no prefix in front of that base unit. Okay?

There is no prefix in front of that base unit. So anytime we're working with measurements, if there's no prefix, then you know that that's gonna be sitting at the base. Okay, that's representing the base right there. All right, king, let's start over here, represents kilo, and the symbol that we use for kilo is a lowercase k. Henry, this is a prefix that's not used just a whole lot.

This is hecta, and the symbol for that is a lowercase h. Now we do have two D's here. We've got one that comes before the base unit and one that comes after the base unit.

The one that comes before the base unit is deca with an A at the end and the one after is deci with an I at the end. Now obviously they both cannot be a single lowercase D or we'll never know which prefix we're talking about and using. Deca is our only two letter prefix.

Deca is D-A and deci is just the single lowercase d. Chocolate represents centi and the symbol for that's a lowercase c. And then milk represents milly represented by a single lowercase m. Okay, now the way that the prefixes work together is in between each of these prefixes, as well as from deca to base, and base to deci. In between each of these prefixes, there's a power of 10. In between each prefix, there's a power of 10. Okay, now what that means...

is that when you've got two prefixes that sit right next to each other, they're separated by only one power of 10. As an example, if we have one kilogram, okay, kilo, there are 10 hectograms. Kilo and hecta are right next to each other, separated by only one 10. So one kilogram has 10 hectograms. Okay, hecta and deca are right next to each other. So one hecta liter, hecta, has 10 deca liters. Hecta and deca are right next to each other, separated by only one 10. So hecta and deca are right next to each other, separated by only one 10 there.

And of course we can keep on going. Deca and base are right next to each other. So one decameter, deca, has ten meters.

Now remember, meters, there's no prefix here. That's your base. So deca and base are right next to each other, separated by only one ten there.

Okay? We can keep going. One second.

has 10 deciseconds. Seconds, there's no prefix on it. Well, when there's no prefix, that's base.

Base and deci are right next to each other, separated by only one 10. One decigram has 10 centigrams. Deci and centi are right next to each other. Okay, one centiliter has 10 milliliters.

Centi and milli right next to each other. Now again, these are prefixes that are right next to each other, so they're only separated by one power of 10. What if they're not right next to each other? What if they're separated by more than one 10? Okay, so if we have one. Kilogram, and we're looking at grams.

Kilo, and grams, there's no prefix on it, so that is base. Okay, one kilo to base. All right, kilo to base. There are three tens from kilo to base. Okay, there are three tens in between kilo and base.

Do not do 3 times 10 and give me 30. Okay, do not do that. Take the three 10s times each other. So 10 times 10 times 10, and you'll give me 1,000. Or if you are already familiar with scientific notation and you want to go ahead and start using that now, you're more than welcome to do so. This could be written as...

10 to the third. Another example, let's say that we have one deciliter and we're going to milliliters. Deci to milli.

Deci to milli. Okay, here's deci, milli. In between those, there are two tens.

Okay, again, do not do two times ten and give me twenty. Take the two tens times each other and give me one hundred. Or, if you want to do scientific notation, that'd be ten squared.

Alright, now, one thing I want to point out is that when you're moving... with these prefixes here. Anytime you're moving to the right, okay? Anytime you're moving to the right, you are multiplying times 10, okay? You're multiplying times 10. Well, when you multiply times 10, all you really have to do is move a decimal to the right, okay?

When you multiply times 10, that's really all you have to do is move your decimal to the right. As an example, now let's say we've got 3.75 meters. and we want to go to millimeters. 3.75 meters to millimeters. Okay.

Well, meters, there's no prefix there. So that's going to be representing your base. And then we're going to milli. From base to milli, we're moving to the right.

So again, we're multiplying times 10. And from base to milli, that is one, two, three places, or one, two, three tens. Okay. So we're going to take our decimal point here, and we're going to move that decimal point three places to the right. Now when we do that, we create this empty spot, or this open spot right here.

And when you create an open spot, you always fill those in with zeros. You always fill those in with zeros. So that 3.75 became 3,750. Okay, or scientific notation, if you want to use that, leave it as 3.75 times 10 to the, and we moved our decimal three places because there's three tens in between base and milli. So 3.75 times 10 to the third could be your scientific notation answer.

Okay, so let's look at another example like that. Let's say that we've got 10 point. eight, nine. And let's do deca liters into deci liters.

