For some reason I have found that American culture views math as something that is only for an elite few. Anything past basic algebra seems to be met with groans of dread. This is unfortunate because math is one of our primary connections to the Universe. The math and problems that we’ll be covering today help to illustrate that point. The examples will present concepts that are basic, but they serve to show us that what we’re really trying to do with math, is understand the world around us.
Love it or hate it chemistry is filled with math, so you’re going to have to get comfortable with solving mathematical problems. The good news is that, the math involved in General Chemistry is relatively easy to understand, it’s just a little bit of basic algebra and learning how to manipulate equations. Except maybe for quantum theory, don’t get me started on that…
Now, here at TYS we are strong proponents of understanding what things mean. If you truly want to learn a science topic, you need to understand how it connects you to your surroundings. It isn’t enough to regurgitate information and hope that you get an “A” on the test, you’re going to need to think about things to truly understand them. Let’s dive right in so you can see what I mean.
What Are Units and What Do We Mean When We say Conversion Factors?
When you go to the store and buy a party size bottle of Coca Cola, what is it that you’re buying? For most of us the obvious answer is 2 liters of Cola. Think about that for a second, you’re not just buying 2 Coca Cola, otherwise you could end up with 2 of anything. Maybe it will be 2 ounces, 2 bottles, or 2 gallons of the stuff (and even then what do any of those words really mean). This is why we need units attached to those numbers in order for us to have a reasonable expectation of what we’re getting, you know so it’s not a surprise.
For any unit out there, someone at some point in time decided that they needed to have a simple way of letting people know what they meant. This resulted in inventing a unit that everyone would know so that it could be used to present information.
Think of a kilogram (Kg). You got it? It’s okay if you didn’t, most people wouldn’t know that when they see Kg there’s actually a definition attached to that unit. The International Prototype of the Kilogram is that definition. When you say 30 kilograms you are actually saying that it is the equivalent of 30 International Prototype of the Kilogram. Though we’ll just call it a kilogram.
Next I want you to think about ratios as they relate to units. What is a ratio? It’s basically a way to quantify (put numbers to) how many times one value contains or is contained in another. When you think about how fast you are driving, you’re not merely thinking I’m going 30 miles. Yes 30 miles might be how far you are going but you need a ratio to tell you how fast you are going. Enter Miles Per Hour (miles/hour). That ratio tells you how many miles are contained in 1 hour of travel, in other words your speed!
Chemistry is largely a problem solving venture, but it’s not mystical in any sense of the word. You use ratios and unit conversions in your every day life all of the time! The only difference is that in chemistry you are given a foreign set of units that you aren’t used to yet. Let’s take a look at an every how you would use a ratio to solve a problem.
Suppose you want to travel from Portland, OR to Los Angeles, CA. According to Google maps that’s 965 miles. You want to know how fast you will get there if you take the new magical freeway that doesn’t have any accidents and doesn’t go through any towns that slow you down. Let’s say you’ll be traveling at an average speed of 65 mph.
- You need to figure out what you’re trying to solve for. In this case you want to know how much time (t) it will take you to get from point A to Point B- 965 miles.
- Next you need to write down what is given. You are given the distance-965 miles, and you are given a speed-65 mph. Now let’s do some math.
Warning: unless you’re super comfortable with the units you’re using, always include them in every step of your problem solving. It will help you double check whether or not you are making a mistake.
Conversions can be scary, as they should be. One tiny mistake on a conversion factor and you’ll blow the question. Now that I’ve got you good and scared, do you want to know a secret? Conversions aren’t actually hard at all. If you know what you have, and you know what you want, then you can effectively convert one unit to another, so long as the two units describe similar phenomena.
There isn’t really a good way to explain conversions, you just have to do it. So let’s convert our answer from the last problem to see how it works. We’re going to attempt to express our answer from the last problem in days and minutes.
Conversions really are that easy. You take what you know or what you are given and you convert a value to another. Think about how you would convert 23 centimeters to inches if you know that there are 2.54 centimeters in 1 inch.
Pro Tip #10: Practice Problems
Yes you read that right. Science isn’t your history class (FYI, I love history). It isn’t enough to get the general gist of a topic, or memorize a bunch of terms and call it good. If you truly want to teach yourself science, then you need to get comfortable with the technical aspects of the material. This means that you need to work on problems with real implications in the field that you’re studying. If you’re curious as to where to start, take a look at our resources page.
[Chemistry 211 section 1.3]