hello everyone today we're going to be discussing chapter 2 which is chemistry and measurements so we're going to go ahead and jump right in and start talking about section 2.1 which is all about the units of measurement and in this section we are not converting but we will learn how to convert in between units today so in chapter 2 table 2.1 we have a wide variety of different measurements we have the metric system and the si system so for volume that is going to measure some type of liquid that's typically measured in a liter or we can say meters cubed for length the metric system is in meters and the si unit is also in meters for mass that is how much an object weighs that would be a gram or in the si unit a kilogram we also have temperature and that in the metric system is as degrees celsius and in the si system calvin and when we get to discussing uh kelvin we'll talk about why converting to kelvin is extremely important right now we just need to know that we can use degree celsius or kelvin and time is measured in seconds in both cases so those are our common units of measurement so let's go ahead and break these down so we have length and that is one meter in terms of the si unit as well as the metric unit and one meter is equal to 100 centimeters so there are 100 centimeters for every one meter in one inch there is equal to 2.54 centimeters so length is measuring uh at the a distance of something and we can again measure that in terms of meters and one meter is equal to 100 centimeters or we can measure things in terms of inches and one inch is equal to 2.54 centimeters when we talk about the mass that is the quantity of material and typically we uh use the term kilograms that's your s i unit so one kilogram is equal to one thousand grams and one pound is equal to let me go ahead and make that one very clear one pound is equal to 454 grams so we are used to thinking about things in terms of pounds and when we weigh things and in one pound there is 454 kilograms excuse me in one pound there's 454 grams not kilograms in one pound there is 454 grams also when we're talking about temperature we're talking about how cold something is so again we're used to thinking about things in terms of fahrenheit so zero degrees celsius is equal to 32 degrees fahrenheit and 100 degrees celsius is equal to 212 fahrenheit zero degrees celsius is equal to 273 kelvin and again we're not talking about converting them yet we're just talking about uh the different units of measurement but we're not talking about how we actually convert them and time for time you have one day which is equal to 24 hours and one minute is equal to 60 seconds so again those are just the different types of units of measurement those are not converting quite yet we didn't talk about volume um we will talk about volume a little bit later volume is a little bit more complicated uh because it has three dimensions so for section 2.2 we want to talk about measured numbers and significant figures so section 2.2 so when we're talking about significant figures we call that sig figs so you'll be seeing me write the shorthand significant figures so you want to include all the digits including the estimate and the estimate is always the last digit and that is because whatever you're trying to measure and we'll talk about this when i actually write this number down so let's look at 4.5 grams your scale is measuring the estimated value of five grams and so that the last digit is always called the estimate digit and so again that is because this number is not exact where the other numbers actually are so that's the estimate so when you're counting significant figures you're looking for all of the digits so again and we're looking at number four uh 4.5 and this happens to be grams this value would have two significant figures if we looked at a different value of 5.008 kilograms again it doesn't matter what the unit is we have an estimated value of 8 because that is your last value and then you have 0 and 0 and 5 and those are all exact numbers so in this case you have four significant figures so it's actually pretty straightforward when you don't have a zero somewhere so let's go ahead and look at the numerical value 850 000 and in this case we happen to be looking at meters what we can do is from chapter one we are going to go ahead and put this in scientific notation so let's move that decimal place over let's move this decimal place over one two three four five positions and that's going to be 8.5 times 10 to the fifth power because we have a number that's larger than one so we have a positive exponent that was from chapter one and when we have our number written in our standard notation versus our scientific notation when we have it written in our scientific notation what we find is that we actually only have two significant figures so these the zeros is when things can get a little bit uh more complicated these zeros are not included in your significant figure count because you when you put it in scientific notation there are in fact only two significant figures now let's go ahead and look at 16.00 milliliters what we're saying is we're actually measuring let's say your you're measuring in a graduated cylinder and you're measuring out and your graduated cylinder here's the tick mark for 15 and here is the tick mark for 16. inside and you put your water or whatever liquid inside your graduated cylinder and you measure it exactly to that 16 tick mark these numbers although they are zeros because they're after the decimal they are significant