Okay, deca into deci, deca into deci. It's going to the right and we'll go two places or there are two tens from deca to deci. So we're going to take our decimal point and we're going to move it. two places to the right and in this case we did not create any empty spots so we don't have to add any zeros or anything like that but that 10.89 becomes 1089. Scientific notation there are actually a couple of ways that you could write this one you can leave it as 10.89 and then times 10 squared since we moved that decimal over two places or 1.08 eight nine times ten to the third the difference between these is the placement of that decimal which then in turn accounts for the difference in the power of ten there when it comes to scientific notation these are both correct answers they both give you the correct answer but this one right here is actually the best way to write it in scientific notation because you want this number out front to be in between one and ten And since 10.89 is just outside of that range slightly, but outside of that range, we move the decimal over a spot, and then that adjusts and changes the power of 10. Okay?

So just watch out for that if you're using scientific notation. Okay, now if you look at all of these examples that we looked at, whether the prefixes were right next to each other or separated out a little bit, in every single one of these examples, I was moving to the right. I started with one prefix. and we moved to the right.

And when you move to the right, you multiply times 10. And when you multiply times 10, that's where you can just move your decimal, okay? So what do you think's gonna happen if we change direction? And now we go to the left. As an example, if we have 11.75 centigrams, and we're headed into grams, okay? Well, centi.

And then grams, there's no prefix there, so that's representing your base. Okay. Centi to base is now moving to the left. From centi to base is now going to the left. And to get there, it takes two places or two tens.

So we're going to take that 11.75, and we're now going to take our decimal and move it to the left two places. Technically, what you're doing now when you move to the left is you're dividing by those tens. You're dividing by those tens. And when we divide by tens, you move to the left. Okay?

So that 11.75 is now.1175. Scientific notation, there's a couple ways you can write this one. You can do 11.75 times 10 to the negative 2. Negative because now we're moving to the left, okay, and then 2 because that's how many places or how many tens we moved.

Or 1.175 times 10 to the negative 1. Again, the difference between these is the placement of that decimal, which in turn affects the power of 10. This second one is actually the best option because, again, you want that number out front to be in between 1 and 10. And since 11.75 is outside of that range, we move the decimal over a spot, but then that adjusts and that changes your power of 10. Okay, one more example of that. Let's look at 4.2 grams into kilograms. Grams, there's no prefix, so again, that's base. To kilo.

Okay, base tequila is moving to the left. Well, base tequila was 1, 2, 3 places, or 3 tens. So now we're going to take that decimal point, and we're going to move it. It's three places to the left.

One, two, three. Now when we do that, that has created a couple of empty spots there. And remember when we create empty spots, we add in zeros there.

So 4.2 becomes 0.0042. Scientific notation, 4.2 times 10 to the negative 3. Negative because again we're moving to the left and then three because it is three places, three tens that we moved. Now your slide number 30 has a few examples on it.

I'm going to do a couple of them with you and then I'll let you do the other two on your own. I'm just going to flip this paper around. Let me get my King Henry and I'm not going to write out all of the words, just my symbols.

Again, your slide number 30, first example is 24 milligrams into decigrams, milli to deci, okay, from milli to now deci. Remember we have two D's here. Deci is the one on the right side of the base unit, okay.

Well, from milli to deci, that means we're moving to the left, and it's going to take us two places, or two tens, to get there. So when you have a whole number, even when that decimal is not written in, it naturally falls at the end of that number. And you're going to take that decimal, and we're going to move it two places to the left. So 24 becomes.24. The next example on your slide number 30, 10.59 meters into millimeters.

Meters, there's no prefix there, so that's representing base. Meters, there's no prefix, so that's representing base. To millimeters.

This time base to milli, we're going to the right. Okay, from base to milli, we're going to the right. And to get there, it'll be one, two, three places to the right, or three tens.

So we're going to take our decimal point and move that decimal three places to the right. And when we do that, it will create an empty spot right there that we're going to fill in with a zero. So ten point. five nine becomes ten thousand five hundred and ninety and of course if you want to use scientific notation you're more than welcome to do so on your slide number 30 there are a couple of more examples i'm going to leave those for you to do on your own okay so slide number 31 There are actually a few more prefixes that we add onto our kilo, onto our King Henry saying. On our King Henry saying, there are some prefixes that come out on this side from kilo.

That's where you get your mega, giga, tera prefixes. There is nothing mega, giga, tera about atoms and molecules. So we really don't work with the prefixes that come out on the left side past kilo. We do, however, work with prefixes that come out on the right side past millie and that's what your slide number 31 is adding so again we have king henry died by drinking chocolate milk okay and then your slide number 31 wants you to put down two dots the dots are important i'll explain why here in just a minute and then we have mac Now the symbol for micro is the Greek letter mu. Kinda sorta looks like a lowercase cursive u in a way.

