# The Experimental Study of Innovative Methods Regarding the Removal of Sm(III)
## 3 Results and Discussion  
### Results of the Ion Flotation Method  
The results of the ion flotation study of the solutions containing Sm+3 \(\mathrm{\SIUnitSymbolMicro}\)DS- are shown in Table 1.  
From the obtained experimental data, it is evident that the Sm3+ removal in acidic mediums is practically non-existent. With the increase of the pH value from 3.5 to 6.0, the distribution coefficient was approximately 16. Not surprisingly, in this pH range, neutral and basic dodecyl sulphates of samarium Sm(C\({}_{12}\)H\({}_{25}\)OSO\({}_{3}\))\({}_{3}\)\(\mathrm{\SIUnitSymbolMicro}\)Sm(OH)(C\({}_{12}\)H\({}_{25}\)OSO\({}_{3}\))\({}_{2}\) floats. From the obtained experimental data, it is evident that at a pH exceeding 6.0, the distribution coefficient (K\({}_{\mathrm{p}}\)) increases rapidly. This value is lower than that previously determined by us through the pH of the hydrate formation (Formula (3). On this basis, it may be considered that in the pH range satisfying the maximum removal, samarium floats mainly in the hydroxide form, with which DS- anions form hydrogen bonds with the admixture of neutral and basic dodecyl sulphate. According to the literature data, in the process of the ion flotation of metal cations, the increase in removal ratio occurs in the pH range of the hydrate formation [29] and notable cations go into the froth in the form of hydroxides. It is assumed that ion flotation non-ferrous metals flow with the formation of their basic salts with anion surfactants. A hypothesis was put forward based on a thermodynamic analysis of ion-molecular equilibriums that cerium (3+) is extracted at pH = 5 by oleic and naphthenic acid solutions in diluents in the form of basic oleates and naphthenates, and yttrium in the form of neutral salts [30]. To identify the process mechanisms and predictions of optimal conditions of metal cations removal and separation by extraction, flotation, and ion flotation methods, one should know the pH of metal hydroxo-complexes and pH of the hydrate formation that can be calculated based on the Gibbs energies of hydroxo-complexes and metal hydroxides formation. The pH value of the Sm(OH)2+ hydroxo-complexes formation can be calculated based on the expression for instability constants:  
\[K_{n}=\frac{\left[\mathrm{Sm}^{3+}\right]\cdot a_{\mathrm{OH}^{-}}\cdot\gamma _{\pm}}{\left[\mathrm{Sm}\left(\mathrm{OH}\right)^{2+}\right]} \tag{2}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**pH**} & **[Sm+]aq\_104** & **[Sm3+]org\_103** & \multirow{2}{*}{**K\({}_{\mathrm{p}}\)**} \\  & **mol/L** & **mol/L** & \\ \hline
1.8 & 5.64 & 1.79 & 3.2 \\ \hline
3.0 & 2.36 & 2.15 & 9.1 \\ \hline
3.5 & 1.39 & 2.24 & 16.2 \\ \hline
4.0 & 1.30 & 2.31 & 17.7 \\ \hline
4.9 & 1.71 & 2.00 & 11.7 \\ \hline
5.4 & 1.83 & 2.18 & 11.9 \\ \hline
6.0 & 1.31 & 2.13 & 16.2 \\ \hline
6.7 & 0.23 & 3.03 & 130.4 \\ \hline
6.9 & 0.25 & 3.27 & 128.9 \\ \hline
7.5 & 0.28 & 3.56 & 128.6 \\ \hline
7.9 & 0.30 & 3.91 & 128.7 \\ \hline
9.5 & 0.30 & 3.91 & 129.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The results of the experimental study of samarium ions’ distribution between aqueous and organic phases. The pH value of hydrate formation is calculated by the formula:  
\[\text{pH}_{\text{hydr}}=14+13(\text{lg}L-\text{lg}C-\text{lg}\gamma_{\pm}) \tag{3}\]  
where \(L\) is the product of hydroxide solubility; \(C\) is the samarium cation concentration; and \(\gamma_{\pm}\) is the salt average ion activity coefficient. Although the Gibbs energy value for Sm(OH)\({}_{3}\) formation is \(-1281.56\)\(\pm\) 3.77 kJ/mol, in [32; 33], this value is missing. The Gibbs energy value of Sm(OH)\({}^{2+}\) hydrate formation is \(-859.95\) kJ/mol, available in [32], which disagrees with the value of \(-848.10\)\(\pm\) 3.35 kJ/mol as specified in [33]. Due to the poor accuracy of values available in the literature data, the pH evaluation of complex formation and hydrate formation by the conductometric titration method was attempted with subsequent calculation of thermodynamic quantities.