Mass action model of solution activity via speciation by solvation and ion pairing equilibria

Abstract

Solutes and their concentrations influence many natural and anthropogenic solution processes. Electrolyte and solution models are used to quantify and predict such behavior. Here we present a mechanistic solution model based on mass action equilibria. Solvation and ion pairing are used to model speciated solute and solvent concentrations such that they correlate to a solution’s vapor pressure (solvent activity) according to Raoult’s law from dilute conditions to saturation. This model introduces a hydration equilibrium constant (Kha) that is used with either an ion dissociation constant (Kid) or a hydration modifier (m) with an experimentally determined ion dissociation constant, as adjustable parameters to fit vapor–liquid equilibrium data. The modeled solvation equilibria are accompanied by molecular dynamics (MD) studies that support a decline in the observed degree of solvation with increased concentration. MD calculations indicate this finding is a combination of a solvent that solvates multiple solutes, and changes in a solute’s solvation sphere, with the dominant factor changing with concentration. This speciation-based solution model is lateral to established electrostatics-based electrolyte theories. With its basis in mass action, the model can directly relate experimental data to the modeled solute and solvent speciated concentrations and structures.

Lithium Concentration from Salt-Lake Brine by Donnan-Enhanced Nanofiltration

“…28,50 Next, the original ion rejection measurements of the present work were used to calibrate the model parameters of DSPM-DE, allowing us to infer differences in the solute transport between the dual cation and multicomponent brines. Mindful of the assumptions and limitations of DSPM-DE, we restricted its use to brines of low concentrations (10 g L −1 ), avoiding ion-pairing 58,59 and coupled diffusion 60,61 phenomena that occur at higher concentrations. Further, the model was calibrated to 72 ion rejection measurements from three unique brine compositions (see Supp.…”

A theoretical study of selective radical relay and coupling reactions for alkene difunctionalization

“…This value is much lower than that for the corresponding process with 5 leading to the major product 10 . According to the law of mass action, 46,47 the ratio at which products 10 and 24 are generated can be obtained using eqn (3) based on the concentrations of radical species 4 and 5 . r 10 = k 9ts [ 5 ][ 8 ] r 24 = k SET [ 4 ][ 8 ]…”

Solvent-driven fractional crystallization for atom-efficient separation of metal salts from permanent magnet leachates

“…Gaseous DME is employed as a saturation agent to induce crystallization of transition metal or lanthanide sulfates from mixed metal salt magnet leachates. DME is not thought to interact directly with other solutes; instead, DME reduces the quantity of the free water (i.e., water that is not bound within a solvation environment) to fulfill its own hydration requirements 62 , 63 . A reduction in free water, reduced water activity, and/or liquid phase microstructuring 79 induce salt precipitation.…”