Nernstian theoretical

Figure 4- Response of an lead-selective electrode based on a calix[6]arene hexaphosphene oxide to sequential 10-fold dilutions of a sample solution demonstrating a very rapid Nernstian response down to sub-nanomolar concentrations of lead. The inset shows a linear Nernstian plot is obtained with almost theoretical slope (25.7 mV per decade) down to 10-10 M.

When the test component content in the samples varies over a wider interval, a calibration curve must be constructed. Calibration curves with ISEs are usually linear over several concentration orders (usually from about 10" m to about 10" m) and their slope is close to the theoretical Nernstian value. Both at high and at low concentrations with respect to the linear part, the caUbration dependence becomes curved and, eventually, independent of the test substance concentration (see fig. 5.1). The upper limit of the ISE response is mostly given by saturation of the active sites in the electrode membrane (for example ion-exchange sites), whereas the lower limit is determined by solubility of the... 

Conventional non-aqueous pH titrations are useful in detecting and determining acidic and basic impurities. On the other hand, the ion-prove method proposed by Coetzee et al. [9] is convenient in characterizing trace amounts of reactive impurities. The principle of the method was described in Section 6.3.5. In Fig. 10.4, the method is applied to reactive impurities in commercial acetonitrile products. The prove-ion and the ISE were Cd2+ and a Cd2+-selective electrode (CdS-Ag2S solid membrane), respectively. The solid line TR is the theoretical relation expected when the ISE responds to Cd2+ in the Nernstian way. The total concentrations of impurities, which were reactive with Cd2+, were estimated to be 4x10 5 M, 8xlO-6M,... 

In order to make the comparison between Ep and Ep/2 measurements summarized in Table 9, the two quantities were measured in separate experiments. A recent study by Eliason and Parker has shown that this is not necessary [57]. Analysis of theoretical LSV waves by second-order linear regression showed that data in the region of Ep are very nearly parabolic. The data in Fig. 9 are for the LSV wave for Nernstian charge transfer. The circles are theoretical data and the solid line is that described by a second-order polynomial equation. It was concluded that no detectable error will be invoked in the measurement of LSV Ep and Ip by the assumption that the data fit the equation for a parabola as long as the data is restricted to about 10 mV on either side of the maximum. This was verified by experimental measurements on both a Nernstian and a kinetic system. 

A significant feature of NPSV analysis is that linear relationships were observed when theoretical data for Nernstian charge transfer were taken as the X axis and theoretical data for various electrode mechanisms were taken as the Y axis. The slopes of the resulting straight lines are indications of the mechanisms of the electrode processes. Some of the slopes are included in Table 25. 

At the same time, the response deviates more from the theoretical value the fewer proton-binding sites are present. On the other hand, both the adsorption effects and the sub-Nernstian behavior vanish if the thickness of the hydrated layer is allowed to increase up to 800 nm (Fig. 6.24). It is seen from this model that as the thickness of the hydrated layer exceeds the thickness of the space the adsorption effects and the sub-Nernstian behavior disappear. 

It is merely an extension of these ideas to demonstrate the conditions that the same membrane, containing MY, should also be responsive, in a Nernstian fashion, to Y activities+in solution. These conditions are again a three-ion situation M, Y and N. The salt NY is the aqueous sample whose Y activity is to be measured. N is typically a hydrophilic ion such as Na. When aqueous NY activity is varied, the interfacial pd is again S-shaped (mV vs log[NY]). These responses are illustrated from a theoretical calculation in Figure 1. The assumed extraction parameters are given in the legend. The similarity with silver halide membrane electrodes are summarized below. 

The pH response was initially tested at 90°C and one atmosphere pressure by immersing the sensor in standard pH buffer solutions. The EMF of the sensor was then compared with the EMF generated by a commercial Ross-type glass electrode. Figure 3 shows the EMF versus pH response of a representative tube, PSU-T1-18. The response over a pH range of 2.5 to 9.5 is linear and displays a slope which is 98% of the theoretical Nernstian slope for this temperature. 

In the microchip ISE, the calibration plot of the measured potential versus log [Ba2+] gives a slope of 36 mV. What is the theoretical value of the Nernstian slope Explain the difference between the experimental and Nernstian slopes. [766] (2 marks)... 

