Male Speaker: Sodium chloride, sucrose, H2O. Well, what's the similarity between three of these compounds right here, certainly in terms of their quantities it doesn't seem to be anything similar or you would be wrong in saying that, even though that there are around 58 grams of salt here over 340 grams of sugar here and 18 grams of frozen water here. Each one of these represents what we call 1 mole of the compound, there is 6.02 times 10 to the 23 sodium chloride ionic units in here, 6.02 times 10 to the 23 molecules of sucrose, 6.02 times 10 to the 23 molecules of water, that's Avogadro's number, here comes the mole.
Now those balancing numbers in front of those equations, I told you they represent something called the mole. Now what is a mole? Well, actually the mole is a convenient number of things in chemistry and okay well it is a convenient number but it looks kind of weird, 6.02 times 10 to the 23. If you have that number of things you have yourself one mole of things and that mole is actually written mole, the abbreviated mol, don't ask me why, we just dropped e and call in abbreviation but this is the number of things there are whatever those things are in a mole.
Now it was Avogadro, who came up with this, so that's his number, Avogadro's number and he came up with this based on gas laws and observations he made by taking elements in their gaseous phase and being able to determine that a certain quantity of these gases had in them 6.02 times 10 to the 23 numbers of molecules or atoms and so therefore we call that a mole. Its actually convenient number because 6.02 times 10 to the 23 atoms of various elements can then help us to get a convenient handle on their masses and we will come to those molar masses in just a minute.
So this number looks kind of imposing but really is going to be able to help us in chemistry but let's take it just out of chemistry for a second, just use it as a number and I am going to show you how to set up calculations with unique cancelation that is absolutely violent to be able to do in chemistry. With that 3.00 moles of trucks, so how many trucks do we have? That's a lot of trucks, okay now that's a crazy amount of trucks and you think with this planet could actually hold those amount of trucks listen to this. If you had one mole of little green peas, a green pea is, look at that big, green peas 250 planets, the size of the earth frozen over as a solid ball, cover that ball one meter deep up to your hip in peas, 250 planets size of the earth one meter deep in peas that 6.02 times 10 to the 23 peas, that's one mole of peas, do you realize that if you believe that the universe is actually 15 billion years old, that there hasn't even been a mole of seconds since the beginning of time, hey I'm not kidding, ask the way the mole is, it is such a enormous number, it is so difficult understand and yet you can hold a mole of something in your hand, that's how small atoms and molecules are, unbelievable.
Now three moles of trucks would occupy a heck of a lot of planets, okay how many trucks would you have, if you have how many trucks I got If I had three moles of trucks this is the way you do the calculation watch this. If you have 3.00 moles of trucks and you want to convert that in -- to be able to just find out how many trucks you have, then what you need to do is multiply by a ratio and is everything is ratio, so watch this, it is just beautiful the way it works. Do you want moles of trucks in the end, no, so you always put the number of moles or the unit, moles of trucks in the denominator, so when you multiply these two out moles of trucks in the numerator and denominator where they will cancel each other and you will be left with what you want in the end which is worth though.
For every one mole of trucks, how many trucks are there, its right, now I have those number 6.02 times 10 to the 23 trucks, so now look at the ratio that I set up, I've got moles of trucks multiplied by 6.02 times 10 to the 23 trucks over one mole of trucks, now you can say, yeah yeah -- I could have done this long time ago by just multiplying three times that number I get the answer. So leave me alone, no, I won't, I wont leave you alone because this is the way to set it up and you have to show unit cancellation and you might not like that, I haven't run into one student that actually likes this in 20 years of doing this or more but I tell you what, this is the best way to be able to get your head around calculations because if you start here the ones that come up later that are so involved and so difficult are going to be but if you just rely by going on the -- not doing unit calculation forget, I am sorry, I didn't mean to -- right batches of teacher but this is very important stuff.
I hope you understand that I only mean good. Now look, 3 times 6.02 times 10 to the 23 over one that's going to equal in the end you are going to get the number 18.06 times 10 to the 23 trucks because the moles of trucks cancel here and here. Now nobody write scientific notation like that, you have to actually move the number the decimal one over because scientific notation its number than decimal in the rest of your digits or we have to be something called significant digits.
We will continually enter into significant digits as we go through calculations here but for now just follow the long, pick it up as we go. This number really is 1.806 times 10 to the one while I actually took this big number, made it smaller so I'm going to make this number bigger to compensate, so its times 10 to the 24 trucks and this number has three significant digits. This number has three significant digits, three here, three here when you multiply or divide, you keep the least number of significant digits or significant figures if you will, so this number has four, you're not allowed to keep four, you are only allowed to keep three here, when you multiply or divide and so one, two, three.
So the answer is going to be 1.80, no it's not because that zero is followed by 6 and that's going to round up, so its 1.81 times 10 to the 24 trucks times a lot of trucks but does the answer make sense. Look three times this number has to be a number that's greater than 6.02 times 10 to the 23, three moles of trucks is more than 6.02 times 10 to the 23 trucks. Oh yeah, its 1.8 times 10 to the 24 trucks, this number is bigger than this number it make sense always go back and think about your answer, see if it make sense. Here is another one.
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