Abstract
Most of the available thermodynamic data concerning radioactive waste disposal are restricted to values of reaction equilibrium constants (logK298°) at 25 °C and 1 bar. Simple estimation methods such as isocoulombic reactions can be used for extrapolating the properties of reactions involving aqueous species and minerals to elevated temperatures. The aim of this study was to validate the applicability of various alternative isocoulombic reactions to estimate logKT° values of aqueous complexation reactions for lanthanides and actinides to elevated temperatures while taking advantage of new additional literature data, and to identify criteria for choosing the “best” reactions. For each chemical species of interest, a systematic approach using dedicated software and database allowed us to identify the isocoulombic reactions and types of extrapolation that yield the best estimates of standard thermodynamic properties at elevated temperatures, when very limited or no experimental data are available. We have tested aqueous complexation reactions for selected lanthanides and actinides of different valences with chloride, fluoride, sulfate, carbonate, nitrate, phosphate and silicate ligands. “Model” complexation reactions, having known temperature trends, were systematically combined with complex formation reactions of interest whose temperature trends are unknown, into many alternative isocoulombic reactions. For each ion, we investigated which of the generated isocoulombic reactions provide the best estimates for logeKT° of the reaction of interest at elevated temperatures in order to compile the guidelines for choosing the optimal ones, then applying these guidelines to “prediction” subsets. In most cases, knowing only logeKT° at 25 °C (for the reaction of interest), it was possible to obtain rather accurate estimates of logeKT° values at elevated temperatures using isocoulombic reactions that exchange ions with similar charge and hydration properties (hydrated ionic radius and structure of the hydration shell) and known logmKT° of model reactions. These ions and their complexes interact with the solvent in comparable ways, so that their similar heat capacity and entropy effects largely cancel out on both sides of an “optimal” isocoulombic reaction.
Highlights
We investigated which of the generated isocoulombic reactions provide the best estimates for loge of the reaction of interest at elevated temperatures in order to compile the guidelines for choosing the optimal ones, applying these guidelines to ‘‘prediction” subsets
A common problem with thermodynamic modeling related to radioactive waste disposal is the lack of thermodynamic data for some relevant aqueous species and minerals, especially for the extrapolation of equilibrium constants to elevated temperature conditions
The temperature trend of the equilibrium constant of a complexation reaction is a function of its standard entropy and heat capacity effects, which both can be related to interactions among the reactants and the water solvent, which affects the structure of water
Summary
A common problem with thermodynamic modeling related to radioactive waste disposal is the lack of thermodynamic data for some relevant aqueous species and minerals, especially for the extrapolation of equilibrium constants to elevated temperature conditions. Even though new experimental data eventually become available, they are by far not enough to cover the large number of aquocomplexes and minerals in broad temperature ranges and for direct evaluation of the required standard-state thermodynamic data In such cases, correlation and prediction methods, such as the isocoulombic method, can provide reasonable estimates of the missing thermodynamic properties before these can be extracted from fitting the models to new experimental data. An isocoulombic reaction has the same number of like-charged species on the reactant and the product side, while an isoelectric reaction has the same total numbers of positive and negative charges on each side Such reactions are adopted in the MULTEQ computer program (Alexander and Luu, 1989) for providing high-temperature estimates of thermodynamic properties with applications in vapor–liquid partitioning and precipitation. There can be many ways in which a reaction of interest can be converted into an isocoulombic reaction; this leads to temperatureand other extrapolations with varying degrees of accuracy
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