Errors in potential

Relationship Between Measurement Error in Potential and Relative Error in Concentration... 

Fig. 10.9 Diagram illustrating the source of the IR error in potential measurements on a cathodically protected structure. BA is the absolute electrode potential of the structure CD is the absolute electrode potential of the anode and CB is the field gradient in the environment due to cathodic protection current flux. A reference electrode placed at E will produce an IR error of EFin the potential measurement of the structure potential. If placed at G the error will be reduced to GH. At B there would be no error, but the point is too close to the structure to permit insertion of a reference electrode. If the current is interrupted the field immediately becomes as shown by the dotted line, and no IR is included...

Figure 3 Errors in potential energies for CH4 in a 6-3IG basis. B3LYP and UB3LYP error curves have been shifted up by 70 kcal mof. ...

This source of error in potential sweep measurements will apply to sweep measurements made for all kinds of electrode reactions, not only those involving intermediates. It will be a strong source of error, particularly when nonaqueous solutions are used because there, the resistance of the solution (and hence the IR error) can be particularly large. 

A 1-mV error in potential corresponds to a 4% error in monovalent ion activity. A 5-mV error corresponds to a 22% error. The relative error doubles for divalent ions and triples for trivalent ions. 

Reference electrode potentials change with temperature. Both electrochemical reactions (Nernstian thermodynamics) and chemical solubilities, e.g. of the inner reference electrode solution, are affected. Accordingly, the temperature coefficient, dE/dT (mV °C4), varies from one type of reference electrode to another. To minimise errors in potential readings the coefficient should be low and at least known. Examples of temperature coefficients are given in Table 2.2. 

For rx = 0.05 cm, and a potential error not to exceed 2 mV, the specific resistance of the electrolyte must be less than 200 fi-cm for currents of 10 /iA. This approximate calculation indicates that the errors in potential due to iR drop will be 200 mV when the specific resistance of the electrolyte is 104 fi-cm. 

We believe that for a considerable time the uncertainty that arises in using models will be still less than that due to errors in potentials. Only in exceptional cases when exact reconstruction of potentials from scattering data is attempted, as is the case in collision spectroscopy, will more refined treatment of nonadiabatic coupling be needed. 

Discrimination Between Folds. Because of the inherent error in potential functions, secondary structure prediction methods, limited sampling, and so forth, one can anticipate that prediction of a variety of alternative structures (perhaps, by several methods) would be more likely to generate a correctly folded structure than any single prediction. The problem then becomes one of discriminating between the correct structure and alterna-... 

The size of the loading error in potential measurements depends on the ratio of the internal resistance of the meter to the resistance of the circuit being studied. The percent relative loading error associated with the measured potential Tm in Figure 21F-6 is given by... 

At UMEs, the picture is quite different, because the currents are extremely small consequently, the error in potential control in a voltammetric experiment is often much smaller than in the same experiment with an electrode of conventional size. Consider, for example, a disk UME with radius tq at which we desire to carry out sampled-current voltammetry. What are the conditions that will allow the recording of a voltammogram in which the half-wave potential is shifted less than 5 mV by the effect of uncompensated resistance ... 

In general, a potentiostat controls E + rather than the true potential of the working electrode (Sections 1.3.4 and 15.6.1). Since i varies with time as the peak is traversed, the error in potential varies correspondingly. If is appreciable compared to the accuracy of measurement (e.g., a few mV), the sweep will not be truly linear and the condition given by... 

Errors in Potential Fxmctions, Equation 7 will yield the correct value of only if the potential energy functions making up A, and A12 are correctly stated there. For example, the question about the use of and 12 has already been mentioned. If, in addition, types of force other than dispersion, induction, and dipole-dipole orientation make significant contributions to the surface energy. Equation 7 will be in error and the results invalidated to the extent of the other contributions. (The Sinanoglu-Pitzer treatment of dispersion forces, which involves a third-order perturbation treatment of three interacting bodies, has not as yet been put in suitable form for application to complex molecules. Hence this effect was not included in the treatment above or in [18].)... 

A wide variety of ion-selective electrodes are now available (see Table 11.7) and the only instrumentation required is a high-impedance voltmeter to monitor the potential difference between the measuring electrode and the external reference electrode. The voltmeter must, however, be capable of accurate measurement since an error of 0.1 mV in the measurement of potential introduces an inaccuracy of almost 1% in the ion analysis (a 1 mV error in potential leads to a concentration error of 4% and 8% for singly and doubly charged ions respectively). 

The small error in potentials used in Equation (2) due to iR drop also results in errors of a values. The potential was corrected for iR drop as suggested in Chapter 2. 

General consideration of membrane potential and LJP in the context of experimental errors in potential measurements is available in a brief review [98]. The specific details for so-called biological liquids (like blood, urine, etc.) can be found in review [99]. 

Leclercq, J. M., Allavena, M., Bouteiller, Y. (1983). On the basis set superposition error in potential surface investigations. I. Hydrogen-bonded complexes with standard basis set-functions. Journal of Chemical Physics, 78, 4606-4611. 

Figure 9 compares the quasielectrostatic potential with the electrostatic potential in the dilute solution model. The plotted potentials are those at the dissolving surface relative to the values at the pit mouth. The concentrated solution model predicts a much larger potential drop in the pit, primarily because it depends on the experimentally measured conductivity, which is again is reduced in concentrated solutions relative to the conductivity according to the dilute solution model. By comparison with Fig. 7, it may be seen that significant relative errors in the dilute solution calculation appear at concentrations less than 1 M. Since pit solutions are usually even more concentrated, large relative errors in potential calculations would be expected. This may be a serious concern because the metal dissolution rate increases exponentially with potential. 

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