# Mini-Mods: General Chemistry - Moles

### Counting by Groups

We often use various methods of counting individual things out throughout our daily lives without realizing it. The most common example of this is the term “dozen”. If someone says they have a dozen roses, you know that they have 12 individual roses. Similarly, if someone has pair of pet guinea pigs you know that they own two individual guinea pigs. This sort of notation helps us quantify large numbers of individual things into nice little packages of information that are easier to work with - this becomes especially useful when we are talking about a large quantity of things like atoms or molecules.

A busy donut shop makes 32 dozen donuts every Saturday morning in anticipation of a large crowd of donut buyers. What is the number individual donuts produced each Saturday?

We start out with 32 dozen donuts, but need to convert to individual donuts - this is a unit conversion problem! So let's set up the problem thinking about units. We need to cancel out dozen and replace the units with individual donuts.

The fraction (or conversion factor) informs us we need to know how many donuts are in a dozen - of course, there are 12 donuts for every 1 dozen.

### Counting by Moles

One aspect of studying chemistry involves being able to
count the number of atoms or molecules within a compound. However, because atoms and molecules are so small, it is not convenient to count them by dozens, or hundred, or thousands, or millions, or even billions. We need a much, much bigger number by which to count - we count by moles! Much like the term “dozen” is used to
mean 12 “things”, a mole of things is simply when you have 6.022x10^{23}
individual things, otherwise known as Avogadro’s number.

How many molecules are there in 0.367 mol of H_{2}O?

Think of the mole just like a dozen and follow the same approach as above.

We need to know how many molecules are in 1 mole of any substance - the answer is of course Avogadro's number - 6.022x10^{23}.

As well as counting molecules, we could instead count the number of one type of atom. As a simple example of this, you can easily see that if you were counting the number of ears in a collection of 5 people, there would be 10 ears. The math is formalized as follows:

We can do the same with atoms in molecules.

How many atoms of carbon are there in 0.200 mol of C_{3}H_{8}O?

First, we can count how many molecules there are by using Avogadro's number, but then we need to account for every one molecule, there are 3 carbon atoms.