## Tuesday, July 17, 2012

### A is for Avogadro's Number (ABC's Wednesday)

Right now, your high school or college chemistry teacher would be very proud if you started mumbling to yourself "pee vee equals en ar tee..."

 These paper lanterns - also known as Kongming lanterns - are taking off due to some of the physical laws that Avogadro was investigating during the late 1700s and early 1800s.

What is Avogadro's number?

Well, one way to look at it is the actual number, which is:

602,214,150,000,000,000,000,000 +/- 1,000,000,000

Or, in shorthand, (6.0221415 ± 0.0000010) × 10^23.

It's actually formally defined as "the number of carbon-12 atoms in 12 grams of unbound carbon-12 in its rest-energy electronic state.

But why do we care how many atoms are in 12 grams of a particular isotope of carbon?

Why Avogadro's number is useful

Long before physicists and chemists had an actual number for Avogadro's number, they were using Avogadro's number to construct theories and physical laws.

In a lot of nature, certain numbers are important because they help define the relative size of different physical phenomenon.

One great example is the constant c in E = mc^2.  In Einstein's famous relationship, c is the speed of light.  We know from this equation that energy is related to mass by a proportional relationship to the speed of light squared.  Even when we really didn't have a good idea of the precise value for the speed of light, we knew this relationship held.

Another great example is Planck's constant, or h.  In an electromagnetic wave, such as light or microwaves, there is a relationship between the energy of the wave (v) and the energy of the wave (E) that is defined as E = hv.

These relationships - such as E = mc^2 and E = hv - are known as "scientific laws" or "physical laws."

In the case of Avogadro's number, one law where the number becomes important is Avogadro's Law:

Avogadro's Law: Under the same condition of temperature and pressure, equal volumes of all gases contain the same number of molecules.

So, knowing the number of atoms or molecules in one gas at a given temperature and pressure will give us a proportion where we can figure out the number of atoms or molecules in all gases.

"pee vee equals en ar tee..."

And that's where "pee vee equals en ar tee..." comes in.

PV = nRT is what's known as the "ideal gas law," the major consequence of Avogadro's Law.  Most gases follow the ideal gas law almost perfectly.  In PV = nRT, P is "pressure," V is "volume," and T is "temperature," R is the universal gas constant and n is the number of moles of molecules or atoms of the substance - counting units in Avagadro's number.

American Scientist article on the history of Avogadro's number

How Stuff Works article on gases

Wolfram Research on Avogadro's number

[Note: correction Aug 4 2012 from "And what's that n?  That' Avogadro's number, who, along with another important constant, Boltzmann's constant R, gives the proportional relationship between most gases." to  "R is the universal gas constant and n is the number of moles of molecules or atoms of the substance - counting units in Avagadro's number."]

1. OK, I have HEARD of this. But I don't remember it from HS chem, and I managed to avoid college chem altogether.
Anyway, WELCOME TO ABC WEDNESDAY!

1. Huh. Where did you hear it? Do you remember? My weird capacity to have a great memory for where I first learned something has served me pretty well in my job.

Anyways... thanks for the visit!

2. I'm guessing the New York Times, back when I used to read it every day. But not swearing to that.

3. Hm. Good shot of that. I can think of a couple concepts I first learned in the news, particularly the BBC.

2. Whew! All new and Greek to me, but fascinating I'm sure to scientists. I did read all the way to the end and if you knew me, you'd know if I don't "get" something right away, I skip it. Have an awesome week,

Leslie
abcw team

1. Thanks for the visit! After looking at the comments I have a better idea of what people might be interested in. I'm trying to cover science this first round of ABC Wednesdays. So thanks for the input! :-)

3. Takes me back to my college days.

1. Thanks for the visit!

4. I'm sure glad someone has the where with all to understand all of that.
Me? I'll accept that as the most original word for ABC Wednesday.
Good stuff.

1. Thanks for the input and the visit. I'm trying to keep it to science for ABC Wednesday, so knowing what's interesting is helpful to me. :-)

5. Again....my brain in being stretched beyond it's limits... Yikes....but very interesting.

1. Thank you for the visit! I'll try to cover better science next time... I'm thinking of more fossils and animals! But math is really interesting to me. :-)

6. You took me right back to my HS and the good old days. Chemistry was always my fav subject though I am not anywhere near it now.

PhenoMenon, ABCW Team

1. Sure you do - do you cook? Bake? Cooking and baking are all about chemistry!

Anyways, welcome!

7. A truly fascinating conglomeration of formulas (formulae?) and explanations (explanationii?) but since I am more of a liberal arts/fine arts/humanities sort or person I cannot comprehend it in any meaningful way. Now that I have this information, what am I supposed to do with it?

In Chemistry my precipitate never did what it was supposed to.

1. :-) I'm not authorized to give you your money back for chemistry experiments that failed. Besides, I'm probably worse than you are. I've accidentally set fire to several benches and once accidentally flooded a lab as well! They keep me safely locked behind a computer now... :-)

Anyways - Welcome! Thanks for dropping by!

8. sort of person

9. You got me... I'm depending on you that all of this is correct!! But your pic is cool:)

1. :-) Thanks. I like the pic, too. It makes the post look deceptively interesting... :-)

You can check out the American Scientist article I cite above. It's a good magazine, like National Geographic. It's been published since 1913.

10. You've got my curiosity going which is always a good thing. Will read this through again, and browse the internet for what I don't grasp, (not that that's a sure-fire way to get answers)!

I love how different your post is, and your page is definitely one of the most beautiful I've seen...:)

Thanks for stopping by to visit!

1. Thank you. The next ABC Wednesday will involve my background. It's part of the constellation Orion.

Thank you for stopping by!

11. I yawned at this in school wahhh..

Aero 360's Arrows
Rose, ABC Wednesday Team.

1. Well, hopefully the next post will be more interesting - it'll have a question and involve astronomy. Everybody loves the stars!

Thanks for dropping by!

12. very important constant in scientific calculations

1. Yes! Even basic ones in chemistry. Thanks for dropping by!

13. I noticed the description of the ideal gas law is a little misleading. Specifically in the equation PV=nRT, n is the number of moles, which when multiplied by avagadro's number gives the number of atoms or molecules.

1. Yes, that's right. I'll add the clarification in a second. The first time I wrote it was rather long and had moles etc. explained, so I deleted a bit, which apparently made it less accurate.

Thank you for the catch!