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:
There are two reasons you will find this method of doing things helpful, according to Ebbing and Gammon:
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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