Avogadro`s Number: an absurdly complex basis for quantifying the number

[DEMVET-USMC]

of molecules in chemistry formulas. I suggest a formula based on something that can be multiplied or divided by 10. If anyone out there knows how to set up a poll as to: I like using Avogadro`s number yes or no please do so. Also, what can anyone come up with as to a formula that has a multiple of ten to replace Avogadro`s number. Avogadro`s number is the number of carbon-12 atoms in 12 grams of carbon 12. It`s value is is approximately .60229 x 10 to the 24th power. Feedback please. I think he woke up pissed off one day and really wanted to make things hard for his students. Fire up those flamethrowers and give it to me big time if you disagree. ...Oscar

[MallRat]

1. If it's any consolation...

...I'm a biochemist, and all of my work is done in terms of moles, molarity, grams, g/ml, and all the variations thereof (i.e., nanomoles, ng/ml, etc.)

I've never had reason to sit down and calculate how many MOLECULES of protein I'm working with. I haven't multiplied or divided anything by 6.02 x 10²³ in a very, very long time.

But that's just me.

-MR

[DEMVET-USMC]

14. You are a lucky man or, I am speculating now, they have software that

does all the calculating for you. I would imagine they do. If this is so any recomendations ? Oscar

[MallRat]

15. No. It's just that I deal in MOLES, not MOLECULES.

The number of molecules is a cumbersome way to work in most areas of biochemistry.

Unless you're getting into ultra-sensitive detection (yoctomoles = 100's of molecules), it's much easier to deal with moles instead.

I would never sit down and write a protocol describing how my enyzmatic assay uses 6.02 x 10¹⁵ molecules of enyzme per liter of buffer. I'd just say the assay uses a concentration of 10nM protein.

This is exactly why the mole was conceived.

-MR

[DEMVET-USMC]

23. Thank you MR

I appreciate your input. Any ideas on a system based on a mulitple of ten ?

[IrateCitizen]

2. Well, since atomic mass units are based on carbon-12...

... it only stands to reason that Avogadro's number would be based on the same.

The argument you seem to be presenting is similar to complaining that pi is too complex of a number to be used in calculating the properties of circles and spheres.

Personally, I've never had any problems with Avogadro's number other than remembering it when I haven't used it for some time. There are plenty of other numbers out there -- Planck's constant, mass and energy conversion factors, etc. -- that I have found much more onerous than Avogadro's number. That one is really pretty simple. Would it really make it easier if a mole was defined as something different than the number of carbon-12 atoms in 12 grams of pure carbon-12 (thus linking it directly to atomic mass number)?

[DEMVET-USMC]

7. Like I said,if it was a multiple 10,obviously it would.

...Oscar

[DrWeird]

33. Um, Avogadro's number is a multiple of ten.

It is roughly 628,000,000,000,000,000,000,000.

Maybe you have a problem with scientific notation, perhaps?

[DEMVET-USMC]

41. You are right, any number can be multiplied by 10,By Using" Oscars #

The number of Boron-10 atoms in 10 grams of Boron-10" you will have a much easier nuber to work with. For instance it will be a simple matter of moving the decimal point in many of these equations.

[treepig]

42. and can you kindly tell us

how many atoms that is?

p.s. on the other thread you admonished me for belittling you, but isn't that exactly what you're looked for? otherwise, why post such nonsense?

[treepig]

46. since it's too late to edit

i'll just acknowledge that i'm most deserving of a good dose of belittling myself for my atrocious spelling and grammar - d'oh!!

[DEMVET-USMC]

48. I gave the number you along with others have corrected me, though with

differing numbers. Using the web site you suggested I hopefully have the correct one. ...As always I appreciate your input and interest.....Oscar

[DrWeird]

45. Oscar, the number of atoms in 10 grams of boron-10...

is 6.02*10^23.

Most people call that Avogadro's number.

[DEMVET-USMC]

17. Please,it was Avogadro who arbitrarily established the standard atomic

mass units are based on. That is my whole point. And if a number that is a multiple of ten can be established it would make all these calculations much simpler.If You PEOPLE DON`T come up with it I will and you will ever after be stuck with referring to Oscar`s number ! !

[Ediacara]

20. who counts molecules?

Jeez..... What's so friggin hard about one mole of something weighs the same (in grams) as its atomic number?

