MGM Chemistry 1 Conversions
Aug 16, 2008
Conversions and Density Problems in Chemistry 1
Hey guys, it's miss Laverne and today we're going to talk about conversions and density problems. But before we get on to conversions and density problems, we're going to talk a little bit about something called accuracy and precision. First of all, we're going to define these two accuracy. Is how close you are to the correct answer. It's how close you how close you've got to what you wanted to get. Now that's different from precision. And I think we talked a little bit about precision when we did significant figures. Precision is not how close you are to the correct answer precision is how close your answers are together.
So for example, let's say that you were measuring a block of wood in the lab and one lap group got the mass as 5 grams, another group or another person in your life group at the mass is 5.1 gram. And a third person in your lab group measured it and got 5 grams. And I told you that the true answer or the correct math for that block was, 5 grams. You would say that these measurements were accurate. They were very close to the answer that you should have gotten, which was 5. They were also very precise because all of the measurements were very, very close together. Now let's say a second lab group tried to measure the mass of the block, and they've got 8.9 grams. 8.8 grams, and 9.0 grams. Now, they did not get the answer of 5 grams that they were supposed to get. So these were not accurate. So they were not accurate in their measurements. However, they were precise in their measurement, which means they did something wrong, but they did that same thing wrong every single time.
All right, the third option was that we have a third lab group, and they measure the math as 10.8 grams, 1.2 grams, and 27.3 grams. We would say that this set of measurements were not accurate and they were not precise. They weren't close to the 5, which made them not accurate, and they're not very close together at all, which also makes them not for size. Let's look at the same thing, but we're going to look at some dark boards and see if we can decide a little more about accuracy and precision. So we've got this dartboard here. And I want to know if the accuracy is good or bad, and I want to know if the precision is good or bad. Accuracy. Don't forget accuracy is how close your to the correct answer and in this case, the correct answer is this bull's eye right here. It's hitting what you want to hit. So we would say the accuracy in this case was very, very good. You hit the bull's eye three times in a row.
Now as far as the precision, don't forget precision is not how close you are to the correct answer, precision is where your answer is close together. We would say that these darts are very close together that our precision is also good. Now let's look at a second example of a dart board. All right, this time we got three more darts. And the darts did not hit the bulls at this time. This time they hit somewhere in the upper right hand corner. Now the accuracy, don't forget accuracy is how close you are to the correct answer. We would say the accuracy was bad here. They did not answer the bull's eye which is exactly what they wanted to hit. They didn't hit that to the accuracy of that. However, the precision and don't forget precision is how close your answers are together. They're darts are very close together, so we're going to say the precision in this case is good. Start one more look at another dartboard. All right, again, the same two questions. Is the accuracy good or bad and is the precision good or bad? This one's probably easy to figure out. None of the darts hit the bull's eye. So we're going to say the accuracy is bad. And none of your darts are close together.
So we're also going to say that the precision is that. Let's talk a little bit about dimensional analysis now. Dimensional now. All right, I'll dimensional analysis is a big long word that means you're going from one unit to another unit. If any of you ever have converted from inches into feet or maybe years into days or years into minutes, then you've done dimensional analysis, all dimensional analysis is, is changing units, changing from one unit to another unit. So dimensional amounts is a method of problem-solving that focuses on changing your units. All dimensional analysis is going from one unit to another unit. Now, when you do dimensional analysis problems, you're going to be using conversion factors. You're going to be using these a lot. Now conversion factors are just an equal ratio that you used to go from one unit to another. And you probably use conversion factors before and never realized they were called conversion factors.
For example, one bud equals 12 inches that's never going to change at the constant, now instead of writing it with an equals sign in between, these conversions factor said, we're going to write them in a ratio and a ratio is kind of like a fraction. It's like writing one over the other. So we're going to rewrite one foot equals 12 inches as one foot over 12 inches. You could have also written that as 12 inches over one foot and it's going to be the same conversion factor. Again, the conversion factor is just equal units or equal ratios in with one over the other. It's a ratio of equal units. Now, the next one is rules for dimensional analysis. This should actually say steps. These are the steps we're going to follow for every single-dimensional analysis problem. And the first one is going to be beat into your head in this class.
Rule number one or step number one is you always always start with a given. Before you do any kind of problem, you need to make sure that you're writing down all of your givens. The next step is you're going to draw an X and a line or multiplication time and align. The third step is you're going to place the unit that you want to cancel on the bottom of that line that you just drew. Step number four, you're going to apply the conversion factor on that line. You just draw it. So you're going to put a unit on the top now, and you're going to fill in some numbers. Step number 5, please don't forget to step you're going to cross out your units and see what you have left. But in order to cross that unit, you have to make sure you have one unit on the top and one unit on the bottom. If you have two at a time, you need it on the top, they do not cross out. You have two on the bottom, they do not cross out.