so these in our 850 000 these numbers were before the decimal so those are not significant in our 16 milliliters these numbers are after the decimal and those are significant because these are not estimates or i should say what i should say more clearly is this 0 right in the tens place is not an estimate and the zero in that hundredths place is an estimate because it's the last number but again both of those zeros are after the decimal so in the case of 16.00 milliliters you have four significant figures so anytime that you have a zero after the decimal it is included in the significant figure count if you can put your number in scientific notation it's not included in that significant figure count so now let's go ahead and look at five zero point zero zero five seven zero now again we are running into this problem where we can actually move this decimal place one two three positions to get that in the significant figure or excuse me into scientific notation so that would be 5.70 times 10 to the negative 3. we moved our decimal place three places now since we were able to move that decimal place we have three significant figures so when you can put your standard numerical value into scientific notation you always do that and then you count your significant figures so even though these two zeros are after that decimal place because you were able to put this numerical value into scientific notation the significant figures are not included another thing that we need to know it will take a lot of practice and you'll have a lot of practice in your homework so beware it takes a lot of practice but soon you'll see the pattern so for exact numbers these are not included in significant figures so an exact number an example of this would be one thousand grams is equal to one kilogram and this is just an exact number so that is not included you do not count these and we'll see when we'll actually be using conversions and you'll have multiple numbers in your system then you have to figure out what is the actual significant value significant bigger value so let's go ahead and work at problem 2.13 together so 2.13 so we want to indicate if the zeros are significant so problem 2.13 so let's just go ahead and look at a first 0.0038 meters so again we could move this decimal place over three positions and that gives you 3.8 times 10 to the negative 3 meters and so these are not significant because again we can move those over into scientific notation so for b you have 5.04 centimeters you cannot put that into scientific notation the zero is in the center yes that zero is significant you have 800 liters because we have this decimal place right here and we're saying okay we measured exactly 800 liters that makes it so that this very this significant the zeros are significant if it's not part of the problem but let's just look at if we just had 800 liters then we could put this into scientific notation and that would be equal to eight point zero times ten to the two and that would be no those would not be significant so having that decimal place there changes the game and again you'll have lots of practice so let's go ahead and look at d and d is 3.0 times 10 to the negative three three point zero times ten to the negative three yes we have that one significant figure and so yes that is going to be an important significant figure and so i'll have you try d on your own so if you find that you're struggling with uh e please come see me in office hours i'm going to have you work on e in your on your own so now let's go ahead and move on to section 2.3 which is significant figures in calculations so significant figures in calculation so let's say you have 5.52 meters and we're going to go ahead and multiply that by 3.58 meters and that's going to give us a value of 19.7616 meters squared so in 5.52 we have three significant figures and in 3.58 we also have three significant figures and here what we have reported currently is six significant figures so you can't have you cannot be more of an exact number than your least exact number so then you should only have three significant figures in your answer so that would be 9.19.8 meters squared now you have three significant figures and you're good to go so you never in your answer should have no more significant figures than the least significant figure so no more let me actually write this out your answer cannot have more significant figures than your least significant figures okay never your answer cannot have any more significant figures than the least amount that you have so let's go ahead and look at 8.00 divided by 2.00 and in this top case we have three significant figures and in our denominator we also have three significant figures so our answer needs to be reported to three significant figures and this should be four but this only has one significant figure and so again we need to report that to three significant figures so 4.00 now you have three significant figures and you're good to go that's for multiplication and division let's look at addition and subtraction let's say you have 2.045 and we're gonna go ahead and to that we're going to add 34.1 in the case of 2.045 you have four significant figures in the case of 34.1 you have three significant figures so it's always helpful to write out how many significant figures you have this added together gives you 36.145 so just looking at the answer currently we have five significant figures and again we can't report a numerical value more than the the least accurate so in this case you have 34.1 that's only