But it is the Greek letter mu. After micro we have two dots, nano. Symbol for nano is the Greek letter eta. Looks like a lowercase m which is kind of a long tail on it.

After nano, put down two more dots, pico. The symbol for pico is the Greek letter rho, and it just looks like more of a rounded lowercase p. These dots are very important because they are placeholders, okay? They're representing prefixes that some of them don't even have names to them, but they're representing prefixes that we don't have to worry about, but they're placeholders to let us know that milli and micro are not right next to each other, separated by only one. 10, milli and micro are actually separated by three tens.

Same thing from micro to nano, there are three tens there as well. And then again from nano to pico, there are three tens there as well. And you know, sometimes when you look at the prefixes, if you can look at them in chunks of three, Sometimes that can really help you count as you're having to move back and forth on this King Henry or move back and forth between prefixes.

What do I mean by chunks of three? Well, from kilo to base, there are three tens there. From kilo to base, there are three tens. From base to milli, there are three tens there as well. From base to milli, there are three tens there as well.

And we've already counted them, but again, from milli to micro. there are three tens there. From micro to nano, there are three tens there.

And then again, from nano to pico, there are three tens there as well. Okay, now these three tens, again, what that means is that, let's look down here at milli and micro. If you have one milliliter, there are a thousand microliters. Milli and micro are three tens.

away from each other. One microgram has a thousand nanograms. Micro and nano are three tens apart from each other. And one nanosecond has a thousand picoseconds.

Nano and pico are three tens apart from each other. Okay, so again those dots are very very important because they're placeholders. Just trying to remind you, let you know that those prefixes are not right next to each other, separated by only one 10, they're actually separated by three 10s.

Now, the whole process of if you move to the right, you're multiplying times 10, and your decimal moves to the right, or if you move to the left, you're dividing by those 10s, therefore your decimal moves to the left, all that stays the same, okay? All of that stays the same. So on your slide, I believe it's now slide number 32, you have some examples using these new prefixes here. And so I'm going to work those out. I'll work a couple of them out, and then I'll leave a couple of them for you to do on your own.

So first we have 11.43 micrometers into millimeters, micro to milli. Okay, well, micro 2 milli is moving to the left. Okay, from a micro, 2 milli is moving to the left, and that's 1, 2, 3 places, or again, 3 tens.

So you're going to take that decimal point, and we're going to move it 3 places to the left. Now, when we do that, we do create one empty spot there that we're going to fill in with zeros. So that 11.43 becomes.01143.

The next example, 9.75 kilograms into picograms, kilo to pico. Okay, well this time going from kilo to pico, we're going from one end of our prefix spectrum here all the way down to the other end. From kilo all the way down to pico.

Okay, well from kilo all the way down to pico is moving to the right. And here's where counting the prefixes and chunks of three is really going to help out. Okay, kilo to base is three. Base to milli is three more, making it a grand total of six. Millie to micro makes it 9. Micro to nano makes it 12. Nano to pico.

Makes it a grand total of 15. 15 places. Now, if you just want to move your decimal over and add in a whole bunch of zeros, you're more than welcome to do that if you'd like to. But this is one of those that I'm definitely going to write in scientific notation. So 9.75 times 10 to the, and we counted a total of 15 places. And we're moving to the right, so that'll be a positive 15. Now again, if you want to move the decimal and add in zeros, you're more than welcome to do so.

On this example, you would have 9, 7, 5, and then 13 zeros following that. Again, slide number 32 has a couple of more examples. I'm going to leave those for you to do on your own. Okay, now the next example that I want to take a look at with you starts our dimensional analysis, which is just a fancy phrase or a fancy saying for conversion problems. And this is where everybody tends to freak out.

Don't freak out. When it comes to dimensional analysis, conversion problems, the key is you just have to take it slow and take it one step at a time. Okay, now the first example I'm going to look at with you is 62 inches into centimeters.

Now we know that we cannot use King Henry here because we're dealing with completely different units. You can only use King Henry as long as your base unit stays the same. So as long as you're staying in meters or in liters or in grams or in seconds.

But the moment your base unit changes completely, King Henry cannot help you. Okay, King Henry cannot help you there. Alright, so instead we have to do what's called dimensional analysis or conversion problem. There is a very important piece of information that we have to know in order to be able to do this conversion problem.

