Isotherms intersection point

It has become fairly common to adopt the manufacture of combinations of internal reference electrode and its inner electrolyte such that the (inner) potential at the glass electrode lead matches the (outer) potential at the external reference electrode if the glass electrode has been placed in an aqueous solution of pH 7. In fact, each pH glass electrode (single or combined) has its own iso-pH value or isotherm intersection point ideally it equals 0 mV at pH 7 0.5 according to a DIN standard, as is shown in Fig. 2.11 the asymmetry potential can be easily eliminated by calibration with a pH 7.00 0.02 (at 25° C) buffer solution. 

If the inner reference of the electrode is such that the iso-pH value (isotherm intersection point) lies at pH = 7 0.5 (according to a DIN standard), which may agree with the Ege vs. pH plot in Fig. 2.11, then the overall potential of this... 

Note from the definition is follows that the pH of the isotherm intersection point in Fig. 2.13 represents the isopotential pHf of the Metrohm EA121 combined electrode.)... 

Since often people who don t even know the charge of the measured ion are entrusted with the job of making measurements, a circuit board with the proper programming should be supplied with the instrument (see Fig. 36). From the standpoint of the customer service it might also be suggested that such circuit boards also adjust for the corresponding isotherm intersection point. In this case the entire flow system must be purchased from the same manufacturer. 

Isotherm intersection point adjustment for industrial instruments (Eiso 10 pActivity units)... 

Fig. 43. Ion meter with digital activity or concentration display, logarithmic amplification, isotherm intersection point adjustment and option for two high ohmic inputs (Metrohm)...

Due to the complex construction of an ion-sensitive electrochemical cell (Fig. 32) the position of the isotherm intersection point cannot be theoretically predicted. It must be empirically determined for each individual electrode cell. Caution must be exercised here to insure that the conditions of this determination match those later to be employed in measurements. (To reproduce the same temperature gradient along the electrodes, even the air temperature should correspond to that which will be used for the actual measurements.)... 

The isotherm intersection point is best determined in a flow cell of the same design as that at the monitoring location. The rate of heat transmission in the temperature sensor used (usually a Pt-100 resistance) should resemble that of the electrode, so that rapid, temporary temperature fluctuations of the sample solution do not result in overcompensation. 

The contradictory statements concerning the validity of automatic temperature compensation via the isotherm intersection point in the literature are based on primarily two arguments It may happen that with more than two isotherms no single intersection point is obtained, but rather a diffuse intersection region, which naturally subtracts from the accuracy of the temperature compensation. In addition, with pH meas-... 

The half-automatic temperature compensation entered by hand, frequently carried out in laboratory practice, also needs adjustments via the isotherm intersection point, but this is usually overlooked. For a desired accuracy of about 1% with a calibration solution differing in concentration from the sample solution by a factor of 5, the temperature potentiometer must be able to be set within an accuracy of l C. For a factor of 100 difference between sample and calibration solutions this tolerance is lowered to about 0.2°C. This illustrates how important these slope potentiometers are for accurate measurements. Unfortunately, they can often only be set to an accuracy of about 2°C. 

If one wants to increase the accuracy to about 0.001 pa units, then the temperature compensation must also be carried out properly via the isotherm intersection point — this is often overlooked. For example, an accuracy of 0.001 pa units over a calibrated range of 0.5 pa units of the measured ion requires a temperature control over both solutions of 0.6°C and an equally precise setting of the temperature potentiometer. For calibration over a 2 pa units range this tolerance is reduced to 0.15 C The temperature compensator, however, is often only calibrated to 1°C. 

As point 4 indicates, a precise thermostating of the measuring cell is recommended for accuracies less than 0.01 pa unit. Due to the unavoidable uncertainties involved in an isotherm intersection point compensation and the fact that only a very few laboratory instruments are equipped for such calibration, this procedure should be avoided by simply making calibration and sample solution measurements at the same temperature. 