accurate to the tenths place you have 2.045 this is reported to the thousandths place so this is your least accurate number because it's only to the tenths place so we're only going to report to the least accurate number so in this case it would be 36.1 so your answer should be 36.1 for your significant figure count and again for addition and subtraction it is going to be that your significant figures and your answer should be the least accurate value in the problem set so in this case your least accurate is one dust one place after the decimal the tenths place so your answer can only be reported to that tenths place so let's go ahead and look again it's going to take a lot of practice and then eventually you'll see the patterns merge you want to for 2.27 we want to report the correct number of significant figures so for problem a we have 45.7 and we're going to multiply that by 0.034 so let's go ahead and look at our first number that has three significant figures let's go ahead and look at our second number our second number has two significant figures so when we multiply this out we're not going to round yet we're going to multiply 1 uh 45.7 times 0.034 that will give us a value of 1.553 we should only have two significant figures so that is going to equal 1.6 and then we're going to look also at problem d so we're going to look at 0.2465 we're going to go ahead and multiply that by 25 and then we're going to divide this whole number by 1.78 so let's go ahead and look at our count so in 0.2465 that has four significant figures 25 has two significant figures 1.78 has three significant figures let me go ahead and move that three underneath so that you don't think it's actually part of the problem it's just our account so when i carry out this calculation i get 3.462079 since we're multiplying and dividing we need to have uh the significant figures with the least numerical value in this case it's 2. so 3.4 i should have this underlined is red so 3.4 and now we need to round that so 3.46 is equal to 3.5 and so now our answer has two significant figures so we're good to go there so again you'll have a lot of practice working on reporting significant figures so let's go ahead and look at section 2.4 section 2.4 is all about prefixes and equalities so the most common prefixes in chemistry is kilo and that's to 1000 or 10 cubed centi is also very common 0.01 which is 10 to the negative 2 and we abbreviate that as a lowercase c milli is abbreviated as a lowercase m and that is 0.001 or 10 to the negative 3 and then micro is the other common uh numerical or prefix in chemistry and that is this greek letter greek symbol mu and that is 0.0001 or 10 to the negative 6. those are the most common prefixes used in chemistry so let's talk about that a little in a little bit more detail so when we're measuring length let's say you have a ruler and you're measuring oops sorry that should be a half so let's say that this is one centimeter on your ruler well you can say that one centimeter is equal to 10 millimeters you can also say that [Music] 0.1 meters is equal to one centimeter sorry 0.001 i missed a decimal place there so i wanted to verify 0.01 meters is equal to 1 centimeter so you can say this distance is 0.01 meters as well you can also say that this distance is 10 millimeters it's all saying the exact same thing again we're not talking about converting in between these units yet we will get there so when we're measuring volume when we're measuring volume that is in three dimensions and that is your length times your width times your height so if you have a cube you have your length [Music] you have your width how far back this goes and then you have your height which is this dimension here up to down so length times width times height let's say your length is equal to one centimeter your width is equal to one centimeter and your height is equal to one centimeter its length times width times height so that'd be one centimeter times one centimeter times one centimeter which is equal to one centimeter cubed and we call this one milliliter so you could have one cubic centimeter is equal to one milliliter and that is because again for measuring volume you have three dimensions so right now we're not talking about interconverting we're just trying to understand the different unit conversions but we're not converting from one size to another size so we can also measure mass and that would be if you have 1000 grams that's like saying that you have one kilogram if you have 1 000 milligrams that's also saying that you have one gram so that is how you can interconvert using mass so we're going to complete the following relationship so problem number 2.39 which is completing the following relationship so if you have one meter that is equal to 100 centimeters and if you have one millimeter that is equal or excuse me one meter if you have one millimeter sorry i had this in my notes um you have one times 10 to the negative three meters so that is that relationship so you'll have a lot more homework problem practice and 2.39 so now we want to talk about writing conversion so section 2.5 so section 2.5 is writing conversions and so this can be the hardest part of this chapter for a lot of students so there will be again lots of practice in writing conversion so you'll want to get very comfortable with this chart so these are very common conversions so i would go ahead and take a screenshot or something of this chart have access to it because we will be using it when we carry out our calculations so let's say we want