Re: SI Units

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

On Tue, 4 Mar 1997, Ian Sefton wrote:

> Gary Karshner wrote
> > ...  Is the mole used and is it the gram-mole, i.e. is there such
> > a thing as the kilogram-mole? My text uses gram-moles and it really throws
> > the students as their IS calculations are off by a factor of one thousand if
> > they are not careful with their units.
>
> A mole is a mole is a mole. It is the SI unit of amount of substance which
> is defined in terms of the number of particles (atoms, molecules, ions,
> electrons or whatever you want to talk about) in a system. The symbol for
> mole is mol.

My, oh my! Sometimes I read things on this newsgroup which make me scurry
to my reference library to find out whether everything I thought I knew
might actually be wrong.

Yes, folks, Ian, and Virginia, too; the kilomole exists, and is alive and
well. Some books use mole, some use kilomole, even when they are otherwise
scrupulous about sticking to SI units, so you'd better watch out! This is
one of the dirty little secrets of physics: Physicists aren't as
consistent or logical as they'd like the world to believe. 

One can quickly find out whether a book is consistently using SI units, or
its compromising them. Just look in the table of constants for the value
of Avogadro's _constant_.

              23     -1                     26     -1
A = 6.022 x 10   mole    , or A = 6.022 x 10  kmole

But then look farther. Some books give Avogadro's constant in reciprocal
kilomoles, then express other units in gram-mole, such as the universal
gas constant, Boltzmann's constant, and Faraday's constant. I.e., they are
using mixed systems. For shame!

Just from my home library I find these examples:

Francis Weston Sears. _Thermodynamics_, Addison-Wesley 1955.
	Uses kilomoles consistently in all cases.
Philip M. Morse. _Thermal Physics_ Benjamin, 1969.
	Mixed mole and kilomole.
Anderson, Elmer E. _Introduction to Modern Physics_ Saunders, 1982.
	Consistently kilomoles.
Arthur Beiser. _Concepts of Modern Physics, 5th ed._ McGraw-Hill, 1995.
	Kilomoles.
Arya, Atam P. _Elementary Modern Physics_, Addison-Wesley, 1974
	Kilomoles consistently.
Espinola, Thomas. _Introduction to Thermophysics_ Wm. C. Brown, 1994.
	Kilomoles consistently.
Nolan, Peter J. _Fundamentals of College Physics_ Wm. C. Brown, 1993.
	Kilomoles consistently.
Wehr, Richards and Adair. _Physics of the Atom_ 4th edition.
Addison-Wesley, 1984.
	Mixed. On p. 7 we find:
"Note that the mole and the Avogadro constant have been defined in terms
of 12 grams of carbon. This is the modern practice. However, these
definitions do not always conform to the Si system of units. Therefore, we
will on occasion use the kilomole, kmole, which is 1000 moles. Obviously a
kilomole of carbon 12 has a mass of 12 kilograms.)"

Another book defines mole as "the amount of substance that contains as
many elementary entities (atoms, molecules, ions, electrons, other
particles) as there are atoms in 0.012 kg of C12." 

You see, when the official definition was made, it was done in the era
when most physicists used cgs units. I haven't kept up with SUN commission
reports recently, so maybe they've gotten on the ball and revised the
official definition to an MKS statement. 

I've listed some older books to demonstrate that the kilomole is not a new
fad, but has been around at least as far back as 1955 (when I entered
college), and was being used consistently in some texts even in those dark
ages.

Note that the term "Avogadro constant" is preferred over "Avogadro's
number", to emphasize that it is a *physical* concept, not merely a
*mathematical* one. (No mathematical analysis can determine the size of a
mole, only a physical experiment can.) To speak of a mole of grains of
sand is pointless, for that much sand has no physical significance
whatsoever. So I cringe a bit when I see chemistry texts trying to make
the concept seem simple by saying "The mole is merely a number," or
referring to "Avogadro's number". 

Avogadro's constant isn't a mole. It has the *units* of reciprocal
mole, being a unitless number divided by a mole (or kmole) of material. 
And in all the books listed above, the value of A is given in mol^-1 or
kmol^-1. If you want to do unit consistency analysis on equations, you've
got to attach the right units to it.

The fact that A is given a physical unit is a strong statement that
it's *not* "just a number".

	-- Donald

......................................................................
Dr. Donald E. Simanek                            Office: 717-893-2079
Prof. of Physics                    Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745          CIS: 73147,2166 
Home page: http://www.lhup.edu/~dsimanek            FAX: 717-893-2047
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