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The Mole & Avogadro’s Number
Posted: 06 October 2007 11:42 PM   [ Ignore ]
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The following are some excerpts from Wikipedia that I need some help on. 

The mole (symbol: mol) is the base unit that measures an amount of substance.

One mole contains Avogadro’s number (approximately 6.022×10*23) entities.

Why that number?  Did the result of a particular experiment insist that it must be that number?  What was the experiment?

A mole is much like “a dozen” in that both are absolute numbers (having no units)

What does it mean for a number to have no units?    Doesn’t a dozen have 12 units?  [shrug]

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Posted: 07 October 2007 09:39 AM   [ Ignore ]   [ # 1 ]
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Have you checked THIS out, or THIS, or THIS, or THIS? Just googling around a little.

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Posted: 07 October 2007 02:19 PM   [ Ignore ]   [ # 2 ]
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Doug, I’m not certain he wants some great big theory that explains a mol.  I’m thinking he maybe thinking as simplistic as I do concerning mathematical things.  If so, then I would think it is a case of the number and theory comes first, then they name it.  Thus why it is not some other number.

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Posted: 07 October 2007 03:06 PM   [ Ignore ]   [ # 3 ]
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CoryDuchesne - 06 October 2007 11:42 PM

The following are some excerpts from Wikipedia that I need some help on. 

The mole (symbol: mol) is the base unit that measures an amount of substance.

One mole contains Avogadro’s number (approximately 6.022×10*23) entities.

Why that number?  Did the result of a particular experiment insist that it must be that number?  What was the experiment?

A mole is much like “a dozen” in that both are absolute numbers (having no units)

What does it mean for a number to have no units?    Doesn’t a dozen have 12 units?  [shrug]


To patch from Doug’s first reference
The name “Avogadro’s Number” is just an honorary name attached to the calculated value of the number of atoms, molecules, etc. in a gram mole of any chemical substance. Of course if we used some other mass unit for the mole such as “pound mole”, the “number” would be different than 6.022 x 1023.

So there is an error in your Wikipedia reference as I understand it.

a. The experiments were done by Avogadro ( LOL )
b.  The number is actually not dimensionless, because it depends on the definition of “mole” and “gram” (as noted in Doug’s reference).  It takes 6.022 x 10^23 atoms to give a mass equal to the atomic weight in grams.
c. So you asked about the specific experiment.

http://www.madsci.org/posts/archives/1998-03/889394526.Ch.r.html  This look like a good reference.

I would also point to an essay by Isaac Asimov:
To Tell a Chemist
Subject: Avogadro’s number
First Published In: May-65, The Magazine of Fantasy and Science Fiction
Collection(s):

1966 From Earth to Heaven

1974 Asimov on Chemistry

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Posted: 07 October 2007 05:02 PM   [ Ignore ]   [ # 4 ]
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Thanks for the leads, Doug.


Mriana,

Mriana - 07 October 2007 02:19 PM

Doug, I’m not certain he wants some great big theory that explains a mol.  I’m thinking he maybe thinking as simplistic as I do concerning mathematical things.  If so, then I would think it is a case of the number and theory comes first, then they name it.  Thus why it is not some other number.

When it comes to understanding scientific ideas, my approach has always been to try bridging the gap between the empirical observable world and the theoretical abstract concepts and numbers. 

For instance, at this point, Avogadro’s number appears to me as merely some arbitrary number.  I want to understand the empirical observations/experiments which left the experimenters/observers no choice but to say, “It must be this number”

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Posted: 07 October 2007 05:18 PM   [ Ignore ]   [ # 5 ]
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The mole is an arbitrary weight of any pure material that chemists define.  The molecular weight of any material expressed in grams is called a mole.  For example water, H2O has a molecular weight of 18.016 so that would be the number of grams that would be called a mole.  It’s not too obvious, but if you think about it carefully, you’ll realize that the moles of any material would have the same number of molecules.  [That’s something you can reason out so I’m not going to explain why].  Avogadro was the first one who calculated that number and it was given his name.

Remember that the weight called a gram is also arbitrary.  It all stems from the distance from the north pole to the equator (even though that measurement was later found to be inaccurate).

Occam

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Posted: 07 October 2007 05:39 PM   [ Ignore ]   [ # 6 ]
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Jackson,

Jackson - 07 October 2007 03:06 PM

To patch from Doug’s first reference

The name “Avogadro’s Number” is just an honorary name attached to the calculated value of the number of atoms, molecules, etc. in a gram mole of any chemical substance.