The only way you can cross out is to get one on the top, and one on the bottom. Let's try an example. We're going to convert 32.5 inches into feet. Now make sure you have your steps out in front of you. The first step was to always start with a given. So we're going to write down our given, which was 32.5 inches. All right, the second step was draw an X and a line. So we're going to draw a little multiplication time. With a line, and the third step was put the unit that you want to cancel on the bottom. Well, we don't want inches and we're going to put inches. On the bottom. All right, you should be able to get through this much before you have any kind of problem. So before you ask me a question, make sure you've at least gotten to this point. Write down your given drawn XL on, put the unit that you wrote across that on the bottom. Now we've got to figure out what we want to get to.
We want to go from inches to feet. So the first question you need to ask yourself is do I know a conversion to go for inches defeat? And you should, we can go from inches to feet. Now you're going to fill in numbers. You should know that one foot is the same as 12 inches. So now you filled in your conversion factor. Now we are going to get a step number 5, which is cross out your unit. Please don't forget this step because when we get on the stoichiometry and limiting reactant problems, you're going to have a lot of these problems going on at once and you're going to need to make sure that you know what unit you have left. So we have an inches on the top and it's just on the bottom that we're going to cross now. And you have the left. And what you wanted and feet is what we wanted. So that means we can stop right there. All right, now the work these problems, you need to make sure you multiply everything across the top, and you divide by everything across the bottom.
So we're going to put 32.5 divided by 12, because I don't need to worry about that one. That gives me the answer is 2.70 8 with some repeating three. Now, we're missing a couple things here to make sure you get full credit for this answer. The first thing you need to make sure of is that your answer is in the right number as significant figures. So make sure you have the right number of safety. Now this conversion factor here is what we call a constant. And we learned the other day that constants have an infinite number of sig figs. Now let's look back at our given. Our given head three safety and we're most flying and dividing here so we look at the number of sake bags. If you're looking between three and infinity three is always going to be smaller than infinity, anything, it's going to be smaller than infinity. So the only thing we're going to look at for sig figs when we're doing dimensional analysis is you're given. So make sure your answer has the same number of sig figs as you're given.
Okay, so if we're going to change this into three sig figs, we're cutting it off after the zero. We're going to look after the zero and we have an 8. So this should become 2.71. The second thing you need to look at is make sure you put your unit. We don't want any numbers without units. That doesn't tell us anything about what's going on with the problem. We had feet left so our unit is going to be defeat. The last thing I want you to do is make sure you circle your answer. Okay, that way I can find it. Either circle it or highlight it, but make sure that it's easy for me to find. So once you've done this, you've got full credit, you move on to the next problem. The next one we're going to do is how many seconds or an 82.95 minutes. We're just going to go step by step. You're sorting out with 82.95 minutes, so we're writing down our given, the next step was drawn X, and a line, and the next step with the unit you want to cancel on the bottom. So we're going to put a minute on the bottom. Now, I want to go from minutes to seconds. And I do know conversion in my head for that. So I'm going to put seconds on top of the line. And now I'm going to fill them on numbers.
I know that there are 60 seconds in one minute. So I'm going to cross out my units, and I'm left with what I wanted, which was seconds, and now I'm going to put that much calculator. Because everything's on the top, I'm going to multiply, so I'm going to say 82.95 times 60, that can be 4977. And I'm going to check my thick mix. I had four in my given, so I want four, and that's what I have. I need to put my unit, which is seconds, and lastly, I'm going to circle my answer. Let's start with where you have to change two units at once. So we're going to convert 65 mph to kilometers per second. And I tell you in the problem that there are .625 miles in one kilometer. Now there's a problem here. Most of you are going to want to write 65 mph at 65 MPH, but that really doesn't give you anything that you know where to cross out what to put on the job what to put on the bottom. But what you need to understand here is that 65 mph means that you're going 65 miles in one hour. So anytime you see a purr, you need to rewrite this kind of as a fraction. Or as a division problem. So we're going to say, when we write our given, we have 65 miles for every one hour or 65 miles per one hour.