to we're asking ourselves how many pounds in 13.6 kilograms you always start with what you know and you always end up to what you want so in this case what we want is pounds and what we know is kilograms so we would take 13.6 kilograms and we know that we have 1 000 grams and 1 kilogram and we also know that one gram excuse me one kilogram uh sorry one gram one pound has 454 grams so let's talk about what i did here because you saw that i actually was moving my numbers around quite a bit so i have my kilogram in the numerator and my kilogram in the denominator so those units need to go ahead and cancel out and remember if you have let's just say 365 divided by 365 that is going to give you a value of 1. so if you have a unit in the numerator as well as the denominator those are going to cancel each other out so you had your kilograms in the numerator so your kilograms needed to be in the denominator of the second portion of your picket fence then you have your grams for every one kilogram you have 1 000 grams so your grams are in the the numerator so therefore you need to put your grams in the denominator and now you have your pounds in the numerator which is exactly what you want so you would carry out this conversion and you would get 29.92 pounds so now let's go ahead and think about our significant figures in our first numerical value we had three significant figures remember this is your exact conversion so we're not going to go ahead and include that in our significant figure count and this is also an exact numerical value or exact conversion so we do not need to count that in our significant figure count so we should have three significant figures so 29.92 rounds to 29.9 pounds and you have three sig figs reported so that's when it becomes really important in understanding when you report those significant figures so you'll get lots of practice um especially in 2.6 about conversions so go let's go ahead and look at sample problem 2.7 and levsin is used to treat stomach problems and is available as 0.125 milligrams per 1 ml solution so the way that we can write this is 0.125 milligrams for every one milliliter of solution or we can say in one milliliter of solution you have 0.125 milligrams of lepsin so there's always two ways to write the unit so one milli one milliliter is it is an exact number and then you have 0.125 so you have three significant figures so that is how you can approach a problem is you're not only looking at what is the actual unit conversion but how many significant figures are there so you always want to ask yourselves both questions so now let's actually work on problem solving so this is the section that can be very difficult so problem solving we've seen a little bit in the last section problem solving using conversions so uh we're going to go ahead and look at our slide because that is where the problem is written down we're looking at problem 2.8 so greg's doctor ordered a pet scan of his heart and in the radiological imaging dosages of the pharmaceuticals are based on your the body mass if greg weighs 164 pounds what is his mass in kilograms so again we're always going to start with what we know and where we want to go so what we know is greg weighs 164 pounds so we're in pounds we know our pounds and what we want is our kilograms so we just need to know how to go from pounds to kilograms we've seen a problem very similar to this so we know greg weighs 164 pounds we also know that one kilogram has 2.02 2.20 sorry 2.20 pounds so in the previous example uh i went through it a little bit longer we're going to go ahead and see that as well in one second so your pounds are in the numerator and your pounds are in the denominator so those units will cancel each other out so 164 divided by 2.20 leaves you at 74.5 kilograms let's say you did not know that exact conversion no problem what you can also say is you have 164 pounds we know that one pound contains 450 grams so your those are going to your units will cancel and then we also know that in one kilogram there is 1 000 grams and your units of grams will also cancel and that should also still give you 75.74.5 kilograms so either way you do it you should be able to get to the exact answer this is a two-step conversion because you're going exactly from pounds to kilograms but you may not have that conversion at hand what you have might have is that you're going from grams to pounds and then grams to kilograms which is no problem this is a three-step conversion but what you'll see is whether you go the two steps or the three steps you'll be able to get into the get the exact same answer so sometimes you're gonna have more than one conversion that you're gonna need to carry out this was nice because you were just going from pounds to kilograms so that was one conversion sometimes you might need two or more conversions for example study check 2.9 so a bottle contains 120 milliliters of cough syrup if one teaspoon which is five milliliters is given four times a day how long will that bottle last before a refill is needed so what we know is that we can think about your bottle and i'm a terrible artist so please forgive me but you can think about your bottle and that has 120 milliliters if one teaspoon is five milliliters so one teaspoon is equal to five milliliters and we need to give that four times a day that means we're going to go through 20 milliliters every day so what we know is that we have 120 milliliters of solution or cough syrup and that is going to last you you're going to you're gonna divide that by 20 