Diffusion Onsager Coefficients L_ij for the NaCl + Na₂SO₄ + H₂O System at 298.15 K

Abstract

The isothermal diffusion Onsager coefficients L ij have been calculated and the Onsager reciprocal relation (ORR) has been tested for 23 compositions of the NaCl + Na 2 SO 4 + H 2 O system at 298.15 K. The calculations are based on our previously reported extensive set of Fick's law based diffusion coefficients measured using the high-quality Gosting diffusiometer and volumetric measurements made with a vibratingtube densimeter or (at a few compositions) with pycnometry. These calculations also require the four chemicalpotential concentration derivatives, which were obtained by reanalysis of available isopiestic data using a hybrid thermodynamic model. This model uses an extended form of Pitzer's ion-interaction model to represent the single-salt thermodynamic activities but uses the mixing terms from Scatchard's neutral-electrolyte model. Because of the ORR, the two cross-term diffusion Onsager coefficients should be equal, i.e., L 12 ) L 21 , on either the solvent-fixed or volume-fixed reference frames. The ORR was actually tested using the experimental volume-fixed diffusion coefficients, with an equation that reduces the propagation-of-errors calculations by removing unnecessary terms. The ORR is found to be satisfied for 22 of the 23 compositions when estimated errors (usually 5 to 10 % for the chemical-potential derivatives, depending on the composition, 4 times the standard errors for diffusion coefficients or scatter observed from cross-plots, whichever is larger) are assigned for the input quantities. † Part of the special issue "Robin H. Stokes Festschrift".

Quasi-Equilibrium and Unsteady Mass Transfer of Low-Grade Bloedite in the Process of Static Water Dissolution

“…For the mass transfer coefficient, when the salt-water interface is farther away, the diffusion coefficient is greater-this is because the solute concentration and viscosity are small, and this causes the mass transfer resistance to be smaller. Such a phenomenon is also consistent with the general law in the diffusion of salt solutes in aqueous solutions [23,31].…”

“…At this point, solute transfer is an unsteady diffusion mass transfer process, and the bulk water solution is not flowing. According to Fick's second law [23], the mass transfer can be calculated as follows:…”

“…Assuming that the diffusion direction is one-dimensional (i.e., diffusion only occurs in the vertical y direction), Equation ( 1) can be transformed into the following form: At this point, solute transfer is an unsteady diffusion mass transfer process, and the bulk water solution is not flowing. According to Fick's second law [23], the mass transfer can be calculated as follows:…”

“…Compared with the dissociation that occurs on the surface of solid-phase salt, studies have shown that the diffusion of the salt component in the liquid phase after dissociation under static conditions is the process control step [13,22]. Research on the diffusion and mass transfer kinetics of salt solutes in the liquid phase has mostly focused on the steady-state process of single-component salts or simple salt-water systems, and the obtained diffusion constant is usually a fixed average value [23]. In contrast, in these studies, the actual hydrostatic extraction of soluble salt is not a steady mass transfer process.…”

Isotopic approaches for quantifying the rates of marine burial diagenesis

“…Diffusion of ions and molecules in simple binary and multicomponent aqueous solutions has been studied both theoretically and experimentally over the years [e.g., Anderson and Graf , 1976; Ben‐Yaakov , 1972; Boudreau et al , 2004; Crank , 1975; Dunlop , 1964; Felmy and Weare , 1991a, 1991b; Lane and Kirkaldy , 1966; Longsworth et al , 1945; Miller , 1966, 1967a, 1967b; Miller et al , 2007; Onsager and Fuoss , 1932; Poisson and Papaud , 1983; Rard et al , 2009; Vinograd and McBain , 1941; Wendt , 1965; Wu et al , 1994]. With regard to diagenetic systems, Boudreau [1997, chap.…”