[PragMantisT]

3. I never knew where it came from

I learned that it was the number of molecules in a MOLE (not the subterranean mammal). Mole being an arbitrary measurement. Knowing that there is a standard for that number makes it more realistic. I had no idea there was a real basis for the count.

[Q3JR4]

4. As it is with most sciences

if you define something away, it only makes other things harder to deal with.

[DEMVET-USMC]

11. I could not agree more wholeheartedly.

I am constantly baffled by obviously unnecessarily complex formulas and definitions. I actually do believe some of these people must have been making that which is relatively simple into something very complex on purpose. ...Oscar

[NNadir]

27. Avogadro had nothing to do with the value of his number.

He merely postulated that the number existed. The concept of the number was brilliant enough to justify naming it after him.

The actual value of could have been an even power of ten, but the number needed to be measured. It is NOT a defined quantity that is arbitrarily picked. The only thing that was "arbitrarily" picked was the value of the gram. The gram was chosen so that water at its maximum density (at 3.98C) would occupy a volume of 1 ml. The ml in turn was defined as a cubic centimeter, and the meter by a "power of ten" fraction of the circumference of the earth (which was actually the wrong value at the time of the invention of the meter, and so a new standard needed to be defined for the meter.) These conventions are a lot more useful in daily life than using Avogadro's number.

Until the early twentieth century, long after Avogadro was dead, the value of Avogadro's number was not known with any accuracy. Planck's quantum hypothesis showed that the constant in an empirical law known as the Wein displacement law was a function of Planck's constant, the speed of light, and the Boltzman constant, k. The Boltzman constant, in turn, is the universal gas constant divided by Avogadro's number. Another empirical law that was known at the time is the Stefan-Boltzman equation relating to the energy density to the fourth power of the temperature times a constant known as the Stefan-Boltzman constant. It can be shown that this constant is also a function of Planck's constant, the Boltzman constant and the speed of light. Since we have two equations and two unknowns, we can solve for both Planck's constant and the Boltzman's constant.

Since the speed of light was accurately known from the Michelson experiment, and the Wein constant and the Stefan-Boltzman constant had all been measured accurately, it was possible to determine k and h. Since k = R/N where R is the universal gas constant (which had also been accurately known) , and N is Avogadro's number, once we know the value of k, we also know the value of Avogadro's number, something which Avogadro himself didn't know.

Happily, Avogadro's number is very close to an integer times a power of ten, the integer being 6. This makes back of the envelope calculations, or calculations done in one's head very easy. Of course, today, almost everyone has access to a computer with which one can easily do very precise calculations. One merely makes a spreadsheet with all the important constants in it.

[AZCat]

29. Calculations with computers...

While computers certainly have improved the speed of calculations, there is a danger in relying on them to do all the work. Certain operations can increase the uncertainty of a particular value and that isn't always taken into account. So while the answer from a calculation may have a dozen significant digits, it may only be accurate to two or three.

And really - how often is it useful to have those extra significant digits? Even if you do know the value of a constant like pi to several billion digits, the other values in consideration will probably be far less precise. I am hard-pressed to think of a time that I needed the value of pi to be more precise than 3.14, because the other values I used were (at most) three significant digits.

I read a good book a couple of years ago that had a chapter on this - A Mathematician Reads the Newspaper, by John Allen Paulos - and he was talking about the absurd precision of calorie counts for recipes listed in the newspaper. He questioned how the author could determine a particular concoction would have 347 calories when the measurements used in preparation are so crude.

[NNadir]

31. It depends on the precision required.

Most computer systems have to be validated for precise work, but they actually work quite well when one does so.

It is particularly important to obtain as much precision as is possible when one is doing sophisticated calculations involving the manipulation of many variables. The high precision with which the Rydberg Constant was known (a factor in measuring the distance between spectral lines) validated quantum theory and raised its status from an ad hoc fudge to solve obscure problems to a demonstration of a fundemental property of the universe. (This was Bohr's work.)

The discovery of the element Argon derives from precise work. Lord Rayleigh the observation that "nitrogen" prepared from air is invariably more dense than nitrogen prepared from decomposition of nitrogen containing chemicals such as ammonium nitrate. It might well have missed this matter if he chose Avogadro's number to be a nice round 6 X 10^23. The discovery of Argon in turn led to the validation of the periodic system, and was crucial in understanding chemical bonding. This insight to chemical bonding lead to the ability to make very elaborate models of complex systems such as protein substrate interactions, folding etc, things that underlie our understanding of medicinal chemistry.

