- #1
Rasalhague
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I'm a bit confused about the terms "mole", "Avogadro's number", "Avogadro's constant" and "the Avogadro constant" and the concept - or concepts - they represent. I'm puzzled about how "amount of substance" differs from "amount", and in what sense this is a dimension if - unlike other dimensions - its units can be used to measure anything.
The terms "mole" and "Avogadro's number" seem to be synonymous (interchangeable), at least for some authors, given statements such as these:
"Definition of the mole: if we measure out exactly 12g of carbon-12, then we have exactly 1 mole of carbon 12 atoms. There will be exactly an Avogadro's number of atoms in the pile" (Atkins & Jones: Chemical Principles, F43).
"Things to understand about Avogadro's number. It is a number, just as is dozen, and thus is dimensionless; you can think of Avogadro's number as the chemist's dozen." (General Chemistry Virtual Textbook http://www.chem1.com/acad/webtext/intro/MOL.html ).
"The Mole is like a dozen. You can have a dozen guitars, a dozen roosters, or a dozen rocks. If you have 12 of anything then you would have what we call a dozen. The concept of the mole is just like the concept of a dozen. You can have a mole of anything" ( http://library.thinkquest.org/19957/atomic/molebody.html ).
"A convenient name is given when there is an Avogadro's number of objects - it is called a mole. Thus in the above example there was a mole of pennies. 1 mole = N_A objects. The mole concept is no more complicated than the more familiar concept of a dozen : 1 dozen = 12 objects" ( http://www.iun.edu/~cpanhd/C101webnotes/quantchem/moleavo.html ).
Atkins and Jones distinguish between Avogadro's number, "a pure number", and Avogadro's constant (or the Avogadro constant - they use both terms), "a constant with units". They designate the latter concept N_A, unlike some of the sites I quoted above who use N_A as their symbol for the former (supposing those other sites make this distinction).
On the other hand, the Wikipedia article Avogradro constant takes a different approach. It says the Avogadro constant was "originally called" Avogadro's number. According to this article, "The change in name to Avogadro constant (N_A) came with the introduction of the mole as a separate base unit in the International System of Units (SI) in 1971, which recognised amount of substance as an independent dimension of measurement. With this recognition, the Avogadro constant was no longer a pure number but a physical quantity associated with a unit of measurement, the reciprocal mole (mol^−1) in SI units."
If a mole is a certain number, approximately 6.022 * 10^23, also called, according to some sources, Avogadro's number, and if - as the Wikipedia article defines it - the Avogadro constant is this same number times mol^-1, its inverse, then the Avogadro constant must equal 1... but that contradicts the statement that the Avogadro constant is not dimensionless. I'm guessing the contradiction arises because some of these definitions I've read conflict with each other. Which is the best or most thorough or more orthodox definition? Are there competing definitions currently in use, and if so could someone explain the differences to me? Or are they all somehow equivalent really?
For those who take "amount of a substance" as a dimension, would it still be correct to talk of a mole of anything (eggs, dollars, meters, radians, tens, troubles...?) or would a mole be limited, according to this definition, to amounts of physical items such as eggs or dollar bills, or would it be limited still further to counting only atoms, ions or molecules?
The Wikipedia article Amount of a subtance
http://en.wikipedia.org/wiki/Amount_of_substance
offers several rationals for having a unit for the amount of a substance. They mention the comparison with "standard batch size" such as reams of paper or dozens of eggs, but say a better analogy is the value of gold held by a bank. In their "rationale for preferring amount-of-substance to absolute numbers", they compare the mole to the astronomical unit. See in particular the paragraph:
"This is somewhat similar to the situation that existed in Solar system astronomy for a time, where one did not know very well the absolute distances of the planets to the Sun, but one did know quite precisely the ratios of these distances to each other and, in particular, their ratios to the distance from the Earth to the Sun. The latter distance became known as the astronomical unit, and one way to describe the situation is to say that one knew quite precisely all the distances in terms of the astronomical unit, while the length of the astronomical unit itself was known quite poorly. [...]"
Perhaps I'm taking this too literally, but surely the AU is a unit of length (however poorly its exact relationship to other units of length may be known), and economic value is measured in dollars (or euros or rupees, etc.); we can't say how many kilograms away the sun is, or how many AU of roosters or guitars there are, or how many dollars of radians make half a circle. If we can say how many moles there are of anything (including units of any other dimension), then a mole seems more like a pure number than a dollar does or an AU. More like pi, for example, since we could express any quantity as a multiple of pi, if not exactly, to as much accuracy as we choose.
So, we can say so many times pi roosters (or so many dozens of roosters, moles of roosters?) and so many times pi meters (dozen meters) and so many times pi dollars (dozens of dollars), but not so many dollars of meters - which leaves me wondering in what sense the value analogy used by the Wikipedia article is preferable to the dozen analogy, except for the technical matter of whether the quantity is literally counted one, two, three...
