 Okay let's try some examples. I'm going to work through these examples using the unit conversion format that I've shown you previously. Remember though that it's just as valid and you may prefer to use the formula that I've shown you on the mole map. Okay, first example, if you have 1.9 times 10 to the 22 molecules of caffeine, how many moles of caffeine is this? So we write down what we know as a fraction. And then we think about what conversion factor we need. If we go back to our mole map, the conversion factor between number of particles and moles is Avogadro's number. So we know that 6.022 times 10 to the 23 particles, in this case our particles are molecules, so I'm going to write molecules, is equivalent to 1 mole. And just as in unit conversions we can write our conversion factor one way or the other. We can have 6.022 times 10 to the 23 molecules over 1 mole, or we could write it the other way up. It is completely equivalent either way. Which version you use depends on which unit you're trying to cancel out in your calculations. Here we want to cancel out molecules and be left with moles. So we're going to choose the version that has the 6.022 times 10 to the 23 molecules on the bottom. We can then cancel out the molecules and we're left with moles. When we run through the calculation it looks like this, and the answer it gives us is 0.03155 moles. Now we should check significant figures. If we look back we find that the number of molecules we were given at the start of the problem has two significant figures, the 1.9. So we need to round our final answer to two sig figs as well. Now just a quick reminder, if you plug these numbers into your calculator and you didn't come up with 0.032 moles, one possibility is this. When you enter the number into your calculator you need to make sure that you use this button to put in the exponent. So for instance to enter 1.9 times 10 to the 22, I would enter 1.9, then I would press the times 10 to the button, and then put in the exponent 22. Now if I add equals you can see that formats the number correctly. Avoid the temptation to use this function here. On some calculators this may actually have its own button. On this particular calculator emulator it has it as one of the shift functions. But it is possible to put in 1.9 times, and we use the shift function to get 10 to the, and then type in the exponent like that. That looks exactly the same. But when you do calculations using this number entered in that way, the calculator doesn't treat it as a single number. It treats it as 1.9 and separately as times 10 to the 22. That may not seem like a big deal but when you get into order of operations it means that the calculator misunderstands what you want to do. You could try it now. Try doing this calculation 1.9 times 10 to the 22 divided by 6.022 times 10 to the 23. Try it first using the times 10 to the button that you've got. And then try it again using the shift function or whatever the equivalent button is on your calculator. You should see a difference in the answer. So let's try the next example. We're given a mass of sodium, 0.21 grams, and we're asked to convert this to moles of sodium. So I'll first write down what I know. There's my mass. Now I want to convert from mass to moles. So the conversion factor that I'm going to need is the molar mass. So I need to go to the periodic table and I need to find sodium and find the molar mass of sodium which is 22.989 grams per mole. Now in this problem I want to cancel out the grams and turn it into moles. So I'm going to have to turn my molar mass conversion factor upside down so that the grams is on the bottom and the moles is on the top like this. The grams now cancel out and I'm left with moles. I just need to run through the calculation and I find that it comes out as 9.1348 times 10 to the minus 3 moles. Now I need to look back at the values that I used in the calculation to find the lowest number of sig figs and that's the mass which is given to two significant figures. So I'm going to round this to two significant figures giving 9.1 times 10 to the minus 3 moles. Okay, another example. This time we have 0.21 moles of chlorine gas filling a jar at STP. Remember that's standard temperature and pressure and we want to know what is the volume of the jar. So this conversion is going from moles of chlorine to volume of chlorine and the conversion factor that we're going to use is the molar volume which is 22.4 liters per mole. What I know from the problem is that I have 0.21 moles of chlorine and I need to arrange my conversion factor so that the moles cancel out and I'm left with liters because I'm looking for the volume. So the way that I've written the conversion factor here with the leaders on the top and the moles on the bottom is the correct way around for this problem because it allows the moles to be cancelled out and I'll be left with liters which gives me 4.704 liters. Again I check my sig figs. I had two sig figs in my original volume so I round my final answer to two sig figs as well.