Experimental assumptions, validity

A significant change in the theoretical treatment of atomic structure occurred in 1924 when Louis de Broglie proposed that an electron and other atomic particles simultaneously possess both wave and particle characteristics and that an atomic particle, such as an electron, has a wavelength X = h/p = h/mv. Shortly thereafter, C.J, Davisson and L.H. Germer showed experimentally the validity of this postulate. Dc Broglie s assumption that wave characteristics are inherent in every atomic particle was quickly followed by the development of quantum mechanics, in its most simple form, quantum mechanics introduces the physical laws associated with the wave properties of electromagnetic radiation into the physical description of a system of atomic particles. By means of quantum mechanics a much more satisfactory explanation of atomic structure can be developed. 

The main advantage of this model is that it does not include any adjustable parameters. Hence, the behavior of the system can be predicted if the experimental conditions (applied current intensity, solution flow rate, and mass-transfer coefficient) are known. The good agreements obtained between model and experimental data validate all the assumptions made in the development of this model. This validation has been carried out with a wide variety of model pollutants including aromatics, nitroaromatics, cloroaromatics, carboxylic acids, alcohols, etc. 

The target efficiencies tj < for the collision velocity and 7g < 1 for the influence of the rotor geometry take into account deviations from a modelling based on assumptions valid for an ideal system. The letter denotes the volume shape factor. Data for the solid material parameters Hy,n, and r/(K and further information can be found in Mersmann (2001). Experimental data on the width of the metastable zone valid for the presence of mother crystals are given... 

This chapter discussed the art of modeling, with a few examples. Regardless of the type of model developed, a mathematical model should be validated with experimental results. Validation becomes very important in the black-box type of models such as the neural network models. Moreover, the model results are valid only within certain regimes where the model assumptions are valid. Sometimes, any model can be fit to a particular set of data by adjusting the parameter values. The techniques of parameter estimation were not presented in this chapter, the presentation was limited to lumped-parameter analysis, or macroscopic modeling. 

To prove our assumptions valid, we plot the experimental data from the reaction as ln([A]/[A],=o) against time. The slope of such a plot is If the plot produces a linear relationship between... 

The extensive use of the Young equation (Eq. X-18) reflects its general acceptance. Curiously, however, the equation has never been verified experimentally since surface tensions of solids are rather difficult to measure. While Fowkes and Sawyer [140] claimed verification for liquids on a fluorocarbon polymer, it is not clear that their assumptions are valid. Nucleation studies indicate that the interfacial tension between a solid and its liquid is appreciable (see Section K-3) and may not be ignored. Indirect experimental tests involve comparing the variation of the contact angle with solute concentration with separate adsorption studies [173]. 

It seems appropriate to assume the applicability of equation (A2.1.63) to sufficiently dilute solutions of nonvolatile solutes and, indeed, to electrolyte species. This assumption can be validated by other experimental methods (e.g. by electrochemical measurements) and by statistical mechanical theory. 

It would clearly be desirable to extend the scope of the Kelvin method to include a range of adsorptives having varied physical properties, especially surface tension, molar volume, molecular shape and size. This would enable the validity of the method and its attendant assumptions to be tested more adequately, and would also allow a variation in experimental technique, for example by permitting measurements at 298 K rather than 77 K. 

The correlations used are based partly on theoretical consideration and partly on empirical observations. The basic filtration data are correlated by application of the classic cake-filtration equation, aided by various simplifying assumptions which are sufficiently valid for many (but not all) situations. Washing and drying correlations are of a more empirical nature but with strong experimental justification. If steam or thermal diying is being examined, additional correlations are required beyond those summarized below for such applications, it is advisable to consult an eqmpment manufacturer or refer to pubhshed technical papers for guidance. 

This type of correlation applies to almost any siibstrate involved in cellular energy metabolism and is supported by experimental data and energetic considerations. However, it is based on assumptions true at or near the steady-state equilibrium conditions and may not be valid... 

Equations (4-5) and (4-7) are alternative expressions for the estimation of the diffusion-limited rate constant, but these equations are not equivalent, because Eq. (4-7) includes the assumption that the Stokes-Einstein equation is applicable. Olea and Thomas" measured the kinetics of quenching of pyrene fluorescence in several solvents and also measured diffusion coefficients. The diffusion coefficients did not vary as t) [as predicted by Eq. (4-6)], but roughly as Tf. Thus Eq. (4-7) is not valid, in this system, whereas Eq. (4-5), used with the experimentally measured diffusion coefficients, gave reasonable agreement with measured rate constants. 

