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Salt (electrolytes) Sorption by Membranes And/or Ion-exchange Resins: Donnan or Partition Equilibrium?
| Content Provider | Semantic Scholar |
|---|---|
| Author | Schumacher, Hans Joachim |
| Copyright Year | 2006 |
| Abstract | The sorption equilibrium of salts (electrolytes) between aqueous solutions and ionexchanging phases (membranes, resins, and/or gels) is analysed. Classically this equilibrium had been treated as Donnan equilibrium with unitary constants (Teorell (1953), Schloegl (1964)). However, as phases of different structure and different thermodynamic standard states are involved a partition equilibrium with non-unitary constants is the correct thermodynamic description, as it is used, p.ex. in the solubility-diffusion theory of membrane processes. Surprisingly a complete thermodynamic description of such equilibrium has not been given. Stating the thermodynamic phase equilibrium conditions directly for the salts (not for ions) and taking into account the molarity (X) of fixed ions in the ion exchanging phase (accountable of the characteristic ion exclusion effect) a limiting sorption law for a binary salt of type Mν1Yν2 is obtained (indices: 1 = counter-ion, 2 = co-ion within the sorbing phase): (qs = ν2 |z2| cs/X; cs = salt molarity in the membrane; _ ms _ γs = external molal salt activity) law which depends on the salt formula (relation ν1/ν2) and the membrane characteristics. Experimental sorption data of different salt/membrane systems (NaBr/NaR; CsBr/CsR; SrBr2 /SrR; MgCl2 /RCl; MgCl2 /MgR; LaCl3 /LaR; Na2SO4 /NaR) follow this law. In log-log graphs of qs vs. _ ms the experimental exponent ns coincides with its theoretical values (1+ ν1/ν2). The partition constants are also obtained as well as the activity coefficient of the salt within the sorbing phase. It is found that this coefficient (>1) is logarithmically linear in √(Is), the ionic strength of the salt in this phase. Finally the complete sorption equations for qs are solved, i.e. eqs. of 2nd. degree (symmetric electrolytes) and of 3rd. degree (1:2 electrolytes), the latter being treated in detail. The expressions of the partition factors of the counter-ion and of the co-ion are also obtained as well as their limiting expressions. 196 Timmermann, E. O. Resumen Se analiza el equilibrio de sorción de sales (electrolitos) entre soluciones acuosas y fases intercambiadoras de iones (membranas, resinas, y/o geles). Clásicamente este equilibrio ha sido tratado como equilibrio Donnan con constantes unitarias (Teorell (1953), Schloegl (1964)). Sin embargo, ya que se tratan fases de distinta estructura y de distintos estados termodinámicos tipo un equilibrio de partición con constantes no-unitarias es la correcta descripción termodinámica, como es usada, p. ej., en la teoría de solubilidaddifusión para procesos de membrana. Sorprendentemente una descripción termodinámica completa de este equilibrio no se ha dado. Planteando las condiciones para el equilibrio termodinámico de fases directamente para sales (no para iones) y teniendo en cuenta la molaridad (X) de los iones fijos en la fase intercambiadora de iones (responsable del característico efecto de exclusión iónica) se obtiene una ley límite de sorción para sales binarias del tipo Mν1Yν2 (índices: 1 = contraión, 2 = coión en la membrana): (qs = ν2 |z2| cs/X; cs = molaridad salina en la membrana; _ ms _ γs = actividad salina molal externa) ley que depende de la fórmula de la sal (relación ν1/ν2) y de las características de la membrana. Datos experimentales de sorción para diferentes sistemas de sales/membrana (NaBr/NaR; CsBr/CsR; SrBr2 /SrR; MgCl2 /RCl; MgCl2 /MgR; LaCl3 /LaR; Na2SO4 /NaR) siguen esta ley. En gráficos log-log de qs vs. _ ms el exponente experimental ns coincide con su valor teórico (1+ ν1/ν2) Se obtienen también las constantes de partición así como el coeficiente de actividad de la sal en la fase sorbente. Se encuentra que este coeficiente (>1) es logarítmicamente lineal en √(Is), la fuerza iónica de la sal en esa fase. Finalmente se resuelven las ecuaciones completas de sorción para qs, esto es, ecs. de 2do. grado (sales simétricas) y de 3er. grado (electrolitos 1:2), tratándose éstas últimas en detalle. Se obtienen además las expresiones para los factores de partición para contraión y coión así como sus expresiones límites. Introduction The sorption equilibrium of an electrolyte between an aqueous solution and a membrane with fixed electrical charges or an ion-exchange resin has been described in different ways in the literature: (a) with an unitary equilibrium constant (Teorell (1953) [1], Schlögl (1964)[2], (b) with non-unitary constants (solubility-diffusion theory for membrane processes (1949) [3,4], but always considering that the phase-equilibrium solution-membrane is characterised by the so-called Donnan equilibrium. In this paper, we revise these formulations through thermodynamics stating directly the phase equilibria in terms of the neutral components the salts involved and not by the usual ionic equilibria. Thermodynamically, only the quantities corresponding to neutral components are measurable, exhibiting concrete physical meaning. The effect of the fixed charges (X) of the membrane (common ion effect) is specifically taken into account, but not the electrical aspects because they compensate each other being not necessary to consider them explicitly. General laws, and their limiting expressions, are obtained and are applied to several experimental cases. The corresponding equilibrium constants are determined as well as the activity coefficients of the salts in the membrane phase. The analysis confirms our description, which is in some aspects differs and in others coincides and complements the findings of the literature [1-8]. 