When solving problems in chemistry, you will always have a quantity and an associated unit for that quantity. More often than not, calculations will not be as simple as performing one addition or one multiplication problem and moving on. Therefore, it is best to not simply fly through calculations with a calculator, without writing anything down on a piece of paper, even if you are not asked to show your work to receive a grade. In chemistry, and in all other quantitative sciences, you have a far greater chance of getting a problem right if you write your problem out on a sheet of paper, placing the proper units where they belong, alongside their quantities. Whatever you do to a measurement, you must also do to its unit. No exceptions! Remember this rule forever. The process of employing the above steps is known as the factor-label method, or dimensional analysis. Concisely, this process involves the changing of units in a problem based on conversion factors, which are essentially statements of equivalence between the two units (Zumdahl and DeCoste 2008). The steps for doing the conversions are as follows, according to Zumdahl and DeCoste: - Start by finding the equivalence statement that relates the two units (the unit that you are presented with, and the unit that you are trying to convert). What you will get is a ratio of the two parts of the equivalence statement.
- Using the rules of cross-multiplication, which I will not go over here but which you can Google, make sure that the units will cancel to get your desired unit when you choose your conversion factor.
- Perform the cross-multiplication and ensure that your result is given in the unit that you would like your answer to be in.
- Make sure that you have the correct number of significant figures and that you rounded correctly. You must ALWAYS do this!
- Go over your answer mentally and make sure that your answer makes sense in the given context.
There are two reasons you will find this method of doing things helpful, according to Ebbing and Gammon: - Your answer will contain the units that you would like your answer to be in.
- Your final answer will be a check of the correctness of your calculations; if you happened to do something wrong in the equation, your units will not make sense and they will not be what you expected. Therefore, you can go back and easily find where you went wrong.
A very simple example of the use of the factor-label method is as follows: John has a dog. He measured that his dog’s toenails grew 2.3 inches in the past month. How many centimeters did his dog’s toenails grow? 2.3 inches must be cross-multiplied by 2.54 centimeters/inch. The final answer is 5.8 centimeters. This is an extremely oversimplified example, but with our first MCAT review question coming up very soon, your knowledge of all of the previous topics will be tested on a far greater level, now that we have almost completed our review of the first chapter of introductory general chemistry! Good luck!
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