How to do Conversions in Chemistry: Part 1- The Conversion Factor

Whether you are going to be an English major, music major, pharmaceutical tech or network engineer, most likely, you will have to take chemistry.  If you have to take chemistry, you will have to know how to convert.

Conversion enables you to compare and find equal quantities of different types of things.   In the simplest of examples, we can compare quarters and dollars and find quantities of each that would be equal.  Finding equivalent quantities will yield the conversion factor which we can use to change dollars to quarters, or quarters to dollars.

Here is an example.  Say we have 352 dollars.  How many quarters are there in 352 dollars? Well that is simple, each dollar has 4 quarters so 352 dollars would be equivalent to 1,408 quarters  (352 * 4).  Or how about this question:  How many dollars are equivalent to 78 quarters?  That’s about 19 and 1/2 dollars ( 78 / 4 = 19.5).

The above question is easy.  You know intuitively whether to multiply or divide because you are familiar with the quantities and understand what they mean.  But what if you were not so familiar with these quantities?  Would you understand the process that you just did to get your answer? Would you divide when you were to multiply?  Or multiply when you should have divided? Chances are the process is not quite as clear as you would like.  And if you don’t get the process on a simple problem with quarters and dollars, how will you ever determine how many milligrams of a substance you will need to weigh in order to make a 0.5M saline solution for your patient?

The process to convert dollars to quarters is called dimensional analysis or the factor-label method.  Basically every number out there is associated with a tag.  This tag describes what the number is all about.  4 what?  4 quarters.  5 what?  5 dollars.  Tags act like numbers.  They can be added: 3 dollars + 3 dollars = 6 dollars.  They can be subtracted: 5 dollars – 2 dollars = 3 dollars.  They can be multiplied: 3 dollars X 3 dollars equals 9 dollars squared.  Or they can be divided: 3 dollars / 3 dollars = 1.

Note: when you divide tags, the tag disappears.  Remember the old rule: a number divided by itself is equal to 1.  Well that rule also applies to tags.  A tag divided by itself is equal to 1 and the tag disappears.  We can use this concept in conversion problems.

Take the above example with dollars and quarters.  We have 352 dollars, and we also have a relationship 4 quarters equal 1 dollar.  We can write this relationship as a fraction:

conv-1

Now we can use this relationship in the following example:

convert-2

 

Multiple straight across and this is our new fraction.  Include your tags!  They haven’t gone anywhere.convert-3

We can multiply the two numbers together as well as the tags.  The equation now looks like this:convert-4

The tag “dollar” is in both the numerator and denominator.  So we can cancel them out.  Put a slash through those words like this:

convert-5

The term “dollar” cancels out and  Poof!  It’s gone.  All you are left with is quarters.  We divide 1408 by 1 (still 1408) and your answer is in quarters.

convert-6

 

The game here is to try to cancel out tags.  One tag on the top, and the same tag on the bottom will cancel each other out.

 

That’s probably enough to digest for now.  Be on the lookout for Part 2!

 

 

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