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The Mole

This lesson was written by Lynda Jones, at http://www.molechemistry.info/


In chemistry, the MOLE is the “name for a number,” and that’s all!

The MOLE is a VERY LARGE number, in fact, it is so large that most people cannot even read it. But here you will LEARN how to read it and understand its meaning very quickly.
It is EASY! Here is the number:


The easiest way to remember this number is first to notice how many commas it has.

How many commas DOES it have? Count them.

Now that you know that, the rest is EASY!

How to Read Large Numbers

In reading numbers, every 3 digits has a section name.
Some section names are hundreds, thousands, millions and billions.
If we have a number such as the one below, for example,


we read it as “231 thousand,” because the “231” is in the “thousands” section.

This next number…


is “458 million,” because the “458” is in the “millions” section.
We use this same pattern to read all large numbers in the United States, no matter how big the numbers get. (The British Isles have a slightly different system for naming large numbers, which we will explain later.)
In the United States, all you need to know is the sequence of section names,
which really isn’t that hard to remember after “millions,”
because the prefixes come from the names for the Latin numbers 1 through 10.
Here is the list of section names with the Latin-derived prefixes written in red.













When you display these horizontally, they look like this:

Chart with 142,000,000,000,000,000,000,000,000,000,000,000 written at the top.  Every 3 digits is written in a column marked off by the comma.  Column colors alternate between yellow and pink.  Under the number are written sideways the names of the 3-digit place values with the Latin prefixes written in red.  Reading from right to left, or from smallest value to largest, we have hundred, thousand, million, billion, trilliion, quadrillion, sextillion, septillion, octillion, nonillion, decillion.

So the number in this example reads “142 decillion.” From here, it should be EASY to read the numerical name for “the mole.” Here it is:

Chart with 602,200,000,000,000,000,000,000 written in it with the 3-digit place value names written underneath.  Names are written sideways in columns of alternating color, pink and yellow.  The names go from smallest to largest and from right to left, 'hundred, thousand, million, billion, trillion, quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion.

So, what is that number? “602 sextillion 200 quintillion.” That’s it!

How large is a mole?

My friend, fellow teacher and colleague, Mike Offutt from Chicago, did some calculations specifically to help us comprehend the sheer magnitude of the mole. He even wrote a song about it, “A Mole is a Unit,” which is very clever and which can be purchased in his album, “Chemistry Songbag I.”

Go to Chemistry is Easy Store

Here are three visualizations calculated by Mike Offutt to help you comprehend the magnitude of “the mole.”

1. The Marshmallows Visualization:

Let’s imagine that we have a mole of large marshmallows, like the ones you roast around a campfire. To get an idea of just how large a mole is using this example, read and imagine the following:

Imagine first a single line of marshmallows between your two hands held about a foot apart. How many marshmallows do you think that would be? 10 or 12?

Now imagine how many marshmallows it would take to make a line on the floor of your classroom which would stretch from wall to wall. Now imagine marshmallows covering the floor of your classroom with a layer just 1 marshmallow deep. How many marshmallows would that be?

Now imagine covering the entire surface of the earth, both land and sea, with a layer of marshmallows just 1 marshmallow deep. The earth is 25,000 miles (or 40,000 kilometers) around its equator. A globe this large gives us 197 million square miles (or 510 million square kilometers) of surface area, which includes both land and sea.

Believe it or not, even with marshmallows covering the entire 197 million square miles of surface area on the earth, that would not be anywhere near a mole.

Now imagine piling the marshmallows up to the ceiling in your classroom and imagine extending this pile all the way around the earth. Even THAT would not be a mole. Imagine piling up marshmallows to the height at which jet planes fly, which is about 6 miles or almost 10 kilometers.

Even a pile that high, covering the entire 197 million square miles of earth’s surface is not yet a mole. You would have to go beyond that another 12 miles more according to my calculations, to a total height of 18 miles, (assuming that the weight of the marshmallows on top did not squash the marshmallows on the bottom).

This would give you a total volume of marshmallows of 195 BILLION cubic MILES of marshmallows. Can you even imagine that?

Drawing of the earth with a circle drawn around it to suggest a distance from the surface of the earth going all the way around the earth.

You can prove this to yourself, if you are mathematically inclined, by downloading and following the step by step instructions on Worksheet 21 from HOLY MOL-EE! Chemistry, “Marshmallow Calculation.” It is available for 99 cents. It is easy to follow and has an answer key in both US and metric units for teachers. And it’s FUN! To download a pdf file of the Worksheet, click here. [Not yet active.]

PS: In the drawing of the earth above, the circle drawn in space around the earth is NOT drawn to scale. It does NOT represent 18 miles up. Since the earth is 8,000 miles in diameter, if we were to draw a circle to scale, it would be drawn so close to the surface of the earth that you could not see it. As the circle IS drawn above, it represents a height of approximately 1000 miles above the earth, or about 1/8 the earth’s diameter. It is drawn the way it is just to get you thinking about a pile of marshmallows.

