Lesson 1: Atomic Mass and Atom Counting

Part c: The Mole

Part a: Atomic Mass
Part b: Measuring Atomic Mass
Part c: The Mole
Part d: Grams-Moles-Atoms Relationship

 

The Atomic Mass Unit

In Lesson 1a, we discussed the atomic mass of elements. We mentioned that the standard for all atomic mass values is the carbon-12 isotope. It is assigned a mass value of exactly 12.00 amu. The masses of all other atoms are expressed relative to the mass of the carbon-12 isotope.
 
The amu is the abbreviation for atomic mass unit. By definition, an amu is 1/12^th the mass of an atom of carbon-12. The unit is useful for comparing masses of atoms. But atoms are small. Very small. Very, very small. And it is not possible to directly measure the mass of an atom. Nor is it even possible to isolate an atom in an effort to determine its mass. The atomic mass unit needs some super-sizing. The particulate (mass of an atom) needs to be scaled up to the macroscopic level so that there is a measurable sample size and a determinable number of atoms.

 
 
 

Avogadro’s Number

Time for a thought experiment: There must be some number of atoms of carbon-12 that when gathered together results in a 12.00-gram sample. Of course nobody could guess what that number is. Let’s represent it by the symbol N_A. There are N_A atoms of carbon-12 in a 12.00-gram sample of carbon-12. The mass of an atom of any element is expressed relative to carbon-12. This relative number, known as the average atomic mass, is listed on the periodic table. And so, …
 

• N_A atoms of helium (He) would have a mass of 4.00 grams.
• N_A atoms of beryllium (Be) would have a mass of 9.01 grams.
• N_A atoms of nitrogen (N) would have a mass of 14.01 grams.
• N_A atoms of neon (Ne) would have a mass of 20.18 grams.
• N_A atoms of calcium (Ca) would have a mass of 40.08 grams.

 
While we don’t know what the value of N_A is, we do know that there must be some number of atoms that provides these measurable masses in grams. In this sense, N_A is the supersizing factor between atomic mass units and grams. It is a way of scaling up from the particulate level (atoms) to the macroscopic level that can be observed and measured.
 
Numerous experiments have been performed to determine the value of N_A. Experiments by Joseph Loschmidt (1865), Robert Millikan (1910), and Jean Perrin (1926) have led to some agreement upon its value. Today, we know the value of N_A to be 6.02214076 x 10²³. We will more commonly use the value of
   
This numerical value is known as Avogadro’s number, named in honor of Italian chemist Amedeo Avogadro (1776-1856).
 
Consider these elements with their listed atomic mass values:
   
Now that we know the value of N_A, we can make the following claims:
 

• 6.022 x 10²³ atoms of helium (He) would have a mass of 4.00 grams.
• 6.022 x 10²³ atoms of beryllium (Be) would have a mass of 9.01 grams.
• 6.022 x 10²³ atoms of carbon (C) would have a mass of 12.01 grams.
• 6.022 x 10²³ atoms of nitrogen (N) would have a mass of 14.01 grams.
• 6.022 x 10²³ atoms of neon (Ne) would have a mass of 20.18 grams.
• 6.022 x 10²³ atoms of calcium (Ca) would have a mass of 40.08 grams.

 
The number 6.022 x 10²³ is equivalent to the number of atoms in a sample of an element having a mass equal to the atomic mass of that element.
 
     

The Mole

You have likely heard of the terms pair, dozen, and gross to refer to a particular number of items. A pair of shoes refers to two shoes. A dozen donuts refers to 12 donuts. A gross of nails refers to 144 nails. We can categorize these three terms – pair, dozen, and gross – as counting units. If the clothing store, the bakery, and the hardware store have their counting units, then it is only fair that chemists have a counting unit. And they do! It is referred to as the mole.
 
A mole is a counting unit that refers to 6.022 x 10²³ items. Just as a pair means 2, a dozen means 12, and a gross means 144, the mole means 6.022 x 10²³. One mole of atoms refers to 6.022 x 10²³ atoms. A mole, abbreviated mol, is the counting unit used by chemists to refer to a number of items. It is a term used to refer to a very large number of very small things. One mole is numerically equivalent to 6.022 x 10²³. It is the chemist's term that represents the supersizing factor between atoms and grams. One mole of atoms of any element has a mass in grams equal to the atomic mass of that element.

