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# Deriving the ideal gas law

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### Deriving the ideal gas law

1. 1. L. Allen Stonington HS Holt Modern Chemistry, Chapter 11
2. 2.  Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Amadeo Avogadro, the ugliest of the dead chemists
3. 3.  If we can fix, for example, the temperature and pressure at STP, we can then compare how many molecules are present by simply comparing volumes. We find that one mole of any gas – ANY gas – has a volume of 22.41410 liters.
4. 4. What does this mean? For starters, if we convert any amount of gas at any temperature and pressure to STP using the combined gas law, we can convert the resulting volume to moles using this conversion factor. Image from TutorVista
5. 5. How many moles of gas are present in 46.5 liters of gas at 28 ° C and 2.75 atm of pressure? Strategy? Use the 4-Step method to solve for V2, then use dimensional analysis to convert from liters to moles  4-Step method Write the given Rearrange the equation  Plug in numbers and units  Solve  
6. 6.       P1 = 2.75 atm V1 = 46.5 L T1 = 28 ° C + 273 = 301 K P2 = 1.00 atm V2 = ? T2 = 273 K 
7. 7. PLUG IN VALUES WITH LABELS  DOES THIS MAKE SENSE?  Notice, BTW, that the pressure goes down, which will make the volume go up. Also, the temperature is lower at STP; that makes the gas shrink. This is consistent with what we see as we disaggregate the parts of this equation.
8. 8. SOLVE  V2 = 116 Liters at STP (3 sig figs) USE DIMENSIONAL ANALYSIS TO CONVERT FROM LITERS AT STP TO MOLES. 
9. 9. Shouldn’t this be easier? If we know that 1 mole = 22.41 L at 273.15K and 1.000 atm, can’t we organize our work so that we don’t have to do this step by step? Can’t we come up with some kind of multiplier, something to include the 22.41, the 1.000 atm, the 273.15 K? Let’s fool around with the math… Random mole from internet, lost url
10. 10.  
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13. 13. Gosh, if I can calculate moles, I can find mass, or number of molecules… wait a sec, isn’t this how the stoichiometry chapter got started?
14. 14.    End of chapter 11, page 392 #40-52 Do NOT ignore sig figs. We always use one more sig fig in “book values” than in the givens, so that when we round back, we get the right answer. There is actually one correct answer for each question. image fromwww.bowlinggreen.kctcs.edu