It may happen that AH is not available for the buffer substance used in the kinetic studies moreover the thermodynamic quantity A//° is not precisely the correct quantity to use in Eq. (6-37) because it does not apply to the experimental solvent composition. Then the experimentalist can determine AH. The most direct method is to measure AH calorimetrically however, few laboratories Eire equipped for this measurement. An alternative approach is to measure K, under the kinetic conditions of temperature and solvent this can be done potentiometrically or by potentiometry combined with spectrophotometry. Then, from the slope of the plot of log K a against l/T, AH is calculated. Although this value is not thermodynamically defined (since it is based on the assumption that AH is temperature independent), it will be valid for the present purpose over the temperature range studied. 

The reverse of Example 16.4 involves finding Rq, of a compound given its solubility. The solubilities of many ionic compounds are determined experimentally and tabulated in chemical handbooks. Most solubility values are given in grams of solute dissolved in 100 grams of water. To obtain the molar solubility in moles/L, we have to assume that the density of the solution is equal to that of water. Then the number of grams of solute per 100 g water is equal to the number of grams of solute per 100 mL of solution. This assumption is valid because the mass of the compound in solution is small. To solve for IQp, find the molar solubility of the solute and determine the concentration of its component ions. Substitute into the IQp expression. 

The receptor compartment is defined as the aqueous volume containing the receptor and cellular system. It is assumed that free diffusion leads to ready access to this compartment (i.e., that the concentration within this compartment is the free concentration of drug at the receptor). However, there are factors that can cause differences between the experimentally accessible liquid compartment and the actual receptor compartment. One obvious potential problem is limited solubility of the drug being added to the medium. The assumption is made tacitly that the dissolved drug in the stock solution, when added to the medium bathing the pharmacological preparation, will stay in solution. There are cases where this may not be a valid assumption. 

The enthalpy values of the displacement in the above solvents were calculated to be — 2.0, — 2.0 and —2.1 kcal mol , i.e., practically identical within the experimental error. These observations verify the validity of the assumption for the cancellation of solvation effects in hydrogen bonds in non-polar solvents6 5b,c. Solvent effects on the hydrogen bond have been discussed by others66 - -80 82. 

While venting technology and methods are improving, considerable uncertainty remains as to the validity of various assumptions and accuracy of the correlations. Nearly all of the experimental data to verify calculations to-date are with air-water-steam systems. 

In considering step polymerisation with polyfunctional molecules a number of assumptions are made. They are (i) that all functional groups are equally reactive, (ii) that reactivity is independent of molar mass or solution viscosity, and (iii) that all reactions occur between functional groups on different molecules, i.e. there are no intramolecular reactions. It is found experimentally that these assumptions are not completely valid and tend to lead to an underestimate of the extent of reaction required to bring about gelation. 

When an analytical method is being developed, the ultimate requirement is to be able to determine the analyte(s) of interest with adequate accuracy and precision at appropriate levels. There are many examples in the literature of methodology that allows this to be achieved being developed without the need to use complex experimental design simply by varying individual factors that are thought to affect the experimental outcome until the best performance has been obtained. This simple approach assumes that the optimum value of any factor remains the same however other factors are varied, i.e. there is no interaction between factors, but the analyst must be aware that this fundamental assumption is not always valid. 

Thus, the Stokes-Einstein equation is expected to be valid for colloidal particles and suspensions of large spherical particles. Experimental evidence supports these assumptions [101], and this equation has occasionally been used for much smaller species. 

The percolation model of adsorption response outlined in this section is based on assumption of existence of a broad spread between heights of inter-crystalline energy barriers in polycrystals. This assumption is valid for numerous polycrystalline semiconductors [145, 146] and for oxides of various metals in particular. The latter are characterized by practically stoichiometric content of surface-adjacent layers. It will be shown in the next chapter that these are these oxides that are characterized by chemisorption-caused response in their electrophysical parameters mainly generated by adsorption charging of adsorbent surface [32, 52, 155]. The availability of broad spread in heights of inter-crystalline barriers in above polycrystallites was experimentally proved by various techniques. These are direct measurements of the drop of potentials on probe contacts during mapping microcrystal pattern [145] and the studies of the value of exponential factor of ohmic electric conductivity of the material which was L/l times lower than the expected one in case of identical... 

In Chapter 3 we will provide experimental verification of expression obtained in this Section linking the concentration of active particles in ambient volume with the change in electric conductivity of adsorbent under stationary and kinetic conditions as well as experimental prove of validity assumptions made while deriving above expressions. 

As with donor particles, in order to resolve the posed problem it is initially necessary to prove experimentally a rigorous validity relationships derived in above domain of parameters (pressure and temperature) based on substantially wide number of experimental results. It is known that when preparing such experiments it is recommended to avoid various reefs which may provoke an experimentalist to take wrong assumptions for real, or to hide from a theorist, for example, simple functions in relationships analysed. Pioneering experiments conducted with acceptors involved such active particles as molecular oxygen which on the one hand possesses strong acceptor properties, and on the other is a fairly widespread and chemically sufficiently stable element. 

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