Problem Solving and Unit Conversions

Problem solving is one of the most important skills you will acquire in this course. Not only will this skill help you succeed in chemistry, but it will help you to learn how to think critically, which is important in every area of knowledge. My daughter, a freshman in high school, recently came to me for help on an algebra problem. The statement of the problem went something like this  

Sam and Sara live 11 miles apart. Sam leaves his house traveling at 6 miles per hour toward Sara s house. Sara leaves her house traveling at 3 miles per hour toward Sam s house. How much time until Sam and Sara meet  

Units are critical in calculations. Knowing how to work with and manipulate units in calculations is a very important part of problem solving. In calculations, units help determine correctness. Units should always be included in calculations, and we can think of many calculations as converting from one unit to another. Units are multiplied, divided, and canceled like any other algebraic quantity. 

Always write every number with its associated unit. Never ignore units they are critical. 

Always include units in your calculations, dividing them and multiplying them as if they were algebraic quantities. Do not let units magically appear or disappear in calculations. Units must flow logically from beginning to end. 

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Basic study skills needed to study chemistry Macroscopic and microscopic properties of matter The SI (Metric) system Basic problem solving techniques Unit Conversion Method Significant figures... 

Most of the applications of artificial intelligence in chemistry so far have not involved numerical computation as a primary goal. Yet there are aspects of the AI approach to problem-solving which have relevance to computation. In scientific computation, one could view the knowledge base as the set of equations, input variable values, and unit conversions relevant to the problem, and the inference engine the numerical method used to solve the equations. This paper describes such a software system,... 

In this chapter, you have seen a few examples of how to solve numerical problems. In Section 2.6, we developed a procedure to solve simple unit conversion problems. We then learned how to modify that procedure to work with multistep unit conversion problems and problems involving an equation. We will now sirni-marize and generalize these procedures and apply them to two additional examples. As we did in Section 2.6, we provide the general procedure for solving nmnerical problems in the left colmnn and the application of the procedure to two examples in the center and right columns. 

Many problems besides strict unit conversions can be thought of as conversion problems and can therefore be solved with the preceding procedure. 

Chemistry is full of calculations. Our basic goal is to help you develop the knowledge and strategies you need to solve these problems. In this chapter, you will review the Metric system and basic problem solving techniques, such as the Unit Conversion Method. Your textbook or instructor may call this problem solving method by a different name, such as the Factor-Label Method and Dimensional Analysis. Check with your instructor or textbook as to for which SI (Metric) prefixes and SI-English relationships will you be responsible. Finally, be familiar with the operation of your calculator. (A scientific calculator will be the best for chemistry purposes.) Be sure that you can correctly enter a number in scientific notation. It would also help if you set your calculator to display in scientific notation. Refer to your calculator s manual for information about your specific brand and model. Chemistry is not a spectator sport, so you will need to Practice, Practice, Practice. 

In this section, we will introduce one of the two common methods for solving problems. (You will see the other method in Chapter 5.) This is the Unit Conversion Method. It will be very important for you to take time to make sure you fully understand this method. You may need to review this section from time to time. The Unit Conversion Method, sometimes called the Factor-Label Method or Dimensional Analysis, is a method for simplifying chemistry problems. This method uses units to help you solve the problem. While slow initially, with practice it will become much faster and second nature to you. If you use this method correctly, it is nearly impossible to get the wrong answer. For practice, you should apply this method as often as possible, even though there may be alternatives. 

Dimensional analysis is a technique for solving problems that involve units or conversions that is taught in many engineering schools. It is a very useful technique in some areas of the emergency services, especially in EMS, where drug and fluid administration rates need to be calculated. 

The dimensional-analysis method and the use of ballpark checks are techniques that will help you solve problems of many kinds, not just unit conversions. Problems sometimes seem complicated, but you can usually sort out the complications by analyzing the problem properly ... 

The conversion factor problem-solving technique has been used throughout this book, especially in the units on moles and stoichiometry. These problem solutions are generally in a format like this ... 

There are a variety of problem-solving strategies that you will use as you prepare for and take the AP test. Dimensional analysis, sometimes known as the factor label method, is one of the most important of the techniques for you to master. Dimensional analysis is a problem-solving technique that relies on the use of conversion factors to change measurements from one unit to another. It is a very powerful technique but requires careful attention during setup. The conversion factors that are used are equalities between one unit and an equivalent amount of some other unit. In financial terms, we can say that 100 pennies is equal to 1 dollar. While the units of measure are different (pennies and dollars) and the numbers are different (100 and 1), each represents the same amount of money. Therefore, the two are equal. Let s use an example that is more aligned with science. We also know that 100 centimeters are equal to 1 meter. If we express this as an equation, we would write ... 

You will see many different types of unit conversions in this chapter, but they can all be worked using the same general procedure. To illustrate the process, we will convert 2 teaspoons to milliliters and solve the problem of how much medicine to give the little boy described above. 

Work on as many of the problems at the end of the chapter as you can. They review and extend the concepts and skills in the text. Answers are given in the back of the book for problems with a colored number, but try to solve them yourself first. Let s apply this approach in a unit-conversion problem. 

Appendix C Units of Measure, Unit Conversion, and Problem Solving... 

Many kinds of numerical problems in everyday life as well as in science can be solved by extending the use of conversion factors and cancellation of units beyond unit conversion. The use of density expressed as mass per unit volume is a simple example of such an extension. Density provides the connection between mass and volume. Given that the density of lead is 11.4 g/cm , you can find the mass in grams of a piece of lead of known volume or the volume of a piece of lead of known mass. If the known information is that a piece of lead has a volume of 25.0 cm and the unknown information is its mass, the problem is set up and solved as follows... 

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