The Mole Unearthed
Over the years when grading the test on chemical quantities, I’ve been surprised to see
that the concept of the mole can still cause some trouble for many. In fact the concept
itself can contribute up to 50% of the errors on the test. I’d like to try and see if there’s a
way of removing some of the confusion for this concept, because as you progress
through this course (Chapter 8, Final exam...), and then into the next Chemistry course,
it never goes away.
We started off our discussions of the mole as a quantity by trying to put the concept into
the same context as the idea of the dozen, the gross, or the case – all of which are
called collection terms, which means they represent some specific quantity. The funny
thing for me, is that the name “Collection Term,” brings to mind gangster movies or TV
shows like the Sopranos, where the Wiseguy has his “collections”. In these shows the
mob guys have cool ways of defining quantities. If you watch these types of shows you
get used to these terms and then they sometimes creep into your everyday language.
For example, Pauli tells Tony that a guy owes him 200 large. What is this large thing?
Well, years ago that would have been called a “grand” or a “G.” which we all know
means $1000. But in the 21-century the mob is trying to keep things interesting so
they change up their terms a bit. So we can have values like 10 large or 50 large, which
are just mob ways of defining $10,000 or $50,000. The use of this term “large” defines
a specific quantity – in this case $1000 - just like the days of old with the “G”
designation.
Now, if Pauli gets arrested for using excessive force ‘collecting’ that dept of 200 large,
he might end up in prison (the can, the pokey, the big house, the crossbar hotel....)
doing, a nickel, or dime, or maybe even a stretch. Which are terms used to define
prison sentence quantities of, 5 years, 10 years, or maybe 20 to life.
With these collection terms they are being used to sound in the know, not to simplify
repetitive quantities or partial quantities. I don’t think you would do 1.5 stretches in
prison, and you’d sound pretty silly calling $500, a half large. But hopefully you get the
idea that defining a specific quantity with a name is fairly common, whether it’s in the
bakery, grocery or brewery industry, or the dark underworld of organised crime.
In Chemistry we have one very important collection term, which just happens to be a
very large quantity. Really, the only difference between using the mole quantity or the
dozen quantity, is the number that goes along with it. A quantity called Avogardro’s
Number (NA) equal to 6.022 x 1023
For fun let’s define our own collection term, let’s call it the Vogon, and give it a value of
42. Of course this is just a number and doesn’t refer to any particular thing. All we’ve
done is to say that if you have 42 of anything you have one Vogon.
We could do our equality thing and get our equation that shows what a Vogon is, and
use this equality to give us some conversion factors so that we could figure out how
many Vogons we might have if we had some count of things.
1 Vogon (things)
=
42 things
1 Vogon (things)
42 things
or
42 things
1 Vogon (things)
Example; I drop a box of toothpicks on the floor, and unlike Rainman I can’t count them
by just looking at them, so I pick them up one at a time and count them and get 63
toothpicks. Ah, but you ask, how many Vogons is that?
Well we know how many things we have so we want to convert that to Vogons, so that
would be the first conversion factor...
= 63 toothpicks
x
1 Vogon
42 toothpicks
= 63 x 1 Vogon
42
= 1.5 Vogon
What about if I told you that I had seen 13 Vogon of Canada Geese sitting in the middle
of the parking lot at the campus. How many geese is that?
= 13 Vogon x
42 geese
1 Vogon
= 13 x 42 geese
1
= 546 geese
That’s a lot of cleanup....
Like all collection terms we could have multiples or part units.
Example: if we had 673 Vogons, that would be
673 Vogons x 42 things/Vogon = 28, 266 things .
Or if we had 1 thing that would be:
1 thing ÷ 42 things/Vogon = 0.024 Vogons.
You get the idea...hopefully
OK, the Vogon thing is stupid, and doesn’t address the problem of the mole and
Avogadro’s number.
