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Chemistry Tips: Conversion Factors

Matthew Simonson

Matthew Simonson, Editor-In-Chief

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Yes, the concept may seem extremely simple.  In fact, it’s considered so simple that it’s rarely taught at the college level.  Hence, those of us who haven’t learned to master it before college often end up struggling tooth-and-nail to get decent grades in our math-based science classes.

If you can identify with this struggle, I would suggest taking a step back to learn the art of unit manipulation.  Although the critical thinking skills necessary to succeed in Chemistry can’t be obtained by simply watching a 5-minute video, the best way to prepare yourself to handle super-complex problems is to spend extra time on the basics.  My purpose in creating this piece was to give students one of the most fundamental building blocks that can be used to analyze more complex problems.

I only made one “loaded statement” in this particular video.  Here’s the explanation of that concept, followed by some tips on handling difficult unit conversions:

Definition of a Conversion Factor. A conversion factor is a fraction with equal quantities on the top and bottom (numerator and denominator).  They MUST be equal, so that we don’t change the value of the number we’re trying to apply our conversion to. This fact can be seen in a more basic example that doesn’t involve units at all. If we multiply 62 by a fraction that can be reduced to 1, we still end up with 62:Conversion Factor Example

Although unit conversions  have seemingly different numbers on the top and bottom of the fraction, the quantities are actually equal.  To refer back to the video: 12 inches is equal to 1 foot, so we can likewise multiply our quantity by a fraction that has 12 inches in the denominator and 1 foot in the numerator.  Since they are equal, we aren’t messing up our value.

Handling Series’ of Unit Conversions. If we wanted to convert 2,015 centimeters to some number of miles, we would need to go through several unit conversions (assuming that we don’t have a conversion factor for going directly from millimeters to feet).  Some people like to go through one conversion at a time, but I think it’s simpler (and far more efficient) to save punching the numbers into my calculator until I have all of the conversion factors written out like this:Numbers 2, CanceledThat way you can just plug all of the numbers into the calculator at once.

Handling Conversions With Multiple Units.  It may seem more complicated to convert 20 miles per hour into some number of kilometers per hour.  What does “miles per hour” even look like?  Here’s a neat little trick.  Whenever we see “per” in a unit, we can rewrite it as a fraction for the purpose of creating a conversion factor.  We can think of “20 miles per hour” as “20 miles per 1 hour.”Numbers 3
So, now that we’ve split up “mph” into its actual units, we can set up a conversion factor that will replace miles with kilometers.Numbers 4aAnd then, as before, we simply cancel the appropriate units.

Numbers 4, Canceled

Even though problems can get more and more complicated, the principles always stay the same.  Get a thorough mastery of these principles, and you’ll be setting yourself up to excel in chemistry!

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Chemistry Tips: Conversion Factors