Chapter Two Conversion Factors

Conversion Factor  A conversion factor is a ratio derived from the equivalence between two different units that can be used to convert from one unit to the other.  For example, 12 eggs = 1 dozen eggs  12 eggs = 1 1 dozen eggs =1 1 dozen eggs 12 eggs

Say you want to make omelets…  For everybody in the class. That’s 28 omelets. A good omelet has 3 eggs in it. So how many dozen eggs should you buy?

Dimensional Analysis  Is a mathematical technique that lets you use units (like a dozen) to solve problems involving measurement.  It comes in handy when you’re cooking!  It also comes in handy when you’re solving lots of different types of problems. Like stoichiometry. (You’ll find out what that is LATER).

Start at the end.  What are we trying to figure out? How many dozen eggs we need to buy. = ______dozen eggs

So, we’re solving for: = _____ dozen eggs Now we know where we want to end up, so where do we start?

Well, what are we trying to make?  Right. 28 omelets. Lets plug that into the beginning. 28 omelets =______dozen eggs Now, make an ‘x’ and draw a line. Bring those units (omelets) down.

 28 omelets x ______ = ______dozen eggs omelets We’ve almost got another conversion factor here. What do we know about those omelets? RIGHT. One omelet requires 3 eggs. Plug that into the numerator.

 28 omelets x 3 eggs = _____dozen eggs 1 omelet Now make another ‘x’, draw another line. Bring those units that are in the numerator (eggs) down. 28 omelets x 3 eggs x _____ = __dozen eggs 1 omelet eggs

Almost done!  Let’s see…………….  28 omelets x 3 eggs x __ = ____dozen eggs 1 omelet eggs We’re solving for dozen eggs. We need one last conversion factor. Right: 1 dozen eggs 12 eggs

Plug it in.  28 omelets x 3 eggs x 1 dozen eggs = ___dozen eggs 1 omelet 12 eggs Now, as you multiply across the top, and divide by the bottom, you’ve got those units starting to cancel out. 28 omelets x 3 eggs x 1 dozen eggs = ___ dozen eggs 1 omelet 12 eggs

So you’re left with….  ___Dozen eggs. Now all you have to do is actually calculate, then you can get started cooking!  Multiply across the top, divide by what’s on the bottom. You should get:  7 dozen eggs. You want toast with that?

Okay.  I know what you’re thinking. That was a lot of math and drawing lines, and making x’s. And you could have figured it out without doing all of that. But remember:  This is a process called dimensional analysis, and when you get really good at it, it’ll make solving big, hard problems seem really easy. Like stoichiometry. And yes, it’s as fun as it sounds

Let’s practice…  We’ll start with an easy one.  Convert 10.7 g to kg  Remember, we want to solve for kg, so : = _____kg

 We’re starting with 10.7 g.  Make an ‘x’ and draw a line.  10.7 g x _______ = _____ kg  Now we need a conversion factor: 1000 g = 1 kg. Arrange it so that the units we are starting with (g) are in the denominator so they will cancel out, and the units we want to end up with (kg) are in the numerator.

It should look like this:  10.7 g x 1 kg = ______ kg 1000 g  Solve-multiply across the top, divide by the bottom, cancel your units.  Answer: Answer:

Hopefully you got  kg