Learning curve, Chapter

To choose the appropriate indicator for a particular titration, you must know the approximate pH of the solution at equivalence. As you learned in Chapter 8, an acid-hase titration curve provides this information. 

The objective of this chapter is to reduce the learning curve for the application of near-infrared (NIR) spectroscopy, or indeed any process analytical technology, to the chemical industry. It attempts to communicate realistic expectations for process analyzers in order to minimize both unrealistically positive expectations (e.g. NIR can do everything and predict the stock market ) and unrealistically negative expectations (e.g. NIR never works don t waste your money ). The themes of this chapter are value and... 

Earlier in this chapter I talked about the important role of families in childhood socialization. However, socialization continues throughout our lives. In our jobs, our role as spouses, parents, and eventually new retirees, we must learn how to function. Learning how to deal with illness, doctors, and medications also involves a steep learning curve. At the outset of an illness, patients often feel helpless and unquestioningly give themselves over to the care of doctors. Despite the proliferation of in-... 

The savings that result from increases in productivity benefit the stockholders by increasing profits and dividends, the employees by increasing salaries and wages, and the consumer by decreasing prices. The experience and learning curves, which are measures of productivity, were discussed in Chapters 2 and 8. 

The World Wide Web is now the most common interface used to submit sequences to the three databases. The Web-based submission systems include Sakura ( cherry blossoms ) at DDBJ, Webln at EBI, and Bankit at the NCBI. The Web is the preferred submission path for simple submissions or for those that do not require complicated armotations or too much repetition (i.e., 30 similar sequences, as typically found in a population study, would best be done with Sequin, see below). The Web form is ideal for a research group that makes few sequence submissions and needs something simple, entailing a short learning curve. The Web forms are more than adequate for the majority of the submissions some 75-80% of individual submissions to NCBI are done via the Web. The alternative addresses (or URLs) for submitting to the three databases are presented in the list at the end of the chapter. 

The most satisfactory solution to such situations would be the establishment of temporary strm-dards. The analyst establishes the standard based on the difficulty of the job and the number of pieces to be produced. Then, by using a learning curve (see Chapter 53 on learning curves) for the woik, as weU as existing standard data, an equitable temporary standard for the work can be established. When released to the production floor, the standard should be clearly identified as temporary and apphcable to only to a fixed quantity or fixed duration. Upon expiration, temporary standards should be immediately replaced by permanent standards. 

This book is not divided into the main themes of aviation psychology. Instead, it is sectioned to reflect the rephrasing and regrouping of aviation research, as explained above, so that relationships between these themes are highhghted. Research on stress is in the company of studies on flying skill, risk assessment techniques side with a stiufy on safety culture, and studies on selection are joined by a chapter on learning curves. 

In this chapter we begin by describing the main principles of CBAS and the use of learning curves in OJT. Next, we explain the method by which learning curves are derived from the assessment results. Finally, we present the results of the analysis of learning curves. 

The industrial cases overviewed in this chapter indicate that by planning a collaborative platform (i.e., with complementary software applications), users can best benefit from the most recent technology developments for establishing meaningful and timely collaboration with minimum technological hindrances and steep learning curves. 

N, Inc. (see Chapter 1) moved forward with its plans to build a plant in Mexico. After these plans were implemented, it found the plant to be extremely effective and efficient. However, the plant did not generate the desired overall cost savings. In the new facility, yields had dropped from 75 to 60 percent, but some of this decrease could be explained by a learning curve. N, Inc. performed a detailed cost comparison analyzing the before and after environments and discovered that transport costs and inventory carrying costs had jumped dramatically. In addition, the supply chain had become enormously complicated. The materials that previously came from companies like C, Inc. now had to be moved across borders, which meant more distribution layers, resulting in increased cost. 

In the overview to this chapter we noted that the experimentally determined end point should coincide with the titration s equivalence point. For an acid-base titration, the equivalence point is characterized by a pH level that is a function of the acid-base strengths and concentrations of the analyte and titrant. The pH at the end point, however, may or may not correspond to the pH at the equivalence point. To understand the relationship between end points and equivalence points we must know how the pH changes during a titration. In this section we will learn how to construct titration curves for several important types of acid-base titrations. Our... 

From Chapter 5 we have learned that with this form of rate-concentration curve we should operate as follows ... 

