The Mole Concept
The Chemist's Dozen: How to Count Atoms by Weighing Them.
This tutorial builds on our knowledge of balanced equations.
← Go back to learn about balancing recipes.
The Problem: The Counting Conundrum
In the last chapter, we learned to balance chemical recipes. For example, to make water, we need 2 molecules of H₂ for every 1 molecule of O₂. That's a 2-to-1 ratio.
But how can a chemist actually measure this out in a lab? Atoms and molecules are impossibly small and numerous to count individually. It would be like trying to count every grain of sand on a beach.
We need a way to connect the microscopic world of atom counts to the macroscopic world of mass that we can measure on a scale.
The Solution: The Chemist's Dozen
How do we count large numbers of small things, like eggs or donuts? We use a group unit: a dozen. A dozen is just a word that means "12". A dozen eggs and a dozen bowling balls both have 12 items, but they have very different masses.
Chemists do the same thing, but with a much, much bigger number. This number is called a mole, and it's the bridge between counting and weighing.
One mole is equal to 6.022 x 10²³ items. This giant number is known as Avogadro's Number.
Your mission is to use the interactive scale below to discover the magic of the mole. Select an element and add one mole to the scale.
The Connection: AMU to Grams
Did you see the "Aha!" moment? The mass of one mole of an element in grams is numerically equal to its atomic mass in atomic mass units (amu) on the periodic table!
- 1 Carbon atom ≈ 12.01 amu → 1 mole of Carbon atoms ≈ 12.01 grams.
- 1 Oxygen atom ≈ 16.00 amu → 1 mole of Oxygen atoms ≈ 16.00 grams.
- 1 Gold atom ≈ 196.97 amu → 1 mole of Gold atoms ≈ 196.97 grams.
This isn't a coincidence; it's the entire reason Avogadro's number is what it is! It was chosen to be the perfect conversion factor.
Diving Deeper: How the Math Works
Let's prove this for Carbon. We need two key conversion factors:
- The definition of an atomic mass unit (amu) in grams:
1 amu = 1.6605 x 10⁻²⁴ g - Avogadro's Number (the number of items in a mole):
1 mole = 6.022 x 10²³ atoms
Now, let's calculate the mass of one mole of Carbon atoms:
Step 1: Find the mass of one Carbon atom in grams.
Mass of 1 C atom = (12.01 amu) × (1.6605 x 10⁻²⁴ g/amu) = 1.994 x 10⁻²³ g
Step 2: Find the mass of one mole of Carbon atoms.
Mass of 1 mole of C = (Mass of 1 C atom) × (Number of atoms in a mole)
Mass of 1 mole of C = (1.994 x 10⁻²³ g/atom) × (6.022 x 10²³ atoms/mole)
Result:
Mass of 1 mole of C ≈ 12.01 g/mole
The numbers cancel out perfectly! This is why the mole is such a powerful and convenient unit for chemists.
You've Learned to Count by Weighing. What's Next?
You now understand the mole. The next step is to use this concept to calculate the mass of any molecule or compound, a skill called calculating Molar Mass.