The terms "mole" and "Avogadro's number" seem to be synonymous (interchangeable), at least for some authors, given statements such as these:
"Definition of the mole: if we measure out exactly 12g of carbon-12, then we have exactly 1 mole of carbon 12 atoms. There will be exactly an Avogadro's number of atoms in the pile" (Atkins & Jones: Chemical Principles, F43).
"Things to understand about Avogadro's number. It is a number, just as is dozen, and thus is dimensionless; you can think of Avogadro's number as the chemist's dozen." (General Chemistry Virtual Textbook http://www.chem1.com/acad/webtext/intro/MOL.html ).
"The Mole is like a dozen. You can have a dozen guitars, a dozen roosters, or a dozen rocks. If you have 12 of anything then you would have what we call a dozen. The concept of the mole is just like the concept of a dozen. You can have a mole of anything" ( http://library.thinkquest.org/19957/atomic/molebody.html ).
"A convenient name is given when there is an Avogadro's number of objects - it is called a mole. Thus in the above example there was a mole of pennies. 1 mole = N_A objects. The mole concept is no more complicated than the more familiar concept of a dozen : 1 dozen = 12 objects" ( http://www.iun.edu/~cpanhd/C101webnotes/quantchem/moleavo.html ).
Atkins and Jones distinguish between Avogadro's number, "a pure number", and Avogadro's constant (or the Avogadro constant - they use both terms), "a constant with units". They designate the latter concept N_A, unlike some of the sites I quoted above who use N_A as their symbol for the former (supposing those other sites make this distinction).
On the other hand, the Wikipedia article Avogradro constant takes a different approach. It says the Avogadro constant was "originally called" Avogadro's number. According to this article, "The change in name to Avogadro constant (N_A) came with the introduction of the mole as a separate base unit in the International System of Units (SI) in 1971, which recognised amount of substance as an independent dimension of measurement. With this recognition, the Avogadro constant was no longer a pure number but a physical quantity associated with a unit of measurement, the reciprocal mole (mol^−1) in SI units."
If a mole is a certain number, approximately 6.022 * 10^23, also called, according to some sources, Avogadro's number, and if - as the Wikipedia article defines it - the Avogadro constant is this same number times mol^-1, its inverse, then the Avogadro constant must equal 1... but that contradicts the statement that the Avogadro constant is not dimensionless. I'm guessing the contradiction arises because some of these definitions I've read conflict with each other. Which is the best or most thorough or more orthodox definition? Are there competing definitions currently in use, and if so could someone explain the differences to me? Or are they all somehow equivalent really?
For those who take "amount of a substance" as a dimension, would it still be correct to talk of a mole of anything (eggs, dollars, meters, radians, tens, troubles...?) or would a mole be limited, according to this definition, to amounts of physical items such as eggs or dollar bills, or would it be limited still further to counting only atoms, ions or molecules?
The Wikipedia article Amount of a subtance
http://en.wikipedia.org/wiki/Amount_of_substance
offers several rationals for having a unit for the amount of a substance. They mention the comparison with "standard batch size" such as reams of paper or dozens of eggs, but say a better analogy is the value of gold held by a bank. In their "rationale for preferring amount-of-substance to absolute numbers", they compare the mole to the astronomical unit. See in particular the paragraph:
"This is somewhat similar to the situation that existed in Solar system astronomy for a time, where one did not know very well the absolute distances of the planets to the Sun, but one did know quite precisely the ratios of these distances to each other and, in particular, their ratios to the distance from the Earth to the Sun. The latter distance became known as the astronomical unit, and one way to describe the situation is to say that one knew quite precisely all the distances in terms of the astronomical unit, while the length of the astronomical unit itself was known quite poorly. [...]"
Perhaps I'm taking this too literally, but surely the AU is a unit of length (however poorly its exact relationship to other units of length may be known), and economic value is measured in dollars (or euros or rupees, etc.); we can't say how many kilograms away the sun is, or how many AU of roosters or guitars there are, or how many dollars of radians make half a circle. If we can say how many moles there are of anything (including units of any other dimension), then a mole seems more like a pure number than a dollar does or an AU. More like pi, for example, since we could express any quantity as a multiple of pi, if not exactly, to as much accuracy as we choose.
So, we can say so many times pi roosters (or so many dozens of roosters, moles of roosters?) and so many times pi meters (dozen meters) and so many times pi dollars (dozens of dollars), but not so many dollars of meters - which leaves me wondering in what sense the value analogy used by the Wikipedia article is preferable to the dozen analogy, except for the technical matter of whether the quantity is literally counted one, two, three...
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