And that piece of information is that 1 inch equals 2.54 centimeters. Now that piece of information right there is called a numerical relationship. And on slide number 33, numerical relationship.

Your slide number 33 in your notes gives you a list of some common numerical relationships. Now that is just kind of a starting list to get us started in the notes and with our problems. As we continue on through the rest of the semester, you'll have some more numerical relationships that you can add to that list. So again, that's just kind of a starting list, but that gives you several of our common. numerical relationships that we're using in our notes right now.

But it's a very important piece of information that you need to have, otherwise you cannot go from inches into centimeters. Now to carry out this problem, always, always start with what you've been given to convert. So in this case, we've been given the 62 inches to convert.

You always start with that times the numerical relationship. Now, the numerical relationship, we are going to set it up like a fraction. So, I'm going to go ahead and draw my dividing line there, so I can clearly see that I will have a numerator and I will have a denominator.

Now, how we set this up completely depends on the units, okay? How you set this numerical relationship up completely depends on the units. Since we are starting in inches, we need inches to cancel. In order for them to cancel, they're going to have to be opposite. So since these inches are in the numerator, they're up top.

In order to cancel them, over here in our numerical relationship, they're going to have to be on bottom. Again, in order for them to cancel, they always have to be opposite. Okay, then we're going to cancel out inches and we're going to go into centimeters.

The numbers stick to the unit. So when you look at your numerical relationship over here, we have one inch, okay, so one inch is 2.54 centimeters. So 2.54 goes with the centimeters on top. Then you always, always want to double check and make sure that the units you want to cancel out does in fact cancel out.

And the units you want to end up with is what you will actually end up with. And then you can carry out the math and when we do 62 times a 2.54 you get 157.48. We cancelled out the inches and that leaves us in centimeters.

So again, there's a list of numerical relationships on slide 33, but that's just kind of a starting list. As we continue throughout the rest of the semester, we'll be learning more numerical relationships that you can add to that list. That gives you a good starting point there. So on your next slide, so it should be slide number 34. slide oh i'm sorry 34 35 let me have my numbers off a little bit you've been given some examples to work out we just did this first one together the 62 inches into centimeters we canceled out inches converted that into centimeters and then we do the math 62 times the 2.54 and we ended up with 157.48 centimeters My general rule of thumb is to go two places past the decimal. I am not picky about significant figures.

For most of our calculations, most of the things that we do, two places past the decimal is enough. And we don't have to worry about that. Sometimes if we have some tiny numbers that are less than one, we may take those out a little bit further.

But generally just two places past the decimal is good for us. Okay, let's go ahead and do the next example. 110 pounds and 2 kilograms.

110 pounds into kilograms. Okay. Always, always start with what you've been given to convert. So we've been given the 110 pounds times numerical relationship. Okay.

When we go to our list of numerical relationships on our list, we have that one kilogram. is 2.2 pounds. So that gives us a direct relationship between kilograms and pounds there.

Because we're starting out with pounds, we want pounds to cancel. So that will go on bottom. We're trying to get it into kilograms. So the kilograms will go on top. To fill in the numbers, remember the numbers are attached to the units in your numerical relationship.

So one kilogram, so wherever kilograms is, that's one kilogram. And the pounds are 2.2 pounds. Double check, make sure the units you want to cancel will in fact cancel out.

Unit you want to end up with is what you'll actually end up with. And then you can carry out the math, which in this case will be 110 times 1, divide by 2.2. In this case, that should come out to be exactly 50 kilograms.

Next example, 50 kilograms. Next example, 1,244 grams into pounds. 1,244 grams into pounds. When you look at your list of numerical relationships, we have one that gives us the direct relationship between grams and pounds, and that is that one pound is 454 grams. Take this 1,244 grams, since that's what we've been given to convert.

Start with it. Times numerical relationship. We want grams to cancel, so that has to go opposite. So that means they'll go on bottom.

Trying to get those into pounds. So pounds will go on top. One pound is 454 grams. Unit of grams will cancel out and we'll turn that into pounds for us.

When you put this into the calculator, again, you'll have 1,244 times 1. Divide by 454 and I have 2.74 pounds. seven four okay that's the last example we've got 6.34 yards going into inches Okay, this one you can do it a couple of ways. And so I'd like to show you both ways and then you stick to whichever method you're most comfortable with. Alright, we have two numerical relationships that will be needed here.

Yards to feet and then feet to inches. And they're both on your list on slide 33. One yard has three feet and one foot has... 12 inches okay now you can do this conversion in two steps or you can combine numerical relationships and then do it into or do it in one step i'm going to show you both okay the two-step process so we still start off with our 6.34 yards that we're trying to cancel out or convert times first conversion factor We want to cancel out yards so that goes on bottom and then this first one we're going to take it from yards to feet.

