This lesson was written by Lynda Jones. It originally was at her website http://www.molechemistry.info. That website no longer exists.

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### In chemistry, the **MOLE** is the name for a very large number,

**We’ll learn **how to read it and understand its meaning:

**602,200,000,000,000,000,000,000**

**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,

**231,000**

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

### This next number…

**458,000,000**

### 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.**

**Hundreds**

**Thousands**

**Millions**

**Billions**

**Trillions**

**Quadrillions**

**Quintillions**

**Sextillions**

**Septillions**

**Octillions**

**Nonillions**

**Decillions**

### When you display these horizontally, they look like this:

### 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:

### 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.”

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?

Note: the circle drawn around the earth here is NOT drawn to scale. 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 that you could not see it. This is drawn just to get you thinking about a pile of marshmallows.

Note on the size of atoms and molecules:

Try thinking about how very tiny molecules actually are. Take all those marshmallows which you have imagined to cover the entire planet – and shrink 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?

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?

### 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, in 2010, to be 6,820,200,000. When Mike wrote the song, it was about 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.

### 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!**

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**How the mole is related to atomic mass:**

**How does one determine how many molecules one has of a certain substance? We can weigh lots of molecules together, so that they add up to something our scales can detect.**

**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.] S**

**o 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 defined such that when you have 1 mole of nucleons (either protons or neutrons, or both), it masses 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:**

Carbon

Argon

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

I asked my good friend and chemistry professor, Dr. David Katz from the University of Arizona in Tuscon, to help find the answer to this question. He directed me to a series of 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.

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### 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.

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

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### Here is the reaction of hydrogen and oxygen to make 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.

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### Here is another reaction of nitrogen with hydrogen.

### 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.

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### 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.)

### An experiment by Avogadro showed us that:

### 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!

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### Here is the reaction of nitrogen with hydrogen gas.

### 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!

### By the way, my friend, colleague and fellow teacher, Mike Offutt from Chicago, has a very catchy song about Avogadro’s Law in his album, “Chemistry Songbag.” I highly recommend it!)

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### Johann Josef Loschmidt of Austria

(Paper written in 1865, 54 years after Avogadro’s paper, explaining how to determine the size of molecules of air.)

### Loschmidt used simple mathematical equations and data to calculate the size of a molecule of air. He calculated it to be .. He used a constant, N, in his equation to represent the number of molecules in a unit volume of air.

### Even though Loschmidt calculated the size of air molecules, there were still many scientists who did not believe that molecules existed. They thought that some materials were continuous.

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Jean Baptiste Perrin of France (Paper written in 1909, 44 years after Loschmidt, talking about Brownian motion and the reality of molecules.)

Brownian motion is the random micro-movement of cells and particles seen through a microscope. Perrin received the Nobel Prize for Physics in 1926 for finally proving in a definitive way that molecules DID, in fact, exist. (Until then there was still discussion back and forth between different scientists about it.) Read the interesting presentation speech which summarizes his life work and for which Perrin won the Nobel Prize.

This lesson was written by Lynda Jones. It originally was at her website http://www.molechemistry.info. That website no longer exists.

https://web.archive.org/web/20151210062751/http://www.molechemistry.info:80/

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