In this paper solubility measurements of synthetic and natural dyestuffs are presented using VIS-spectroscopy. The investigations concentrate on two different methods. I. P-carotene was measured as a function of temperature and pressure in near- and supercritical C02 (289 to 309 K, 10 to 160 MPa) and CC1F3 (297 to 326 K, 12 to 180 MPa), respectively, using a static method. II. Additionally, the solubilities of l,4-bis-(n-alkylamino)-9,10-anthraquinones (with n-alkyl = butyl, octyl) were determined with a dynamic method in temperature and pressure ranges from 310 to 340 K and 8 to 20 MPa, respectively this method permits a continuous purification from better soluble impurities as well as the measurement of solubilities at the same time. For both anthraquinone dyestuffs intersection points of the solubility isotherms were found in the plot of concentration versus pressure. This behavior can be explained by a density effect. 

The pressure-composition diagram is related to the composite pressure-temperature diagram previously described in the following manner. In Figure 28 let Ti represent the fixed temperature at which the pressure-composition diagram is to he constructed. This isotherm intersects the two-phase loop of a particular composition at the bubble-point pressure and the dew-point pressure. If these two pressures and the composition are plotted, two points on the pressure-composition... 

FIGURE 5.13 Sketch of a disjoining pressnre isotherm of the DLVO type, O vs. h. The intersection points of the n(/t)-isotherm with the line H = correspond to equihhrium films /j = /j, (primary film), /j = /jj (secondary film). Point 3 corresponds to unstable equilibrium. 

The intersection points of the pure natural convection and pure forced convection equation also provide valuable information on the conditions for which forced and natural convection are equally important. For example, for laminar flow along the heated isothermal vertical plate in Fig. 4.6 if Eq. 4.33a for NulV is equated to the forced convection Nusselt number given by... 

Colloid Titration A method for the determination of charge, and the zero point of charge, of colloidal species. The colloid is subjected to a potentiometric titration with acid or base to determine the amounts of acid or base needed to establish equilibrium with various pH values. By titrating the colloid in different, known concentrations of indifferent electrolyte, the point of zero charge can be determined as the pH for which all the isotherms intersect. See also Point of Zero Charge. 

The effect of temperature on solubility is more complex and involves both a consideration of the solute vapor pressure as well as the density of the SCF. The solubility isotherms shown in Figure 1.2-9 are typical of most solid-SCF systems in that they intersect within a narrow range of pressure. For any two isotherms, the point of intersection, or crossover pressure, represents a change in the temperature dependence of solubility. 

Deviations from the above properties have been observed attributed to various factors. For example, the reorientation of the solute molecules on the electrode surface is a factor that may disturb seriously the above picture, especially when the area covered by a solute molecule on the electrode surface changes upon reorientation. " In this case the maximum in adsorption is concentration dependent and for this reason the plots of a v.y.. E do not exhibit a common intersection point, the capacitance plots show characteristic humps in the region between the adsorption-desorption peaks, and the validity of the Frumkin isotherm is questionable. 

Figure 5 demonstrates the kinetic evaluation of these results. On the left-hand side, the initial velocity Vp (intersection points with the ordinate) is plotted versus the concentration of the Al component while the Ti concentration was kept constant. The result is the Al isothermal curve of the second equilibrium reaction generating the active species. It demonstrates in the initial part the demanded sigmoid curve course according to the location of the two successive equilibria. This induction period is enlarged in Fig. 6. It can be clearly seen how sensitively the initial polymerization rate responds to the ratio Al/Ti. With a ratio >1 (i.e., here [AlEtCl2] > 3x10 mol L ), the formation of the active species increases drastically.

Starting from a homogeneous polymer solution with concentration Cp, the LL phase separation sets in by decreasing the temperature below Tc, for instance, at temperature Ti. The tie line (isotherm) intersects the binodal at points A and B (see Fig. 4), and these points deline the concentrations of the polymer-poor and polymer-rich phases in equilibrium at Ti, originating from the LL phase separation. 

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