Well it’s good to get that out of the way.  My interest is understanding how they managed to calculate number, as that will help me understand what the bloody point of it is.  smile

For instance, I don’t quite understand what the difference is between a gram and a ‘gram-mole’

Based on what I read, my guess is that since Avogadro’s number is so huge, it must refer to the amount of atoms in a gram?

Of course if we used some other mass unit for the mole such as “pound mole”, the “number” would be different than 6.022 x 1023.

And is that because a pound mole refers to how many atoms are in a pound?

So there is an error in your Wikipedia reference as I understand it.

a. The experiments were done by Avogadro ( LOL )

Ok, so you mean wikipedia is wrong to suggest that avogadro did the experiments required to establish Avogardo’s number?

b.  The number is actually not dimensionless

I don’t remember reading or considering anything to do with the number ‘having dimension’ or lacking in dimension.  So I’m a bit puzzled in that regard.

because [the number] depends on the definition of “mole” and “gram” (as noted in Doug’s reference).  It takes 6.022 x 10^23 atoms to give a mass equal to the atomic weight in grams.

Or in other words, there are 6.002 x 10^23 atoms in 1 gram? 

Much like there are 12 eggs in what we consider a carton of eggs (a dozen?)

c. So you asked about the specific experiment.

Precisely

http://www.madsci.org/posts/archives/1998-03/889394526.Ch.r.html  This look like a good reference.

I’ll check it out.

I would also point to an essay by Isaac Asimov:
To Tell a Chemist
Subject: Avogadro’s number
First Published In: May-65, The Magazine of Fantasy and Science Fiction
Collection(s):

1966 From Earth to Heaven

1974 Asimov on Chemistry

I suppose such an essay would be most obtainable at most university library’s.  I’ll see if they have it where I’m at. 

Thanks!

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Posted: 07 October 2007 06:25 PM   [ Ignore ]   [ # 7 ]
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Occam,

Occam - 07 October 2007 05:18 PM

The molecular weight of any material expressed in grams is called a mole.

I don’t understand this whole concept of ‘molecular weight’.  I understand the metric system.  Therefore, I understand how molecules probably weigh picograms or nanograms.  But I feel like I’m really missing something here.

For example water, H2O has a molecular weight of 18.016

Huh?  18.016 picograms, nanograms?   

So that would be the number of grams that would be called a mole.

Are you saying that there is 18.016 grams in a mole? 

I’m quite sure you aren’t, but I have no idea how else to interpret what you’re saying.  [shrug]

It’s not too obvious, but if you think about it carefully, you’ll realize that the moles of any material would have the same number of molecules.

 

Based on what you said above, my impression is that a mole isn’t so much a weight, but it’s a certain amount of occupied space.  Am I right?

That being said, when a person is interested in determining the amount of moles, really, they are interested in determining the amount of space that a substance occupies.  Am I right?

It’s not too obvious, but if you think about it carefully, you’ll realize that the moles of any material would have the same number of molecules. [That’s something you can reason out so I’m not going to explain why]. 

Well, that’s based on the assumption that all atoms are the same size.  I don’t think it’s unreasonable to think that maybe some elements are bigger or smaller than others. That being said, a mole of carbon might contain more or less atoms than a mole of Iron. 

Avogadro was the first one who calculated that number and it was given his name.

If the number is arbitrary, then why did it require him to calculate it?  He could have just picked one.

Remember that the weight called a gram is also arbitrary.  It all stems from the distance from the north pole to the equator (even though that measurement was later found to be inaccurate).
Occam

What was the logic behind that?  How the distance from the north pole to the equator gives us a bearing on deciding how much a gram should be, eludes me.

[ Edited: 07 October 2007 06:46 PM by CoryDuchesne ]
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Posted: 07 October 2007 06:54 PM   [ Ignore ]   [ # 8 ]
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Any unit of measure is arbitrary. That doesn’t matter so long as it is clearly defined and consistent. As I understand it, a gram is the weight of 1 cubic centimeter of water at 4 degrees centigrade. Nothing special about that except that it is easy to define and is consistent over time so it provides a useful unit system.

The same is true with moles. If you define a mole as the amount of something that weighs, in grams, the same as the molecular weight of a molecule of that something in atomic mass units, then you consistently end up with 6.02 x 10 to the 23rd molecules of that something in a mole. Think of a mole like you would think of a dozen. It’s a relatively arbitrary, but convenient, unit of quantity that lets you compare amounts of things. So the molecular mass of water is 18.016. If you have 18.016 grams of water, that’s one mole, and it will contain Avagadro’s number of water molecules. It actually gets a little fancier when you start considering isotopes and such, but that’s more than good enough for me as a biologist.