This is the same thing as writing it at 65 miles MPH, but it's going to give us a little more information when we're trying to do this dimensional analysis. So I've written my given down in the next step was draw X and along. And you put the unit you want to cancel where it needs to cancel. Now you got two problems here. Number one, you need to get rid of miles and change it to kilometers. And number two, you need to get rid of hours and change in two seconds. Does not matter which one you do first. We're going to start with miles. Miles is on the top. So in order to cross it out, we need to put it on the bottom. And we're going to go from miles to kilometers because I was given the conversion factor in the problem. So we're going to go for miles, to kilometers. Now in this problem, I see that the one, you guys with kilometers, and .625 .625 goes with miles. So now we're going to cross out mild to miles, and we're left with kilometers per hour. That is not what we wanted, so we're going to draw another X and another line. We're going to keep going. Now don't want to get rid of this kilometers. But I do want to get rid of this hour. If you look hours of on the bottom. So to get rid of hours now, I'm going to have to put it on the top.
Now, most of you don't know conversion to go straight from hours to seconds, but you can go from hours to minutes. So we're going to convert from hours to minutes, knowing that one hour is 60 minutes. Now I need to cross out. So I'm going to cross out hours on the bottom, with hours on the top. Now I'm left with kilometers per minute that is still not what I wanted. I want to kilometers per second. So I'll keep going. Draw another X and another line. I want to keep the kilometer, so I'm not going to mess with it, but I don't want the minute. I need to get rid of it, and right now it's on the bottom. So to get rid of it, I need to put it on the top. And I'm trying to get to seconds, and hopefully you do know in conversion between minutes and seconds. You know that there is one minute for every 60 seconds. So we cross out minutes and minute, and when the more left with kilometers over seconds, which is exactly what we wanted. So make sure you multiply everything across the top and divide everything across the bottom. So we're going to say 65 divided by .625 divided by 60 divided by 60. And that gives us our answer is point. Two with repeating 8. So that's going to thick big, round two, two, 9, and my unit is kilometers per second. And you circle that, you're done with this problem. Now we're going to talk about how to convert with prefixes. They're done in the exact same manner.
You start with your given, you keep drawing X's and lines until you get to what you want. You keep crossing out till you get to what you want with the problem is you have to know your prefixes. And yes, ladies and gentlemen, you must memorize these easy way to do it is to go ahead and make yourself a set of flashcards. All right, you need to memorize the prefix. You need to memorize the symbol and you need to memorize the value. Which is a number in scientific notation. All right, so make sure you pass this and you copy this down and make yourself out some flashcards to remember these. Now, when you do these problems, which prefixes the steps are exactly the same, you start with your given, you draw an X in the line, you keep crossing out until you get what you want, but there are a few differences. If you're working them out, we're going to try and work them out in the same way every time.
You need to remember that the number one is always going to go with your prefix. So those are prefixes like Giga, mega kilo, desi senti, any of those words, you're going to stick the number one with. The number and scientific notation is going to go with your base unit. So there's numbers in that column that said value that one times ten to the 9, one times ten to the 6th, one times ten to the third. That's always going to go with your base unit. The other thing you need to know is that you can only go from a prefix to a base unit. In one step, you can't go straight from Giga to femto in one step. It's going to be two steps. All right, so let's look at an example. We're going to convert a hundred nanometers into meters, and we're going to use the exact same steps, which was number one, start with your given. We're going to start with a hundred nanometers. We're going to draw an X in a line. We're going to put the unit. We want to cancel out, which is nanometers, on the bottom.
Now, you can only go from a prefix to a base unit, the prefix is nano, which means the only thing we can really go to here is meters, which is good because that's what we wanted. Now that you have your unit filled in, we need to put in the numbers. I said that the number one always needs to go with the prefix. The prefix in this case is nano. So one is going to go with nanometers. That number in scientific notation is always going to go with the base unit. So if you look up NATO, this number in scientific notation was one, times ten to the negative 9. That's going to go with the base unit. All right, we're going to cross out and animators in the animators. We have what we wanted left, which is meters. So we're going to put this in our calculator. So we're going to just have to 100 time. Don't forget to put this in your calculator as one EE negative 9. And that leaves me with one times ten to the negative 7th, my unit is meters and my fig figs are correct because this given had one thickening. So I'm going to circle my answer and I am done with that problem.
Now this time we're going to go from a prefix to another prefix, but remember I said, if you could not do that in one step, it was going to take two steps for this. So we're going to start with our given, which is 785 millimeters. We don't act in a line. Millimeters is going to go at the bottom, but you can not go from millimeters to kilometers. You can only go from a prefix to a base sheet. And if you have millimeters, the base unit of that is going to be meters, right? So now we're going to put it on numbers. The number one goes with the pre banks. In this case, the prefix is Millie, so we're going to just take a one there. And the number that goes with the base unit with Millie is one times ten to the negative three. Now you're going to cross that. You can cross out Millie and Millie, and you're left with meters, but that's not what you wanted. You want it to kilometers. So you're going to draw another X and a line. You put the you want to cancel, which in this case is meters. It's going to go on the bottom, and we want to go from meters to kilometers. So that's going to go on the top. And we have to fill in our numbers and don't forget the number one always goes with the prefix.
