Problem solving unit conversion problems

Solve unit conversion problems by following these steps. 

Solve unit conversion problems using the problemsolving strategies outlined in Section 2.6. 

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 ... 

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. 

This is a unit conversion problem. You should come up with the following strategy to solve the problem. 

We can diagram conversions using a solution map. A solution map is a visual outline that shows the strategic route required to solve a problem. For unit conversion, the solution map focuses on units and how to convert from one unit to another. The solution map for converting from inches to centimeters is ... 

EXAMPLE 2.10 Solving MuKistep Unit Conversion Problems... 

EXAMPLE 2.13 Solving Multistep Conversion Problems Involving Units Raised to a Power... 

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. 

Strategize. This is usually the most challenging part of solving a problem. In this process, you must develop a conceptual plan—a series of steps that will get you from the given information to the information you are trying to find. You have already seen conceptual plans for simple unit conversion problems. Each arrow in a conceptual plan represents a computational step. On the left side of the arrow is the quantity you had before the step, on the right side of the arrow is the quantity you will have after the step, and below the arrow is the information you need to get from one to the other—the relationship between the quantities. 

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... 

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. 

When solving a problem by the Unit Conversion Method, the question mark in the following should be replaced by. ... 

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 the present book, for magnetism we use the SI unit that is based on the MKS A (meter, kilogram, second, ampere) system. In accordance with that, the tesla (1T = 10" gauss) was presented as the magnetic unit in Chapter 17 (see Fig. 17.10a and b). It is useful to know both the SI and Gaussian systems and be able to convert between them. Thus, when one attempts to solve a magnetics problem, to avoid errors one is well advised to stick to a single convenient unit system. A useful conversion table of... 

The conversion values corresponding to optimal conditions calculated may be considered low for industrial units. If one includes a constraint in conversion (conversion > 0.99) and solves the optimization problem using the SQP technique again, the following values are calculated S0 = 180 kg/m3, tr = 1 h, R = 0.42, and r = 0.52. Productivity is 13 kg/ (m3-h), conversion is 0.99, and % yield is 0.89. In this case, the extractive process has productivity only a little higher than the optimized conventional process. Kalil et al. (9) optimized the conventional process of Andrietta and Maugeri (4) and obtained productivity of 12 kg/(m3h), conversion of 0.99, and % yield of 0.86. 

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. 

To convert one unit to another, we must set up a conversion factor or series of conversion factors that relate two units. The proper use of these conversion factors is referred to as the factor-label method. This method is used either to convert from one unit to another within the same system or to convert units from one system to another. It is a very useful problem-solving tool. 

Most sea water conversion plants now in operation are outside the United States. Many countries are not only water-short but also fertilizer-short. Water alone does not solve an agricultural problem. Fertilizers are usually necessary too. Combining fertilizer production with sea water conversion may have particular value in these countries, which are not necessarily have-not nations. Those which can economically support sea water conversion as a source of fresh water could probably support a premium quality fertilizer. Its low solubility, nonburning, nonleaching in sandy soils, and trace element content make it more valuable than ordinary fertilizers and could be of great merit in the future development of these nations. 

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