As for why the number is what it is, Occam is clearly smarter than the rest of us, because it doesn’t matter how hard I think about it I can’t figure out why. I do remember having a professor do the math for me in college, and for one brief shining moment I understood it. The light has faded, but I am content to accept that the number is what chemists say it is because of that little transient moment of comprehension. I realize that may not be good enough for you, but it suffices for me.

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Posted: 07 October 2007 07:32 PM   [ Ignore ]   [ # 9 ]
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A proton or neutron is assigned unit mass, i.e., 1 (really it’s based on oxygen having an arbitrary atomic weight of 16, but I won’t get into that).  A proton or neutron weighs 1 atomic unit.  A hydrogen atom consists of one proton and one electron (which weighs a hell of a lot less) so the atomic weight of hydrogen is 1.008.  If you have water at a M.W. of 18.016 and you take enough molecules of water to weigh 18.016 grams you have a certain number of molecules.  If you use, say, hydrogen gas, H2, it has a M.W. of 2.016.  If you take enough of those molecules to weigh one mole, 2.016 grams, then it seems obvious that you would have the same number of molecules in the one mole of water and the one mole of hydrogen.  They wouldn’t be the same volume, and they wouldn’t be the same weight, but they would have the same number of molecules in each of the two moles.

Off-hand I don’t recall the technique used to determine the weight in grams of a proton, etc. but obviously it’s 1 divided by Avogadro’s number.

I hope this clarifies everything.

[As I think of it, possibly the 0.008 is because of the small amount of deuterium and tritium rather than the electron, because of using oxygen as 16.000, but I’m not about to dig my freshmen chem text out of storage.  You can check Wikipedia, Cory.]

Occam

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Posted: 08 October 2007 11:41 AM   [ Ignore ]   [ # 10 ]
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Mckenize, thanks for the reply - keep in mind that many of the following questions are directed at readers in general, and not specifically at you.  Many of my questions you have said near the end of your post that you don’t know, and so I’m just asking the questions simply to help focus the thread in a particular direction.  But if you suddenly have an epiphany or realize you forgot to mention something that might be edifying, then by all means.  smile

mckenzievmd - 07 October 2007 06:54 PM

Any unit of measure is arbitrary. That doesn’t matter so long as it is clearly defined and consistent. As I understand it, a gram is the weight of 1 cubic centimeter of water at 4 degrees centigrade. 

Ok, so initial unit of measure is arbitrary.  However, all measurements which follow from that are not arbitrary.  The relative, observable difference between the weight of a brick and the weight of a feather is not random. 

That’s why I don’t think it’s correct to consider avogadro’s number arbitrary.  There are very specific reasons why Avogadro’s number is the number that it is.  I just have yet to fathom these reasons.

The same is true with moles. If you define a mole as the amount of something that weighs, in grams, the same as the molecular weight of a molecule of that something in atomic mass units, then you consistently end up with 6.02 x 10 to the 23rd molecules of that something in a mole.

The part I bolded is what I’m confused by.  It sounds like you are saying that 1 mole is (an enormous, but very specific number) of molecules.  Why molecules?  Don’t you mean atoms?  The reason why I make the distinction is that molecules often refers to compounds which can vary in size.  And don’t atoms vary in size depending on what element they are?  If so, then I’m VERY confused about the point of Av’s number.

Think of a mole like you would think of a dozen. It’s a relatively arbitrary, but convenient, unit of quantity that lets you compare amounts of things.

But I can actually count a dozen eggs in contrast to a 6 pack of beer.  The concept of 6-pack or a dozen actually refers to the empirical world that I can see.  I can actually see what the concepts are pointing to.  A mole is much more confusing.  I don’t understand how they decided on such a specific number.  My guess is that math is not going to be the vital thing for me to consider, but rather, it’s the experiments they did in order to ‘feel out’ the microcosm.  It’s the experiments that will prove to be most helpful and edifying.  The math will just be icing on the cake. 

But, maybe not. 

So the molecular mass of water is 18.016.

You mean the amount of moles in 18.016 grams of water is 1?  36.032 grams of water = 2 moles?  Etc.

And if the amount of grams per/mole varies depending on the element or compound, does the volume always remain constant? 

(e.g:  1 mole of mercury and 1 mole of water may occupy the exact amount of space in a test tube, yet those two identical volumes have differing weight)

In other words, am I right to conclude that identical volumes of liquid or solid, despite they vary in weight, contain an identical number of atoms?   

