Unit analysis method

The unit analysis method of problem solving is extremely versatile. You can use it to convert between units or to solve some formula problems. If you forget a formula during a test, you may still be able to solve the problem using unit analysis. 

The unit analysis method involves analyzing the units and setting up conversion factors. You match and arrange the units so that they divide out to give the desired unit in the answer. Then you multiply and divide the numbers that correspond to the units. 

Use the unit analysis method to solve each problem. 

COMPOUND STAB. NO. CODE DATA AVG S.D. UNITS ANALYSIS METHOD NO. NUMBER ... 

Your colleagues who are responsible for the first step, the production of pure phosphorus, estimate that they can supply you with 1.09 X lO kg of phosphorus per day. The production manager asks you to figure out the maximum mass of P4O10 that can be made from this amount of phosphorus. The tools described in this chapter, in combination with the unit analysis method, enable you to satisfy this request. 

Preliminary models are required to identify significant measurements and the complexity of model required and to test the analysis methods that will be used during the unit analysis. Effort must be devoted during the preparation stage to develop these preliminaiy models. 

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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, sometimes called the factor label (unit conversion) method, is a method for setting up mathematical problems. Mathematical operations are conducted with the units associated with the numbers, and these units are cancelled until only the unit of the desired answer is left. This results in a setup for the problem. Then the mathematical operations can efficiently be conducted and the final answer calculated and rounded off to the correct number of significant figures. For example, to determine the number of centimeters in 2.3 miles ... 

The dimensional analysis method involves multiplying a series of fractions that are all equal to a value of one, with unwanted units alternately on... 

Now, solve the problem using the dimensional analysis method. We want the answer to be in inches per second. Set up the fractions with inches on the top and seconds on the bottom, so that the centimeter and minute units cancel. 

The time required to conduct an interfacial tension experiment depends largely on the properties of the surfactants and less on the chosen measurement method. A notable exception is the drop volume technique, which, due to the measurement principle, requires substantial ly more time than the drop shape analysis method. Regardless of the method used, 1 day or more may be required to accurately determine, e.g., the adsorption isotherm (unit D3.s) of a protein. This is because, at low protein concentrations, it can take several hours to reach full equilibrium between proteins in the bulk phase and those at the surface due to structural rearrangement processes. This is especially important for static interfacial tension measurements (see Basic Protocol 1 and Alternate Protocols 1 and 2). If the interfacial tension is measured before the exchange of molecules... 

Probably the most important carbohydrate polymer in food, certainly from a nutritional standpoint, is starch, and Chapter E2 presents three units that can be used for starch isolation and characterization. UNITE2.1 condenses many different starch isolation methods into one scheme for starch isolation from virtually any plant source. In this protocol, the author notes the care that must be taken to prevent starch degradation during isolation. unite2.2 presents a simple enzymatic analysis method that can be used for estimation of starch in food. Finally, unit E2.3 describes a colorimetric method to determine starch amylose content. Again, different combinations of the units in this chapter can be used to characterize starch from any source. 

Dimensional analysis is also known as unit analysis or the factor label method. 

The simplest way to carry out calculations that involve different units is to use the dimensional-analysis method. In this method, a quantity described in one unit is converted into an equivalent quantity with a different unit by using a conversion factor to express the relationship between units ... 

The dimensional-analysis method gives the right answer only if the equation is set up so that the unwanted units cancel. If the equation is set up in any other way, the units won t cancel properly, and you won t get the right answer. Thus, if you were to multiply your height in inches by the incorrect conversion factor inches per meter, you would end up with an incorrect answer expressed in meaningless units ... 

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 known information is the speed in kilometers per hour the unknown is the speed in miles per hour. Find the appropriate conversion factor, and use the dimensional-analysis method to set up an equation so the km units cancel. 

Because many experiments involve numerical calculations, it s often necessary to manipulate and convert different units of measure. The simplest way to carry out such conversions is to use the dimensional-analysis method, in which an equation is set up so that unwanted units cancel and only the desired units remain. It s also important when measuring physical quantities or carrying out calculations to indicate the precision of the measurement by rounding off the result to the correct number of significant figures. 

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