## 3 Results
At the maximum recovery pH 7.0, the Y(OH)\({}_{2}\)DS goes into froth, as pH\({}_{\text{compl}}\) Me(OH)\({}_{2}\)\({}^{+}\) equals 6.97 [36], and pH\({}_{\text{hydr}}\) equals 7.2. The pH of the maximum recovery at the chloride concentration of 0.05 M shifts insignificantly to the higher values in the nitrate medium, ranging from 6.9 to 7.0. As was mentioned above, the recovery of yttrium (III) by ion flotation takes place at pH = 7.0, exceeding the values fitting the formation of hydroxo complexes in the form of \begin{table}
\begin{tabular}{c c c c} \hline
**pH** & **[Y3+]\({}_{\text{aq}}\times\) 10\({}^{4}\) mol/L** & **[Y3+]\({}_{\text{org}}\times\) 10\({}^{3}\) mol/L** & **\(K_{distr}\)** \\ \hline
4.0 & 6.43 & 1.35 & 3.0 \\
5.2 & 6.35 & 1.40 & 3.1 \\
6.4 & 6.23 & 1.33 & 3.1 \\
7.0 & 2.42 & 1.81 & 9.4 \\
7.4 & 2.78 & 1.94 & 7.2 \\
7.9 & 4.67 & 1.56 & 4.5 \\
8.5 & 10.82 & 0.99 & 1.1 \\ \hline \end{tabular}
\end{table} 
Table 4: The results of the experimental study of yttrium (III) cations recovery to froth pulp in nitrate-chloride medium at the NaCl concentration of 0.05 M. \begin{table}
\begin{tabular}{c c c c} \hline
**pH** & **[Y3+]\({}_{\text{aq}}\times\) 10\({}^{4}\) mol/L** & **[Y3+]\({}_{\text{org}}\times\) 10\({}^{3}\) mol/L** & **\(K_{distr}\)** \\ \hline
3.9 & 5.94 & 1.44 & 3.4 \\
4.5 & 4.79 & 1.60 & 4.6 \\
5.1 & 4.89 & 1.31 & 4.3 \\
6.0 & 5.37 & 1.50 & 3.8 \\
6.7 & 5.83 & 1.31 & 3.9 \\
7.4 & 0.01 & 2.05 & 279.3 \\
7.8 & 0.08 & 2.09 & 379.5 \\
8.1 & 0.55 & 1.95 & 50.6 \\
8.5 & 3.05 & 1.57 & 8.4 \\
9.0 & 5.32 & 1.31 & 3.1 \\ \hline \end{tabular}
\end{table} 
Table 3: The results of the experimental study of yttrium (III) cations recovery to froth pulp in nitrate-chloride medium at the NaCl concentration of 0.01 M.  
basic dodecyl sulfates. Consequently, the influence of chloride ions on the distribution coefficient can be explained if we compare the instability constants of chloro and hydroxo complexes. The former were calculated using the following equation:  
\[\Delta_{\text{f}}\text{G}_{298}^{0}\Big{\{}\text{MeCl}_{\text{aq}}^{2+}\Big{\}}= \Delta_{\text{f}}\text{G}_{298}^{0}\Big{\{}\text{Me}_{\text{aq}}^{3+}\Big{\}}+ \Delta_{\text{f}}\text{G}_{298}^{0}\Big{\{}\text{Cl}_{\text{aq}}^{-}\Big{\}}+ \text{RTInK}_{\text{n}}\]  
If we express the instability constant from the equation, we find the following:  
\[\text{K}_{\text{n}}=\text{e}^{-\frac{\Delta_{\text{compl}}\text{G}_{298}^{0}}{ \text{R}\cdot\text{I}}}\]  
Gibbs energies of chloro complexes and lanthanides cations formation in aqueous solution were accepted in accordance with the database [40]. Instability constants of hy-droxo complexes were calculated by the authors (Table 5). When chlorides are added, lanthanides are partially fixed in chloro complexes, which are not florable. A decrease in concentration level in hydroxo complexes brings about flotation suppression and alteration of the maximum recovery to the range of higher pH values. To calculate the concentrations of chloro and hydroxo complexes, let us write down the following set of equations:  
\[\left\{ \begin{array}{c}\text{C}_{\text{Ln}}=\,\Big{[}\text{Ln}^{3+}\Big{]} \,+\,\Big{[}\text{LnCl}^{2+}\Big{]}\,+\,\Big{[}\text{LnOH}^{2+}\Big{]}\\ \text{K}_{\text{n},\,\text{Cl}}\,=\,\frac{\big{[}\text{Ln}^{3+}\big{]}\cdot \big{[}\text{Cl}^{-}\big{]}}{\big{[}\text{LnCl}^{2+}\big{]}}\\ \text{K}_{\text{n},\,\text{h}}\,=\,\frac{\big{[}\text{Ln}^{3+}\big{]}\cdot \big{[}\text{OH}^{-}\big{]}}{\big{[}\text{LnOH}^{2+}\big{]}}\end{array}