Some definitions and concepts

Solution. Hydrochloric acid is a gas under normal conditions, but it is a strong electrolyte that dissolves in water to form equal numbers of H (aq) and Cl (aq). Therefore, when 0.02 mole of HCl dissolve in 1 L of water, 0.02 mole of H (aq) and 0.02 mole of Cl (aq) will form [we can neglect the small additional number of H (aq) produced by the dissociation of the water]. Hence, [H (aq)] = 0.02 M. Since we can apply Eq. (4.22) to the solution 

In both cases, an acid reacts with a base to produce water and a third class of substance called a salt (e.g., NaCI and CaS04). 

The acidity (or alkalinity, as the case may be) of water is very important because H (aq) and OH (aq) ions play crucial roles in many reactions in aqueous solutions. For example, the acidity (or alkalinity) determines the ability of water to sustain fish and plant life it also determines the solubility of many materials in water. 

In addition to the acids we have already mentioned, some other common acids are sulfuric acid (H2SO4), nitric acid (HNO3), formic acid (HCOOH), phosphoric acid (H3PO4), hydrogen fluoride (HF), 

Some common bases are sodium hydroxide (NaOH), potassium hydroxide (KOH), magnesium hydroxide (Mg(OH)2), calcium oxide (CaO), sodium carbonate (Na2C03), and ammonia (NH3). We could postulate that, like acids, a common property of bases is their ability to dissolve in water to produce ions. Also, since bases counteract acids, we might conclude that one of the ions they produce can remove the hydrogen ion. For NaOH, KOH, and Mg(OH)2 this ion is clearly OH (aq). But what is it for Na2C03 and NH3 To answer this question let us consider what happens when ammonia dissolves in water. It reacts with water molecules to form ammonium ions, NHJCaq), 

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The concept of complex variables is used widely in mathematical and engineering analysis. Some definitions and concepts commonly encountered in the field of impedance spectroscopy are presented in this section. 

Hartley, G. S., and J. Crank Some fundamental definitions and concepts in diffusion processes. Trans. Faraday Soc. 45, 801 (1949). 

Some of these definitions and concepts are shown schematically in Fig. 8.2, which describes a simple hydrologic cycle. The figure introduces the important concept of a perched water table, which may result from ponding of infiltration on a clay layer or impervious lens. Also shown is... 

In this Chapter, we quickly review some basic definitions and concepts from thermodynamics. We then provide a brief description of the first and second laws of thermodynamics. Next, we discuss the mathematical consequences of these laws and cover some relevant theorems in multivariate calculus. Finally, free energies and their importance are introduced. 

Many of the terms, definitions, and concepts used in polymer science are not encountered in other branches of science and must be understood in order to fully discuss the synthesis, characterization, structure, and properties of polymers. While most of these will be discussed in detail in subsequent chapters, some are of such fundamental importance that they must be introduced at the beginning. 

The next section, entitled Basic Aspects of Molecular Similarity, gives a general overview of molecular similarity and the usual vocabulary used by chemists in this field. In the section entitled The Electron Density as Molecular Descriptor, some elements of quantum chemistry will be presented. These sections should not be expected by the reader to offer a rigorous discussion of all aspects of such broad fields, and therefore, only the most important definitions and concepts will be introduced. The following sections will then address extensively the subject of molecular quantum similarity in both theoretical and practical aspects. An ample references list will help the interested reader to look up the more specialized literature. 

The development of Eq. (Iz3), including the necessary definitions and concepts, is the subject of a large portion of many books on thermodynamics (e.g., Balzhiser et al.. 1972 Denbigh. 1981 Elliott and Lira. 1999 Sandler. 2006 Smith et al.. 2005 Walas. 19851 but is beyond the scope of this book. However, Eq. (Iz3) does require that there be some relationship between liquid and vapor conpositions. In real systems this relationship may be very conplex and experimental data maybe required. We will assume that the equilibrium data or appropriate correlations are known (see Chapter 2). and we will confine our discussion to the use of the equilibrium data in the design of separation equipment. 

We begin the discussion with some key definitions and concepts in solving MCSP. We will assume that all the criteria in Table A.l are to be maximized. 

In the next section, I introduce the concept of power, confronting some different definitions of power from different realms of social science. Section 3 surveys economic literature on power, stemming from the view of the standard model to the newest theories developed by the new institutional economics and to power definition and concepts suggested by different strands of social network analysis. Section 4 uses different concepts of power to address some organizational problems in the food system. 

Alternatively, in faculty development workshops and other contexts involving some sustained discussion, it would be prudent to acquaint faculty with multiple SJ definitions, and even ask them to discuss which definitions apply most aptly to particular social justice contexts or scenarios. Faculty in one of our SJ workshops found the given definitions useful but inadequate and created hybrids, pulling concepts from some definitions and grafting them onto others. A sample of SJ definitions is provided in the Appendix. 