197 Salt (Electrolytes) Sorption By Membranes and/or Ion-Exchange Resins... Thermodynamic foundations The Donnan equilibrium [9,10] describes the osmotic equilibrium between two aqueous electrolytic solutions separated by a membrane, one of the solutions containing a polyelectrolyte the macro-ion of which cannot permeate through the membrane. The presence of the macro-ion and its non-permeability through the membrane determines at equilibrium, on one side, an osmotic pressure difference between both solutions and, on the other side, an asymmetric ion distribution between the two solutions (essentially for the counter-ions of the macro-ion). Besides, this ionic asymmetry determines an electrical potential difference (Donnan potential) between both solutions. It must be pointed out that, in the Donnan equilibrium formulation, only the thermodynamic properties of the components of the electrolytic solutions are involved, being all these welldefined [9,10]. The role of the membrane is then merely the one of a device preventing the access of the macro-ion to the other solution. This means that the membrane is completely passive (black box) being of no interest any of its other properties. On the other hand, if we concentrate our attention to the two solution/membrane interfaces involved in the Donnan equilibrium the situation is different. To formulate thermodynamically these phase equilibria the characteristics of the membrane phase must be specifically stated. These interfaces are permeable to the salts and the solvent and the membrane substance now takes the role of the macro-ion if it possesses fixed electrical charges. Consequently, differences arise from the fact that phases of different physical constitution are considered. In the membrane, the poly-ionic membrane substance is the major component, sorbing the substances (salts and solvent) of the external aqueous solution. Thus, one deals directly with a partition or distribution equilibrium of genuine nernstian type, while the fixed charges of the membrane determine the ion exclusion effect. As usual, the equalities of the chemical potentials of the substances which partitionate or distribute through the interface between the two involved phases describe thermodynamically the equilibrium and the corresponding standard potentials in each phase must be carefully characterised. These standard potentials are identical for the Donnan Equilibrium as phases of identical physical constitution (the two external solutions) are considerated and, therefore, the corresponding equilibrium constants are unitary. But, if the involved phases are physically different as in the solution/membrane equilibrium, these standard potentials are different and correspondingly the partition constants become non-unitary. For very dilute external solutions, the membrane in equilibrium tends to the sorption equilibrium stage of pure water, constituting this state the thermodynamic reference state of infinite dilution of the salts in the membrane. It is the water saturated (swollen) state which is characteristic of each membrane system. Thereby, the nonunitary partition constant is specific for each solution/membrane equilibrium. This condition differs from the conventional Donnan equilibrium and establishes the basis of the present work. Moreover, its results are requisites for the analysis of the transport phenomena within the membrane in terms of phenomenological mobilities [11]. Definitions and general formulations Let us consider the sorption of a single salt s from an aqueous solution by a membrane or ion exchange resin. A mole of the salt s is formed by ν1 ions 1 of electrical charge number z1 and ν2 ions of charge number z2, being νs (= ν1+ν2) the salt dissociation number and the electroneutrality condition ν1 z1 = ν2 z2. 198 Timmermann, E. O. On the other hand, the membrane substance presents X equivalents of fixed electrical charges per unit of volume (X equiv./dm3) neutralised by 1/|z1| moles of counter-ions 1. Thus, the salt has the counter-ions 1 in common with the membrane and the co-ions 2 constitute the characteristic ions of the salt. Moreover, the solvent water (index w) is present in both phases. The properties of the binary external solution are indicated with a bar ( ̄) over them. The external salt molality is _ ms , its molarity _ cs and the external water molarity is _ cw ; hence _ ms = _ cs / Mw _ cw , where Mw is the |
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| Resource Type | Article |