Related comment on the size of atoms and molecules:

Try thinking about how very tiny molecules actually are. Do this next imagination exercise. Take all those marshmallows which you have imagined to cover the entire planet 18 miles deep and shrink them down.

Keep shrinking them down until each marshmallow becomes the size of a single water molecule. How much water do you think that would be? Would a mole of water molecules be an ocean? A lake? A swimming pool? A cup? A single drop?

It turns out that one mole of liquid water occupies a volume of only 18 milliliters, less than half the volume of a single old-time film cannister as shown to the right. Given the extremely huge volume of marshmallows we started with, does that give you some idea of just how teeny tiny atoms actually are?

Photograph of 35-mm film cannister less than half filled with water.

2. Money to the Moon Visualization:

Here is another imagination exercise to help you gain a feeling for the magnitude of a mole. This visualization is also from Mike’s song. What if we piled a mole of dollar bills from here to the moon? How many times would we have to go to the moon and back with our piles of money to add up to a mole of dollar bills?

The moon is ~ 239,000 miles away (~ 384,000 kilometers), a distance of 30 times the diameter of the earth. Any guesses? Mike says we would have to go back and forth 80 BILLION times to use up all our dollars. Isn’t that amazing?

Graphic showing the earth as a small sphere in the lower left hand corner with a dotted line going up to a smaller circle in the upper right hand corner, representing the moon.  The dotted lines represent dollar bills piled up to reach the moon.

3. Pennies Visualization:

Here is a third visualization taken from Mike’s song, “A Mole is a Unit.”
What if we had a mole of pennies and wanted to spread the wealth around so that every single man, woman and child on earth gets some.
The population of the world is estimated, as of May, 2010, to be 6,820,200,000.
When Mike wrote the song, it was about 6 billion.
Because of the simplicity of using the number 6 billion, let’s use that and see how much money each living person would get.

Here is a comparison between the mole and the population of the world when Mike wrote the song.

Chart showing 3-digit place values with columns of alternating pink and yellow with the names written sideways.  Names are, going from smallest to largest and from right to left, 'hundred, thousand, million, billion, trillion, quadrillion, quintillion, sextillion.'  At the top of the columns are written two numbers:  602,200,000,000,000,000,000,000 the mole, and 6,000,000,000  the population of the world.

Notice how many more zeros the mole has than the entire population of the world! So if you start with a penny in the “billions” place, where the “6” is in our world population shown above, and count over place by place multiplying by 10 each time, until you get to 600 sextillion, you can see that if we had even one mole of pennies to distribute to everyone on the planet, each person would end up with…..

Well, we would multiply by “10” 14 times! So $0.01 x 10 x 10 = $1.00.

$1.00 x 10 x 10 = $100

$100 x 10 x 10 x 10 = $100,000

$100,000 x 10 x 10 x 10 = $100,000,000

$100,000,000 x 10 x 10 x 10 = $100,000,000,000, which is already $100 billion for each person.

We have already mutiplied the population of the earth by “10” 13 times. One more time will give us….

$100,000,000,000 x 10 = $1,000,000,000,000

So if we had one mole of pennies to distribute around the planet, each man, woman and child would end up with $ 1 trillion!

Mike’s song, “A Mole is a Unit” is really worth getting.

How the mole is related to atomic mass:

Considering how infinitesimally teeny tiny molecules are, how does one go about determining how many molecules one has of a certain substance? Certainly we cannot weigh just one molecule. That would be harder to weigh than a puff of smoke! The only way we can tell how much we have is to weigh lots of molecules together, so that they add up to something our scales can detect.

Perhaps you know already that atoms are made of three different particles: Protons, neutrons and electrons. Protons and neutrons weigh about the same and are almost 2,000 times more massive (heavier) than electrons. [Being exact: protons = 1836 electron masses and neutrons = 1837 electron masses.] So the mass of any atom that has a few extra electrons, or is missing a few electrons, really doesn’t change in any noticeable way. Electrons are so light compared to protons and neutrons that electrons don’t really count in determining atomic mass. The mass of an atom is determined almost exclusively from how many protons and neutrons it has. Since protons and neutrons are both found in the nucleus of the atom, they are collectively referred to as “nucleons.”

The “mole” is a number scientifically determined such that when you have 1 mole of nucleons (either protons or neutrons or both), it weighs exactly 1 gram. There is a near perfect correlation between the total number of nucleons in an atom and how many grams 1 mole of those atoms weighs. Here are some examples:


hydrogen atom showing 1 proton in the center

Total Nucleons = 1

Grams in one mole = 1



helium atom showins 2 protons and 2 neutrons in the center.

Total Nucleons = 4

Grams in one mole = 4



carbon atom showing 6 protons and 6 neutrons in the center

Total Nucleons = 12

Grams in one mole = 12



argon atom showing 18 protons and 22 neutrons in the center

Total Nucleons = 40

Grams in one mole = 40

The history of how the number in a “mole” was determined.

