Valency electrolytes

It is accurate for simple low valence electrolytes in aqueous solution at 25 °C and for molten salts away from the critical point. The solutions are obtained numerically. A related approximation is the following. 

The theory of strong electrolytes due to Debye and Htickel derives the exact limiting laws for low valence electrolytes and introduces the idea that the Coulomb interactions between ions are screened at finite ion concentrations. 

The osmotic coefficients from the HNC approximation were calculated from the virial and compressibility equations the discrepancy between ([ly and ((ij is a measure of the accuracy of the approximation. The osmotic coefficients calculated via the energy equation in the MS approximation are comparable in accuracy to the HNC approximation for low valence electrolytes. Figure A2.3.15 shows deviations from the Debye-Htickel limiting law for the energy and osmotic coefficient of a 2-2 RPM electrolyte according to several theories. 

Rasaiah J C 1972 Computations for higher valence electrolytes in the restricted primitive model J. Chem. Phys. 56 3071... 

In general, for mixed valency electrolytes, we can express the individual transference numbers in terms of the experimentally accessible equivalent ionic conductivities from (6.17) and (6.19) as... 

These data require extension but in a tentative manner the conclusions can be summarized in Figure 8 where the domains of coagulation and flocculation are represented. Moreover, these ideas have only been applied to sodium chloride. With higher valency electrolytes more specific effects may occur which could dominate the phenomena. 

It is well-known that the traditional double layer theory is valid in a limited range of concentrations for monovalent electrolytes, but is much less valid for higher valency electrolytes.15 The traditional theory starts from the Poisson equation... 

It is necessary to call attention to the fact that equation (69) was deduced for symmetrical valence electrolytes for unsymmetrical types the corresponding equation is of a still more complicated nature. 

N NaCl has been used. Conversely, for brackish water desalination a 0.1 N NaCl/membrane/0.2 N NaCl may be used. The membrane potential is measured using a potentiometer or high impedance voltmeter (more than 2 MQ). In general, the membrane potential is high when the ratio of the concentration of the concentrated side solution to that of the dilute side solution is high and becomes low when salt solutions of high concentration are used. Transport numbers are calculated by Eq. (4.1) when a 1 1 valence electrolyte solution is used and the potentials between the probe electrodes and their ambient solutions are subtracted ... 

When a 2 1 valence electrolyte is used, the membrane potential is as follows,... 

Examination of the terms to O(k ) in the SL expansion for the free energy show that the convergence is extremely slow for a RPM 2-2 electrolyte in aqueous solution at room temperature. Nevertheless, the series can be summed using a Pade approximant similar to that for dipolar fluids which gives results that are comparable in accuracy to the MS approximation as shown in figure A2.3.19(a). However, unlike the DHLL + i 2 approximation, neither of these approximations produces the negative deviations in the osmotic and activity coefficients from the DHLL observed for higher valence electrolytes at low concentrations. This can be traced to the absence of the complete renormalized second virial coefficient in these theories it is present... 

Equation 2.18 effectively incorporates the retardation effects into the mobility determination for high concentration solutions. As an example, for aqueous solution at room temperature T = 298K), using D = 78.56 and t] = 0.008948, the variation of the mobility of the positive ion with concentration in 1,1 valency electrolytes of HCl, KNO3, and NaCl are plotted in Figure 2.5 according to Equation 2.18. The variation of the transference numbers of the cations with the concentration are also plotted to discern its effect on the mobility of each ion. As observed, the square root model represents the reduction of the mobility of each ion with increasing concentration, where the reduction appear to be mostly dependent on A. ... 

For simplicity, we consider a charged cylindrical microcapillary of radius / w packed with charged mono-sized microparticles of diameter dp. The liquid in the microcapillary is assumed to be an incompressible, Newtonian, mono-valence electrolyte of density p and viscosity p,. The zeta potentials of the inner wall surface and the particle... 

The second of these relations is exact the first is an approximation which assumes the asymptotic form of the direct correlation function for all separations beyond the hard core diameter. By implication the solutes molecules are assumed to have hard cores, e.g., charged hard spheres (RPM) or sticky charged hard spheres (SEM). An advantage to the MSA is that the thermodynamic properties can be determined analytically, and are quite accurate for low valence electrolytes in aqueous solution at room temperature. The thermodynamics of the MSA for simple fluids is discussed by Hdye and Stell (1977). 

The forces binding the atoms A and B together in AB are chemical in nature and must be introduced, at least approximately, in the Hamiltonian. Then it should be possible to apply the same theoretical methods (e.g., HNC and MS approximations) used to study strong electrolytes to investigate incomplete dissociation in weak electrolytes as well. The binding between A and B is quite distinct from the ion pair formation observed for higher valence electrolytes (Fig. 9). In these cases no alterations in the Hamiltonian models already discussed were required to account qualitatively for the experimental observations. 

The Debye thickness decreases with increasing electrolyte concentration and it decreases more for the high-valency electrolytes. The surface potential is estimated, sometimes indirectly, via electrokinetic experiments (see Section 10.6). Through these experiments we can measure the electrophoretic mobility, which for very small or very large particles can be related by theory to the so-called zeta potential (Hiickel and Smoluchowski equations. Equation 10.10). The zeta potential is approximately equal to the surface potential. 

---