The prefix in this case is kilo. The number one times ten to the three is going to go with the face unit, which is meters. You're going to cross out meters and meters in your left with kilometers, which is exactly what you wanted. So now all you need to do is plug this into your calculator. Excuse me. So we have 7 85. It's a 185 times one EE negative three divided by one EE three. That gives a 7.85 times ten to the negative four. You're going to put your units kilometers, and you're saying things you want at three and you have three, so you are perfectly good with this problem. A couple more conversions we need to do are temperature convulsions. Three ways to measure temperature. Degrees Celsius, degrees, Fahrenheit, and Calvin, there's no debris line in front of Calvin, it's just Calvin. And there are three formulas you need to make sure you memorize in order to convert between these three. The first one is degrees Fahrenheit equals 1.8 times degrees Celsius plus 32. Now sometimes in your book or in other places you'll see this written as 9 fifths.
I know you guys sometimes have problems with fractions in your calculator and forgetting these parentheses. So I just went ahead and put that as 1.8 in your calculus or in your problem. Second one is degrees Celsius is .56 Fahrenheit -32. Again, sometimes in your book, you'll see this written as 5 9. So I just went ahead and divided that out for you. Now, in this problem, don't forget your order of operations. You have to do your parentheses first. You need to subtract first and then multiply by .56. And the last one is easy. It's Kelvin equals Celsius plus 273. So let's work a couple of these problems. First one we're going to do is convert 35°C into Kelvin. Well, I want Kelvin and I know that that was degree Celsius plus 273. So that gives me 35 plus 273, which in your calculator should give you three O 8. Now don't forget we're looking at 6. But in this problem, we're actually doing addition. In addition, you need to make sure you look at the number of death mode places. But you can not look at this two 73 for decimal places because that's a constant in this equation. So the only thing that we're going to look at, the only thing that would have some sort of error is this 35°C.
It has no decimal places, which means your answer needs to have no decimal places, but we do need to put our unit after it and make sure that you circle. That was going to be an easy peasy for you. Next one we're going to do is 55°C to paranoid. So we're looking for degrees Fahrenheit. And if you look back at your formulas, which make sure you memorize, you get 1.8 degrees Celsius, plus 32. So that gives us 1.8 times 55 plus 32. Then we have to do this in steps because you're doing multiplication and addition to here. So we're going to say 1.8 times 55 and because we're multiplying it, we're going to use sig figs and you can only look at your given and that gives me 99 and I still need to add my 32. But now what I'm adding about 32, I'm not looking at 6 figs anymore.
Now I'm looking at decimal places. So when I add those together, I get a 131, and that should be degree Fahrenheit. So you can baby step these little problems to make sure you get the right number of sick things. Next thing we're going to convert 95.8 Fahrenheit to Celsius. So we have degrees Celsius equals 0.56. Fahrenheit, -32, that gives us 0.56 times 95.8 -32. Now here's a little different you're doing the subtraction photos. So we're going to keep our .56 there and we're going to subtract these two. We got 95.8 -32, which gives us and don't forget because you're subtracting your looking at decimals, but the only difference when you look at is you're given because that 32 is going to be constant north equation. So we've got 63.8. Because we needed one decimal there. Now you multiply by the .56. And we need three 6 6 because this number has three 6 6. You don't look back at that .56. And that's going to give us our answer is 35.7° Celsius.
One more temperature example and then we'll get on to density. We're going to convert 75.0 Fahrenheit to Kelvin. But there's probably if you look back at your formula sheet, the only way you could get to Kelvin was to go from Celsius. There wasn't a Fahrenheit straight to Kelvin so we're going to have to do this in two steps. First thing we're going to have to do is convert this to Celsius. So we have degrees Celsius equals .56 airline -32. All right, so that's going to be .56 times 75.0 -32. Got to do this in baby steps. So that's going to give us .56 and the 75 -32 gives us 43, but make sure you keep that .0 there for your depth of light. Then a multiply that by point 5 6. That gives us our Celsius answer as 24.1°C. But that's not what I wanted. I wanted it in Kelvin. Now to get Kelvin, you just say Celsius, plus two 73, which was 24.1 plus two 73. And that gives us what you stick it in your calculator. 297.1 Kelvin. All right, you should be converting temperature pros by now. Now we're