Quantitative problems

Finally, quantitative problems involving multiple analytes and back titrations also can be solved by applying the principle of conservation of electron pairs. 

Quantitative problems that require a calculator and some algebraic manipulations. 

Apply the seven-step strategy to this quantitative problem. The first two steps are part of the strategy the rest are part of the solution. 

Solving quantitative problems about gases requires only one equation, the ideal gas equation. 

This is a quantitative problem, so apply the seven-step strategy. As a review of the process, we present the steps as a list. 

We are asked to calculate two quantities, so this is a quantitative problem to which we can apply the... 

The seven-step method described in Chapter 16 provides the strategy for working any quantitative problem that involves equilibria. As a reminder, we detail each step in this first example of acid-base equilibria. 

This is a quantitative problem, so we follow the standard strategy. The problem asks about an actual potential under nonstandard conditions. Before we determine the potential, we must visualize the electrochemical cell and determine the balanced chemical reaction. The half-reactions are given in the problem. To obtain the balanced equation, reverse the direction of the reduction half-reaction with the... 

In spite of quantitation problems, SIMS can give useful information if one uses appropriate reference materials. The spectra in Fig. 4.18 indicate that the relative intensities of the Zr02, ZrO and Zr", contain information on the chemical environment of the zirconium the zircomum ethoxide (O Zr = 4 1) shows higher intensities for the and ZrO" signals than the calcined Zr02 (O Zr = 2 1). 

All available methods (TG-MS, PyGC-MS and LDI-MS) suffer from difficult quantitation, although for different reasons. In TG-MS, selective volatilisation may not reflect the composition in the solid the quantitation problem of PyGC-MS requires assessment of the importance of matrix effects. Laser ablation methods cannot easily be calibrated. Quantitation is simplified in case of dual detection (MS for identification, FID for quantitation). A general drawback of many direct methods, which allow only small sampling volumes, is granule-to-granule variations. 

The notes that form the basis for the bulk of this textbook have been used for several years in the undergraduate course in chemical kinetics and reactor design at the University of Wisconsin. In this course, emphasis is placed on Chapters 3 to 6 and 8 to 12, omitting detailed class discussions of many of the mathematical derivations. My colleagues and I stress the necessity for developing a seat of the pants feeling for the phenomena involved as well as an ability to analyze quantitative problems in terms of design framework developed in the text. 

Several other approaches to solve the quantitation problem have been proposed. Hoppe et al. [2] determined y/ by calibrating it against constructs with known FRET efficiency. We and others [3, 6] have used data from a cell before and after acceptor photobleaching to relate the FRET-induced sensitized emission in the S channel to the loss of donor emission in the D channel by factors termed or G, respectively. For the CFP/YFP pair this works very well on confocal microscopes with a 514-nm Argon ion laser line, but on wide-held systems, selective acceptor photobleaching reportedly causes problems [ 14]. F inally, G can also be determined by comparison of several constructs that differ in FRET efficiency, a bit analogous to the Yellow Cameleon calibration described above [10,14],... 

The boundary conditions too were known. It would not be as easy as handling an infinite periodic solid, but a number of us set to work. The special demand of chemistry was to quantify very small molecular changes. Successes came slowly, but with the development of computers and a lot of careful, clever work, by the 90s the quantitative problem was essentially solved. The emergent hero of the chemical community was John Pople, whose systematic strategy and timely method developments were decisive. The methods of what is termed ab initio quantum chemistry became available and used everywhere. 

The quantitative environmental analysis of surfactants, such as alcohol ethoxylates, alkylphenol ethoxylates (APEOs) and linear alkylbenzene sulfonates (LASs), is complicated by the presence of a multitude of isomers and oligomers in the source mixtures (see Chapter 2). This issue bears many similarities to the quantitation problems that have occurred with halogenated aromatic compound mixtures, e.g. polychlorinated biphenyls (PCBs) [1]. 

In the case of PCBs, the solutions to the quantitation problem have been ... 

The reasoning above allows us to find good qualitative answers, but in order to be able to do quantitative problems (how much is present, etc.), the extent of the dissociation of the weak acids and bases must be known. That is where a modification of the equilibrium constant is useful. 

While in classical statistics (univariate methods) modelling regards only quantitative problems (calibration), in multivariate analysis also qualitative models can be created in this case classification is performed. 

