Dimensional Analysis:

We are now going to introduce dimensional analysis, which we will use to do many of the molar conversions in much of the work from this point forward.

Consider the first question from yesterday's work:

How many trunks are found in one dozen elephants?

This conversion would be set-up in the following manner using dimensional analysis:

To set this up, you need to think about the necessary steps:

1. We are beginning with 1 dozen elephants.

2. We need to convert dozen elephants into how many elephants there are in one dozen (12 elephants/1 dozen elephants)

3. We need to convert from elephants to how many total trunks there are (1 trunk/1 elephant).

Mathematically, the process plays out like this:

1. Multiply 1 x 12 elephants per 1 dozen elephants; the "dozen elephants" will divide out with the "dozen elephants" in the denominator of the first fraction. This changes the units from "dozen elephants" to "elephants".

2. At this point, we should have 12 elephants. Multiply 12 elephants x 1 trunk per 1 elephant. The "elephants" unit will divide out into the "elephants" unit in the denominator of the second fraction. This will change the units from "elephants" to "trunk".

3. This would result in a solution of 1 dozen elephants = 12 trunks.