Okay this first one we're going to go from yards to feet and one yard has three feet. That will cancel out our units of yards and get us into feet but we're not staying there because remember we're trying to ultimately get to inches so we're just pausing for a moment at feet. Okay times the next Numerical relationship, next conversion factor, we want to cancel out feet, so those have to be opposite of each other, and take that into inches, and one foot has 12 inches, and it'll cancel out the unit of feet and get us into the inches, which is what we ultimately are trying to end up with.

And then when you do the math, I always recommend go all the way across the numerator and all the way across the denominator and then divide. So we have 6.34 times 3 times 12 all over and we just have 1s down here in the denominator. So divide by 1 and I have 228.24 inches.

So that's an example of a multi-step problem. And what I recommend is you get all those numerical relationships in there and get those conversion factors in there and then do all the math at the very, very end. The other way that you could do this is you can combine these numerical relationships right here into one and then do this conversion problem in one step. So we still have our 6.34 yards that we are.

starting with that we've been asked to convert, but we're going to combine a couple of numerical relationships into one here, okay? Now to combine them, you're basically just going to carry out the math problem that I've got in brackets here, okay? So 3 times 12 gives us 36 on top.

1 times 1 gives us 1 on bottom. The unit of feet have canceled and we have our inches up here on top we had yards on bottom so one yard is 36 inches that will cancel out the unit of yards get our answer into inches which again is what we're looking for take your 6.34 times 36 and you should still end up with your 228.24 So if you want to do a problem like this in multi-steps or if you would rather can combine a couple of numerical relationships and do the conversion in one step that's completely up to you that's just your personal preference whatever you want to do there okay it doesn't matter to me. So that was that last example there. Alright, now sometimes, sometimes the numerical relationship that we need, you're not going to find it on a list. Or you're not going to find it in any kind of textbook or reference book.

Because sometimes the numerical relationship that you need is in a word problem. And you have to pull that information out in order to be able to use it. Example I've got on number 36 here. Okay, the example I've got on slide number 36. We have a patient who needs 0.024 grams of a sulfa drug. There are eight...

milligram tablets in stock, how many tablets do we give him? So our patient needs 0.024 grams of a sulfa medication, but what the question is asking us to find is how many tablets do we give him? Okay, we're told how much of the medication our patient needs, but we're being asked, okay, how many tablets do we give him?

That relationship there between the medication and the tablets, that is something that you're going to have to pull out of this work problem because you're not going to find it just in any book or any reference chart or on any list. You're going to have to pull it out of the work problem. And what this tells us here is that there are 8 mg tablets in stock, meaning that one tablet contains 8 mg of our sulfa medication. Alright, now there's something we need to address here.

The amount of medication our patient needs has been measured in grams, but our tablets have the medication in milligrams. So we're going to have to convert one of those. Really, ultimately, it doesn't matter which one, but we've got to convert one of them so that they match up.

Now, grams, milligrams, those are the same base unit of grams. We've got base unit over here because there's no prefix. And then we've got milli is what our tablets are measured in. So what I'm going to do is I'm going to take that 0.024 grams, and I'm going to get that converted into milligrams using King Henry. Okay, using King Henry.

So I'm going to come out to the side to work this one out. King Henry. Died by drinking chocolate milk. Again, our grams right here, there's no prefix, so that's at base.

We need to get that into milli. Okay, well, base to milli is moving to the right. Going to the right, that's one, two, three places to the right. So we're going to take that decimal and move it one, two, three places to the right.

Point 024 becomes 20. Again, the.024, we moved our decimal three places to the right, and we end up with 24 milligrams. Now, we don't stop there, because that's not what the question asked. The question didn't ask how many milligrams of medication does our patient need. The question wants to know tablets.

How many tablets do we give him? So the conversion problem comes in next. Where we need to cancel out the amount of medication, so in this case we need to cancel out milligrams of sulfa, and turn that into the number of tablets that we should give our patient. And this information comes from the numerical relationship that we had to pull out of the word problem. And one tablet, so one tablet, contains eight.

milligrams of the medication. The amount of medication is going to cancel out and leave us with tablets, which is perfect because that's exactly what we're trying to determine. And when you do the math you have 24 times 1 divided by 8. That leaves you with 3 tablets.

