Molar conductivity diffusion coefficient

Figure 2. Conductivity diffusion coefficient (mobility) of protons and water self-diffusion coefficient of aqueous solutions of hydrochloric acid (HCl), as a function of acid concentration (molarity, M) (data are taken from ref 141).

The physical property monitors of ASPEN provide very complete flexibility in computing physical properties. Quite often a user may need to compute a property in one area of a process with high accuracy, which is expensive in computer time, and then compromise the accuracy in another area, in order to save computer time. In ASPEN, the user can do this by specifying the method or "property route", as it is called. The property route is the detailed specification of how to calculate one of the ten major properties for a given vapor, liquid, or solid phase of a pure component or mixture. Properties that can be calculated are enthalpy, entropy, free energy, molar volume, equilibrium ratio, fugacity coefficient, viscosity, thermal conductivity, diffusion coefficient, and thermal conductivity. 

A second solution, likewise 1 04 molar with respect to HCl and simultaneously o 67 molar with respect to NaCl, diffused into a solution of NaCl, 067 molar The diffusion coefficient of the hydrogen ion was now 351 When diffusion took place into pure water the diffusion coefficient was 2 09. Similar results were obtained with NaOH 1 The presence of electrolyte appears to increase the rate of diffusion of the ion The change in the diffusion coefficient here observed is large, much, larger than the effect considered above in dealing with equivalent conductivity It is remarkable, howevei, that no adequate explanation of the behaviour observed by Arrhenius has as yet been suggested... 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Ionic mobility — Quantity defined by the velocity of an ion moving in a unit electric field (SI unit m2 V-1 s-1). The ionic mobility of ion i (uf) is related to its molar ionic conductivity (A ) by A = zfFui, where Z is the charge number of the ion. The ionic mobility is also related to the -> diffusion coefficient (A) by the Nernst-Einstein... 

MOLAR CONDUCTIVITY AND ITS CORRELATION WITH DIFFUSION COEFFICIENT... 

Note. V is the molar volume, JVyi is Advogadro s number, is the equilibrium concentration, D is the diffusion coefficient, sub-s surface, hHfiB the heat of fusion, t) is the Damkohler number. Ah is the thermal conductivity, i die area shape factor for surface nuclei , y, is the distance between steps, n is the equilibrium surface concentration, p = 1 - o-JS is one minus the maximum surface supersaturation divided by the solution supersaturation, and p is the density. ihG - pl- fPMpAkBT In S)... 

By listing the ratios of the molar conductivities versus the conductivities calculated from the NMR self-diffusion coefficients A m /ANV(R, they were able to propose a useful parameter to characterize various properties of ILs with different anions, such as quantitative information on how much individual ions contribute to ionic conduction. 

The relationship between ionic conductivity and Onsager s theory can now be presented in terms of the electrochemical potential. By expressing the force leading to the transport of ions in terms of the gradient of jr,-, one finds important relationships between the diffusion coefficients of the ions, and the molar conductivity and mobility. Furthermore, when the force has the correct Newtonian units, one is also in a position to calculate the rate of entropy production. On the basis of the thermodynamics of irreversible processes, the relationship between the flux of ion i and the force Vp,- is... 

These equations repeat those previously set down. Flete, u is the kinematic viscosity, and a is the thermal diffusivity. The subscripts have been dropped in the convective diffusion equation, and D can be the binary diffusion coefficient, the effective electrolytic diffusion coefficient, or the diffusion coefficient of the fth species. The molar concentration is to be interpreted in the same context. In the energy equation, sometimes referred to as the heat conduction equation in the form written, heat flux due to interdiffusion and due to viscous dissipation have been neglected as small. Heat sources are also absent. 

This table gives the molar (equivalent) conductivity X for common ions at infinite dilution. All values refer to aqueous solutions at 25°C. It also lists the diffusion coefficient D of the ion in dilute aqueous solution, which is related to X through the equation... 

By replacing Ui in the Einstein equation by its value from Eq. (31.26), Ui = XJZiF, we obtain the relation between the molar conductivity and the diffusion coefficient. 

Probably the most systematic and complete study on the influence of temperature on water transfer has been performed on mammalian red cells [10,20,28]. The dependence on temperature of both the tracer diffusional permeability coefficient (cotho) 3 nd the hydraulic conductivity (Lp) of water in human and dog red-cell membranes have been studied. The apparent activation energies calculated from these results for both processes are given in Table 2. The values for the apparent activation energies for water self-diffusion and for water transport in a lipid bilayer are also included in the table. For dog red cells, the value of 4.9 kcal/mol is not significantly different from that of 4.6-4.8 kcal/mol for the apparent activation energy of the water diffusion coefficient ( >,) in free solution. Furthermore, it can be shown that the product L — THOV )rt, where is the partial molar volume of water and the viscosity of water remains virtually independent of temperature for dog, hut not for the human red-cell membrane [20]. The similarity of the transmembrane diffusion with bulk water diffusion and the invariance of the... 

What is the stmcture of neat ionic liquids. Even though the stmcture of liquids, such as water, has been studied for many years, the study of room-temperature ionic liquids is still in its infancy [58]. Purified [BMIM][PFj], probably the most studied IL, has been shown to be purely monophasic, with no aggregates, but to have a local stmcture [47]. Imidazolium groups are positioned in pairs with a plane-to-plane separation of 4.5 A. The stmcture of ILs is also characterized by a degree of anion-cation association. Thus, in [EMIM][NTf2] and [BP][NTf2], the self diffusion coefficients of the anions and the cations measured by pulsed-gradient spin-echo N M R are superior to the diffusion coefficients deduced from the molar conductivity, which demonstrates the existence of ion pairs which cannot contribute to the ionic conduction [53]. 

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