Factors Limiting Accuracy

This chapter opened with a photo of a nearly perfect silicon sphere that is being used to determine Avogadro s number. Use your Web browser to connect to http //chemistry.brookscole.com/skoogfac/. From the Chapter Resources Menu, choose Web Works. Locate the Chapter 4 section and click on the link to the Australian National Measurement Laboratory. Read the article on Avogadro s number and the silicon kilogram. What factors limit accuracy in the determination of this number What are the present and ultimate uncertainties in the measurement of the molar mass of silicon, the number of atoms per unit cell, the mass, the volume, and the lattice parameter of silicon ... 

What calibration needs are required These factors limit accuracy and precision. The specifics of calibration have been discussed in detail in Chapters 3 and 6. 

The factor limiting the resolution in ultraviolet photoelectron spectra is the inability to measure the kinetic energy of the photoelectrons with sufficient accuracy. The source of the problem points to a possible solution. If the photoelectrons could be produced with zero kinetic energy this cause of the loss of resolution would be largely removed. This is the basis of zero kinetic energy photoelectron (ZEKE-PE) spectroscopy. 

A number of factors limit the accuracy with which parameters for the design of commercial equipment can be determined. The parameters may depend on transport properties for heat and mass transfer that have been determined under nonreacting conditions. Inevitably, subtle differences exist between large and small scale. Experimental uncertainty is also a factor, so that under good conditions with modern equipment kinetic parameters can never be determined more precisely than 5 to 10 percent (Hofmann, in de Lasa, Chemical Reactor Design and Technology, Martinus Nijhoff, 1986, p. 72). 

RMC can be selectively extracted into butyl acetate. Concentration coefficient 50 was achieved. Factors affecting accuracy and reproducibility of the proposed method were investigated. Method is simple and fast. Detection limit is 0,3 p.g/1 for P(V). 

The theory developed for perfect gases could be extended to solids, if the partition functions of crystals could be expressed in terms of a set of vibrational frequencies that correspond to its various fundamental modes of vibration (O Neil 1986). By estimating thermodynamic properties from elastic, structural, and spectroscopic data, Kieffer (1982) and subsequently Clayton and Kieffer (1991) calculated oxygen isotope partition function ratios and from these calculations derived a set of fractionation factors for silicate minerals. The calculations have no inherent temperature limitations and can be applied to any phase for which adequate spectroscopic and mechanical data are available. They are, however, limited in accuracy as a consequence of the approximations needed to carry out the calculations and the limited accuracy of the spectroscopic data. 

Several attempts were performed to determine the accuracy of in silica prediction tools developed for lipophilicity (for a recent review, see [34]). The main factor limiting the accuracy of all predictive methods is the training sets used to generate the models, in terms of population and quality of the experimental data they contain. Since most of the methods proposed in commercial software were built with data available in the public domain, their accuracy can be expected to be comparable. Thus, in order to select the most suitable prediction tool, other criteria than accuracy have to be used such as the speed of the calculation for large databases, the price of commercial software or the application domain of the model. 

If the activation energies of surface diffusion vary over a wide range from one element to another and from one surface to another, the diffusivity, or the pre-exponential factor, D0, does not. Within the very limited accuracy of the field ion microscope measurements, usually no better than one order of magnitude because of the narrow temperature range within which a measurement can be conveniently done, all measured values of D0 are consistent with eq. (4.22) by taking AS = 0, and v0 = kTIh where h is the Planck constant, or D0 are about a few 10-3 cm2/s. This has been pointed out repeatedly by the author126 since there is... 

In practice, the selection tends to be a combination of equipment and methods, as portability is as great a factor in the selection process as are detection limits, accuracy, and reproducibility. Also, each operator and field engineer will have a slightly different opinion concerning what constitutes the optimum balance. As a result, it is difficult to propose any hard-and-fast rules some mere observations therefore are presented here. 

Site populations of less abundant cations estimated from X-ray diffraction measurements have limited accuracies particularly when iron is present, since diffraction phenomena involve the cooperative scattering effects of many atoms in the unit cell. It is very difficult, and sometimes impossible in X-ray structure refinements, to distinguish between cations of different valences, such as Fe2+ and Fe3+, Mn2+ and Mn3+ or Ti3+ and Ti4+, and between neighbouring elements in the periodic table with similar scattering factors, such as iron... 

Calibration is performed by measuring Rm for a number of standard mixtures with a known concentration of analyte x. Depending on the type of ion interference, linear regression analysis is applied if both C1 and C2 (type 1 ion interference, Section 3.1) or only C2 (type 2) are negligible. In all other cases (types 3 and 4), a NONLIN computer program is used to calculate the nonlinear calibration curve after experimental determination of Clt C2, and C3 on the pure components. Apart from the fact that the exact form of the NONLIN data regression was not specified, the experimental determination of ion interferences and the assumption that qj = pt are limiting factors to accuracy (Jonckheere, 1982). 

Accuracy and precision of filling with liquids vary with the method. Therefore, a method is selected to provide the degree of accuracy and precision required. A slight excess is required in each container to compensate for losses that occur at the time of administration resulting from adherence to the wall of the container. Danger of overdose and economic factors limit the amoimt of excess desirable in a given container. 

Alternatively, fluid characteristics other than Zc can be used as the additional parameter in the generalization of the simple corresponding-states principle. In fact, since for many substances the critical density, and hence Zc, is known with limited accuracy, if at all, there is some advantage in avoiding the use of Zc-Pitzer has suggested that for nonspherical molecules the acentric factor co be used as the third correlative parameter, where co is defined to be... 

Except for the factor 312flep -, this equation is quite similar to Eq. (3.4.24), and only leads to slightly higher values of the pressure drop in a medium range of RCp (10-1000). With regard to the limited accuracy of an exact calculation of a pressure drop this is an acceptable deviation, and thus we may use either Eq. (3.4.31) or Eq. (3.4.24) for spherical particles. 

Sangiorgi, R., Caracciolo, G., Passerone, A., 1982. Factors limiting the accuracy of measurements of surface tension by the sessile drop method. J. Mater. Sci. 17, 2895-2901. 

Cases 9 and 10 illustrate the type of convergence study which is possible with methods in which the local approximation error has a known parameter dependence. In case 9 the error should be at least a factor of (1.5) = 5 times larger than case 10. Thus one can confidently and conservatively ascribe RHF-limit accuracy to the digits that are stable in the two calculations. That is, in case 10 the uncertainty should be no greater than the fifth decimal place for the total and orbital energies and the third-fourth for the moments. 

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