How are galvanic and electrolytic cells built, and how do they function What equations are used to describe these types of cells How can you solve quantitative problems related to electrolysis ... 

The next quantitative problem is to understand the basic mechanism of interaction between the regulator (in this case x) and its binding to the target enzyme (i.e. the enzyme that regulates the flux through the pathway). 

In general the mathematical formulation of the quantitation problem is shown in Table 2 for n-components. The matrix equation, H=AW G, can be solved for the total polymer Gp and... 

Tsaparlis (117) carried out a correlation study of the role of various cognitive factors (variables) in the solution of non-algorithmic quantitative problems in elementary physical chemistry. The cognitive variables were scientific reasoning (developmental level), working-memory capacity functional mental capacity (M-capacity) and disembedding ability. 

Studies of short-lived radionuclide generators (4-6) do not adequately treat the quantitative problems of the daughter nuclide elution or those specific to their optimal clinical use. Two essential physical characteristics of a generator are the yield of the daughter nuclide and its radiochemical and radionuclidic purity. To realize the full potential of a short-lived radionuclide generator for medical studies requires that these two characteristics are optimized and are compatible with parameters important to clinical use such as total perfused volume and duration of the scintigraphic examination. 

We now consider problems of a quantitative analysis of multiphonon transitions. Here an exact treatment seems hopeless at the present time, and to make headway at all a fair number of approximations are required. We shall give an overview of the general difficulties, discuss some (unfortunate) confusion on Born-Oppenheimer terminology, and then illustrate some quantitative problems using the adiabatic formulation (see below). The present discussion will also be used as a basis for subdividing the various papers, to be discussed in Section lOd, into various (perhaps somewhat arbitrary) categories. 

Qualitative ways of analyzing a problem in molecular vibrations, that is, methods for determining the number of normal modes of each symmetry type which will arise in the molecule as a whole and in each set of equivalent internal coordinates, have been developed. There is also the quantitative problem of how the frequencies of these vibrations, which can be obtained by experiment, are related to the masses of the atoms, the bond angles and bond lengths, and most particularly the force constants of the individual bonds and interbond angles. In this section we shall show how to set up the equations which express these relationships, making maximum use of symmetry to simplify the task at every stage. 

At this meeting Axelrod and Fransson both have shown synthetic nebular spectra based on the Wolf-Rayet model, and both find good qualitative agreement with observation. The main quantitative problem seems to be that since in this model the oxygen is concentrated into a... 

Another alternative solution to circumvent the detection and quantitation problems of classical TLC involves the use of silica-coated quartz rods, so-called chromarods. This has been pro-... 

Other methods of estimating total amino acids exist but have not been widely applied to citrus. Various ninhydrin colorimetric methods are published, but different colors produced by individual amino acids caused quantitation problems. Ting and Deszyck (63J attempted to reduce this problem by using two wavelengths, 400 and 570 nm, for proline and the "ninhydrin blue" amino acids. Differences in molar absorption made the results dependent upon the composition of the standard mixture. 

Karamushko, L.I. and Shatunovsky, M.I. (1993). Quantitative problems of temperature effect in relation to energy metabolism rate in Gadus morhua, Anarhichas lupus and Pleuronectes platessa (In Russian). Voprosy Ikhtiologii 33,111-120. 

Hyphenated thermogravimetric techniques have been used in a wide variety of qualitative and quantitative problem-solving cases for elastomeric materials ... 

Note Many chemistry essays on certification exams consist of quantitative problem solving with the requirement to show your work. The first of the two sample essays is of this type. For additional practice, I recommend solving quantitative problems from the multiple choice sample test with an essay mindset and comparing your essays to the solutions shown in the Answers with Solutions section. Some chemistry essays require little or no quantitative problem solving, but they ask for an experimental design or analysis of a design. The second of the two sample essays is of this type. These essays usually have no single correct solution. 

Besides this quantitative problem (which may seem a luxury problem to many other industries) the very idea of focusing on just the negative outcomes of process control deviations neglects the valuable lessons to be learned on the basis of positive outcomes. Every time an operator, manager, procedure, or piece of equipment behaves in an unexpected way and thereby prevents a likely breakdown of the production system (e.g. as in reduced product quality, environmental releases, etc.) or restores the required levels of safety and reliability, these positive deviations could be detected, reported and analysed in order to improve the qualitative insight into system functioning on the whole. 

Apply your understanding of stoichiometry to solve quantitative problems involving solutions. 

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