It can be seen that cyclic voltammograms at low scan rate have peak-to-peak separations close to the value theoretically expected for a reversible process of A p = 2.218 X 7 r/ = 57 mV at 298 K [47] and the peak current increases with the square root of the scan rate. Under these conditions, the process is diffusion controlled and termed electrochemically reversible or Nernstian within the timescale applicable to the experiment under consideration. Hence, as with all reversible systems operating under thermodynamic rather than kinetic control, no information concerning the rate of electron transfer at the electrode surface or the mechanism of the process can be obtained from data obtained at slow scan rate. The increase of A p at faster scan rate may be indicative of the introduction of kinetic control on the shorter timescale now being applied (hence the rate constant could be calculated) or it may arise because of a small amount of uncompensated resistance. Considerable care is required to distinguish between these two possible origins of enhancement of A p. For example, repetition of the experiments in Table II.l.l at... 

The normalized potential LSV is based on a direct comparison of normalized currents, = I/Ip at normalized potentials, E = E —Ep/j. The normalized experimental data are compared with theoretical ones. The comparison of a reversible wave with the Nernstian data (see Appendix G) gives the correlation coefficient 1.0. In the case of an irreversible (or quasi-reversible) process the parameters of the electrode process, k° and can be estimated using working curves for different combinations of these quantities. For the reduction of benzonitrile in DMF at a mercury electrode the working curves were best fitted with ranging from 0.47 to 0.50 and corresponding k° values (5.8-4.9) X lO- ms- [126]. 

This value is selected, since at the scan rates considered a voltammogram half-width exceeds generally 60 mV, the theoretical value for a Nernstian one electron voltammogram, owing to limited rate constants of electron transfer (compare Figures 2-4). TTierefore, a 10 mV error represents generally an error comparable to or even smaller than the actual experimental uncertainty on defining the peak potential position. 

The Nernst factor, 0.059 V for room temperature, does not always reach its theoretical value. In experimental work, it is better to use the expression Nernstian slope S of the function E = f(a). The slope must be determined empirically. The constant const in Eq. (7.8) is a combination of all terms not dependent on concentration. In practical work, the name asymmetry potential ( as) is preferred. This expression is derived from the expectation that the constant should be zero for a completely symmetric cell, i.e. if inner and outer solutions are of equal pH and if inner and outer reference electrodes are of identical types. In practice, Eas is not always zero but must be calibrated empirically by means of buffer solutions with known pH. By setting - log alHsO" ) = pH, the common form of the Nernst equation for the glass electrode results ... 

It can be seen that cyclic voltammograms at low scan rate have peak-to-peak separations close to the value theoretically expected for a reversible process of A p = 2.218 X RT/F = 57 mV at 298 K [47] and the peak current increases with the square root of the scan rate. Under these conditions, the process is diffusion controlled and termed electrochemically reversible or Nernstian within the... 

The theoretical implications of using ultrathin sensing membranes is of utmost importance as these so-called space-charge membranes have a different behavior than conventional thick membranes with bulk electroneutrality and thin space charge regions only at their boundaries. In fact, the previously mentioned experimental studies could not benefit from the recent comprehensive theoretical description of the potentiometric behavior as well as potential and concentration profiles in ultrathin non-electroneutral membranes by Morf. This study showed clearly that only space-charge membranes contacted with aqueous solutions on both sides will exhibit a Nernstian response. While unfortunately such membranes are rather unstable mechanically, their stabilized counterparts, that is, solid-contacted thin membranes, are theoretically predicted to have a sub-Nernstian slope. 

This section describes the various calibration and evaluation methods which can be used with ion-selective electrodes. The specific procedure chosen determines whether the activity or concentration of the indicated ion is obtained as a result of the measurement Fundamental to all analytical methods is the Nernst equation. We have seen in Chap. 1.2 that the Nernst equation is a theoretically derived relationship. In practice it is usually the case that an electrode deviates somewhat from the Nernst equation. As long as this deviation is reproducible, the electrode can still be used for analytical applications. Testing an electrochemical cell for exact Nernstian behavior is quite painstaking, and is often impossible. Standard solutions of precisely known activities are needed. This, in turn, requires the individual activity coefficients of the corresponding measured ions, and these are not always known with sufficient accuracy. Instead, one usually uses an empirical form of the Nernst equation for analytical applications ... 

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