Avogadro’s Number
Tienne Moriniere-Myers
Chemistry 511
Amedeo Avogadro (1776-1856)
Gay-Lussac’s law of combining volumes (1808) (when two gases react, the volumes of
the reactants and products-if gases-are in whole number ratios) tended to support
Dalton’s atomic theory. Dalton did not accept Gay-Lussac’s work, but the Italian
chemist Amedeo Avogadro saw it as the key to a better understanding of molecular
community.
In 1811 Avogadro hypothesized that equal volumes of gases at the same temperature
and pressure contain equal numbers of molecules. From this hypothesis it followed that
relative molecular weights of any two gases are the same as the ratio of the densities of
the two gases under the same conditions of temperature and pressure. Avogadro also
reasoned that simple gases were not formed of solitary atoms but were instead compound
molecules of two or more atoms. Avogadro was able to overcome the difficulty that
Dalton and others had encountered when Gay-Lussac reported that above 1000C the
volume of water vapor was twice the volume of the oxygen used to form it. According to
Avagodro, the molecule of oxygen had spit into two atoms in the course of forming water
vapor.
Avogadro’s hypothesis was neglected for half a century after it was first published.
His hypothesis wasn't generally accepted until after 1858 (after Avogadro's death), when
the Italian chemist Stanislao Cannizzaro was able to explain why there were some
organic chemical exceptions to Avogadro's hypothesis. One of the most important
contributions of Avogadro's work was his resolution of the confusion surrounding atoms
and molecules (although he didn't use the term 'atom'). Avogadro believed that particles
could be composed of molecules and that molecules could be composed of still simpler
units, atoms. The number of molecules in a mole (one gram molecular weight) was
termed Avogadro's number (sometimes called Avogadro's constant) in honor of
Avogadro's theories. Avogadro's number has been experimentally determined to be
6.023x1023 molecules per gram-mole.
Introduction
The new television hit is Deal or No Deal. Contestants have the ability to win a million
dollars. What does it really mean to be a millionaire? Our students hear about this
number in their daily lives, but do they really know how much that really is? The
challenge of helping students to understand the concept of a huge numbers increases
when we begin discussing atoms.
What is a mole?
Atoms and molecules are very tiny and difficult to count. Less than 100 years ago,
scientist were able to come up with a “constant” to use when determining the number of
atoms or molecules in a substance: 6.02x1023(also know as Avogadro’s number) This
number was named after an Italian scientist (Amadeo Avagadro) who had done some
preliminary reasoning about this idea in the 18th century. The number was termed
“mole”, which is Latin for “lump”. A mole is a very big number, but atoms are small, so
you don’t necessarily have to have a big lump of something to have a mole of it. This
number has a great deal of significance for chemistry. It’s worth celebrating every
October 23 (10^23) from 6:02 in the am to 6:02 in the pm. (Mole Day)
In the English language we use words like decade, gross, and dozen to describe specific
numbers. If Mike has a dozen doughnuts, we know he has twelve. If Mike were to have a
mole of doughnuts he would have 6.02 x1023 doughnuts, enough for everyone in the
world to each have over a trillion doughnuts. The mole is a unit commonly used when
describing a number of atoms or molecules. (Hewitt, Suchocki, and Hewitt, 1999, 4669) Atoms and molecules are so tiny in size, that we need a huge number like the mole to
quantify them. The concept of mole is difficult for students, not only for its tremendous
size, but also because it refers to atoms and molecules, which are extremely small.
The lesson will begin with an activity designed to help students to understand what it
means to have a million of something The students will predict how long it will take to
count to a million if they were to increase a number every second. Students use the
factor- label method to calculate the times to be 11.6 days for a million. . (Educators’
Science and Mathematics Institute Series)
1 million seconds x ___1minute___ x___ 1hour ____ x____1day____= 11.6 days
60seconds
60minutes
24 hours
Next, students will be asked to determine an accurate estimate for the number of
Cheerios in a box of Cheerios cereal without counting each piece. This lesson gives
students a chance to grasp the idea that atoms are so small we need ways of quantifying
them without physically counting each piece. It also gives them a chance to work with a
concrete object. Each student counts and masses an equal number of Cheerios. Students
then calculate the class’s average mass of Cheerios per number of Cheerios. Students can
make an estimate of the number of Cheerios in a box, given the mass of Cheerios using
the factor-label method, illustrated below, using an example where 15 Cheerios had an
average mass of 3.0 grams and the box of Cheerios had a mass of 425 grams.
425g Cheerios x 15 Cheerios =2100 Cheerios
3.0g Cheerios
It is time to introduce Avogadro’s number and the definition of a mole. (see Powerpoint
Presentation) Next, determine the number of boxes required for a mole of Cheerios.
6.02 x 1023 Cheerios x 1 box Cheerios = 2.9 x 1020 boxes of Cheerios
2100 Cheerios
Stacked end to end, the boxes containing a mole of Cheerios would reach a distance equal
to 7.5 million trips from the Sun to Pluto!
Now connect the analogy to calculating the number of moles in aluminum. No one can
directly count the number of atoms in aluminum foil, but if you know how many atoms
there are in a certain number of grams, like the Cheerios, the job can be done.
Finally, have students calculate and ask students to calculate the number of atoms
contained in the penny based on the molar mass of 63.546 grams. (Minted before1982)
The students will answer questions in their notebooks.
Examples
If you were given a dollar a second, how long would it take you to have a million dollars?
Which has more atoms, a mole of helium or a mole of copper atoms?
If you had one mole of copper atoms, how many atoms would you have?
What does the size of Avogadro’s number tell us about the size of atoms?
Explain with an example.
To build student mole enthusiasm students will create and stuff moles at home. A pattern
and instructions will be provided. We can celebrate Mole Day by sharing our moles.
Figure 2. Cut out two pieces like this for the
body sides.
Figure 3. Cut out one piece
base.
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are needed to see this picture.
QuickTime™ and a
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are nee ded to s ee this picture.
http://www.smanet.org/online.nov.18/moles.htm
http://students.resa.net/bhsmc/ClassClicks/Diehl/diehls.htm
References
Hewitt, P., Suchocki, J., and Hewitt, L. 1999. Conceptual Physical Science. Menlo Park,
California: Addison Wesley Longman: 433, 466-9.
Bowden, Mary Bowden 1997 Chemical Achievers Philadelphia, Pennsylvania: Chemical
Heritage Foundation
http://www.smanet.org/online.nov.18/moles.htm
http://students.resa.net/bhsmc/ClassClicks/Diehl/diehls.htm
http://www.ed.mtu.edu/pd/lessonplans.html