Predicting the Distribution Coefficient of Solvent Extraction of Rare Earth Elements Based on the Gibbs Free Energy and Thermodynamic Theory for Equilibrium Constant

Abstract

Rare Earth Elements (REEs) are a class of 17 elements, including the lanthanides (15 elements), scandium (1 element), and yttrium (1 element). REEs minerals consist of 9-10 REEs excluding promethium. The separation of REEs minerals into their components is achieved by the solvent extraction process, consisting of the organic phase and aqueous phase. Leaching is a process by which REEs are dissolved in acid. The final product of the leaching process (leachate) is sent to the solvent extraction process. The leachate and extractant are mixed well with diluents and left until it produces the two phases. The distribution of REE between these two phases is determined by the distribution coefficient and depends on extractant type, pH, temperature, extractant concentration, diluent type, and diluent concentration. A typical REEs solvent extraction process consists of several stages and is determined by the separation factor of REEs. The separation factor for a binary mixture of REE1 and REE2 is the ratio of the composition of REE1 and REE2. The distribution coefficient is used to determine the separation factor and extraction efficiency.

The intercept difference between two adjacent lanthanides in log D vs. pH plot was analyzed to propose a model. The mean value of the intercept difference between two adjacent lanthanides was determined by using experimental results. The ionic radius of lanthanides deviates linearly according to their atomic number. However, the yttrium position based on the ionic radius is between holmium and erbium. Many experimental results revealed that the intercept position of yttrium in log D vs. pH plot was between holmium and erbium. Based on the mean value difference of two adjacent lanthanides and yttrium’s position, a model was proposed to determine the lines of the entire REEs series except for scandium in log D vs. pH plot. It was found that the proposed model can be applied to the log D vs. log (H2R2) plot. The theoretical background for REEs deviation in log D vs. pH plot is the standard Gibbs free energy that gradual changes with its atomic number. The proposed model can be utilized to calculate the separation factor of the lanthanides and yttrium. A model was presented to determine any lanthanide extraction efficiency with the aid of the extraction efficiency value of another lanthanide. The present study discusses the theoretical background of the separation factor and the extraction efficiency of two lanthanides.

The model performance was tested with various intercept values of REEs in the log D vs. pH plot and log D vs. log(H2R2) plot. It was found that experimental results deviate from the proposed model with reasonable errors. The proposed model can be used to calculate the separation factor of REEs. However, the model is only valid for a specific range of extractant concentrations and pH from 2 to 4.