We're going to give our patient 3 tablets. Next slide, next example. We have the daily dose of ampicillin for the treatment of an ear infection is 115 milligrams per kilogram of body weight.

What is the daily dose for a 34-pound toddler? So we have a 34-pound toddler. Toddler, that 34 pounds, that's how much he weighs.

So that's 34 pounds of body weight. I'm doing a little bit of abbreviating here, okay? 34 pounds of body weight.

And we're trying to calculate how much of the medicine, ampicillin, I'm going to abbreviate that as well, amp, do we give him? How much of the medication do we give him? Well, the medication tells us, give him 115 milligrams of ampicillin for every kilogram, so for every 1 kilogram of body weight.

Give him 115 milligrams of ampicillin for every 1 kilogram of body weight. Okay, a little detail we're going to have to work with here. We weighed our toddler in pounds. The medication has body weight measured in kilograms. We're going to have to convert one of those to match the other.

Again, ultimately, it really doesn't matter which one, because in the end, the math will take care of everything, but we've got to convert them so that they match. Okay, for the extra practice, we're going to take our 34 pounds, and we're going to get that into kilograms of body weight. Now, in order to do that, pounds and kilograms, those are definitely not the same base unit, okay?

So King Henry is not going to be able to help us here. So we're going to have to do a conversion to get that from pounds to kilograms first. before we can then continue to get to the medication. Okay, so I'm going to come out here to the side and do this in a different color.

34 pounds of body weight, and we need to get that into kilograms. So we want to cancel out the pounds and get that into our kilograms. Okay, going back to your list of numerical relationships, one kilogram has 2.2 pounds. Pounds will cancel out and leave us with kilograms, which is good because that's where we're headed. That's what we need.

You'll take your 34 times 1, divide by 2.2, and I have 50. 15.45 kilograms of body weight. Okay, now we don't stop there because that's not what the question asked for. The question did not ask how much does our toddler weigh in kilograms.

The question is asking us all about how much medication do we give him. Okay, so our next conversion, now we want to cancel out the whole body weight completely. kilograms of body weight and this time we want to convert it into the medication of ampicillin. Now again the problem told us give him 115 milligrams of ampicillin for every one kilogram of body weight.

Okay kilograms of body weight will cancel out completely. And we'll be left with milligrams of the medication ampicillin. Now this is going to look like a huge number because you are taking 15.45 times 115. Okay. But remember this is a daily dose.

It would be split up over three or four doses in a 24-hour period. But you're taking 15.45 times 115. 1,777.27, and that comes out in milligrams of ampicillin. So again, sometimes that numerical relationship that you need to do the conversion problem is not going to be on any list.

Okay, sometimes you have to be able to pull that out of the word problem in order to be able to use it. Okay, all right, the next slide I've got it is number 38. Okay, we're going to be dealing with conversion of units in numerator and denominator. So here we have the speed of sound and error. It's about 343 meters per second.

What is this speed in miles per hour? So we're going to have to go from meters to miles. And then we're also going to have to take our seconds to hours. And I went ahead and listed those numerical relationships. So this one mile is 1609 meters.

That's one you can add to your list that previous slide. And then the minutes to seconds, hour to minutes, I figure you know those, but I went ahead and wrote them down anyway. Okay, so we are taking 343 meters per second.

And we ultimately want to get that into miles per hour. So I always take care of the unit that's in the numerator first. It really doesn't matter which one you work with first as long as they all get taken care of. Just out of habit, I take care of the numerator first.

So my first conversion, I want to cancel out the meters and get that into miles. Okay, and the relationship that's given to us, one mile is 1609 meters. That will cancel out meters and get us into miles there. I'm going to go ahead with my next conversion factors and then do all the math at the end. So next conversion.

Now we're going to try to get seconds to hours and we're going to do this one in two steps. We're going to go seconds to minutes and then minutes to hours. So seconds we want to cancel out.

Now pay attention here. The seconds that we're given are starting out in the bottom. They're starting out in the denominator.

So in order for them to cancel, they have to go on top. And again, we're going to go from seconds to minutes first. And one minute has 60 seconds in it.

That'll cancel out our seconds and get us to minutes. But we're not staying there. So I'm not going to circle it.

I just underlined it because we're just pausing there for a moment. Because then the very next conversion factor, we're going to cancel out minutes. Now again, minutes here is in the bottom in the denominator.

