Errors due to

When the assumption F ty = 2.303 is no longer valid, instead of eq. (5.137) the relationship 

One can assume that Kf stays constant during the progress of the reaction as a first approximation. Thus the differentiation of this equation yields 

Intensity quotient diagram of the photoreaction of CPTC, irradiated at 254 nm in 

For this derivation the Napierian absorbance units are taken for convenience (the molar absorption coefficient e is decadic). Using eqs. (4.2), (5.152), (5.153) and a rearrangement of eq. (5.150) 

Using the mean value theorem within the time limits ti and 0, eq. (5.154) can be integrated to 

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In fact a sensor measures a flow and proceeds an integration of across a surface, which operates as a spacial lowpass filter. To avoid a critical deconvolution, the error due to this integration must be kept negligible. 

A Hbasis functions provides K molecular orbitals, but lUJiW of these will not be occupied by smy electrons they are the virtual spin orbitals. If u c were to add an electron to one of these virtual orbitals then this should provide a means of calculating the electron affinity of the system. Electron affinities predicted by Konpman s theorem are always positive when Hartree-Fock calculations are used, because fhe irtucil orbitals always have a positive energy. However, it is observed experimentally that many neutral molecules will accept an electron to form a stable anion and so have negative electron affinities. This can be understood if one realises that electron correlation uDiild be expected to add to the error due to the frozen orbital approximation, rather ihan to counteract it as for ionisation potentials. 

The way out of this dilemma is to make measurements at several (nonideal) molarities m and extrapolate the results to a hypothetieal value of at m = 0. In so doing we have extrapolated out the nonideality because at m = 0 all solutions are ideal. Rather than ponder the philosophical meaning of a solution in which the solute is not there, it is better to concentrate on the error due to interionic interactions, which becomes smaller and smaller as the ions become more widely separated. At the extrapolated value of m = 0, ions have been moved to an infinite distance where they cannot interact. 

The comparatively inexpensive long-scale thermometer, widely used by students, is usually calibrated for complete immersion of the mercury column in the vapour or liquid. As generally employed for boiling point or melting point determinations, the entire column is neither surrounded by the vapour nor completely immersed in the liquid. The part of the mercury column exposed to the cooler air of the laboratory is obviously not expanded as much as the bulk of the mercury and hence the reading will be lower than the true temperature. The error thus introduced is not appreciable up to about 100°, but it may amount to 3-5° at 200° and 6-10° at 250°. The error due to the column of mercury exposed above the heating bath can be corrected by adding a stem correction, calculated by the formula ... 

This is sometimes made of mirror glass in order to eliminate the error due to parallax, t Manufactured by Edwards High Vacuum Ltd. This is essentially a form of McLeod gauge. 

The temperature compensator on a pH meter varies the instrument definition of a pH unit from 54.20 mV at 0°C to perhaps 66.10 mV at 60°C. This permits one to measure the pH of the sample (and reference buffer standard) at its actual temperature and thus avoid error due to dissociation equilibria and to junction potentials which have significant temperature coefficients. 

An error due to limitations in the analytical method used to analyze a sample. 

The regression models considered earlier apply only to functions containing a single independent variable. Analytical methods, however, are frequently subject to determinate sources of error due to interferents that contribute to the measured signal. In the presence of a single interferent, equations 5.1 and 5.2 become... 

If Sm is significantly greater than Sj, then we only need to collect and analyze a single sample. The number of replicate analyses, r, needed to minimize the error due to the method is given by an equation similar to equation 7.7... 

Note that a negative determinate error introduced by failing to recover all the analyte is partially offset by a positive determinate error due to a failure to remove all the interferent. 

Finally, values of sx are directly proportional to transmittance for indeterminate errors due to fluctuations in source intensity and for uncertainty in positioning the sample cell within the spectrometer. The latter is of particular importance since the optical properties of any sample cell are not uniform. As a result, repositioning the sample cell may lead to a change in the intensity of transmitted radiation. As shown by curve C in Figure 10.35, the effect of this source of indeterminate error is only important at low absorbances. This source of indeterminate errors is usually the limiting factor for high-quality UV/Vis spectrophotometers when the absorbance is relatively small. 

The rate of a reaction is temperature-dependent. To avoid a determinate error resulting from a systematic change in temperature or to minimize indeterminate errors due to fluctuations in temperature, the reaction cell must have a thermostat to maintain a constant temperature. 

Partitioning of random error, systematic errors due to the analyst, and systematic error due to the method for (a) replicate analyses performed by a single analyst and (b) single determinations performed by several analysts. 

Typical two-sample plot when (a) random errors are larger than systematic errors due to the analysts and (b) systematic errors due to the analysts are larger than the random errors. 

A visual inspection of a two-sample chart provides an effective means for qualitatively evaluating the results obtained by each analyst and of the capabilities of a proposed standard method. If no random errors are present, then all points will be found on the 45° line. The length of a perpendicular line from any point to the 45° line, therefore, is proportional to the effect of random error on that analyst s results (Figure 14.18). The distance from the intersection of the lines for the mean values of samples X and Y, to the perpendicular projection of a point on the 45° line, is proportional to the analyst s systematic error (Figure 14.18). An ideal standard method is characterized by small random errors and small systematic errors due to the analysts and should show a compact clustering of points that is more circular than elliptical. 

The data used to construct a two-sample chart can also be used to separate the total variation of the data, Otot> into contributions from random error. Grand) and systematic errors due to the analysts, Osys. Since an analyst s systematic errors should be present at the same level in the analysis of samples X and Y, the difference, D, between the results for the two samples... 

Relationship between point In a two-sample plot and the random error and systematic error due to the analyst. 

If systematic errors due to the analysts are significantly larger than random errors, then St should be larger than sd. This can be tested statistically using a one-tailed F-test... 

Spike recoveries for samples are used to detect systematic errors due to the sample matrix or the stability of the sample after its collection. Ideally, samples should be spiked in the field at a concentration between 1 and 10 times the expected concentration of the analyte or 5 to 50 times the method s detection limit, whichever is larger. If the recovery for a field spike is unacceptable, then a sample is spiked in the laboratory and analyzed immediately. If the recovery for the laboratory spike is acceptable, then the poor recovery for the field spike may be due to the sample s deterioration during storage. When the recovery for the laboratory spike also is unacceptable, the most probable cause is a matrix-dependent relationship between the analytical signal and the concentration of the analyte. In this case the samples should be analyzed by the method of standard additions. Typical limits for acceptable spike recoveries for the analysis of waters and wastewaters are shown in Table 15.1. ... 

Several micromanometers, based on the liquid-column principle and possessing extreme precision and sensitivity, have been developed for measuring minute gas-pressure differences and for cahbrating low-range gauges. Some of these micromanometers are available commercially. These micromanometers are free from errors due to capillarity and, aside from checking the micrometer scale, require no cahbration. See Doolittle, op. cit., p. 21. 

Data Limitations The process of measuring Xy t) adds additional error due to the random error of measurement. Or,... 

Errors due to lack of communication during shift change leading to an incident. 

Shortly after this time, it was discovered that Bridgman s static high-pressure scale was in error due to calibration problems, and the shock-induced 13 GPa transition became the new calibration standard. 

The error due to diffusion potentials is small with similar electrolyte solutions (cj = C2) and with ions of equal mobility (/ Iq) as in Eq. (3-4). This is the basis for the common use of electrolytic conductors (salt bridge) with saturated solutions of KCl or NH4NO3. The /-values in Table 2-2 are only applicable for dilute solutions. For concentrated solutions, Eq. (2-14) has to be used. 

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