The precise knowledge of atomic weights (and isotopic composition) depend sensitively on the value of Avogadro's number. Believe it or not, this has considerable bearing on ordinary life, where mass spectrometers are critical tools in thousands of industries. You would be surprised at how much of your health, safety, wealth and knowledge depends on the use of mass spectrometers.

It is our habit to report values without respect to the precision (or significant digits) that we actually know, but it is a small price to pay for the convenience and speed at which ordinary people can do sophisiticated work. Sometimes the computer leads one to make extraordinary claims like that you've given about calories, but this is a reflection on the user, not the value of the equipment itself.

[treepig]

5. and while we're at it

let's get rid of the bizarre way that a second is defined, which is currently the natural resonance frequency of the cesium atom of 9,192,631,770 Hz - that's completely bonkers!

and the meter, which is defined by the distance light travels in a vacuum in 1/299,792,458 'ths of a second - how ridiculous is that?

and pi - i'm all for going along with those georgia politicians who want to turn it into the even integer of 3.

i could go on, but the point is that "fundamental physical constants" such as those listed at http://physics.nist.gov/cuu/Constants/index.html (or in the table presented) may indeed be complex and inconvenient to keep in memory, but unfortunately they can no more be redefined at the drop of a hat just to make life easier for you than can, let's say by picking an example out of the blue, re-difining the definition of the angular momentum of the earth to correspond to one's pet theories.

[DEMVET-USMC]

8. I have learned to appreciate your interest and input.

...Oscar

[treepig]

35. suppose an apology to georgians is in order

it actually was indiana that tried to simplify the value of pi:

Did a state legislature once pass a law saying pi equals 3?

--------------------------------------------------------------------------------

Dear Cecil:

In Science magazine a while back an article about the latest attempts to calculate pi to the umpteen zillionth decimal place made a passing reference to a curious Oklahoma law. It said Oklahoma legislators had passed a law making pi equal to 3.0. I also remember Robert Heinlein in one of his novels mentioning that Tennessee had passed a similar law. Did either of these states ever pass such a law? Are they still on the books? What are the penalties if I proclaim that pi equals 3.14159...? --Wulf Losee, Andover, Connecticut

Dear Wulf:

Cecil had heard this story too, only the state in question was Kansas, leading him to believe the whole thing was made up by big-city sharpies having a little fun at the expense of the rustics. However, with the help of Joseph Madachy, editor of the Journal of Recreational Mathematics, I've learned the story does have a germ of truth to it.

It happened in Indiana. Although the attempt to legislate pi was ultimately unsuccessful, it did come pretty close. In 1897 Representative T.I. Record of Posen county introduced House Bill #246 in the Indiana House of Representatives. The bill, based on the work of a physician and amateur mathematician named Edward J. Goodwin (Edwin in some accounts), suggests not one but three numbers for pi, among them 3.2, as we shall see. The punishment for unbelievers I have not been able to learn, but I place no credence in the rumor that you had to spend the rest of your natural life in Indiana.

Just as people today have a hard time accepting the idea that the speed of light is the speed limit of the universe, Goodwin and Record apparently couldn't handle the fact that pi was not a rational number. "Since the rule in present use fails to work ..., it should be discarded as wholly wanting and misleading in the practical applications," the bill declared. Instead, mathematically inclined Hoosiers could take their pick among the following formulae:

(1) The ratio of the diameter of a circle to its circumference is 5/4 to 4. In other words, pi equals 16/5 or 3.2

(2) The area of a circle equals the area of a square whose side is 1/4 the circumference of the circle. Working this out algebraically, we see that pi must be equal to 4.

(3) The ratio of the length of a 90 degree arc to the length of a segment connecting the arc's two endpoints is 8 to 7. This gives us pi equal to the square root of 2 x 16/7, or about 3.23.

There may have been other values for pi as well; the bill was so confusingly written that it's impossible to tell exactly what Goodwin was getting at. Mathematician David Singmaster says he found six different values in the bill, plus three more in Goodwin's other writings and comments, for a total of nine.