We now turn our attention to details of precipitation titrations as an illustration of principles that underlie all titrations. We first study how concentrations of analyte and titrant vary during a titration and then derive equations that can be used to predict titration curves. One reason to calculate titration curves is to understand the chemistry that occurs during titrations. A second reason is to learn how experimental control can be exerted to influence the quality of an analytical titration. For example, certain titrations conducted at the wrong pH could give no discernible end point. In precipitation titrations, the concentrations of analyte and titrant and the size of Ksp influence the sharpness of the end point. For acid-base titrations (Chapter 11) and oxidation-reduction titrations (Chapter 16). the theoretical titration curve enables us to choose an appropriate indicator. 

From an acid-base titration curve, we can deduce the quantities and pK.d values of acidic and basic substances in a mixture. In medicinal chemistry, the pATa and lipophilicity of a candidate drug predict how easily it will cross cell membranes. We saw in Chapter 10 that from pKa and pH, we can compute the charge of a polyprotic acid. Usually, the more highly charged a drug, the harder it is to cross a cell membrane. In this chapter, we learn how to predict the shapes of titration curves and how to find end points with electrodes or indicators. 

Figure 11 -5 shows an autotitrator, which performs the entire operation automatically.4 Titrant from the plastic bottle at the rear is dispensed in small increments by a syringe pump while pH is measured by electrodes in the beaker of analyte on the stirrer. (We will learn how these electrodes work in Chapter 15.) The instrument waits for pH to stabilize after each addition, before adding the next increment. The end point is computed automatically by finding the maximum slope in the titration curve. 

In this chapter we introduce a more useful equation for the surface tension. This we do in two steps. First, we seek an equation for the change in the Gibbs free energy. The Gibbs free energy G is usually more important than F because its natural variables, T and P, are constant in most applications. Second, we have just learned that, for curved surfaces, the surface tension is not uniquely defined and depends on where precisely we choose to position the interface. Therefore we concentrate on planar surfaces from now on. 

Excel provides several ways to find the coefficients that provide the best fit of a function to a set of data points — a process sometimes referred to as curve fitting. The "best fit" of the curve is considered to be foimd when the sum of the squares of the deviations of the data points from the calculated curve is a minimum. In the field of statistics, finding the least-squares best-fit parameters that describe a data set is known as regression analysis. In this chapter you ll learn how to perform simple and multiple linear regression... 

In this chapter you ll learn how to use the Solver, Excel s powerful optimization package, to perform non-linear least-squares curve fitting. 

Overview In this chapter we learn about nonideal reactors, that is, reactors that do not follow the models we have developed for ideal CSTRs, PFRs, and PBRs. In Pan I we describe how to characterize these nonideal reactors using the residence time distribution function (/), the mean residence time the cumulative distribution function Fit), and the variance a. Next we evaluate E t), F(t), and for idea) reactors, so that we have a reference proint as to how far our real (i.e., nonideal) reactor is off the norm from an ideal reactor. The functions (f) and F(r) will be developed for ideal PPRs. CSTRs and laminar flow reactors, Examples are given for diagnosing problems with real reactors by comparing and E(i) with ideal reactors. We will then use these ideal curves to help diagnose and troubleshoot bypassing and dead volume in real reactors. 

Many readers have probably had some exposure to calculus, which involves derivatives and integrals. Although both derivatives and integrals are used in developing PK models, this chapter will not go into detailed derivations of model equations, and you may be happy to learn that an extensive review of calculus is not forthcoming. This section will instead focus on the simple fact that the integral of a function f f) represents the area between the plot of the curve y = f t) and the horizontal axis represented by y = 0. This is illustrated in Figure 10.5. This area is called the area under the curve AUC) in pharmacokinetics, which can then be written as... 

Before we discuss redox titration curves based on reduction-oxidation potentials, we need to learn how to calculate equilibrium constants for redox reactions from the half-reaction potentials. The reaction equilibrium constant is used in calculating equilibrium concentrations at the equivalence point, in order to calculate the equivalence point potential. Recall from Chapter 12 that since a cell voltage is zero at reaction equilibrium, the difference between the two half-reaction potentials is zero (or the two potentials are equal), and the Nemst equations for the halfreactions can be equated. When the equations are combined, the log term is that of the equilibrium constant expression for the reaction (see Equation 12.20), and a numerical value can be calculated for the equilibrium constant. This is a consequence of the relationship between the free energy and the equilibrium constant of a reaction. Recall from Equation 6.10 that AG° = —RT In K. Since AG° = —nFE° for the reaction, then... 

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