Uncertainties sample positioning

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. 

According to (2.29) the effect of dissipation is to reduce the space sampled by the harmonic oscillator, making it smaller than the quantum uncertainty of position for an undamped oscillator (de Broglie wavelength). With exponential accuracy, (2.27) agrees with the Caldeira-Leggett formula (2.26), and similar expressions may be obtained for more realistic potentials. 

The maximum search function is designed to locate intensity maxima within a limited area of x apace. Such information is important in order to ensure that the specimen is correctly aligned. The user must supply an initial estimate of the peak location and the boundary of the region of interest. Points surrounding this estimate are sampled in a systematic pattern to form a new estimate of the peak position. Several iterations are performed until the statistical uncertainties in the peak location parameters, as determined by a linearized least squares fit to the intensity data, are within bounds that are consistent with their estimated errors. 

Comparison of the results allows calculation of kj6/ki8. Obviously there are drawbacks to this procedure. The major one is the necessity of a costly and tedious isotopic synthesis of labeled materials. Optimally those compounds should be as close as possible to 100% enriched. This can seldom be achieved and using partially enriched samples requires substantial corrections to the raw data and increases experimental uncertainty. A rule of thumb used in remote labeling experiments is that the remote (reporting) position should be reasonably far from the reaction center (the phenolic oxygen in the present example). For the case where there is no isotope effect at the reporting site (e.g. no 15N-KIE), the double-label experiment leads directly to the isotope effect of interest. This is more probable when the reporting site is remote, (i.e. well isolated from the reaction coordinate). 

The negative peak in the baseline at 4520 cm-1 proved to be a convenient reference position. Its origin is presently unknown, but it likely arises from slight differences between the silica DIT cell used for the sample and that used for the carbon tetrachloride reference. Band integration did not work veil for quantitation in this study, probably because of uncertainties in the data above 5264 cm-1 where the discontinuity due to the electronic filter in the spectrometer occurs. 

The logarithmic response of ISEs can cause major accuracy problems. Very small uncertainties in the measured cell potential can thus cause large errors. (Recall that an uncertainty of 1 mV corresponds to a relative error of 4% in the concentration of a monovalent ion.) Since potential measurements are seldom better than 0.1 mV uncertainty, best measurements of monovalent ions are limited to about 0.4% relative concentration error. In many practical situations, the error is significantly larger. The main source of error in potentio-metric measurements is actually not the ISE, but rather changes in the reference electrode junction potential, namely, the potential difference generated between the reference electrolyte and sample solution. The junction potential is caused by an unequal distribution of anions and cations across the boundary between two dissimilar electrolyte solutions (which results in ion movement at different rates). When the two solutions differ only in the electrolyte concentration, such liquid junction potential is proportional to the difference in transference numbers of the positive and negative ions and to the log of the ratio of the ions on both sides of the junction ... 

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