Monday, March 16, 2009

A Pleasant Surprise!

This week's chapter of chemistry was fun! We learned about the ideal gas laws and the ideal gas equation. When I heard my professor lecture about it, I was completely freaked out. It looked like a bunch of equations to be memorized, without any rhyme or reason. (Nothing rhymes nicely when my professor speaks. His accent is a bit obnoxious.)

Then I finally got home and read the chapter, and by golly, it works! Joy!

Before continuing, I must note that my audience is composed of two groups: the pursuers of knowledge (ch"ch, as CA would say) and the ignoramuses (or theYoshvei Ohel , as the holy books call them). I can't write a post that will interest the former while being wholly understandable to the latter. I'd love to explain things well enough so that the yeshiva-educated can understand, but that would require more time than I have. So sorry, y'all! E-mail me, and I may be able to explain things further. Now back to business...

The first surprising thing was how proportions get transformed into equations. It's a neat trick. You can't do anything with a proportionality, but add in a constant, and viola! You've got a nifty equation.

While this trick was neat, it got kind of burdensome after we had transformed around four or five proportionalities into equations. There's Boyle's Law, and Avagadro's Law, and all the others that I can't remember. Each one got its equation that needed to be remembered. Plus I was a little perturbed that they never told us what these constants were. It seemed like cheating. Kind of like making calculations in moles, without knowingAvagadro's number.

But then they lumped all these equations into one mother of an equation: The Ideal Gas Equation. How many equations out there get a name with a word as nice and important-sounding as "ideal"? Not many, I bet. Anyhow, now that everything is compressed into one equation,PV = nRT , you only need one constant, R. It's one of the funniest constants I've ever encountered, with all those units tacked onto it. What is it? 0.082058 Moles Kelvin Atmospheres^-1 Liters^-1? Yeah, those are lot of units for one constant. But I'm glad that R has all those units.Cuz now I don't need to worry about them. I plug in the units, and friendly old Mr. R cancels all the units.

That's another nice thing about this equation: no messy conversions. A nice figure like 2.00 grams can become really ugly when those grams are actually 0.0991101396 moles of neon. But in ideal gases, the conversions are a breeze.Celisus to Kelvin? Just add 273! mL to L? C'mon, that just 1/1000! And you don't even need to bother with Torres to Atm . You just use a different value for R, and you're good to go! With my handy-dandy TI-83, I stored 0.082058 in the variable R, and 62.36396119 (i.e. the R value necessary for calculations involving Torres) in the variable Q. So all in all I dealt with normal numbers.

Now here's the real thing I like: Everything is so Goddamn linear! The algebra is a breeze. From PV = nRT, you can get V = nRT/P, T = PV/nR, or whatever. You only need to memorize one equation, and the others are derivable with the snap of the fingers! And because it's linear, you can estimate it all in your head. You can say things like, "Well, if it's 8 liters atSTP , it ought to still be in the neighborhood of 8 Liters with 770 Torres and 265 K. You can't make those estimations in other equations.

Last thing: The questions sound so bloody confusing--but they weren't. There are so many figures in each question. Here's an example: How many grams of N2 (g) at 25.0 degrees C and 734 Torr will occupy the same volume as 25.0 g O2 (g) at 30.0 degrees C and 755 Torr? If you got a molarity problems with this many numbers, you know you're heading into trouble. But with this, you just got to figure out your unknown variable, solve the equation for that variable, and then plug in your constants--and you can do the conversions while entering the stuff into thecalc! That's one of the most elegant things about mathematics: things which look scary turn out to be really simple. It's like transforming 3(X + 2)/6 = 6 into X = 10. Simplifying scary-looking expressions is what math's all about.

Now I just got to read the end of the chapter about kinetic-molecular theory and real gases. I don't know what that's about, but I saw variables getting squared and radical signs, so I fear things will not longer be so linearly predictable. Plus "real" sounds so ominous when contrasted with "ideal." And tomorrow we start the next chapter, which I haven't even looked at. So the horizon seems a bit cloudy, but at least I'll share the jubilation with you as long as it lasts.

13 comments:

  1. This is evil. This post is way too long? Who's gonna have patience to read such stuff? Oh well, maybe next time.

    ReplyDelete
  2. Well I read the whole thing.

    1) I always convert things to atm so that way I only need to remember R as 0.0821.

    2) I never even bothered to learn all the other equations.

    3)The real gas law equation isn't sooo confusing if you stare at it a bit.

    4)The kinetic molecular theory junk I still don't understand.

    ReplyDelete
  3. Hilarious.

    (funny that you used to rail against people's inability to subscribe to comments without leaving one of their own, and now that you have your own blog!)

    ReplyDelete
  4. Strange I never thought my chemistry experiences would be part of good memories.

    ReplyDelete
  5. Good ol' R and Q. And that Avogadro, I haven't seen him in years, he's still the same ol' Avogadro I knew back in college, hasn't changed a bit.

    ReplyDelete
  6. 1. The problem with converting to atm is that you lose a lot of precision, because you need so many more digits in atm. For example 655 Torr is 0.97761194 atm. I stored both values in my ti-83 and now i don't lose any precision. Just another reason to get a graphing calculator.

    2. Precisely my point. pv = nrt gives you everything you need with only the simplest algebra! (although it gets messy when you include molecular weights and density instead of n)

    3. I have yet to experience that on my own. I still haven't opened the book.

    4. sucketh

    TRS: glad you liked it. How do i change that comment/subscription business?

    ReplyDelete
  7. Ah well we're not allowed graphing calculators...

    ReplyDelete
  8. @Dovid re: Avagrado

    are you surprised?

    On a serious note, they probably got a more precise version of Avagrado's number, dontcha think?

    ReplyDelete
  9. LE7: at least when you're learning chemistry lishmah you should be able to be precises.

    ReplyDelete
  10. It's in the settings page-look around a little, shouldn't be too hard to find.

    ReplyDelete
  11. i skimmed this... but you actually reminded me that (aside from the memorizing) i liked chemistry. and algebra (except i hated my teacher). because they made sense. they just fit together.
    trig and physics, however... it wasn't pleasant.

    ReplyDelete

Forth shall ye all hold.