Problem solving systematic approach

If we wish to calculate the solubility of barium sulfate in a system containing hydronium and acetate ions, we must take into account not only the solubility equilibrium but also the other three equilibria. We find, however, that using four equilibrium-constant expressions to calculate solubility is much more difficult and complex than the simple procedure illustrated in Examples 9-4, 9-5, and 9-6. To solve this type of problem, the systematic approach described in Section llA is helpful. We then use this approach to illustrate the effect of pH and complex fonna-tion on the solubility of typical analytical precipitates. In later chapters, we use this same systematic method for solution of problems involving multiple equilibria of several types. 

Besides equilibrium constant equations, two other types of equations are used in the systematic approach to solving equilibrium problems. The first of these is a mass balance equation, which is simply a statement of the conservation of matter. In a solution of a monoprotic weak acid, for example, the combined concentrations of the conjugate weak acid, HA, and the conjugate weak base, A , must equal the weak acid s initial concentration, Cha- ... 

The solubility of a precipitate can be improved by adding a ligand capable of forming a soluble complex with one of the precipitate s ions. For example, the solubility of Agl increases in the presence of NH3 due to the formation of the soluble Ag(NH3)2°" complex. As a final illustration of the systematic approach to solving equilibrium problems, let us find the solubility of Agl in 0.10 M NH3. 

You should be able to describe a system at equilibrium both qualitatively and quantitatively. Rigorous solutions to equilibrium problems can be developed by combining equilibrium constant expressions with appropriate mass balance and charge balance equations. Using this systematic approach, you can solve some quite complicated equilibrium problems. When a less rigorous an-... 

Problem Solving Methods Most, if not aU, problems or applications that involve mass transfer can be approached by a systematic-course of action. In the simplest cases, the unknown quantities are obvious. In more complex (e.g., iTmlticomponent, multiphase, multidimensional, nonisothermal, and/or transient) systems, it is more subtle to resolve the known and unknown quantities. For example, in multicomponent systems, one must know the fluxes of the components before predicting their effective diffusivities and vice versa. More will be said about that dilemma later. Once the known and unknown quantities are resolved, however, a combination of conservation equations, definitions, empirical relations, and properties are apphed to arrive at an answer. Figure 5-24 is a flowchart that illustrates the primary types of information and their relationships, and it apphes to many mass-transfer problems. 

The logical approach to problem solving for rubber analysis at Polysar Ltd was described by Chu [73] (cf. Schemes 2.4 and 2.5). Systematic analysis involves sampling, elimination of interference and measurement. Methods employed include chromatography (GC, HS-GC, HPLC, SEC, IC), spectroscopy (AAS, UV/VIS, IR, NMR), MS, microscopy and thermal analysis. The specific role of each of these techniques for the analysis of rubber compounds with or without... 

A more systematic approach was developed by Romagnoli and Stephanopoulos (1981) and Romagnoli (1983) to analyze a set of measurement data in the presence of gross errors. The method is based on the idea of exploiting the sequential processing of the information (constraints and measurements), thus allowing the computations to be done in a recursive way without solving the full-scale reconciliation problem. 

Fire protection is a science that stretches as far back as the Roman Empire. The aqueducts and the Corp of Vigilantes gave the Romans what they needed for fire protection and control. Through the years, the practice of fire protection has evolved from a problem-solving approach to a mature, systematic discipline. 

This first sample question is followed by a step-by-step analysis that shows you how to use common sense and a systematic problem-solving approach to select the best possible answer. You might want to try working out the answer yourself before you read the explanation that follows. 

Figure 15.7 summarizes the steps followed in solving this problem. This same systematic approach is applied to all aqueous equilibrium problems in this chapter and in Chapter 16. 

Route to Improvement. As one route to solving problems that perplex FTMS, we have made use of a systematic approach illustrated in Figure 1. The "Development Cycle" enables us to define clearly problems and to arrive at solutions through an organized combination of theoretical and experimental work. The most difficult aspect of... 

Apart from the heat bath mode, the harmonic potential surface model has been used for the molecular vibrations. It is possible to include the generalized harmonic potential surfaces, i.e., displaced-distorted-rotated surfaces. In this case, the mode coupling can be treated within this model. Beyond the generalized harmonic potential surface model, there is no systematic approach in constructing the generalized (multi-mode coupled) master equation that can be numerically solved. The first step to attack this problem would start with anharmonicity corrections to the harmonic potential surface model. Since anharmonicity has been recognized as an important mechanism in the vibrational dynamics in the electronically excited states, urgent realization of this work is needed. 

In this appendix, we consider how an organic chemist systematically approaches a mechanism problem. Although there is no formula for solving all mechanism problems, this stepwise method should provide a starting point for you to begin building experience and confidence. Solved problems that apply this approach appear on pages 158, 316,491, 858,1007,1066, and 1089. 

This SPS team was empowered to improve their system. Upper management simply said, OK, see if you can fix it The team s solution used a simple path of least resistance. For a more complex solution set, they may have selected multivariate regression modeling or hired an outside statistical consultant.The main point is that they used a scientifically proven, systematic approach to solving a complex problem, through teamwork and simple observational and analytical techniques. 

The two aspects of documentation are documenting care delivered to patients and documenting progress toward meeting practice plan objectives. The problem-oriented medical record is used by health care professionals to convey information about patient care. The problem-oriented medical record is a means to organize observations into a systematic, problem-solving approach that can be conveyed to others. The problem-oriented approach to documentation is intended to streamline the amount of reading that practitioners must do to update themselves on a patient s status. 

There are many ways you can predict trends in an industry, and there are numerous trend gurus whose work could be helpful. We like the work of Genrich Altshuller, the founder of the Theory of Inventive Problem Solving (TRIZ), because it s one of the most empirical approaches. We also favor the work of U.K.-based author Darrell Mann, who has built on Altshuller s paradigm oi systematic innovation to refine it for further use. 

Any self-developed method or discipline will consist of personal features and individual points of view that may or may not reflect the opinion of the majority which may not necessarily be the most valid position. One should expect, therefore, that the criteria of those readers who have already created their own systematic approach to problem solving in mechanistic organic chemistry may be in conflict with some sensitive points expressed here. In addition, there are those who feel that rules in general jeopardize their ability to create and thus to find original solutions to problems. 

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