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The Mole & Avogadro’s Number
Posted: 09 October 2007 01:54 AM   [ Ignore ]   [ # 16 ]
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Goodbye Cory.  I’m putting you on Ignore because I don’t enjoy bothering with a troll.  I figure others will learn to do that and you’ll have to find some other forum to act like an ass on.

Occam

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Posted: 09 October 2007 11:32 AM   [ Ignore ]   [ # 17 ]
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Occam - 09 October 2007 01:54 AM

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.

(And then later)

I’m putting you on Ignore because I don’t enjoy bothering with a troll.  I figure others will learn to do that and you’ll have to find some other forum to act like an ass on.

Hmm, I’m a bit puzzeled by Occam’s hostile reactions. 

Is it possible that he himself actually has a rather superficial understanding of nature?  Perhaps that’s why my very basic, fundamental questions have caused him such irritation; perhaps he fancies himself to know more than he really does and hence gets frightened and hostile toward anyone who doesn’t mirror the smug, pedantic attitude which stablilizes his unconsciously bewildered mind. 

If not, it’s a pity, because that’s the impression he has given.

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Posted: 10 October 2007 01:01 AM   [ Ignore ]   [ # 18 ]
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The value of A.‘s number is arbitrary in that it is tied to the units of mass we choose to use.  If we used, say, pounds, we’d have to calculate how many atoms of a given element are in the number of pounds corresponding to the atomic weight.  If we used a unit of mass of pithyfeathers (I don’t know what they are either!), we’d calculate the number of molecules or atoms in a atomic-number’s mass worth of pithyfeathers.

Atomic weights are essentially counting numbers, they measure the number of (roughly) proton-sized masses in an atom or molecule.  Logical thought leads to the idea that one can “unitize” the counting number by making it grams, kilograms, pounds, slugs, or pithyfeathers.  So instead of “atomic mass 16” we end up with “16 kilograms”.  It’s also clear that in atomic (or proton) mass units, it takes exactly one atom/molecule to have “enough” mass to add up to it’s atomic weight.  When we decide to count in kilograms or pithyfeathers, we need a number of atoms/molecules identical to the ratio of 1 AU expressed in the weight unit to 1 weight unit (in our case, 1 AU = how many kilograms, or lbs, or pithyfeathers).

To put it simply: to have exactly 1 atomic weight of a molecule, you need only one molecule.  To have enough molecules to make exactly one unit of mass in another set of units (say, 1 kg), the number you need is equal to the ratio between the weight of one atomic-mass in kilograms, and the arbitrary unit in question (say, a kilogram).

So   (1 AU) is to (1 Kg)  as (1 atom) is to (n atoms) where we solve for “n”.

1 AU / 1 Kg = (1.660538782(83) × 10−27 kg)  /  1kg  

If it takes 1 atom to make 1 AU, how many atoms to make one kg?

1AU (in kg) / 1 kg =  1 atom / n atoms

n = 1 / 1AU(in kg)  = 1 / 1.660538782(83) × 10−24 kg = 6.023x10+23   Notice that A.‘s number is just = 1 / (1AU mass expressed in kg)

Similarly, if I said a single AU was 1/100th of a pithyfeather (notice how completely arbitrary this is, just like the kilogram), I’d need 100 1AU atoms to make one pithyfeather of mass.  Analogously, if I had molecules each weighing 16AU, 100 of them would equal 16 pithyfeathers.  If I had huge protien molecules, each weighing 205 AU, then 100 of them would weigh 205 pithyfeathers.  In any case, the “magic” number either 100 or Avogodro’s comes from understanding the mass of a single AU expressed in my arbitrary unit system.

As an interesting aside, here’s a question for you:  Does Avogadro’s number HAVE to be an integer?  If you can think about and answer this question clearly, you’ve almost certainly got a great grasp of the “magic” number.

-Scott

[ Edited: 10 October 2007 01:07 AM by tscott ]
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Posted: 10 October 2007 01:31 AM   [ Ignore ]   [ # 19 ]
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Oh, CoryDuchesne, regarding the idea of “units”.  Any time you have 12 “things” the things are units.  You can have 12 beers, 12 drummers drumming, 12 Krispy Kreme donuts, 12 secons, 12 lightyears or 12 kilograms.  The number “12” is without units until you specify a “thing” you’re counting.

With a 12AU mass atom,, the “thing” we’re counting are Atomic Units of mass. One can convert one unit to another by simple arithmatic as long as the units have the same fundamental dimension (e.g. mass, length, time, etc.).  In some cases we can even convert between dimensional units, say by changing distance into time or vis-versa (i.e. one light-year), but such conversions between dimensional quantities are fairly rare. 

Related to all that is the notion of dimensionles units, which are often specific ratio-values that let us convert from one unit of a given dimension to another unit of the same dimension (say, lbs to kg or light-years to angstroms, or AU to kg).

If I wanted you to bring me 12 in a small shopping bag, you wouldn’t know whether to bring elephants, apples, centimeters, volts of electricity, Dawkins books or Sponge-Bob action-figures.  When we specify units, we make things clearer.  When we assign dimensions to the units, we can begin to talk about commonalities between the various entities (say, the weight of apples vs. elephants or the length of Dawkins books vs action-figures). 

Physics typically boils down to dealing with the universe in terms of mass, energy, field-strength, time and distance units.

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