Potential measurements, precision

Precision Precision is determined by the uncertainties of measuring current, time, and the end point in controlled-current coulometry and of measuring charge in controlled-potential coulometry. Precisions of +0.1-0.3% are routinely obtained for coulometric titrations, and precisions of +0.5% are typical for controlled-potential coulometry. 

A much more reliable method involves the use of two standards. From the point of view of the measuring precision, it is best when the potential measured in the sample solution, E, lies midway between the potentials obtained in the two standard solutions, E and 2. Consequently, for the corresponding concentrations it holds that Cx Provided that all samples measured fall in... 

The limit of determination is commonly estimated by finding the intercept of extrapolated linear parts of the calibration curve (see point L.D. in fig. 5.1). However, it is often difficult to construct a straight line through the experimental potentials at low concentrations and, moreover, the precision of the potential measurement cannot be taken into consideration. Therefore, it has been recommended that, by analogy with other analytical methods, the determination limit be found statistically, as the value differing with a certain probability from the background [94]. 

Cx = (CsFo//xF3)(1-10- ) = Ac (1-10- ) (ASM). (5.20) The double and multiple addition methods are introduced in an attempt further to improve the measuring precision, because with three or more experimental potential values the slope value S need not be knowa Under the same assumptions and with the same symbols as above, provided the same volumes are always added, it holds for the nth addition of the determinand standard solution that... 

Note that (Os) is expressed in percent, not parts in 104, as in the case of epsilon neodymium, primarily because the variations can be large and the measurement precision is typically somewhat lower than for the 147Sm/143Nd system. Occasionally you will see osmium data presented as s(Os) in units of parts in 104. Although most work has been done on terrestrial systems, there is potential for applications to the Moon and Mars. 

Lately, some reports appeared about a new potential measurement technique with application of electric field scattering (frequency 1 MHz) [84,85]. This method is very interesting, for the possibility of the measurements in the condensed suspensions. It will allow to determine the stability of the suspension and developed investigations of the edl structure. To obtain precise values of the potential by this method, the knowledge of particle size distribution of the suspension is necessary. Previously used electrophoretic techniques, enabled the measurements to be taken only in the dilute solutions, which do not characterize the systems properly. 

Deformation density maps have been used to examine the effects of hydrogen bonding on the electron distribution in molecules. In this method, the deformation density (or electrostatic potential) measured experimentally for the hydrogen-bonded molecule in the crystal is compared with that calculated theoretically for the isolated molecule. Since both the experiment and theory are concerned with small differences between large quantities, very high precision is necessary in both. In the case of the experiment, this requires very accurate diffraction intensity measurements at low temperature with good thermal motion corrections. In the case of theory, it requires a high level of ab-initio molecular orbital approximation, as discussed in Chapter 4. 

As already stated in Section 3.3.2, the precise values of the potential of the diffuse electric layer (po can be obtained by the method of equilibrium foam film . The results correlate well with the values of the electrokinetic potential, measured by the method of the rotating bubble [65], Table 8.1 presents the -potential values and the surface charge density Oo for foams from various surfactant kinds [65]. 

Both derivative CV and SHAC voltammetry require specialized instrumentation. A much more simple experimental procedure has been described for electrode potential measurements which can be done with respectable precision using rudimentary instrumentation. The measurement of peak potentials during LSV is normally carried out to a precision of the order of 5 mV. This is because the peak resembled a parabola with a rather flat maximum. On the other hand, the half-peak potential where the current is half the peak value, has just as much thermodynamic significance and can be measured to about 1 mV using x-y recording with a suitable expansion on the potential axis. When used in conjunction with a digital data retrieval system the method is as precise as derivative cyclic voltammetry (Aalstad and Parker, 1980). 

The applications described in the following paragraphs are taken from examples where the measurement techniques were the newer more precise methods or in some cases less precise CV peak potential measurements. In many of the applications precise measurements were not necessary and when this is the case it is often most convenient to make CV measurements without any refinements. 

Parker and Bethell, 1980. Measurements made at a platinum electrode at 23°C with a supporting electrolyte (BU4NBF4) concentration of 0.1 M. Measurement precision was better than 0.2 mV in the peak potentials. The E" values are the mean of 15 determinations and are referred to a bias setting of —1.50 V vs an Ag/Ag+ reference electrode in acetonitrile... 

A frequent complication is that several simultaneous equilibria must be considered (Section 3-1). Our objective is to simplify mathematical operations by suitable approximations, without loss of chemical precision. An experienced chemist with sound chemical instinct usually can handle several solution equilibria correctly. Frequently, the greatest uncertainty in equilibrium calculations is imposed not so much by the necessity to approximate as by the existence of equilibria that are unsuspected or for which quantitative data for equilibrium constants are not available. Many calculations can be based on concentrations rather than activities, a procedure justifiable on the practical grounds that values of equilibrium constants are obtained by determining equilibrium concentrations at finite ionic strengths and that extrapolated values at zero ionic strength are unavailable. Often the thermodynamic values based on activities may be less useful than the practical values determined under conditions comparable to those under which the values are used. Similarly, thermodynamically significant standard electrode potentials may be of less immediate value than formal potentials measured under actual conditions. 

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