about

moles and molecules and atoms

and

Avogadro's Number

(C) - Copyright, 2000 F.W. Boyle, Jr., Ph.D.

Then I hope this works for you!

Of course, the mole is a chemistry counting unit and is equal to
Avogadro's Number (not that Avogadro guessed the number; we just
honored his contributions to chemistry by naming the number after
him.) Avogadro's Number (**A.N.** for short) has a magnitude (this
means numerical value) of 6.022 x 10^{23}. This is THE
number of parts (usually atoms or molecules) that must be
gathered together to have what we chemists call a mole of
"stuff". Stuff is my way of saying "matter".

So if one could count **A.N.** of atoms of any element (Yep! The
number stays the same regardless of the element, dealing with
atoms or molecules dealing with compounds.) and could place those
6.022 x 10^{23} atoms in a pile, one would have a mole of
that "stuff".

Here are some examples:

OR

6.022 x 10^{23} atoms of sulfur (S)

OR

6.022 x 10^{23} atoms of helium (He)

OR

6.022 x 10^{23} atoms of gadolinium (Gd)

OR

6.022 x 10^{23} atoms of uranium (U)

OR

6.022 x 10^{23} atoms of silicon (Si)

I will come back to what chemists do to "count" out moles or
substances but first lets look at some mathematical
manipulations of moles, molecules, atoms, and **A.N.**

One of the simplest ways to deal with multiples and parts of moles is to use ratios. We all ready know one side of every ratio regardless of element and that is:

------------------

6.022 x 10

Example:

How many atoms are in 3 moles of Ag (silver)?

Solving for X, we find it to be 18.066 x 101 mole 3 moles

------------------ = ------------------

6.022 x 10^{23}atoms X atoms

How many moles are in 0.37 mole of Cu (copper)?

And X is found to equal 2.228 x 101 mole 0.37 moles

------------------ = ------------------

6.022 x 10^{23}atoms X atoms

Note that only the names were changed to protect the innocent. Sorry, my fingers slipped. Note that the only change was to replace the mole value on the right side of the equality.

This same ratio can be used to solve for the number of moles that are equal to a given number of atoms. Here are a couple of examples.

How 3.011 x 10 ^{22} atoms of Na (sodium) is equal to how
many moles of Na?

We solve for Y and find that 3.011 x 101 mole Y moles

------------------ = ------------------

6.022 x 10^{23}atoms 3.011 x 10^{22}atoms

How many moles of Ne (neon) contain 3.6132 x 10^{23} atoms
of Ne?

Completing the mathematics, one finds Y equal 6 moles.1 mole Y moles

------------------ = ------------------

6.022 x 10^{23}atoms 3.6132 x 10^{23}atoms

Once again, the above ratio equality can be used for any calculation of moles for any element.

Now, you say what about those darn compounds. They have to be
harder to deal with than this. Compounds have so many different
elements in them. I reply, "No, the same ratios above works
because **A.N.** is 6.022 x 10^{23} molecules when
dealing with compounds. (I won't confuse you at this point by
adding to the discussion the concept of formula units. They are
really the same thing as a molecule only different. ;o)

How about some examples you exclaim!!!

The first question is: How many molecules are there in 5.35
moles of sucrose (table sugar, C_{12}H_{22}O_{11}?

Of course, this must be a hard one, sucrose is such a "big" molecule. But the answer is, "No way! Hombre"

Multiplying and solving for X (just like we did for atoms), we find that 5.35 moles of sucrose (or any other substance) is equal to 32.218 x 101 mole 5.35 moles

----------------------- = ------------------

6.022 x 10^{23}molecules X molecules

Need I do more?? I think not!

A place where these calculations sometimes really get confusing is when the question, how many atoms of H at there in 5.35 moles of sucrose? "Whoa, you say! What are you trying to do to me?" How can a find the number of atoms of a substance when we are talking about molecules.

Just remember that all molecules are atoms stuck (chemists call it bonded) together in a semipermanent form. In sucrose as in all compounds, the subscript numbers following each atom tell us how many aomts of that particular element are in a single molecule of a particular substance.

So lets try figuring out how many atoms of each element are in a
single molecule of sucrose. The formula is
C_{12}H_{22}O_{11}. We note that the
subscript number are 12 for C (carbon), 22 for H (hydrogen) and
11 for O (oxygen). Translating to English, the formula tells us
that there are 12 atoms of C, 22 atoms of H, and 11 atoms of O in
each and every molecule of sucrose. And you probably ask, "So
what?"

This means that once we know the number of molecules of sucrose in a given number of moles of sucrose, we can quickly calculate the number of each kind of atom.

From above, we find that 5.35 moles of sucrose contain 3.2218 x
10^{24} molecules of sucrose. We can set up another
ratio like so.

For C:

Solving for W, one finds that there are 38.6616 x 1012 atoms C W atoms C

------------------ = --------------------------

1 molecule sucrose 3.2218 x 10^{24}molecules

I hope this helps. Good luck on your studies.