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Avogadro's Number: Using the Mole to Count Atoms

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  • 0:04 Counting Atoms
  • 2:18 The Mole
  • 5:02 Practice
  • 8:17 Lesson Summary
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Lesson Transcript
Instructor: Kristin Born

Kristin has an M.S. in Chemistry and has taught many at many levels, including introductory and AP Chemistry.

How do we move from the atomic world to the regular world? Because atoms are so tiny, how can we count and measure them? And what do chemists celebrate at 6:02 AM on October 23rd each year? In this lesson, you will be learning how Avogadro's number and the mole can answer these questions.

Counting Atoms

'Go to a balance and measure out 56 trillion iron atoms. Then combine them with 108 billion oxygen molecules.' Hopefully you could see the flaws in these statements. How are you supposed to measure out 56 trillion iron atoms? There has to be a way to count and measure atoms, but because they are so small and we will usually be dealing with so many of them, a different method needs to be used to count out and measure these little guys.

If a dozen oranges weigh about 5 pounds, and I wanted you to get me 50 dozen oranges, what could you do? Well, you could either count out 600 oranges, which would take a while, or you could keep adding oranges to a scale until you reached 250 pounds (that's 50 dozen x 5 pounds per dozen = 250 pounds). I would opt for the second choice, because then I wouldn't have to worry whether I lost count and I wouldn't have to keep track of oranges. I would just have to focus on getting 250 pounds of oranges.

The top arrow shows the atomic number; the bottom arrow points to the atomic weight.
Atomic Number Atomic Weight Examples

This exact same idea is used in chemistry because it would be ridiculous to count out individual atoms. Again, just like the oranges, we will rely on their weight as a tool to help us count them. So will we be grouping them in dozens and weighing them in pounds? Probably not. We will be using what we already know about the weight or the mass of an atom. We can find the atomic weight right under its symbol on the periodic table. What do you notice as the atomic number (the top number in each box) increases? You should see that as you move from left to right and top to bottom on the periodic table, the atomic number (the number of protons) increases by 1 and the atomic weight also increases. Atoms of each element get heavier because they are holding more protons and neutrons (well, and electrons too, but this really doesn't have an impact on the mass).

The Mole

So atoms of each element have a different mass. For example, the average iron atom will have a mass of 55.8 amu. Remember that 1 amu is very small, about the mass of a proton or neutron. Because balances in the chemistry lab don't measure in amu, we are going to need to scale this up to something they do measure: grams. Just how many amu are equal to 1 gram? The answer to this is a very, very large number: 6.02 x 1023. That is 602,000,000,000,000,000,000,000. I don't even know what that number is called. That's okay, because this number has its own special name (kind of like 12 has its own special name: dozen). Its special name is Avogadro's number, which is named after this guy. Avogadro's number is more commonly called the 'mole.' The mole is just a large number, a way to count how many of something you have, and obviously a very large number. It is always equal to 6.02 x 1023. It is the number of amus in 1 gram, so 1 mole of amus equals 1 gram.

This is a relatively simple concept, but it tends to be one of the biggest hurdles to learning chemistry because it is a number so large your brain has trouble even comprehending it. Here's an example: if I had a mole of basketballs (6.02 x 1023 basketballs) it would be nearly the same volume as the Earth! Ready for another? If I had a mole of dollars, and I spent a billion dollars every second, it would take over 19 million years to spend it all!

The mole is used to count very large numbers of something, such as iron atoms.
Mole Iron Example

Okay, back to chemistry. If 1 mole of amus is the same mass as 1 gram, and 1 hydrogen atom has a mass of 1 amu, then 1 mole of hydrogen atoms would have a mass of 1 gram! What about our iron from the beginning of this lesson? If 1 iron atom has a mass of 55.8 amus, then a mole of iron atoms (6.02 x 1023 of them) will have a mass of 55.8 grams!

Practice

Let's take this concept and do a little more practice with it. Get your periodic table handy and feel free to pause the video to figure out the answers on your own before I explain the answer.

First, find gold on the periodic table. It has the symbol Au and is located slightly to the right of the center of the table. Say I have a pile of gold and it has a mass of 197 grams. How many moles of gold atoms do I have? The answer is 1 mole of gold atoms. If I could count each individual atom, how many would I have? The answer is 6.02 x 1023 atoms of gold! Notice how I started out with what I was given and then I multiplied by a conversion factor, which is really just an equality that I turn into a fraction in order to be able to cancel out the units I don't want and turn it into the units I do want.

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