Opening segments of the IP2 PRA data analysis section describe the definitions of terms and concepts employed, the assumptions made, and limitations recognized during the data base construction. A set of 39 plant-specific component failure mode summaries established the basis for component service hour determinations, the number of failures, and the test data source for each failure mode given for each component. Generic data from WASH-1400, IEEE Std 500, and the LER data summaries on valves, pumps, and diesels were combined with plant-specific failure data to produce "updated" failure information. All the IP2 specialized component hardware failure data, both generic and updated, are contained in Table 1.5.1-4 (IP3 1.6.1-4). This table contains (by system, component, and failure mode) plant-specific data on the number of failures and service hours or demands. For some components, it was determined that specifications of the system was warranted because of its impact on the data values. 

Thus, two interpretations based on two different concepts of the effect of temperature on dipole orientation have been put forward. The two views clash with each other on physical as well as chemical grounds. However, the view based on the correlation of Fig. 25 introduces chemical concepts that are absent in the other, which ignores some definite facts. For instance, although a value for dEa=0/dT is not available for Ga, the temperature coefficient of C is apparently small.905 Ga is universally recognized as a strongly hydrophilic metal. Therefore, according to the simple model of up-and-down dipoles, the effect of temperature should be major, which is in fact not the case. 

This chapter focuses on types of models used to describe the functioning of biogeochemical cycles, i.e., reservoir or box models. Certain fundamental concepts are introduced and some examples are given of applications to biogeochemical cycles. Further examples can be found in the chapters devoted to the various cycles. The chapter also contains a brief discussion of the nature and mathematical description of exchange and transport processes that occur in the oceans and in the atmosphere. This chapter assumes familiarity with the definitions and basic concepts listed in Section 1.5 of the introduction such as reservoir, flux, cycle, etc. 

Here we present and discuss an example calculation to make some of the concepts discussed above more definite. We treat a model for methane (CH4) solute at infinite dilution in liquid under conventional conditions. This model would be of interest to conceptual issues of hydrophobic effects, and general hydration effects in molecular biosciences [1,9], but the specific calculation here serves only as an illustration of these methods. An important element of this method is that nothing depends restric-tively on the representation of the mechanical potential energy function. In contrast, the problem of methane dissolved in liquid water would typically be treated from the perspective of the van der Waals model of liquids, adopting a reference system characterized by the pairwise-additive repulsive forces between the methane and water molecules, and then correcting for methane-water molecule attractive interactions. In the present circumstance this should be satisfactory in fact. Nevertheless, the question frequently arises whether the attractive interactions substantially affect the statistical problems [60-62], and the present methods avoid such a limitation. 

In this chapter, we focus on the use of lanthanides as spin-based hardware for QC. The remainder of this introductory section provides some essential concepts and definitions and then it succinctly describes some of the existing proposals for QC. The second section provides a brief overview of results obtained with spin-based systems other than lanthanides. The following two sections review experiments made on qubits and quantum gates, respectively, based on lanthanides, highlighting their specific properties and advantages for QC applications. 

Before scientifically sound research can be performed on a subject, clear definitions must be set. Although, this may seem a logical step, Osborn (Osborn et al., 1988) highlighted that this has been a stumbling block for research in safety science since its inception. Definitions of concepts like accidents, incidents, near misses, risk, and safety, are known in the field of safety science, but interpreted differently in various situations. Unclear and ambiguous definitions lead to misinterpretations and confusion and must be avoided. Therefore, some general concepts used in safety science and the definitions used in this thesis are discussed in this Section. In the remainder of this thesis specific concepts will be defined where appropriate and can also be found in a list of acronyms and definitions presented in the beginning of this thesis. 

Let us first introduce some important definitions with the help of some simple mathematical concepts. Critical aspects of the evolution of a geological system, e.g., the mantle, the ocean, the Phanerozoic clastic sediments,..., can often be adequately described with a limited set of geochemical variables. These variables, which are typically concentrations, concentration ratios and isotope compositions, evolve in response to change in some parameters, such as the volume of continental crust or the release of carbon dioxide in the atmosphere. We assume that one such variable, which we label/ is a function of time and other geochemical parameters. The rate of change in / per unit time can be written... 

Although the explicit definition was new, the term had been around for some years, and ten years later in another memoire on the same topic, Rouelle provided a brief history of the concept. ... 

In this chapter, we explore acids and bases and the chemical reactions they undergo. We begin with a definition of these two important substances and then explore how some acids and bases are stronger than others. After learning about the pH scale, we close by looking at some environmental and physiological applications of acid-base concepts. 

This chapter introduces the reader to elementary concepts of modeling, generic formulations for nonlinear and mixed integer optimization models, and provides some illustrative applications. Section 1.1 presents the definition and key elements of mathematical models and discusses the characteristics of optimization models. Section 1.2 outlines the mathematical structure of nonlinear and mixed integer optimization problems which represent the primary focus in this book. Section 1.3 illustrates applications of nonlinear and mixed integer optimization that arise in chemical process design of separation systems, batch process operations, and facility location/allocation problems of operations research. Finally, section 1.4 provides an outline of the three main parts of this book. 

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