• 1 mole of He atoms has a mass of 4.00 grams.
• 1 mole of Be atoms has a mass of 9.01 grams.
• 1 mole of C atoms has a mass of 12.01 grams.
• 1 mole of N atoms has a mass of 14.01 grams.
• 1 mole of Ne atoms has a mass of 20.18 grams.
• 1 mole of Ca atoms has a mass of 40.08 grams.

 
 

 
 

Making Cents of Avogadro’s Number

Atoms are very, very small. If 12.01 g of carbon contains 6.022 x 10²³ atoms, then it should be no surprise to say that this is a very, very large number. Let’s entertain the idea of the enormity of this number to see if we can make some cents sense of its magnitude.
 
Analogy #1:
Suppose that you had a mole of pennies gifted to you at birth. And suppose that you used those pennies to spend $1 million every second of your life. If you lived to be 75 years old, then you would have more than one-half of the penny pile remaining.
 
Analogy #2:
Suppose that you had a mole of pennies to distribute equally to every individual on planet Earth. And suppose that the planet population was 8.2 billion (as it was in 2024). Each person on the planet would then have 730 billion dollars.
 
Analogy #3:
Suppose that you had a mole of pennies and decided to make a tall penny tower. And suppose that you had the time to stack every penny on top of each other. If you were able to stack one million pennies every millisecond, then it would take 20 million years to stack all the pennies. And how tall would that penny tower be? It would be tall enough to reach to the nearest star - Alpha Centauri – 26 trillion miles away.
 
Hopefully this gives you a cents sense for the enormity of the number 6.022 x 10²³.
     

Molar Mass

Atomic mass is the mass of one atom. The average atomic mass values for each element are listed on the periodic table. For carbon, the average atom has a mass of 12.01 amu. With our supersizing factor of 6.022x10²³, the atomic mass values have new significance. The atomic mass values also indicate the mass of 1 mole of carbon in grams. A mole of carbon atoms has a mass of 12.01 grams. We refer to this as the molar mass of carbon. The molar mass of a substance is the mass of one mole of particles of that substance.
   
Molar mass is one of the most commonly used quantities in chemistry. The units associated with molar mass are grams per mole, shortened to g/mol. The periodic table can be used to retrieve the gram-per-mole relationship for any element. It is simply equivalent to the average atomic mass value listed for that element on the table.
   
Molar mass is not limited to elements. We can also determine the molar mass of compounds. It is simply the sum of the molar mass of all the individual atoms found in the compound. We will discuss this in detail in Lesson 2a.
 
 
 
Counting Atoms by Mass
The ideas on this page – Avogadro’s number, the mole, and molar mass – provide the means by which chemists can count atoms. The mass (in grams) of any sample of a pure element can be used to determine the number of moles of atoms. Avogadro’s number can be used to determine the number of atoms from the number of moles. Together, the concepts of molar mass and Avogadro’s number can be used to determine the number of atoms in a sample of an element. In two steps, a sample mass in grams can be converted to the number of atoms of that element. We will investigate these relationships in Lesson 1d.
   
 

 
Mole Fun Ahead
We would be doing a disservice if we failed to include some mole jokes, mole memes, and mole art in this chapter of the Tutorial. We have dug up some of our best mole jokes and have massed them together on their own page. We think you will find them amolesing.
 
Visit: Mole Jokes Page.
 
 
 

Before You Leave

• Download our Study Card on The Mole. Save it to a safe location and use it as a review tool. (Coming Soon.)
• The Check Your Understanding section below include questions with answers and explanations. It provides a great chance to self-assess your understanding.

 
 
 

Check Your Understanding

Use the following questions to assess your understanding. Tap the Check Answer buttons when ready.
 
1. Use a Periodic Table to complete the following statements. (N_atoms = number of atoms)

1. The N_atoms in ________ g of Mg (magnesium) is equal to the N_atoms of 12.01 g of C (carbon). 
   
   Check Answer
   Answer: 24.31
   
   12.01 g of C represents a mole of C. One mole of Mg has a mass of 24.3050 grams. (We just rounded to the second decimal place and that's not an important detail.)
   