So to cancel it out, it has to go on top. We're going to get those to hours. An hour, that's 60 minutes. So now those unit of minutes will cancel and get us into hours. Take a look at your units.

all the way across the top all the way across the numerator so we canceled out meters we got that into miles seconds have canceled minutes have canceled so all the way across the top the only unit we still have are these miles and then all the way across the bottom all the way across the denominator the only unit we have left are the hours over here miles per hour that's perfect that's exactly what we need that's exactly what we want So again, when you do the math, I always recommend go all the way across the top, all the way across the denominator, and then divide last. So we have 343 times 1 times 60 times 60. Divide by, we've got 1609 down here at the bottom. So I have 767.43.

767.43 miles per hour. Okay, so again, units that we're dealing with in the numerator and units in the denominator, just take it a step at a time. Okay, you can do the math all at the same time at the end, but do each conversion factor just a step at a time. And then remember, wherever your unit is that you want to cancel, it must go opposite.

So if it starts out in the denominator to get it to cancel in your numerical relationship conversion factor, it's got to go on top in the numerator. Now one thing that I want to talk to you about before we do the next example are dealing with units that are squared or units that are cubed. First of all, how do we even get units that are squared or cubed?

okay all right we've got a box here it is not a perfect box okay not a perfect cube but if we want to solve for area okay if we want to solve for area that formula is two measurements length times width well if we take both of those measurements let's say in centimeters we would have centimeters times centimeters Or what we more commonly write down would be centimeters squared. My point here is that units that are squared, that means you're really dealing with two of those units. So when you're doing a conversion with units that are squared, you're going to have to be very, very careful because you'll have to do that conversion two times to take care of each one of those units. Okay, volume. For calculating volume, that's three measurements.

Length, width, and height. And if we're taking those in centimeters, we'll have centimeters times centimeters times centimeters. which we more commonly write down as centimeters cubed. My point here is that when units are cubed, that means you're really dealing with three of those units.

So when you're converting units that are cubed, you're gonna have to do that conversion three times to take care of each one of those units. Okay, as an example, let's take a look at 9.8. inches squared into centimeters squared. 9.8 inches squared into centimeters squared. Okay, so we've been given this 9.8 inches squared in order to convert.

And one thing that I do that may just kind of help you remember how many times to do this conversion, when units are squared like that, separate them out. Okay, expand that. So we've got inches times inches. That way you can clearly see each one of those units that you're going to have to convert. Times conversion factor.

We want to cancel out inches so that goes on bottom. Trying to get that into centimeters so that goes on top. Looking back at your numerical relationships, 1 inch is 2.54 centimeters. But this one conversion here is only going to take care of one of those units. Okay?

It only cancels out one of those unit of inches and only gets us into one unit of centimeters. The units were squared, which meant that we had two of them, which means we have to do that conversion two times. So we're going to have to do this again.

in order to take care of that second inches unit. Okay, so in the second conversion, it'll take care of that second inches unit and get us into that second centimeters unit. So now both of our inches have canceled. We have centimeters times centimeters, which we more commonly write down as centimeter squared.

Math-wise, what that means, you have to do 9.8 times 2.54 times another 2.54. Okay, so again, 9.8 times 2.54 times 2.54, and I have 63.23 centimeters squared. Okay, another example.

We're going to look at is 11.8 centimeters squared into meters squared. There's a couple ways you can do this one. I'll show you both ways and then you stick to whichever method you're most comfortable with. But 11.8 centimeters squared into meters squared. Okay.

Alright, 11.8 centimeters squared, I'm going to expand that, so centimeters times centimeters, times conversion factor. We want centimeters to cancel, and we want to get that into meters. Okay, now let's talk about this relationship here. Centimeters, meters, those are the same base unit. So to find their relationship, We'll be able to use King Henry.

So I'm going to come up here. King Henry died by drinking chocolate. Meters. There's no prefix there, so that's your base.

And then centi. There's more than one way that you can look at this relationship. Here's what I recommend. Alright, so again meters, that's your base because there's no prefix, and then centi.

Now look at these two measurements here, base and centi. The one that is further to the left, the one that is further to the left is the larger measurement. In this case, that would be our base.

Our base is to the left, it's the larger measurement. Set that as 1. The measurement further to the left is your larger measurement. Set that as one. So we would have one meter. Okay.

To find that relationship, to get to centi, we're going to the right. two places. So when we go to the right, we move the decimal to the right and for a whole number that means that decimals at the end. We're going to move it to the right two places.

Fill in empty spots with zeros. So that means one meter has a hundred centimeters. Okay, again, the measurement that's further to the left is your larger measurement. Set that as 1, and then move your decimal over however many places you need to go to find that relationship to that second measurement. So in this case, 1 meter is 100 centimeters.

