Molar conductivity density dependence

Due to the fact that K2TaF7 - KF is considered to be part of the TaF5 - KF binary system, while the K2TaF7 - KCI system is a component of the interconnected ternary system K+, Ta5+//F", Cl", the single-molecule conductivity and activation energy of the systems was calculated based on density and specific conductivity data [322, 324]. Molar conductivity (p) depends on the absolute temperature (T), according to the following exponential equation ... 

Instruments with indirect pressure measurement. In this case, the pressure is determined as a function of a pressure-dependent (or more accurately, density-dependent) property (thermal conductivity, ionization probability, electrical conductivity) of the gas. These properties are dependent on the molar mass as well as on the pressure. The pressure reading of the measuring instrument depends on the type of gas. 

Figure 1. Molar conductivity A of KCl in KCl-H20-solutions in its dependence on density p and temperature (in C). Mole fraction of KCl 1.8 x 10 0.01 molar at normal conditions) [15]...

The fitting of the experimental data beyond the limit imposed by the condition Kr4 <0.1 could yield large over-estimation of A in the low-density supercritical region, as discussed in the following section. In this region the contribution of the electrophoretic effect to the concentration dependence of the molar conductivity is expected to be lower (Ibuki et al., 2000) and the difference among the equations for associated electrolytes becomes less important. 

The dependence of the molar conductivity with concentration is primarily dominated by ion-ion interactions which, in the Umit of low density, could lead to extensive clustering of the ions. 

It is recognized that FHFP equation accounts for the concentration dependence of electrolyte solutions up to moderate concentrations and yields more reliable association constants than the Shedlovsky or Fuoss-Kraus equations. However, it was observed that the FHFP Equation (4.18), or the more simple Shedlovsky Equation (4.16), give similar fitting results, for some supercritical electrolyte solutions at low density (p < 0.3 g cm" ). The contribution of the electrophoretic effect to the concentration dependence of the molar conductivity is expected to be lower in supercritical water than in ambient water because of the much smaller viscosity and dielectric constant. Moreover, the higher-order terms in Equation (4.18) nearly cancel each other at moderate concentration in supercritical water (Ibuki et al., 2000). This could be the reason why differences among several conductivity equations vanish at supercritical conditions. 

In general, the magnitude of electrical conductivity of polyelectrolyte gels depends on carrier concentration (that is, the crosslink density or degree of swelling) and the type of carrier ions in addition to physical factors such as temperature. Therefore, as is similar to the situation with electrolyte sulutions, we use the value of conductivity a divided by the carrier concentration c, that is, the molar conductivity A, where thte unit of L is Scm mol , a is S/cm and c is mol/1. 

The limiting ionic conductivity is a transport property of an ion, which does not depend on concentration but depends on tanperature and pressure (or density of the solvent). Contrary to any tliamodynamic property of an individual ion, the limiting ionic conductivities of individual ions can experimentally be obtained and are tabulated in [Chapter 10, Table 10.12] for a number of anions and cations. Therefore, the molar conductivity of an electrolyte at infinite dilution. A , is an additive value and can be calculated using the limiting ionic conductivities. This possibility is particularly useful for the weak electrolytes, whai A cannot be experimentally obtained using Kohlrausch s law by an extrapolation to the infinite dilution. For example, the limiting molar conductivity of acetic add, CHjCOOHCaq), can be calculated as follows ... 

Since the molar concentrations of cations in the investigated system could be calculated from density measurements performed by LiCko and Dangk (1982), the mobility of cations can be calculated. Using the multiple linear regression analysis, it was determined that for Ci = 0 the electrical conductivity is not equal to zero, but attains negative values. The dependence of electrical conductivity of cations on concentration corresponds to the equation... 

