Monday, May 21, 2007

On the Conundrum of Mathematical Science, or, How Stupid Math is

Okay, okay, math isn't stupid, but something rather interesting appeared in my math book today.

According to my textbook (Algebra 2, Bob Jones University press), 2 grams of hydrogen contains 6.02 x 10>23* molecules. Wait a minute. Did they just say two? Yes, they did!

So, what's wrong with that? Well, the number 6.02 x 10>23 is called a "mole," just like the way we say that the number 12 is a "dozen." So, how do we know how many grams of any given element exist in a sample? Simple. Look at a chemist's best friend:

Behold, ye peasants, the mighty Periodic Table of the Elements, ruler of all the land!



First, since we are dealing with the element hydrogen, we need to know the abbreviation for Hydrogen. This is "H" (this one is unusually simple, I assure you). See if you can find it on what is often called "the chart." Can you?

Okay, if you can't it's on the very top left of the chart. Now, never mind that all that info in that little box, check out that number on the top left of the "H." What is it? 1.01. This number is in a unit called "atomic mass units" (abbreviated amu), which, for today, you'll just imagine as grams (they are similar in this sense). Basically, it tells us the mass of one atom of that particular element. So what's that mean? Well, this is where the "mole," that long 6.02 x 10>23 number, comes into play.

If you noticed, every element on the chart has this amu number. The amount of molecules in one "mole" of hydrogen, or any other element, is whatever that amu number is. Thus there are not two grams of hydrogen molecules in a mole (6.02 x 10>23). There are 1.01! You might say it comes from rounding errors, but why don't you try rounding 1.01 to make it into 2? Yeah, you can't.

So, just in case none of that made any sense, they made a big boo-boo in the book. Naughty math people!

Dr. Paleo Ph.D.


* Since I unfortunately cannot have superscripts on blogger, "10>23" means "10 to the 23rd power," a notation system I was taught by a very helpful member of the email help line at Apologia Science (www.highschoolscience.com) [I am taking the brilliant Dr. Jay L. Wile's Exploring Creation with Chemistry]

Disclaimer: I am stupid as well, so there might very well be a dreadful scientific error in this post. :-P

4 comments:

Corky Marie said...

wow.

Dr. Paleo Ph.D. said...

So what dost thou thinketh of mine essay?

freakazoid said...

I think they meant there are two grams of the molecule hydrogen (H2, where the 2 is a subscript), not the element.

I thought you were right at first, but then I had a fairly rare moment of brilliance.

Dr. Paleo Ph.D. said...

Hmm...

Aha, Lydia you're a genius! I see...they meant molecules, not atoms. I see, it's due to homonuclear diatomics. Hmm...they should have explained it better...maybe I'm just stupid!

I told you all in the disclaimer I could have been wrong. :-P

I didn't know you read my blog!