milliliters per day that means that the solution will give you will last you six days total so let's go ahead and set that up we have 125 mil 120 milliliters of cough syrup and in one day we're going to go through 20 milliliters of cough syrup so 120 milliliters divided by 20 is going to be that that will last you six days your units cancel your milliliters of cough syrup are going to cancel and now you're left with how many days that you have so there is definitely sometimes you'll need to carry out more than one type of conversion and that was our second conversion was that we were using five milliliters four times a day so we needed to take that into account so again there will be lots of practice in your homework i would strongly recommend getting working on that and then you can ask me any questions that you might have um with in office hours so now the last thing that we want or the last section that we want to look at is density so 2.7 which is density density is equal to mass per volume that is the definition of density so let's go ahead and look at some types of uh excuse me at calculating a problem and then we're gonna we're looking going to look at two different problems so again your density let's um remember that density is equal to mass per volume that is your equation so you have your hdl is a type of cholesterol sometimes called good cholesterol and it's measured in blood tests so if you have a 0.258 gram sample of hdl and that is in 0.215 milliliters of your blood what is the density per milliliter so your density is equal to mass over volume so we're told that we have 0.258 grams of hdl 2.58 grams and we have that's our mass our volume is 0.215 milliliters so 0.215 milliliters so that is going to be 0.258 divided by 0.215 is equal to 1.20 grams per milliliter and let's go ahead and look at our significant figure count you have three significant figures in the numer numerator and you have three significant figures in the denominator so your answer should be reported in three significant figures and it is so that is one way of looking at density the other way of looking at density is through volume displacement and this was discovered by archimedes so we'll go ahead and look at that example so he had a crown and this crown was an odd shape and it was made of gold he wanted to know what how much gold was in his crown so what he did was he discovered that he could do volume displacement when he was in the bathtub he actually discovered this so let's say for example you have a known volume and you measure this in a graduated cylinder because this crown is an odd shape you can't just measure the length times width times height because remember volume is length times width times height but again because your crown is oddly shaped you can't just simply measure that so what you can do is you can have a known volume so you start with 100 milliliters then you're going to put the crown inside that graduated cylinder and then you're going to see how much volume was displaced and read the new measurement so let's say for example this happened to go up to 167 milliliters so what we know is that the volume displaced is 67 milliliters and i'm getting that by 167 milliliters is your final reading minus 100 milliliters which was your initial reading that's going to give you 67 milliliters so again your 167 is your volume your final volume subtracted that from the initial volume is equal to the volume displaced okay that is how you know how much volume was displaced you also are given that the mass of the crown this has to be given was 1293 93.1 grams so you need to have two out of the three values otherwise you can't solve the equation so remember that density is equal to mass over volume we know the mass of the crown was 1293.1 grams the volume of the crown the volume displaced excuse me was uh the volume of the crown as well was 67 milliliters so if we take that value what we find is that we have 19.3 grams per mil and in fact that is the density of gold so his crown is made of gold so there are two different ways of calculating volume one is through volume displacement and one is through uh if you already have everything in terms of the way that uh hdl for example of hdl where you had a certain gram per unit volume it's two ways of calculating density excuse me so just to summarize in today's lecture lecture we went over chapter two and we talked about the units of measurement in section 2.1 in section 2.2 we talked about significant figures and when they're significant so you'll have lots of practice in section 2.3 we talked about significant figures in calculations so you'll want to know how to do that in section 2.4 we talked about prefixes and we talked about um kilo we talked about excuse me spell this correctly we talked about kilo we talked about senti milli and micro are the most important prefixes for this class we talked about writing conversions which is section 2.5 which was writing conversions in section 2.6 we've actually talked about problem solving using conversions and then i'm going to go ahead and highlight this in this hot pink color this is super important this is one of the most important skills in this class and then in section 2.7 we talked about density and in when we talked about density we talked about uh mass per volume and we also talked about volume displacement so lots of practice in your homework if you are still finding that you're struggling on some of the homework problems please do not hesitate to come see me in office hours and that wraps up chapter 2.