It is clear that from the integrated form of Equation (4) the volume of reaction can be obtained if the equilibrium constant can be determined over a range of pressure. If the volume of activation is not experimentally accessible for one of the directions of the reaction, A V can be used to calculate its value. Under certain conditions and with suitable properties of reactants and/or products it may be possible to determine their partial molar volumes, hence allowing development of a volume profile on an absolute volume basis, as noted above. Even if A V can be determined either from the pressure dependence of the equilibrium constant and/or from use of Equation (5), it may be possible to confirm its value by determination of the partial molar volumes from density measurements. The conditions for conducting successful determinations of partial molar volumes are rather stringent and will be described in Section 2. The method depends on measuring the density, d, of several solutions of different concentrations of the reactant or product. The following equation is used to obtain... 

The membrane water and hydronium content, M and P, are nondimensio-nalized by the acid molar density a = 1200 moles/m. The anode and cathode vapor molar densities, and C, are nondimensionalized by the vapor saturation molar density, Csat T) this is the principal dependence of the model upon the temperature. The cathode oxygen concentration Co is nondimensionalized by the inlet oxygen concentration The external voltage, F, is nondimensionalized by the open circuit voltage Eo while the local through-plane current density I y) is nondimensionalized by h = where ao is a reference value for the membrane conductance and is the thickness of the membrane. 

Concentration dependencies of permittivity, viscosity, density (molar volume) and conductivity described here permit to select with certainty the composition of mixed solvent, characterized by any value of mentioned properties. 

Oa, Ka, and R Ka and R must be known from independent measurements (e.g., conductance or heat of dilution measurements). Figure 7 shows the apparent molar volume of CdS04 in water and the extrapolation to zero concentration based on Eq. (115). The quantity AVa = Va is the molar reaction volume of ion-pair formation it is related to the pressure derivative of the association constant of Eq. (102) and can also be obtained from the pressure dependence of the association constant of conductance measurements at various pressures, for example, AVA(CdS04) = 9.4 cm mol from density measurements and 11.7 cm mol" from conductance measurements, which is fairly good agreement when the mutual limits of error are taken into account. 

The ao value depends on the electron-phonon-coupling constant, while Tq is in connection with the localized density of states near the Fermi level and the decay length of the wave function, respectively. It can be seen that conductivity increases with temperature in contrast to that of the metals. This type of conductivity behavior has been verified for many conjugated polymer systems. The problem of locaKzation is less important if the molar mass of the polymer is high and only a few defects are present, as well as a relatively intense interchain coupKng prevails. In... 

The electrolyte solution used to grow the graft copolymer in a one-compartment electrochemical cell with two platinum electrodes contains 0.1 M tetra-butylammonium tetrafluorborate, 0.1 M pyrrole, and different amounts of random copolymer with 6% possible grafting sites in dichloromethane. The conductivity of films grown at a current density of 0.1 mA cm depends on the ratio of pyrrole to linear copolymer. For example, the conductivity of films grown from a 1 1 mixture is 5 x 10 S cm and the conductivity of films grown from a 6 1 (pyrrole/linear copolymer) molar mixture is 0.4 S cm". Both products are 100% insoluble in methylene chloride, indicating that polystyrene is chemically incorporated. 

Numerous experimental studies have been conducted on solute-solvent interactions in supercritical fluid solutions. In particular, issues such as the role of characteristic supercritical solvent properties in solvation and the dependence of solute-solvent interactions on the bulk supercritical solvent density have been extensively investigated. Results from earlier experiments showed that the partial molar volumes 02 became very large and negative near the critical point of the solvent (4-12). The results were interpreted in terms of a collapse of the solvent about the solute under near-critical solvent conditions, which served as a precursor for the solute-solvent clustering concept. Molecular spectroscopic techniques, especially ultraviolet-visible (UV-vis) absorption and fluorescence emission, have since been applied to the investigation of solute-solvent interactions in supercritical fluid solutions. Widely used solvent environment-sensitive molecular probes include Kamlet-Taft jt scale probes for polarity/polarizability... 

Chung-Lee-Starling expression for thermal conductivity of low pressure gases. The molar density, pj, can be calculated using and equation of state model (for example, the Peng-Robinson-Wong-Sandler equation of state) where the mixing rule for b is obtained as follows. The second virial coefficient must depend quadratically on the mole fraction ... 

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