Rob Lederer: Avogadro's law is pretty straight forward. If you keep the pressure and the temperature constant for a gas, then the only way that you are going to actually expand the volume is to actually put more moles of gas in and so therefore, at constant temperature and pressure, the volume of the gas and the number of moles of that gas are directly proportional. So V1 over N1 equals V2 over N2 and that's Avogadro's formulae. Don't use it too much because it is kind of obvious. but anyway, if you were to graph that, well if you had a zero on number of moles, you'd zero volume, so you can start down there at the zero mark and you work up in the a directly proportional manner. Here is the thing. Avogadro came out with 6.02 times 10 to the 23 because, all gases at pretty much room temperatures and pressures can be treated ideally. that means pretty much the same as each other. So, there is an ideal gas law that can be formed from Charles law and Boyle's law and Avogadro's law all combined. You need not memorize the other formula, though you should know those graphs. those other three formulas, get them on your head because, you can use only this one to derive all the others and then some Pv=nRT, PvnRT, that's what its called and PvnRT, where R is universal gas constant will actually be able to solve all of your mathematical needs in the gas unit. Now, 8.314 is the collected constant K for all of those other formulas together and we call that rnl. 8.314 kilopascals times meters divided by Kelvins divided by moles. So kpals per kmole. If you memorize this number and just have it handy all the time. 8.314 kilopascals liters per Kelvin mole, you can solve problems like this. And watch this. There are 30 milliliters of gas at 200k and 150kpa and you are going to warm it to 300K, the temperature is going to go up and the volume goes up to 40mils. But what's the new pressure? Now that's not a Boyle's law to question or Charles law question. Its kind of combine both of them. So, what do you use to figure out the answer. PvnRT, you use PvnRT. that's all you need. PvnRT. But, here is the thing. You are going from an initial pressure and volume and temperature to a final pressure, volume and temperature. So, how do you use this formula. Watch the manipulation of this formula. PV equals nRT, okay. If I take every one of the variables that undergoes a change in this question and isolate them on one side. Then the other side must equal a constant number when multiplied to get it, watch. P and V change in this question so does T, temperature changes too. So we divide each side by T. here is what we get. PV over T equals nR. These all change, V stands the same. if those two numbers stay the same, in this question from the initial to the final state, then Vs are a constant K and remember, if V is our constant K, then here is what happens. If you change this from an initial condition to P2V2 over T2, you get a final condition and ladies and gentleman that mean then, that PvnRT just gave you P1V1 over T1 equals P2V2 over T2. Some people memorize that formula and call it the combined gas law. I will memorize anything expect PvnRT. Now let's plug in the numbers. Here is your combined gas formula. There it is right there. P1V1 over T1 equals P2V2 over T2. In our solvent for P2 here, the new pressure. So, we have to divide each side by V2 to get the rid of the V2s and we have to multiply each side by T2 to get the rid of the T2s. so, see that's how you do that formula manipulation in order to solve for P2. So, P2 equals P1 V1 T2 over V2 T1. Okay, that's a lot of stuff to actually put in. now, a lot of people will write down all of the numbers in the question down the side then plug them in, that's fine if you do that. So, P1V1 is your 150KPA your volume 1 is 30 milliliters your temperate 2 is 300K, your volume 2 was 40 mills and your temperature 1 was 200K right there. You do that math right there, plug everything in, where milliliters cancels mil