 I take it from all the emails that I'm getting, the more positive emails, I'm glad that you guys are finally past the math section, you know, and we're doing chapter one stuff that's much easier, I guess, I take it for you guys. And I appreciate all the positive responses on the videos. I'm glad that I was able to get them up, finally, that we did a patchwork on the summer ones, so they're all being put up right now, and of course the ones that you guys see. So they should all be working from now on, everything it seems is working. Again, thanks for all the positive feedback, and keep going. It'll just keep getting easier, I promise you, I promise you, I promise you, okay? So we've done our first week of baby steps, and I think we're starting to walk now, you know, and we'll eventually be off and running, okay? So why don't we get started on, or get finished, I guess, with chapter one, okay? So let's talk about some of the basic units of time, temperatures, specifically temperature. Time, when we're talking about metric, the cool thing about time is that metric and English units are the same. It's the second, that's the basic unit. Temperature, we're going to have to do a little bit more work with, because of course in the United States, again, we're more familiar with dealing with the Fahrenheit scale, so most of the temperature readings that we see are in Fahrenheit. Of course, you know, the metric system isn't going to make it easy on us for anything, right? So we've got to learn the metric system of temperatures, and that is Celsius, okay? So what we're going to be learning is actually three different temperature scales. The last one is Kelvin. The Kelvin temperature is an absolute temperature scale. The other two temperature scales, Celsius and Fahrenheit, are based on things that people have found through nature, like for example, the Celsius scale is based on the freezing and boiling point of water, okay? So they set zero at the freezing point of water, and 100 at the boiling point of water, and they just made degree increments, 100 of them in between. The cool thing about the Kelvin scale is that the degree unit is the same amount, if you will, as the Celsius scale. Unfortunately, the Fahrenheit scale is really kind of far out. The Fahrenheit scale was based on body temperature with 100 being average body temperature. Of course, this was before we could get very good temperature measurements, and probably you guys know that normal body temperature is in 100 degrees Fahrenheit. It's a little bit low, right? So they based it on that. So we're going to kind of want to be able to convert from Fahrenheit to Celsius, and we'll probably be using Celsius and mostly Kelvin in this class, okay? So most of our temperature readings, when we start doing chemistry problems, are going to be in the Kelvin scale, but I think it's very beneficial to go from Fahrenheit to Celsius and then to Kelvin, okay? So you can see these three thermometers here. You see body temperature, 98.6 degrees Fahrenheit, 37 degrees Celsius, boiling point of water, 212 degrees Fahrenheit, 100 degrees Celsius, freezing point of water, 0, 32, 273. Those are three numbers you're going to want to remember. It'll make your life a lot easier. And then you've got these two equations here, and these equations will help you convert from Celsius to Kelvin. In fact, this is how you do it. Let's try to do some conversions. I'll throw the temperatures up there or the conversions up there. So these are two equations, probably the first two equations, that you're going to need to memorize for the test, okay? So you're not going to have any sort of no part or anything for the first test. So I want you to commit these things to memory, because of course you're going to have to convert from Celsius to Fahrenheit on the first test. Let's go ahead and convert 75 degrees Celsius to Fahrenheit. So how do we do that? Which one of these two equations do you think we'll use, the top or the bottom one? The bottom one, right? Because we want to get Fahrenheit. So let's just, first of all, write that equation down. So degrees Fahrenheit equals 1.8 times degrees Celsius plus 32. Zero degrees Celsius. So this number has, remember, three significant figures. So our final answer is going to have three significant figures. So let's just go ahead and plug this number into this equation. 1.8, 75.0. For this other one, negative 10 degrees Fahrenheit. Let's do a different one. That one's up there. Let's do negative 40 degrees Fahrenheit, okay? Let's do a negative 40 decimal point, okay? So it'll be two significant figures. Okay, so which one of these equations will you use? The top one, of course. Degrees Celsius. And remember, we can manipulate this equation to make that equation. Let's do that. Let's just do that for a little bit of practice with algebra. This is good because, of course, you're going to be manipulating equations quite extensively, and as you guys probably have already figured out in this class. So let's just take this equation. Degrees Fahrenheit equals 1.8 plus 32. And manipulate it to get that other equation. So the first thing we're going to do is subtract 32 from both sides, or as Al would say, like add the negative 32, right? Okay, so we're going to take 32 off the both sides. 