Substitute the word mole for Vogon and the number 42 with Avogadro’s number – which
is 6.022 x 1023, and we have exactly the same thing. We could use the mole to talk
about the number of toothpicks, or geese, but they are such large macro objects, it
would be unreasonable. The mole is used for counts of the extreme nanoscale, where
a huge number of things don’t take up much space. That’s why it’s used for quantities
of atoms and molecules, because they are so small that even if you have 6.022 x 1023
of an atom or molecule, you’re not filling the known universe with it. In fact a mole of
any element would barely cover the palm of your hand. The mole is a big number,
because we are dealing with such small things we need a large number of them to be
visible and usable.
Try to picture the scale.
An atom is on the order of 0.1- 0.5 nanometers across or 1 to 5 Å (x 10-10 m). That’s
really, really small. It takes the combination of millions of atoms to make a molecular
thing large enough to reach the micro-scale, and be barely visible under a light
microscope - like a ribosome. So we don’t want to use this large Avogadro’s number for
anything we can see - even with a microscope.
Just a quick example.
Let’s think about pollen grains, which we normally can’t see and according to Wikipedia
can be anywhere from 0.6 to 100𝜇m (x 10-6 m) in diameter. Let’s use the smallest sized
one (radius of 3 x 10-7m) and determine the volume (assuming it’s a sphere). Trust me
on the math…
Volume of one grain = 4/3πr3
= 4/3(3.14159)(3 x10-7)3
= 1.13 x 10-19 m3
Volume of one mole of grains:
= 1.13 x 10-19 m3 x 6.022 x 1023
= 68100 m3
Thats over 68000 cubic metres! Which, if it was a cube, would be a cube that was 41 m
long, wide and high…that’s the size of an apartment building for just one mole of pollen
grains.
So you can see why it is only used for atoms and small molecules, since moles of
atoms and molecules are macro in size without needing a postal code. And this macro
size quantity is directly related to the mass of the atoms or molecules - aka the molar
mass
So, let’s say I told you that I had 1.27 mole of gold atoms in the palm of my hand, how
would you know that I was right?
According to the Avogadro’s Number (NA) equality:
1 mole
=
1.27 mole gold atoms
6.022 x 1023
x
6.022 x 1023 gold atoms
1 mole gold atoms
= 1.27 x 6.022 x 1023 gold atoms
1
= 7.6 x 1023 gold atoms
Even if you could get some kind of microscope to visualize each individual atom
(possible) and start counting…that would take a long time.
But it just so happens that the atomic mass of any element on the periodic table – in this
case gold - is actually the number of grams for one mole of atoms, or 6.022 x 1023
atoms. That’s kind of convenient and very helpful because we can infer how many we
have by weighing them, which is a macroscopic activity and something we’ve all done.
In the case of the gold, I only have to weigh the gold and compare it the molar mass
(MM) from the periodic table, and I’d know how many moles I had.
Let’s say I weigh the gold and it turn out to be 250 grams, I look up on the periodic table
and see that gold is shown to have an atomic mass of 197 g/mol . Using my favourite
MM triangle.
moles = grams you have ÷ molar mass
= 250 ÷ 197
= 1.27 mol
grams
MM
mol
And with that proof I could say for sure that I had the 7.6 x 1023 gold atoms without
counting
Of course the same relationship of molar mass, number of moles and mass applies to
molecules (compounds) too. In those cases you need to determine the molar mass of
each of the elements (and the number that are present in the compound) and then add
them all up for the molar mass of the compound.
Once you know the molar mass, you can relate the mass (in grams) that you have, to
how many moles that represents. And once you know the number of moles, you could
actually say how many individual molecules you had, without the need of sitting down
with a strong magnifying glass and counting them individually.
So maybe the problem that many people have with the moles and Avogadro’s number
is relating the two equalities/relationships that have the word “mole” in them.
There’s Avogadro’s number:
1.
6.022 x 1023 things = 1 mole of things
And the Molar Mass relationship:
2.
MM = # grams (atoms or molecules)
1 mole (atoms or molecules)
But try to remember, the first item is just a count – a collection term, which is just a
name for a specific number. And the second term is a specific value for each element or
compound (found on the periodic table), that gives you the number of grams in one
mole.
While they both have the term mole in them, it’s the molar mass concept that we’ll
spend most of our time dealing with, since it is mole ratios that we get out of an
equation for a chemical reaction.
…the dreaded “Stoichiometry”…not to be confused with actual dread…