A lot of students get scared when they hear the phrase dimensional analysis but in reality this concept is every chemistry student s best friend It is just a fancy way of saying cancel out units and provides a very organized approach for doing so This tutorial will call dimensional analysis the train tracks Before we do some heavy examples let s get comfortable using the train track setup and practice with our metric units and their associated scientific notations A chart that you should be comfortable with is below This chart should be read in the following manner one prefix unit equals blank units For example one gigaunit is equal to 1x10 9 units Let s do some practice Example 1 Convert 5 3 nanometers to megameters For this we will need to use the train tracks We must also remember that there is no direct way to convert nanometers to megameters and that the two prefixes are related through the base unit In other word we have to go from nanometers to meters and then from meters to megameters because this is how our prefixes relate to one another Notice that we begin by canceling out nanometers which puts us into meters The next step is to cancel out the meters and convert them into megameters Once we have cancelled out all of the units and are left with the units we want we multiply all the numbers on the top then divide the everything on the bottom Be very careful here If you are using a scientific calculator you will want to use the EE button to ensure that the order of operations is followed Example 2 Convert 2 47 cm to km Let s do a more complex example Remember train tracks make it easy not difficult Just do what you know you can do and you ll be fine Example 3 The density of the core of earth about 13 1 g mL Convert this density to milligrams per cubic meter mg m 3 You probably have questions Let s try to answer some of them How did I convert mL to cm 3 That is an equivalence that you have to know 1 mL 1 cm 3 Next why did I write the cm m step 3 times It s because we are starting in units of cm 3 and I want to go to m 3 I only have a relationship between cm and m not their cubic forms So I had to cancel each cm out by doing the step 3 times Equivalently you could have cubed that whole step the first time you write it to save space on you paper Example 2 The concentration of atoms in interplanetary space is about 7 3 x 10 2 kiloatoms L What is this concentration in centiatoms mL Example 3 Given that 1 Sterling 2 6 Keto 4 6 Keto 2 9 Henry and 3 7 Henry 8 1 Mia how many Sterlings equal 92 8 Henry These units are based on the names of my neighborhood dogs The point of this question is to show you that the units don t matter at all when you use the train tracks As long as you only use equivalences and cancel one unit at a time the problems will work out nicely Let s see what happens
View Full Document
Unlocking...