32 minus 32 cancels. And what I like to do is put the negative behind. So we got degrees Fahrenheit minus 32. Then we'll go ahead and divide both sides by 1.8 minus 32 over 1.8. So the cool thing about this is you only really need to memorize one of those equations. You don't need to memorize both of them, and then you can algebraic manipulate back and forth. Okay, so let's go ahead and plug this number in. Negative 40 degrees Fahrenheit into this equation. Negative 40? Calculate around? Okay, so that's the only temperature. This is the only temperature on both scales. That's the same number. Okay, so negative 40 degrees Celsius. It'll be negative 40 degrees. A lot of you already knew that. This number two here, if we look at this answer here, it's got one too many significant figures. Okay, so what I like you to do is just put a decimal point behind that zero there, and that'll make it all good. So I was referring to the Kelvin temperature scale a few minutes ago. The Kelvin temperature scale is an absolute temperature scale. What does that mean? So what we really want to think about in temperature, or what temperature is actually telling us, is that it's the amount of energy, the particles, that are that temperature past. Okay, so temperature is actually a measurement of energy. I know we think it's a measurement of being hot or being cold, but what it really is, is the vibrational energy of the particles. Okay, so the more vibrational energy you give them, the hotter they become. The more energy you take away from these particles, the less they vibrate. Okay, so the temperature scale is based on that. It's based on an absolute measurement. So what does that mean? That means at absolute zero, or zero on the Kelvin scale, there is no more particle or molecular vibration. The absolute zero has never been able to get to. Nobody has ever been able to get to it. I think that the lowest temperature people have been able to get to in the lab is like 0.0004 or something like that, Kelvin. So it's very, very close to absolute zero, but not to where particle motion actually stops. So it is very important, and in fact, what you'll find is most of the calculations you do in this class will depend on the absolute temperature. So I want you to get a really good feel for the absolute temperature. The cool thing about the Kelvin scale is that the degrees are exactly the same magnitude as the Celsius scale. So they're only off by this number here, 273. So what does that mean? That means that water freezes at 273 degrees above absolute zero. Water boils at 373 degrees Celsius, that is, above absolute zero. So, thank you, we have some. Let's convert 75 degrees Celsius to Kelvin. Go back here, right down that equation. So we've got 75.0 degrees Celsius. We want to convert it to Kelvin. Just plug in the 75.0 plus 273. We aren't doing this. This is probably the easiest calculation you could do in this class. I would hope that everybody brings a calculator from now on and starts calculating with me because it'll really help you out. I know that some of you probably have no desire to even do it, but I really want you to get into the habit of doing this because I can guarantee you that the more and more you do these calculations, the more and more it will help you. So let's bring a calculator to class. Whenever we do a calculation, do it on your own. Notice I have this temperature to three significant figures. It also has the units associated with it. So let's try this other one. Convert 502 Kelvin to degrees Celsius. Now remember, you only have to memorize the one equation because you can algebraically manipulate that to give you degrees Celsius. So we'll start with that equation. A equals degrees Celsius plus 273. And all we got to do is subtract 273 from both sides. Celsius equals Kelvin minus a Fahrenheit to Kelvin. Because that one, we actually have to go through the Celsius scale first and then go to the Kelvin. So let's do this one here. Yeah, let's convert absolute zero to degrees Fahrenheit. And hopefully, we all get negative 250. Actually, it's zero Kelvin. Kelvin doesn't have the degrees. You don't say zero degrees. That's a mistake by mine. My degrees are Celsius and Fahrenheit. You both say degrees, but Kelvin is an absolute scale. So we got zero Kelvin and we're trying to convert that to Fahrenheit. So the first thing we got to do is convert that to Celsius. Okay, we remember this equation. Remember when we manipulate this, we get degrees Celsius equals Kelvin minus 273. So we're going to have to do that first. So we plug in zero to there to Celsius. And now what we want to do is convert this to degrees Fahrenheit. Okay, the cool thing is we've already manipulated the equation over here, so we'll just plug in numbers to here. So we've got this equals negative 273 minus 32 divided by... We're going to have to manipulate this equation. Okay, multiply this by 128. We've got to do it in the proper order of operation. So we've got, since this is addition and subtraction, we've got to do this first, okay? We've got to do the division multiplication first. Then we're going to add 32 to both sides of this equation. Let's go back and forth, back and forth. If you can't yet, do