The reason I do it that way is to avoid having a decimal in a conversion fraction like this. Okay, that'll give us nice pretty numbers, and we don't have to mess with a decimal in a fraction. Okay, but there's more than one way that you could find that relationship.

Again, now, this one conversion factor here is only going to take care of one of those units. This one conversion factor only takes care of one of those centimeter to meter units. Because it was squared, that means there's two of them. That means we've got to do this again.

Because it was squared. When there's two of those units, we've got to do that conversion a second time. That'll cancel out that second unit of centimeters and get us in the meters there. So now we have 11.8 times 1 times 1. Divide by 100. Divide by another 100. Be very careful about that. 11.8 times 1 times 1. Divide by 100, divide by another 100, and this should come out to be.00118 meters squared.

The other way that you could do this one is because centimeters and meters are in the same base unit, and we can use King Henry, you can just move the decimal point around. You just have to be very careful about... how many times to move the decimal point around, okay?

11.8 centimeters squared to meters squared, okay? So we're going from centi to base, and from centi to base is moving to the left two places. Okay, from Senti to base is moving to the left two places, so we can move that decimal two places to the left, but that only takes care of one of those conversions.

That only takes care of one of those conversions. In order to take care of the second unit, the second conversion, we've got to move that decimal two more times. And then, of course, fill in those empty spots with zeros. You still end up with the same answer.

To be on the safe side, I always recommend when you're dealing with units that are squared or cubed, write out that conversion long version. Okay, write out that conversion factor long version so that you can see those relationships, even if it's King Henry, but then that way you can see each one of those relationships there. So on the next slide, I have it labeled as slide number 39. Okay, we're dealing with units that are in the numerator and denominator. And we're dealing with units that are cubed as well. So we've got several things going on here.

Okay, all right, we've got 10. grams per, and it's centimeters cubed, and I'm going to expand that out so we can see each one. Trying to get it into grams per meters cubed. Now notice the numerator stays the same, grams and grams. So we're not going to have to convert the numerator at all. It's perfect, it's great the way that it is, okay?

What we are having to convert is from centimeters cubed into meters cubed. So first conversion factor. We want to cancel out centimeters.

Now again, pay attention. They're in the denominator to begin with. So to get them to cancel, they have to go opposite. You're going to have to go in the numerator over here. And we're trying to go from centimeters to meters.

But that one conversion there is only going to take care of one of those units. Because it's cubed and there are three of them, we're going to have to do this conversion three times. Now to find that relationship with centimeters and meters, they are dealing with the same base unit, so we can use King Henry to help us out here. Centi and meters, there's no prefix there, so that would be base. To find their relationship, again we're comparing those two, centi and base.

That base is the one that's to the left, so it's the larger measurement, so we're going to set that one as 1, so 1 meter. And if we have 1 at the base, then to get to centi, that is 2 places, which would be 2 zeros or 100 centimeters. You still want to make sure that units cancel. So the first unit of centimeters is canceled out in that first conversion and gives us meters there. Second unit of centimeters canceled out in that second conversion and give us meters there.

Last unit of centimeters canceled out in last conversion and give us meters there. And remember the grams in the numerator, we didn't touch it, we didn't change it, so it stays the same. So as you look at your units all the way across the numerator, everything's been canceled out except those grams.

So we still have those grams. And in the denominator, we have meters times meters times meters, which we more commonly write down as meters cubed. And in math, we've got 10.9 times 100 times 100 times 100. Okay, again, you've got 10.9. times 100 times 100 times 100, 10,900,000. Or if you'd rather write that in scientific notation, that can be 10.9 times 10 to the sixth, or 1.09 times 10 to the seventh is the better scientific notation.

Again, all of those are expressing the same number. They're all expressing the correct answer. Just in scientific notation, one format is a little bit better than the other because you want that number to be in between 1 and 10. Okay, there's another example on this slide here dealing with units in the numerator and denominator and then units that are cubed as well.

I'm going to leave that one for you to do on your own, but I am going to give you the answer so you can check yourself. This one should come out to be 3,750 kilograms per meters cubed. 3,750 kilograms per meters cubed on that last example there. Okay, now we do still have a few problems left in chapter one dealing with density, specific gravity, and then our temperature. conversions.

I'm going to do that in a second video. So this first video was all about conversions, measurements and conversions, and then that second video will take care of the density, specific gravity, and temperature.

Transcript for:Fundamentals of Chemistry Concepts

Transcript for:
Fundamentals of Chemistry Concepts