Error margins

Are the equilibrium constants for the important reactions in the thermodynamic dataset sufficiently accurate The collection of thermodynamic data is subject to error in the experiment, chemical analysis, and interpretation of the experimental results. Error margins, however, are seldom reported and never seem to appear in data compilations. Compiled data, furthermore, have generally been extrapolated from the temperature of measurement to that of interest (e.g., Helgeson, 1969). The stabilities of many aqueous species have been determined only at room temperature, for example, and mineral solubilities many times are measured at high temperatures where reactions approach equilibrium most rapidly. Evaluating the stabilities and sometimes even the stoichiometries of complex species is especially difficult and prone to inaccuracy. 

Let us now turn to the density functional methods. All of them correctly predict the para-ortho ordering, but considering that this is the case even for a Hartree-Fock treatment this is a somewhat hollow victory. Without exception, all functionals wrongly predict p-protonation. Arguably, this small energy difference falls within the error margin of any type of calibration for (semi-) empirical DFT functionals. 

Note Error margin ( ) of last decimal given in parentheses nd = not determined. 

Some argue that Equations (2) and (3) lead to an overcorrection of the BSSE, and, indeed, this is still under considerable discussion. Sufficiently large basis sets, usually with multiple sets of polarization functions, seem to overcome most of the BSSE. Therefore, we computed the magnitude of the BSSE for the dissociation energies separately to evaluate our basis set error margins approximately. 

The detection of thorium in stars of very low metallicity by Patrick Frangois and Monique and Frangois Spite has opened the way to a direct determination of the age of the most ancient stars, and hence also of the age of the Galaxy. The age of some of the oldest halo stars has been estimated at 15.6 billion years, with an error margin of 2 billion years. This agrees with the classic determination of the age of the oldest globular clusters at 14.9 1.5 billion years, and the age of the Universe by means of remote type la supernovas at 14.2 1.7 billion years (Arnould Takahashi 1999). 

The results of the simulations are shown in Figures 1 and 2, superimposed on the experimental results. The agreement between calculated and experimental spectra is very good. Numerous simulations were performed in order to assess the effect of the various parameters. The results indicate that the simulated spectra are very sensitive to the choice of the distribution parameters and to the values of the residual widths AH and AH . Given the limited possibilities of measuring ESR spectra at S-band, we believe that computer simulations are a viable alternative. We also feel that the error margin in the parameters deduced by computer simulation can be decreased if ESR spectra of isotopically enriched Cu are measured and Simulated 4. 

It should be noted, however, that the linearization process introduces significantly nonconstant error margins, both on the y-axis value (A w-A obs) and on the x-axis value ([S]-cmc) As a result, unless datafits are carefully weighted, results from the nonlinearized model should be considered more reliable. 

Figure 2(a) shows how the adsorbed amount of HPAM on kaolinite increased with bulk concentration HPAM. For clarity, the 200 ppm measurement was omitted, but the peak intensity was not seen to rise above 50 ppm. It would appear that there is surface saturation above this 50 ppm threshold limit. Figure 2(b) shows an HPAM adsorption isotherm for both kaolinite and feldspar. Neither the quartz or mica showed any adsorbed HPAM up to a bulk concentration of 200 ppm. The N is atomic percent did not vary from the background adsorption at 0 ppm, at least within the error margin in these experiments. 

FIGURE 4. Experimental equilibrium structure of silene 25, deduced from the rotational constants of six different isotopomers (for error margins see Table 13)31 —33. 

In the fifth and final test, of which the results are shown in Fig. 5.13, the metering pumps (until then manually operated) are coupled to the regulating unit of the sensor system. It can be observed that the hydrogen peroxide concentration during the measuring period of 5 h is maintained between 0.940 and 0.955 mol F1 with error margins between sensor output and titration of less than 2%, which demonstrates the advantages and the possible applications of the sensor. 

However, repetition of the concentration studies demonstrated that this current is highly reproducible for the modified electrodes, which is not the case for the unmodified ones. This explains why the error margins (Fig. 7.9) for unmodified electrodes were relatively high, particularly for low concentrations. 

From the data in Tables9.9-9.12 and from Fig. 9.15, it can be seen that the resistance of the system decreases as a function of time when textile electrodes are used. This behaviour is contradictory to the behaviour of the palladium electrodes, the resistance of which is constant within the previously obtained error margins (see Table 9.4). Only at t=0 is comparison of the resistances obtained at textile and palladium electrodes possible. 

Stomatal density and index show great potential for paleoelevation reconstructions with low error margins, if additional error sources such as the presence of sun and shade morphotypes and especially uncertainty in sea-level C02 concentrations can be well constrained. Unlike other paleobotanical methods, stomatal frequency analysis is not restricted to angiosperm dominated floras, and has no requirements for a minimum amount of taxa present. The method will be most reliable when applied to fossil taxa that are closely related to extant species, and suitable taxa are most likely to be found for periods when C02 concentrations were not much higher than ambient (380 ppmV). 

Calculate the applicable and taxon-specific error margins ... 

The test should be reproducible. Testing a filter under the same conditions should give the same results within the error margins inherent in the test. 

A detailed study was performed by Berwanger - Oil, gas petrochemical consulting - in order to evaluate how safe the installations were. It should be stated that the study was done in the United States, but with our experience I believe we can transpose the results to other parts of the world, perhaps taking into account about a 10% error margin to be on the safe side for Western Europe, where other (old) codes also still apply above the PED (TuV, ISPESL, GOST, etc.). 

I am not going to explain basic statistical laws of diffusion here. This law is so commonly known that anybody interested in it might look it up in any physics book. Maybe the iterative steps I used where a bit too big, so there is an error margin in my calculations, but if so, it affects all series, so it should not make a difference regarding my comparisons. 

If copper interactions were minimized in real seawater, abundant metals of lesser sulfide affinity would take up some of the slack. ITiis is partially evident from analyses of the type in Table III. For example, nickel has mixed layer concentrations on the order of nanomolar (22), and its sulfide equilibria and inorganic seawater speciations may resemble those of zinc (lv-19.31.32). Titration, however, should only lower free sulfide to a Table m SH equivalence point, or, to roughly picomolar. In a follow up to 1Z, Dyrssen and coworkers treat Cu(II) as a variable parameter, and find that in its absence, nickel, zinc and lead can all become sulfides while the bisulfide ion still hovers well above pM (18). Again, it must be emphasized that error margins in the various equilibria remain to be investigated. 

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