In researching the answer to this question, I asked my good friend and chemistry professor, Dr. David Katz from the University of Arizona in Tuscon, to help me find the answer to this question. He directed me to a series of original scientific papers, originally written in either French or German between 1800 and 1920, and translated into English so we could read them. It was exciting to read the translations of the original papers, because I felt like I was standing alongside the scientists who were doing the ingenious experiments to discover the facts we now take for granted. It continues to amaze me how these scientists, not being able to see anything, were able to learn so much about the nature of atoms and molecules.

Joseph Louis Gay-Lussac of France (Paper written in 1809 about how different gases combine with each other — Mind you, he wrote this more than 200 years ago!) He studied how different volumes of gases combined during chemical reactions to make products. He measured and reported simple relationships between the beginning and ending volumes for the gases in his chemical reactions. 200 years ago, scientists only knew that different substances existed with different densities. They assumed that gases were made of molecules, but they did not know at all what molecules were like. To them it was a mystery. Remember, they couldn’t see anything. Gay-Lussac did experiments, made measurements and reported the facts for a number of different chemical reactions. Three of these experiments are shown in the diagrams below. portrait of Gay-Lussac

This first reaction is of an acid and a base, which always react to make a salt.

Green square labeled 'muriatic acid' + purple square labeled 'ammonia gas' -> white pile of neutral salt.

1 volume of muriatic acid + 1 volume of ammonia gas = 1 pile of salt which is exactly neutral. (This means that the acid and base above exactly cancelled each other out, implying there was exactly the same amount of each.)

Here is the reaction of hydrogen and oxygen to make water vapor.

Two light blue squares labeled 'hydrogen' + 1 red square labeled 'oxygen' --> 2 blue squares labeled 'water vapor.'

2 volumes of hydrogen + 1 volume of oxygen = 2 volumes of water vapor.

Gay-Lussac reported this, but he could not quite figure out WHY these volume relationships existed. He could not yet consistently predict from the volumes of reactants how many volumes of product would result.

Here is another reaction of nitrogen with hydrogen.

1 brown square labeled 'nitrogen' + 3 light blue squares labeled 'hydrogen gas' --> 2 purple squares labeled 'ammonia gas'

1 volume of nitrogen + 3 volumes of hydrogen = 2 volumes of ammonia.

Why in did you need only 2 volumes of hydrogen to give 2 volumes of water in the previous reaction, but need 3 volumes of hydrogen to make 2 volumes of ammonia? This is something Gay-Lussac could not answer.

portrait of Amedeo Avogadro Amedeo Avogadro of Italy (Paper written in 1811, only 2 years later, explaining how Gay-Lussac’s work pointed to the existence of atoms.) Avogadro studied Gay-Lussac’s data and deduced that in order for Gay-Lussac’s data to make sense, it had to be true that equal volumes of gases under the same conditions (namely, the same temperature and pressure) would always have the same number of particles. Once he figured that out, he thought it would be a simple step to find the relative masses of the different molecules, because the ratios of the masses of the molecules would simply be the same as the ratios of masses of the equal volumes of gases. And they could measure the masses of the gases!
Avogadro deduced that in order to explain Gay-Lussac’s data, both oxygen and nitrogen gas must be composed of two molecules stuck together to make one (They did not use the term “atom” in those days.), and that during chemical reactions the “two molecules” would break apart before they combine with something else. That is why one volume of oxygen will give you two volumes of water and one volume of nitrogen will give you two volumes of ammonia. See the drawings below.

(Avogadro’s personal life is interesting. If you have a few minutes, to learn more about this man and about how he fit into the scientific community click here.)

2 white squares, labeled 'hydrogen gas,' each showing 4 diatomic molecules of hydrogen gas inside + 1 square, labeled 'oxygen gas' with 4 red diatomic oxygen molecules inside --> 2 squares labeled 'water vapor' each showing 4 molecules of water inside.  Each molecule of water has 1 red oxygen atom and 2 white hydrogen atoms.

2 volumes of hydrogen + 1 volume of oxygen = 2 volumes of water vapor.

A “molecule” of pure oxygen must be made of two smaller “molecules” of oxygen stuck together as shown above, and when the larger “molecule” of oxygen reacts with hydrogen to make water, it breaks apart, each smaller “molecule” joining with hydrogen to make a “molecule” of water. So from 1 “molecule” of oxygen, we get 2 “molecules” of water. Remember, Avogadro deduced all this without being able to “see” the molecules at all. He was figuring out how it HAD to be in order to account for the data. Pretty smart!

Here is the reaction of nitrogen with hydrogen gas.

1 square labeled 'nitrogen gas' showing 4 diatomic molecules of nitrogen inside + 3 squares labeled 'hydrogen gas' with each square showing 4 diatomic molecules of hydrogen inside --> 2 squares labeled 'ammonia gas' each showing 4 molecules of ammonia (1 brown nitrogen atom and 3 white hydrogen atoms in each molecule).

1 volume of nitrogen + 3 volumes of hydrogen = 2 volumes of ammonia.

Again, Avogadro figured out that pure nitrogen “molecules” HAD to be composed of two smaller nitrogen “molecules” which broke apart to combine with the hydrogen to make ammonia. Otherwise, there could not be two volumes of ammonia at the end. This was brilliant thinking!


What is a mole



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