Lord knows how all this was supposedly to clarify pi or anything else, but as we shall see, they do things a little differently in Indiana. Bill #246 was initially sent to the Committee on Swamp Lands. The committee deliberated gravely on the question, decided it was not the appropriate body to consider such a measure and turned it over to the Committee on Education. The latter committee gave the bill a "pass" recommendation and sent it on to the full House, which approved it unanimously, 67 to 0.

http://www.straightdope.com/classics/a3_341.html

[slutticus]

6. Actually....

...Avagadro's number was initially defined as the number of atoms in one ml of gas (assuming ideal behavior of course), but has since been revised using light scattering measuremnts....I think to 7 significant figures. So now the atomic weight of carbon is actually 12.0107 g/mol.

[DEMVET-USMC]

9. That number I provided specicaly stated the number of CARBON-12

atoms in 12 grams of CARBON-12.Many periodic tables factor in the isotopes of any given element when determining atomic weights. Avogadro`s number does not factor them in by definition. ...Oscar

[MallRat]

16. Atomic weight of carbon depends on your application.

The "average mass" of carbon is 12.0107 g/mol, but that's because you're taking into account the natural abundances of other carbon isotopes.

Pure, monoisotopic ¹²C has an "exact mass" of 12.00000 g/mol.

-MR

P.S. Isn't one mole of ideal gas at STP about 22.4 liters? 1 ml sounds pretty small.

[DEMVET-USMC]

18. Avogadro`s number does not allow for averaging in isotopes

It is specifically defined as the number of carbon-12 atoms in 12 grams of carbon-12. ...Oscar

[MallRat]

21. Right... I was just answering another post.

I got a little off-topic. Sorry if I confused you, Oscar.

-MR

[DEMVET-USMC]

22. Hi Malrat, no appoligies please,we are just having a little fun with

this topic. ...Oscar

[slutticus]

25. Your right...

...my bad. It's 22.4L...standard pressure.

It's been a while since CHEM 1

LOL

[DEMVET-USMC]

26. I understand, a lot of people have that same problem. I keep all those

old books to refer to when I`m not sure. You have a very interesting forum name. Anyway , take care Oscar

[Speck Tater]

10. While we're at it...

let's change pi to 3.0000...

[DEMVET-USMC]

12. purely out of curiosity ,did anyone ever come up with the exact value

of pi ? I figured it may be possible with computers and all. ...Oscar

[midnight armadillo]

13. It's a transcendental number

The value is infinite and non-repeating.

More specifically, a transcendental number is a number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree.

[DEMVET-USMC]

19. Are you refering to pi ?

ARE YOU TALKING ABOUT pi, I think I probably misunderstood what you were refering to. If so please let me know as I am interested. ...Oscar

[DEMVET-USMC]

24. I Know you are referring to pi, can you define the words in layman's words

I want to understand what you are saying. ...Oscar

[Lucky Luciano]

40. transcendental definition

A number, "A" is called "algebraic" if there exists a polynomial ( the underscroe is a subscript used for indexing and the ^ is a superscript for exponents):

p(x) = a_n*X^n + a_(n-1)*X^(n-1) + ... + a_1*X + a_0

where the a_i are integers and p(A) = 0. In other words, it is algebraic if there is a polynomial with integer coeffiecients where A is a root.

So the square root of two is irrational, but it is algebraic since it is a root of x^2 - 2 = 0.

A number is transcendental if it is not algebraic. So, pi is transcendental since there does not exist a polynomial equation with integer coefficients such that pi is a root.

Is that layman terms?

[DEMVET-USMC]

44. Thank you Lucky Luciano, it definately helps.

Oscar

[hunter]

32. It's actually more complicated than that...

A lot of our common "mysteries of pi" are actually "mysteries of five." It is easy to write a computer program that will pick out any particular digit of pi in binary, but not so easy (yet?) to do that in decimal.

http://www.sciencenews.org/pages/sn_arc98/2_28_98/mathland.htm

Anyways, Avogadro's number, and a bunch of other stuff, would be a lot cleaner if God had given us eight fingers instead of ten, along with the keys to the planet.

Oh wait, He did give us eight fingers, and two thumbs, and the keys to the planet.

We humans can hardly do anything right, can we? All thumbs we are, kicking the space bars.

Good night, all...

[LARED]

34. Thanks for that link

Very interesting.

I've always wondered if the value of pi is a transcendental number when calculated or derived from other base systems.

I've always thought there was some flaw in how mathematical computations were developed because it seemed to me that the ratio of the circumferance to the diameter should not be an irrational number.

