Precision of rate measurements

Precision of Rate Measurements for Simple Irreversible Reactions... 

Bardsley [28] and Childs and Bardsley [29] have provided a substantial body of mathematical theory to facilitate the categorisation of detailed curve shapes in cases where the data do not fit the linear transformations of Eqn. 4. This approach may be seen as essentially inductive. It is an attempt to set up rigorous procedures for empirical mathematical description of enzymes kinetic behaviour. Such description should in theory define minimum levels of complexity for physical models. Application of this approach will severely test the precision of rate measurements in real cases, and there is a risk that vaUd mechanisms may be ruled out on the basis of apparent subtleties of curve shape that are no more than experimental error. This, however, is certainly no excuse for ignoring genuine non-linearity. 

Eq. (1) has potential application to other types of measurements of substituent effects besides those specifically considered in this paper e.g., nmr coupling constants and shifts for other nuclei, ir and uv spectral shifts and intensities. We caution (with emphasis) in these applications the needed use of data sets of high quality, both with respect to the precision of the measurement and substituents considered (i.e., a full complement of substituent o/ and Or properties must be encompassed for a meaningful correlation to be obtained). There is, of course, no requirement that all data sets will be uniquely fitted by eq. (1) using one of the four or scales of Table V. For example, the data for the ionization of the conjugate acids of pyridine-N-oxides (30), HjO, 25° is found to fit equally well the or(ba.) or Or scales (SD=. 14 /=. 072). The data (31) for the rates of alkaline ("OMe) cleavage of ArSnMea are not fitted to acceptable precision (fs >. 23) by any of the Or parameters. This data set is nevertheless indicated... 

Twenty-three kinetics have been carried out at 25°C for pH values from 8.25 to 11.25. The rate constant, calculated as the average of all the ks, was of 27.2 9.0 mol 1 min. The pH correction according to equation (2) was not perfect, as there was a tendency to obtain higher k values at lower pH values. However, this was specially true for extreme vdues of our pH range, where the buffer capacity of ethanolamine was limited (higher pHs) or the reaction proceeded very slowly (low pHs), impairing the precision of the data. Another factor that might explain the dispersion of the data is lack of precision of pH measurement (no better than 0.02 pH units). 

The precision of the measured Nx values can be influenced by inertia. All Nr values of shear rates higher than 10 s 1 can be corrected for inertia effect using Eq. (43) ... 

At certain positions in the flame, the background flame luminescence received by the photomultiplier tube can be 15% of the Rayleigh scattered intensity. A large reduction of this noise would be achieved by replacing the 1 nm bandpass filter with a monochrometer. Use of a multipass cell (12) or intracavity laser (13) would raise the signal above the flame luminescence. In addition, the increased scattered photon count rate would increase the precision of each measurement. 

The isomerization reaction A B is found to go to completion at 65°C. The reaction is found to be of % order in A on the basis of two measurements of the half-life determined on initial concentrations of A differing by a factor of 2. The analytical accuracy is 2 per cent, the error due to time is negligible, and the temperature control is 0.1 C, with Boat = 20 Kcal. (a) What is the expected precision of measurement of the half-life (6) Do you believe that the precision of these measurements is sufficient to tell whether the rate is % order or % order Explain. 

The selection of a calorimetric method suitable for the measurement of heat effect of the investigated process is affected by several factors. Almost all of these factors influence the precision of the measurement. Such factors are for example, the rate of the measured... 

First-order Complex Reactions 2-11 Chain Reactions 2-12 Rate Constants and Equilibrium 2-13 Precision of Kinetic Measurements... 

C ODE the theoretical characteristic velocity for one-dimensional equilibrium flow. The precision of measured Fy can be estimated to be within 0.12 %. The precision of the calibration factors for the turbine-flow meters were generally within 0.25 % at a nominal flow rate, and the long term variation of K-factors were within 0.2 %. The overall precision of the measured Igpy, is calculated to be within 0.4 %. 

To conclude this section we summarize that, in general, the kinetic rate constants obtained from SPR sensors may not agree with those obtained in solution. The SPR technique seems to be better suited to performing comparative studies of molecules according their affinity and other interaction characteristics. However, improvements in the precision of SPR measurements and of their theoretical description may soon lead to new approaches for ex-... 

Kinetic data for a chemical reaction is gathered in different type of reactors and we will briefly mention some requirements for chemical reactors from the viewpoint of kinetic analysis. A high precision of the data is needed as large deviations in the values of the experimentally measured rates will be a serious obstacle for quantitative considerations. Reproducibility of rate measurements over a broad range of parameters is also of importance. Another necessary feature is the possibility to reach a goal of obtaining the maximum amount of kinetic information in minimum time. Analysis of products as well as reactor lay-out should preferbably be as easy as possible. 

Since the ruthenium catalyst exhibited virtually the same rate for the growth of in Cj and higher carbon number products, the upper limit for the values of the time constants was obtained assuming that the difference in rates corresponded to the precision of the measurements. The upper limits for x, Xj, X2, and X3 so determined were 1.5, 0.5, 0.3, and 0.3, respectively. Note that the time constant Xj, is much smaller than x for cobalt, whereas it is greater than x for ruthenium. 

Our same research group used tracer to measure the rate of inorganic N-uptake by phytoplankton to evaluate the relative importance of nitrogen cycling mechanisms for phytoplankton productivity in aquatic ecosystems (17), We measured nitrate uptake rates of 54.2 it 14.6 ftg-N/h in an oligotrophic lake. The precision of these measurements as well as the wide range over which they have been effectively used demonstrate the advantages of short-lived radioisotopes for tracer biochemistry. 

Experimental results on reaction kinetics are sometimes characterized by a large amount of scatter in the measured information and corresponding uncertainty in associated rate constant and reaction orders. Such a situation is not necessarily the result of careless experimentation, because these quantities are generally very sensitive functions of the precision of experimental measurements. The following example [S.W. Benson, The Foundations of Chemical Kinetics, McGraw-Hill Book Co., New York, NY, (I960)] provides a clear illustration of this sensitivity. 

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