them, do them, do them until you can. Okay, so let's talk about our first derived quantity. All the quantities that we've been talking about so far have been directly measured, okay, directly measurable. We can take something, put it on a balance, get the mass of it. We can take something, dunk it under water, and get the volume of it, okay? We can put a thermometer on something and get the temperature of it, okay? The first derived quantity, something that we have to take, goes basic quantities and use them to manipulate a new quantity that we're going to learn is density, okay? So notice, for those of you who have already done the lab, you know how to take mass, you know how to get the volume of something, and how to find the density is, you just take that mass and then divide it by the volume, okay? So, this is the way to get the mass of a substance is a physical property, okay? So, every is going to have the same density if it's pure water, okay? Every gold ingot is going to have the same density if it's pure gold, okay? Inget being these bars of gold, okay? Any lead block is going to have the same density as another lead block if they're pure lead, okay? So it's an inherent physical property of substance, okay? So there's a few different types of density units that you will come into contact with. The two we'll be using in this class is grams per milliliter, and you usually use that when you're discussing liquid density, okay? Because liquids usually measure volume in milliliters, and the other one would be grams per cubic centimeter, and that would be when you're talking about solids, because solids are more easily measured with a length measuring device than a volume measuring device, okay? Unless again, if you want to don't do under water. Another unit you may see, and probably will see in this class is grams per liter. You'll use that when you're talking about gases, because gases are so voluminous that a milliliter isn't an appropriate unit to use, because it's too small, okay? So you want to use grams per liter. Notice here, we've got four substances, four pure substances, that is, cork, water, brass, and mercury. Notice how they're each floating on top of each other, okay? One's floating on top of another one, which is on top of another one, which is on top of another one. What you find is things that have the greatest density fall to the bottom of any mixture that you have, okay? So in this case, what you find is mercury with a density of 13.6 grams per mill has a very, very dense substance, okay? In fact, it's the most dense liquid that I know. Must be less than 13.6 grams per mill, or grams per cubic centimeter. Why is that? Because it's floating on top of the mercury. Does that make sense? The water must be less dense than the brass. Why is that? Because the brass did sink in the water, right? So if you throw a rock in water, it sinks, right? That's because the rock is more dense than the water. It's not heavier than the water, right? If I throw a rock in a river, the river is enormous, right? The river is enormous. How much mass of water is there in a river? Much more mass than that rock, right? So it's not the mass that's doing this. It's the mass per unit volume, okay? So the mass per unit volume of water is much, much less than the mass per unit volume of brass. That's why it sinks. And then, of course, quart must be the least dense of these materials. That's why it's floating on top of the water, okay? Does that make sense? So it's inherent property of these substances, okay? And it's this property of mass per unit volume that you need to think about, not just mass, not just volume. So let's calculate the density. Let's calculate the density of aluminum. Aluminum is usually a solid, right? Usually a solid at room temperature. It definitely is a solid. So it's going to be in units of grams per cubic centimeter. So let's go ahead and figure this out. So what I would always do, what I always do, is take the initial measurement, or the initial equation, density equals mass over volume. And then what I'll do is say, okay, the volume equals 2.00 equals 5.40 grams. Notice this has three significant figures. This has three significant figures. Our answer is going to have three significant figures. Plug this number in, 5.40 grams divided by, let's go ahead and take our density calculator here, 2.7. You'll be able to figure this out with anything if you can take its volume and take its mass. So you can figure out the inherent density of anything. And in fact, like I was saying on Monday, this is, there was a very famous experiment that went along with this, some guy, Archimedes. So here's some more density calculations. In this one, we actually, the air density is given and the mass is given, so, or the volume is given. So we need to find the mass, okay? So how would we do that? We just take this equation and manipulate it. So we don't have to remember all three of these equations. We don't have to memorize the equation for mass from density, the equation for volume from density, and the equation of density from mass and volume. All we got to remember is d equals m over v and we can get any of these units. Okay, so we know this and we know the density of air. So density of air. So