Potential of Concentrated Solutions

According to Equation (6-3), the chemical potential of the solvent is defined as the derivative of the Gibbs energy of mixing with respect to amount of solvent. Consequently, with the condition = 1 — 02, differentiation of Equation (6-32) gives 

A is obtained from the argument that at the point 01 the value of A G is also given by Equation (6-38), i.e., by 

if a tangent is drawn to the AG =f (02) curve at a volume fraction of 02 = 02, then the extrapolation of this tangent to the A G axis for values of 02 = 0 and 02 = 1 gives quantities from which the chemical potentials of solvent and solute, respectively, are obtained. 

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Here, Ws is the work function of electrons in the semiconductor, q is the elementary charge (1.6 X 1CT19 C), Qt and Qss are charges located in the oxide and the surface and interface states, respectively, Ere is the potential of the reference electrode, and Xso is the surface-dipole potential of the solution. Because in expression (2) for the flat-band voltage of the EIS system all terms can be considered as constant except for tp (which is analyte concentration dependent), the response of the EIS structure with respect to the electrolyte composition depends on its flat-band voltage shift, which can be accurately determined from the C-V curves. 

As seen from Eq. (130) an activity coefficient may deviate significantly from unity at higher salt concentrations. The activity coefficient can therefore also be used as a measure of the deviation of the salt solution from a thermodynamically ideal solution. If the chemical potential of a solute in a (pressure-dependent) standard state of infinite dilution is /x°, we find the standard partial molar volume from... 

Although Pb tends to - °o as Xb tends to 0 (and In Xb also tends to - °o), the difference on the right-hand side of Eq. (2.18) tends to the finite quantity pi, the standard chemical potential of B. At infinite dilution (practically, at high dilution) of B in the solvent A, particles (molecules, ions) of B have in their surroundings only molecules of A, but not other particles of B, with which to interact. Their surroundings are thus a constant environment of A, independent of the actual concentration of B or of the eventual presence of other solutes, C, D, all at high dilution. The standard chemical potential of the solute in an ideal dilute solution thus describes the solute-solvent interactions exclusively. 

Consider now two practically immiscible solvents that form two phases, designated by and ". Let the solute B form a dilute ideal solution in each, so that Eq. (2.19) applies in each phase. When these two hquid phases are brought into contact, the concentrations (mole fractions) of the solute adjust by mass transfer between the phases until equilibrium is established and the chemical potential of the solute is the same in the two phases ... 

Morita C., K. Sano, S. Morimatsu, H. Kiura, T. Goto, T. Kohno, W. Hong, H. Miyoshi, A. Iwasawa, Y. Nakamura, M. Tagawa, O. Yokosuka, H. Saisho, T. Maeda, and Y. Katsuoka (2000). Disinfection potential of electrolyzed solutions containing sodium chloride at low concentrations. Journal ofVirologial Methods 85 163-174. 

Thus, u.°A for the solute in Eq. (II) is the chemical potential of the solute in a hypothetical standard state in which the solute at unit concentration has the properties which it has at infinite dilution. 

Redox potential (E). The relative tendency of a pair of molecules to release or accept an electron. The standard redox potential (E°) is the redox potential of a solution containing the oxidant and reductant of the couple at standard concentrations. 

When the concentration of a multicomponent system is expressed in terms of the molalities of the solutes, the expression for the chemical potential of the individual solutes and for the solvent are somewhat different. For dilute solutions the molality of a solute is approximately proportional to its mole fraction. (The molality, m, is the number of moles of solute per kilogram of solvent. When two or more substances, pure or mixed, may be considered as solvents, a choice of solvent must be clearly stated.) In conformity with Equation (8.68), we then express the chemical potential of a solute in a solution at a given temperature and pressure as... 

If we use the concentration scale of molality m instead of mole fraction x, the chemical potential of a solute constituent i is expressed by Eq. 5.26 ... 

Usually, the analytical chemist needs to determine the concentration of the ion of interest rather than its activity. The obvious approach to converting potentiometric measurements from activity to concentration is to make use of an empirical calibration curve, such as the one shown in Figure 5.3. Electrodes potentials of standard solutions are thus measured and plotted (on a semilog paper) versus the concentration. Since the ionic strength of the sample is seldom known, it is often useful to add a high concentration of an electrolyte to the standards and the sample to maintain approximately the same ionic strength (i.e., the same activity coefficient). The ionic strength adjustor is usually a buffer (since pH control is also desired for most ISEs). The empirical calibration plot thus yields results in terms of concentration. Theoretically,... 

Figure 9.8. Schematic of the electric double layer under two different electrolyte concentrations. Colloid migration includes the ions within the slipping plane of the colloid denotes the electric potential in dilute solution denotes the electric potential in concentrated solution (adapted from Taylor and Ashroft, 1972)...

At pH = 6 the potential of a solution containing arsenate and arsenite ions at equal concentrations decreases to +0-20 V. Under such circumstances therefore the opposite reaction will occur ... 

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