Calculations factor-unit method

Notice that the milliliter units canceled in the calculation. This conversion to liters is an example of the factor-unit method of problem solving, which is discussed in Section 1.9. 

Use the factor-unit method and numerical relationships from Table 1.3 to calculate the number of yards in 100 m. 

In this textbook, the factor-unit method discussed in Section 1.9 is used for most problems that require mathematical calculations. This method simplifies problem solving and should be mastered so it can be used where it applies. The beauty of this method is that it mimics your natural, everyday way of solving problems. This real-life method usually involves identifying where you are, where you want to go, and how to get there. The factor-unit method follows the same pattern Step 1, identify the given number and its units Step 2, write down the unit of the desired answer Step 3, put in factors that will convert the units of the given quantity into the units of the desired answer. 

The factor-unit method for doing calculations is based on a specific set of steps. One crucial step involves the use of factors that are obtained from fixed numerical relationships between quantities. The units of the factor must always cancel the units of the known quantity and generate the units of the unknown or desired quantity. 

The density of a substance is the number obtained by dividing the mass of a sample by the volume of the same sample. Measured values of density provide two factors that can be used with the factor-unit method to calculate the mass of a substance if the volume is known, or the volume if the mass is known. 

Obtain a factor from Table 1.3 and calculate the number of liters in 1.00 gal (4 qt) by using the factor-unit method of calculation. 

You need 3.00 lb of meat that sells for 3.41/lb (i.e., 1 lb = 3.41). Use this price to determine a factor to calculate the cost of the meat you need using the factor-unit method. 

Determine the following using the factor-unit method of calculation and factors obtained from the preceding three relationships given for sulfur (S) ... 

We will use the factor-unit method of calculation from Section 1.9, and the necessary factors from Table 6.3. 

The stoichiometry calculations of solution reactions can be done using the factor-unit method. The sources of the needed factors will be the mole interpretation of the reactions introduced as statement 2 in Section 5.9, and the molarities of the solutions involved in the reactions. Each known solution molarity will provide two factors. For example, the following two factors can be obtained based on a 0.400 M HCl solution ... 

However, if you must calculate the molarity of a solution that contains 5.00 g of NaCl in enough water to give 100 mL of solution, the units of the numbers do not match those of the formula. The factor-unit method can be used to convert each quantity into the units needed by the formula... 

Therefore, our task will be to calculate the number of moles of acid reacted in each case. The methods described in Section 7.6 will be used. We will begin with the volume of NaOH solution used in each titration, and convert that volume to moles of acid using the factor-unit method. 

Fig, H8. (a) Partial rale factors of free radical phenylation, relative to benzene (397). (b) Free valence calculated by HMO method (117). (c) Radical localization energy (in units) calculated by HMO method (117). 

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. 

By using specific catalytic activities, the differences in V ax due to any factor are automatically compensated for in the calculation. Because this method establishes relative contribution, there is no a priori need to use the same units for both components of the RAF calculation as long as the same units are used within the cDNA-expressed enzyme data set and the human tissue data set. Moreover, knowledge of the P450 content in either the cDNA expression system or in human liver microsomes is not necessary in order to make an interpretation. 

Factor-Label Method This method has the advantage of allowing you to write down the solution as one step. There is also the added advantage of having the calculation laid out ready to be put through your calculator. As you read this setup from left to right, cross out the units that cancel and notice that the units on the answer are those that are to be on the final answer. 

This book is designed to help you leam the fundamentals of chemistry. To be successful, you must master the concepts of chemistry and acquire the mathematical skills necessary to solve problems in this quantitative science. If your algebra is rusty, you should polish it up. Appendix 1 reviews the algebra used in basic chemistry and also shows how to avoid mistakes while solving chemistry problems with your scientific calculator. The factor label method is introduced in Chapter 2 to show you how to use units to help with problem solutions. You can help yourself by using the standard symbols and abbreviations for various quantities (such as m for mass, m for meter, mol for moles, and M for molarity). Always use the proper units with your numerical answers it makes a big difference whether your roommate s pet is 6 inches long or 6 feet long ... 

To use the factor label method effectively, we must know the units of all the quantities being dealt with and write them down as part of the calculation. 