For such a simple geometeric shape to have an irrational number for a simple ratio always seemed too complex.


Maybe if we had 3.243F6A8885A308D313198A2E0 fingers it would make more sense. :)

[DEMVET-USMC]

37. Thanks for the link hunter, I get the gist of what this article is about

though my mathematical skills are not enough to fully understand all that is being discussed there. Thanks, ...Oscar

[Lucky Luciano]

39. yes pi is transcendental,

but the proof of it being transcendental is nontrivial...actually it is even hard to prove it is irrational!

Being transcendental can also be defined by saying that the smallest field containing the rational numbers and pi when thought of as a vector space over the rationals is infinite dimensional.

[treepig]

36. don't know if there's any point to coming up with an "exact" value

for pi, since it apparently changes depending on gravity . . .

"So you're saying that pi is 3.1416 because that's what it is?"

"Yes. It's an experimental fact."

"But could it have come out differently?"

"Yes. There are places in this universe where it does. Draw a circle around an ultra-dense neutron star and you will find that pi is different--or rather that the ratio of the circle's circumference to its diameter is something different from pi. Pi has a unique and stable value only in those parts of the universe where gravity is weak."

"But why is pi equal to 3.1416 in those parts of the universe where gravity is weak?"

http://www.j-bradford-delong.net/movable_type/2004_archives/000733.html

[slutticus]

38. Isn't that the value...

...of Pi quoted in the bible?

[Festivito]

28. Why expect a power to # of fingers and thumbs per person?

I think we use base 10 because historically counting could be done with our handy appendeges, which does not necessarily empirically coincide with the number of molecules in a mole. But 10 can represent any number depending on the chosen base.

Perhaps if we had an exact 23-digit number, there would be a nice set of prime factors and you could write your numbers with the least common denominator and divide by 10(base whatever it turns out to be) to your hearts content.

[hunter]

43. Counting on five or ten fingers makes math more difficult...

It obscures many important numerical relationships.

If we had eight fingers and we used a base eight system we probably wouldn't have wasted so much time gazing at all those digits of pi like it was some deep mystery.

Of course (I'm speculating here, heh, heh...) in the universal scheme of things intelligent species that have eight, sixteen, and other number systems based on the powers of two, tend to destroy themselves with anti-matter bombs, teleportation devices, etc., before they develop the social skills to handle such powerful and sophisticated technologies.

Intelligent species that base their number system on powers of three have a different sort of problem.

[DrWeird]

30. Look, just because some students are stupid and lazy...

doesn't mean we should dumb down the curriculum.

An Avogadro's number of hydrogen atoms, a mole, weighs one gram, and an Avogadro's number of ethanol molecules, a mole, weighs 46 grams, and an Avogadro's number of hydrogen molecules weighs 2 grams.

What's the problem? Saying a mole of atoms is Avogadro's number is like saying a dozen eggs is twelve eggs.

[NNadir]

47. Maybe we should declare a dozen equal to ten.

Actually the selection of base 10 was rather foolish and of course, an arbitrary selection based on the number of fingers.

Base 12 is superior because it has more factors, to wit 1, 2, 3, 4, 6 and 12. Base 10 has 4 factors 1, 2, 5 and 10.

Were we to use base 12, we could avoid all those unnecessary repeating digits in fractions.

The superiority of base 12 is demonstrated by the existence of a concept of a "dozen." Is there a similar one word designation for any other number? There of 360 degrees in a circle, twelve inches in a foot, 36 inches in a yard. A "gross" is 144. A day is 24 hours long; an hour, 60 minutes; a minute, 60 seconds. All of these units are multiples of 12, and all are units for which it is convenient to have lots of factors.

I demand we change our base system, because base 10 is too confusing! How the hell can reasonable people use a base system that requires a decimal when you divide it four ways? Three ways? (And in the case of three ways, it's not just a decimal but - gasp - an endlessly repeating decimal).

This is outrageous.

If John Kerry doesn't promise to change the base system, I'm going to seriously consider voting for Ralph Nader.

[Salviati]

49. As far as I'm concerned, there are 10 types of people in the world...

Those that see the superior nature of converting to the binary system

and those who are just plain ignorant...

:evilgrin:

[NNadir]

50. That's hilarious. Do you mind if I steal that line sometime?

[Salviati]

51. No problem, it was shamelessly stolen by me in the first place...

So who am I to complain...
:)