If you have 18.016 grams of water, that’s one mole, and it will contain Avagadro’s number of water molecules.

Why such a specific number?  It seems appropriate to arbitrarily establish a unit for weight.  While on the other hand, the amount of atoms occupying a given space doesn’t seem arbitrary at all.  It just seems like something that you have no choice but to acknowledge.     

As for why the number is what it is, Occam is clearly smarter than the rest of us, because it doesn’t matter how hard I think about it I can’t figure out why. I do remember having a professor do the math for me in college, and for one brief shining moment I understood it. The light has faded, but I am content to accept that the number is what chemists say it is because of that little transient moment of comprehension. I realize that may not be good enough for you, but it suffices for me.

Well, regardless, you have been helpful - thanks.  I’m a little bit clearer about the factors that are vital to consider, and that’s good enough for now.

[ Edited: 08 October 2007 09:55 PM by CoryDuchesne ]
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Posted: 08 October 2007 11:55 AM   [ Ignore ]   [ # 11 ]
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Occam - 07 October 2007 07:32 PM

A proton or neutron is assigned unit mass, i.e., 1 (really it’s based on oxygen having an arbitrary atomic weight of 16, but I won’t get into that).

I don’t think I’ll even be remotely satisfied until I get into that.  smile

When you say atomic weight of 16, what, is that like 16 picograms or nanograms?

Or do you mean that 16 grams of pure oxygen is 1 mole?

How much does an atom weigh?  Does it vary depending on the element?

How do I relate the atomic weight of 16 to what I already know(basic metric system stuff)? 

A proton or neutron weighs 1 atomic unit. 

How did they determine that?  Certainly it’s not arbitrary, because doesn’t it conform to the metric system?  The origins of the metric system are arbitrary, but the contrasting weight differences from big to small are not arbitrary. 

This all must have something to do with how they determined the atomic weight of oxygen.  Perhaps that is the crux of the mystery here.

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Posted: 08 October 2007 12:37 PM   [ Ignore ]   [ # 12 ]
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Right, 16 grams per mole. Scientists rarely work with weight, which is dependent on gravity. Rather, mass is far more common. The mass of an atom is roughly the sum of its protons and neutrons, each counted as 1. If you look at a table of the elements, you’ll find that the atomic number is half its atomic mass. The number represents the number of protons in an atom. The atomic mass, however, considers both protons and neutrons since they’re about the same mass. Electrons are much tinier and almost arbitrary with respect to atomic mass.

An atomic unit is defined as the mass of a proton or neutron, which is constant from element to element. There’s no unit of measure, metric or otherwise, associated with it.

I’m sure I’ve oversimplified, but for the layperson these things are generally true.

[ Edited: 08 October 2007 12:40 PM by Isherwood ]
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Posted: 08 October 2007 01:30 PM   [ Ignore ]   [ # 13 ]
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I’m through.  Until you take and understand a number of highschool and college general science and chemistry courses, it’s a waste of my (and everyone else’s) time trying to explain anything to you.  You may think you are bright and searching, but I assure you that your questions demonstrate the lack of even the most elementary understanding of any facet of science.

Occam

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Posted: 08 October 2007 10:58 PM   [ Ignore ]   [ # 14 ]
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Occam - 08 October 2007 01:30 PM

You may think you are bright and searching, but I assure you that your questions demonstrate the lack of even the most elementary understanding of any facet of science.

Why don’t you tell me what these ‘most elementary understandings’ are, Occam?

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Posted: 08 October 2007 11:39 PM   [ Ignore ]   [ # 15 ]
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Isherwood,

Isherwood - 08 October 2007 12:37 PM

Right, 16 grams per mole. Scientists rarely work with weight, which is dependent on gravity. Rather, mass is far more common.  The mass of an atom is roughly the sum of its protons and neutrons, each counted as 1. 

Ok, so if hydrogen has a mass of approximately 1, then it would seem that one should simply multiply Avogadro’s number by the mass of the element, and that will tell you how many grams is in one mole of hydrogen.  There is one gram in a mole of hydrogen.  I think I’ve made some progress here.  Or have I?

An atomic unit is defined as the mass of a proton or neutron, which is constant from element to element. There’s no unit of measure, metric or otherwise, associated with it.

Well, it does seem as if the atomic mass of an element relates very directly with the metric system (grams). 

The big question that remains for me is how they managed to discover/detect the proton and neutron.  Not to mention, how they managed to tell apart one atom from another by identifying which ones had certain numbers of protons/neutrons.  Quite a feat if you ask me.

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