The Mole Concept Explained By Analogy


This is a chemistry analogy that will help explain the concept of the mole

The premise for this analogy is really simple. You have a box. Inside the box there are bowling balls.

Concepts Explained

mass to number conversion, Avogadro's number, mole, molecular mass, molar mass, gram to mole conversion
Here's a quick math problem:

Let's say you know that each bowling ball in the box weighs 1 kg and the total weight inside the box is 2 kg. Can you figure out how many bowling balls are in the box without opening it?

closed boxj

Of course you can! The answer is 2 bowling balls.


Easy right? If each bowling ball weighs 1 kg and we have 2 kg of bowling balls, we have 2 bowling balls.

In this situation we used the total
mass of the bowling balls in the box along with the mass of each individual bowling ball to determine the number of bowling balls. This is what we call a mass to number conversion.

A general equation for this conversion is:


Key Concept:

In chemistry, atoms are way too small to count. However, in many situations we need to know the number of atoms we have in a sample. Just like what we did with the bowling ball problem, we use the total
mass of a chemical sample along with the mass of each individual atom (known as the atomic mass) to determine the total number of atoms in the sample. We can do the same thing with molecules.
The mass to number conversion for atoms follows the same general equation:


Calculate how many hydrogen atoms there are in a 1 kg sample of hydrogen. The atomic mass of hydrogen is 1.01 amu.

We learned in the the analogy Balls that 1 amu = 0.00000000000000000000000000199 kg, or 1.99 x10-26 kg in scientific notation. Therefore, using the equation above:

Wow, 5.07 x 1026 is a huge number! It would be a real pain if you had to deal with numbers that large throughout your chemistry class. Luckily, chemists have invented an easy way to deal with the incredibly large numbers that exist in samples of atoms. Read on...
Everyone, meet Amedeo Avogadro:


Avogadro made some important discoveries in the 1800's that eventually led scientists a century later to determine the number of carbon atoms in a 12g sample of 12C (C is the atomic symbol for carbon). This number is equal to 6.02 x 1023 and became known as Avogadro's number.

So, in other words, if you had a box with 12g of carbon in it, there would be 6.02 x 1023 atoms in that box.


"Dozen" is another word for the number 12. A dozen eggs is equal to 12 eggs.

In chemistry the word mole is another word for Avagadro's number, 6.02x1023. A mole of eggs is equal to 6.02x1023 eggs (wow, that's a lot of eggs!). A mole of carbon atoms is equal to 6.02x1023 carbon atoms.

We use the term mole to quantify things in chemistry such as atoms or molecules. The mole makes dealing with large numbers much easier. You will encounter this term a lot in your chemistry class.

For instance, let's say we had 12.04 x 10
27 atoms in a sample. Instead of writing a large number like 12.04 x 1027 we can simply write 2 moles (12.04 x 1027 = 2 x 6.02 x 1023). This is similar to writing 2 dozen instead of the number 24 (24 = 2 x 12).
When you put atoms together to form molecules, the molecules have a mass of their own. This mass is known as molecular mass and is usually expressed in amu. The molecular mass is calculated by adding together the atomic masses in the molecule.

Consider the following analogy. Let's say you formed a "bowling ball molecule" by attaching two 1 kg bowling balls to one 3 kg bowling ball:


How much would the total "bowling ball molecule" weigh? The answer is 5 kg. This is equal to the sum of the "bowling ball masses" = 3 kg + 2 x 1 kg = 5 kg. You could say that the "bowling ball molecular mass" of this "bowling ball molecule" is 5 kg.

Calculating the molecular mass of a molecule is no different or any more complicated. To calculate molecular mass you simply add up the atomic masses of the atoms in the molecule.

Calculate the molecular mass of a molecule of H2O. Assume that the molecule is made up of the 1H isotope of hydrogen and the 16O isotope of oxygen.

The atomic mass of 1H (hydrogen-1) is 1.01 amu. The atomic mass of 16O (oxygen-16) is 16.00 amu.

The molecular mass = 16.00 amu + 2 x 1.01 amu = 18.02 amu.
Molar mass tells you the total mass of an atom or molecule present in 1 mole of that atom or molecule. The units of molar mass are usually g/mole.

In the case of atoms, the molar mass of an element is equal to the atomic weight of the element expressed in the units of g/mole. See the examples below:

The atomic weight of hydrogen (atomic symbol = H) is 1.01. The molar mass of hydrogen is 1.01 g/mole.

The atomic weight of silver (atomic symbol = Ag) is 107.87. The molar mass of silver is 107.87 g/mole.

The atomic weight of iron (atomic symbol = Fe) = 55.85. The molar mass of iron is 55.85 g/mole.
When figuring out the molar mass of a molecule you go through the same general steps we described above, but the key is you use atomic weights instead of atomic mass. See the example below:

Calculate the molar mass of CaCl2.

The first thing we want to do is find the atomic weights of the elements in the molecule on the periodic table.

We see that Ca (calcium) has an atomic weight of 40.08
We see that Cl (chlorine) has an atomic weight of 35.45

We now add the atomic weights together. We multiply the atomic weight of Cl x 2 because there are 2 Cl atoms in the molecule:
40.08 + 2 x 35.45 = 110.98 g/mole
For detailed instructions and more examples of calculating molar mass click below:
Like we said above, atoms and molecules are too small to count. As a result, in order to figure out how many atoms or molecules are in a sample, we have to use the same method we used to figure out how many bowling balls were in the closed box. That is, use the mass of the sample along with the mass of each individual atom or molecule to figure out the number (in moles) in the sample.

When doing this you are converting from mass (usually in grams) to numbers (in moles). This is a very important skill that you will need to know for your chemistry class.

When we convert from grams to moles we use the general equation we talked about above:


When converting between from grams to moles we use the molar mass as the "mass of the thing". This is very important to remember.

How many moles are present in 2.0 g of CaCl2?

The first thing we need is the molar mass. We figured out above that the molar mass of CaCl2 is 110.98 g/mole.

2g/110.98 g/mole = 0.018 moles of CaCl2
For detailed instructions and example problems on how to convert between grams and mole click below:
Yes, we know what you're thinking, Amadeo was a weird looking dude. To learn more about him click here.