The previous calculation is an example of the use of the factor label method, also called dimensional analysis, in which a quantity is multiplied by a factor equal or equivalent to 1. The units inclnded in the factor are the labels. In the previous example, 9 is equivalent to 1 hour (h), and the calculation changes the number of hours worked to the equivalent number of dollars. To use the factor label method, first put down the given quantity, then multiply by a conversion factor (a rate or ratio) that will change the units given to the units desired for the answer. The factor may be a known constant or a value given in the problem. 

Worked Examples. A large number of worked examples serve as aids in understanding the concepts of analytical chemistry. As in the seventh edition, we follow the practice of including units in chemical calculations and using the factor-label method to check their correctness. The examples also are models for the solution of problems found at the end of most of the chapters. Many of these use spreadsheet calculations, as described next. 

Multiplication by unity (by one) does not change the value of an expression. If we represent one in a useful way, we can do many conversions by just multiplying by one. This method of performing calculations is known as dimensional analysis, the factor-label method, or the unit factor method. Regardless of the name chosen, it is a powerful mathematical tool that is almost foolproof. 

The factor label method doesn t change the value of the physical quantity because you are multiplying that value by a factor that equals 1. You choose the factor so that when the unit you want to eliminate is multiplied by the factor, that unit and the similar unit in the factor cancel. If the unit you want to eliminate is in the numerator, choose the factor which has that unit in the denominator. Conversely, if the unit you want to eliminate is in the denominator, choose the factor which has that unit in the numerator. For example, in a chemistry lab activity, a student measured the mass and volume of a chunk of copper and calculated its density as 8.80 g/cm. Knowing that 1000 g = 1 kg and 100 cm = 1 m, the student could then use the following factor label method to express this value in the SI unit of density, kg/m. ... 

The factor label method can be extended to other types of calculations in chemistry. To use this method, you first examine the data that you have. Next, you determine the quantity you want to find and look at the units you will need. Finally, you apply a series of factors to the data in order to convert it to the units you need. 

Careful measurements and the proper use of significant figures, along with correct calculations, will yield accurate numerical results. But to be meaningful, the answers also must be expressed in the desired units. The procedure we will use to convert between units in solving chemistry problems is called the factor-label method, or dimensional analysis. A simple technique requiring little memorization, the factor-label method is based on the relationship between different units that express the same physical qnan-tity. 

In the factor-label method the units are carried through the entire sequence of calculations. Therefore, if the equation is set up correctly, then all the units will cancel except the desired one. If this is not the case, then an error must have been made somewhere, and it can usually be spotted by reviewing the solution. 

An extremely useful tool for scientific calculations (for everyday calculations too) is dimensional analysis, also called the factor label method. This system enables us to convert from a quantity in one set of units to the same quantity in another set, or from a quantity of one thing to an equivalent quantity of another. For example, if we have 2.00 or 200 cents, we have the same amount of money. We can change from one of these to the other with a factor—a ratio—of 100 cents divided by 1.00 dollar, or the reciprocal of that ratio. 

The first application of mathematics to chemistry deals with various physical quantities that have numerical values. In this chapter, we introduce the correct use of numerical values to represent measured physical quantities and the use of numerical mathematics to calculate values of other quantities. Such values generally consist of a number and a unit of measurement, and both parts of the value must be manipulated correctly. We introduce the use of significant digits to communicate the probable accuracy of the measured value. We also review the factor-label method, which is a routine method of expressing a measured quantity in terms of a different unit of measurement. 

The use of conversion factors in calculations is known by various names, such as the factor-label method or dimensional analysis (because units represent physical dimensions). We use this method in quantitative problems throughout the text. 

Hansch and Leo [14] do not give the uncertainties for each of their f and F values, but a typical value of 0.03 log K w unit can be assumed for common fragments and factors and 0.05 for less common ones. The total uncertainty in any estimate derived via the method outlined in Eq. 1-4 can then be calculated by the method outlined in Appendix C of this handbook. Since simple addition and subtraction of terms is involved here, the total method error is the square root of the sum of the squares of the individual uncertainties. Using the example given previously in Eq. 1-5, and assuming that the uncertainties for fci and fBr are both 0.03 log K w unit (Cl and Br are common fragments), the total uncertainty is (0.03 + 0.03 ) = 0.04 log Kow unit. Note that this does not consider any uncertainty in the measured value of log Kow for the base chemical. Accordingly, method errors of 0.04 to 0.1 log K w unit should be expected when this method is used. 

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