    
   
    
2. The N_atoms in ________ g of N (nitrogen) is equal to the N_atoms of 28.09 g of Si (silicon). 
   
   Check Answer
   Answer: 14.01 grams
   
   28.09 g of Si represents a mole of Si. One mole of N has a mass of 14.0067 grams. (We just rounded to the second decimal place and that's not an important detail.)
   
    
   
    
3. The N_atoms in ________ g of Ar (argon) is equal to the N_atoms of 79.90 g of Br (bromine). 
   
   Check Answer
   Answer: 39.95 grams
   
   79.90 g of Br represents a mole of Br. One mole of Ar has a mass of 39.948 grams. (We just rounded to the second decimal place and that's not an important detail.)
   
    
   
    

 
 
2. The value of N_atoms in the above statements is ________.  (That is, find the number of atoms in 12.01 g of carbon, 28.09 g of silicon, 79.90 g of bromine, etc.)

1. 12
2. 10⁹
3. 6.022 x 10²³
4. … nonsense!  It varies from statement to statement.

  ​

 
 
 
3. We know that N_A atoms of helium (He) has a mass of 4.00 grams. (Here, N_A is 6.022 x 10²³.) Complete the following statements:

1. 2•N_A atoms of He has a mass of _________ grams. 
   
   Check Answer
   Answer: 8.00 g
   
   Two times the number of atoms would result in two times the original mass.
   
    
   
    
2. 5•N_A atoms of He has a mass of _________ grams. 
   
   Check Answer
   Answer: 20.00 g
   
   Five times the number of atoms would result in five times the original mass.
   
    
   
    
3. 10•N_A atoms of He has a mass of _________ grams. 
   
   Check Answer
   Answer: 40.00 g
   
   Ten times the number of atoms would result in ten times the original mass.
   
    
   
    
4. 0.5•N_A atoms of He has a mass of _________ grams. 
   
   Check Answer
   Answer: 2.0 g
   
   One-half the number of atoms would result in one-half the original mass.
   
    
   
    

 
 
4. The mole is a counting unit like the pair or the dozen. If a person orders a dozen donuts, then ...

1. ... how many donuts has she ordered?  
   
   Check Answer
   Answer: 12
   
    
   
    
2. If a person orders a mole of donuts, then how many donuts has she ordered?
   
   Check Answer
   Answer: 6.022 x 10²³
   
    
   
    

 
 
5. The number of items in a mole of items is 6.022x10²³. This number is known as _____.

1. A google
2. A mollian
3. The chemist's dozen
4. Avogadro's number

 
 
6. Complete the following statements. Use a Periodic Table.

1. 12.01 g C   →  ________ mol of C   →  ___________ individual C atoms 
   
   Check Answer
   Answer:
   12.01 g C   →  1.0 mol of C   →  6.022 x 10²³ individual C atoms
   
    
   
    
2. 24.02 g C  →  ________ mol of C  →  ___________ individual C atoms 
   
   Check Answer
   Answer:
   24.02 g C  →  2.0 mol of C  →  12.044 x 10²³ individual C atoms
   Twice as much mass means twice as many atoms. 
   
    
   
    
3. 120.1 g C  →  ________ mol of C  →  ___________ individual C atoms 
   
   Check Answer
   Answer:
   120.1 g C  →  10.0 mol of C  →  6.022 x 10²⁴ individual C atoms
   Ten times as much mass means ten times as many atoms. 
   
    
   
    
4. __________ g Al  →  1.0 mol of Al  →  __________ individual Al atoms 
   
   Check Answer
   Answer:
   26.98 g Al  →  1.0 mol of Al  →  6.022 x 10²³ individual Al atoms
   
    
   
    
5. 16.04 g S  →  ________ mol of S  →  ___________ individual S atoms 
   
   Check Answer
   Answer:
   16.04 g S  →  0.5 mol of S  →  3.011 x 10²³ individual S atoms
   The 16.04 g is approximately one-half the atomic mass of sulfur. And so that means one-half of a mole of atoms.