notice, one thing I want you to notice right away is that we've got milliliters here and liters here. Okay, so we're going to have to convert one to the other because we can't do it. We need to cancel out this volume unit. So let's go ahead and convert this to liters since we're talking about a gaseous sample. And liters is a more appropriate volume term to use. So how would we do that? How many milliliters are there in a liter? Everybody? A thousand, right? Make sure you guys know that because that's a conversion I'm not going to give you. So we've got 1,000 milliliters per one liter. Notice milliliters cancel. And what do we get? This divided by that, multiplied by that. So we'll take 0.0013 times 1,000. Notice I only put two significant figures in that calculation. Why? Because there's only two significant figures here. So we're looking for mass here. We're not looking for density. So we're going to have to do something to this equation to get mass to isolate the m variable. That's the way you would want to think about it. So what would we do? Multiply both sides by v. v cancels there. And we get m equals 4 here. We've got volume in liters and density in grams per liter. So when liters cancel out, we're going to get a mass unit. And that's cool too because we're looking for a mass. So volume 6.0 liters multiplied by 1.3 grams per one liter. So that's why I write it this way. So I'll have it actually on the denominator already. So when we do that, remember this is the numerator. There's only one below there. Leaders cancels with leaders. And what do we end up with? Grants over here. So if you do this in the appropriate fashion, you can't help but get the right answer because the units will cancel out for you. So we do this. We multiply 6 times 1.3. Why do you only say 7.8 and not 7.8? 0, 0, 0, 0. 2, 6, 6. Right? Why? Because we've got 2, 6, 6 here. 2, 6, 6 here. So the answer is going to have 2, 6. Okay? Got it? Got it? Got it? Cool. I'll let you guys do the other one on your own. I think you guys can do it. There's some more density calculations. Let's do this lead brick one. This is why solids are usually given densities in grams per cubic centimeter because it's easy to measure, you know, if I have a brick or something. Say this is a lead brick. I could measure that many millimeters to that many millimeters to that many millimeters. Okay? It's very easy to measure because the meter stick is quite readily available. So let's just set this problem up. And then I'll let you calculate it on your own. Remember, you've got to memorize this B equals M over B. So now we have two, three equations that you need to know. The Kelvin to Celsius, the Celsius to Fahrenheit, and density equals mass over volume. Okay, what does it say? The dimensions of the brick. Remember, these dimensions are going to be length times width times height. Okay? That gives you the volume, of course. Or width or height, whatever it is. This is 20.3 centimeters. It's going to be here at the end. 10 meters cubed. Why do you say that? Why do you say that? Because it's what? 10 meters times centimeters times centimeters. Okay? So that would be centimeters cubed. This one we can approximate for right now because what we'll do is we'll take the significant figures at the end of the calculation. Okay? That's the best way to do it is to just go along with your however many numbers your calculator gives you until the very end and then cut your significant figures. Okay? Because that way you won't be estimating, estimating, estimating. And then at the end you've got a different answer than what you would have had. Okay? Well, okay. If this was the final answer, right? But our final answer is in volume. It's going to be density. Okay? So that's what we're really looking for. So we're not really concerned with the significant figures here because this isn't the answer we're going to box on our test, if you will. Okay? So I mean, honestly, what you could do is go 1051.8648 centimeters cubed, if you prefer. Okay? And in fact, this might be the best way to do this the rest of this problem. But yeah, you're absolutely right. We want to make sure, since this has 366s, this has 366s, that has 366s, that we got to go to 366s at the end at the very end. Okay? So we're looking for the density, right? So we've got equals mass to volume. So we don't know what the density is, but we know what the mass is, right? What is this? What is this? 11.950 kilograms. So remember, density is only mass per unit volume. I didn't say you have to specify... Oh, it does say it. Okay? It does say you have to specify in grams. If it doesn't say specifying grams, then you could keep it in kilograms if you prefer. But since the problem says specifying grams, what are we going to have to do with the kilograms here? Change it to grams, convert it to grams through dimensional analysis. And again, how many kilograms are there in a kilogram? A thousand. A thousand. Very good, guys. So one kilogram, one thousand grams to take this number, divide it by this number here, and then take it down to three significant figures. Okay? So I'll let you guys do that on your own. Yeah, so... Okay, I'll just do it for you. No, no. No, no. Yeah, let's do it. I'll set it up for you. And you guys can calculate. Okay? So 11.950 grams. Divide it by 105164. And you're going to want to take this number here, which is going to give you grams for a human denominator, to three significant figures. So practice with these. Remember this. If you don't know, the volume equals the length times width times height of a salt. Okay? And another way to figure out volumes, if you were like in the laboratory or something, is you could take a body of water or a body of liquid and dump the solid in the liquid, and it'll raise the volume up, just like you did in lab, hopefully. And it'll tell you what the volume of it is. Let's talk about error. So there's different types of error. There's random error and systematic error. Unpredictable. It's not going to go specifically to one side of the calculation. They're all scattered about. So if you pretend this line here, this dashed line is the correct answer. You see that we've got these points that are all around it. Okay? So you can't predict where that random error is going to come in. Systematic error, on the other hand, is errors that contain a bias either above or below the accurate measurement. Okay? This would be like if you, I don't know, get maybe five pounds under zero. So you might think, oh, I'm losing weight. I'm losing weight. Or five pounds above zero. I'm gaining weight. I'm gaining weight. Okay? I know I used to do that one when I was much younger. Okay? So you see all the points here systematically will be above the correct value because your balance is inherently incorrect. Okay? So you've got some sort of systematic error in your measuring device. Your measuring device is consistently giving you an answer that's above the correct answer. Okay? So notice the difference between this and this. A precision, this tells you how close is my value to another value, the other values I get. Okay? So here we see we got high precision. All the values are essentially the same. Okay? Here we've got high precision too. All the values are essentially the same. Okay? So even if you have a systematic error, you can still be very precise. This is like if I'm a dart thrower and I don't consistently hit the bullseye but I consistently hit the number 11 on the outside of the board. Okay? So like that, I'm very precise always hitting that 11. Okay? I'm not very accurate because I want to hit the bullseye but I keep hitting the wrong spot. So I'm very precise. Here you see on the other hand would be can I hit the bullseye? Can I hit that right target? And in fact it's the average measurement of all of your different attempts. So here, even though none of the attempts actually hit the bullseye, the average of them would be hitting the bullseye, if you will, right? Hitting this number. If we averaged all those points out, you can imagine it would get close to that dashed line. Okay? So we would say that's very accurate. And another one. Whoops. This, here, both precise and accurate. Okay? Because they're all consistent and the average hits that dashed line. High precision, high accuracy. High precision, low accuracy. Low precision but high accuracy. Okay? Because it's the average of all of your points. And the scientific method, this is the approach that you're going to be using in this class and any other science class that you ever take and any other anything, really, that you ever do, right? Because if you do something and it doesn't work, you're not going to do it again, right? If I, I don't know, touch this thing and it shocks me, right? I'm not going to do it again. I've used the scientific method. Or if I do it and I say, oh well, it didn't happen again. If I do it, bam, and it shocks me again, I'll stop doing it. Okay? That's what a scientific, the scientific method is in a nutshell. You observe a natural phenomenon. I touch that thing and it shocks me. I formulate a question. I wonder if it'll shock me every time I touch it. You recognize the pattern? Oh, it shocked me again when I touched it. It shocked me again. So I'm going to formulate a hypothesis. It's going to shock me every time I touch this thing. So I can perform an experiment. Touch it, touch it, touch it. If it shocks me every time, then I'm proving my hypothesis true. Or if maybe one time it doesn't shock me, right? Then my hypothesis needs to be changed a little bit, right? Maybe every tenth time it doesn't shock me, you know? So if true, if it shocks me every time or shocks me nine out of ten times or something like that, then, and I've made this statement and I've experimented it years and years and years and years, then that hypothesis becomes a model. And then further experimentation by many, many other people, many other scientists doing the same experiment as me will take that model and add further validity to it if they get the same results, right? And that model then becomes a theory. And then, of course, after a while, after hundreds of years of doing these same experiments, that theory then becomes a law, okay? The very few laws of nature. You summarize findings in the theory for people to understand very easily. So they don't have to perform the experiment anymore. Okay? Read this on your own. Okay, good job, guys. We're done with chapter one. We'll start with chapter two next time.