## 1 Introduction
This phenomenon is well reported by [PERSON] et al. [19]. In fact, the authors found that by reducing the L/S (liquid to solid) ratio by a factor of 10, it only increases the pH values from 11.2 to only 11.9. This means that at alkaline pH values, using 10 times the mass increases the pH value by less than a unit value. Similar results were obtained by [PERSON] et al. [20], which showed that only at L/S = 100 L/kg the slag is significantly dissolved. Contrary, for L/S = 10 L/kg the reactions between liquid and solid phases are only cortical, meaning that the dissolution of the mineral phase is stifled substantially by the alkalinity of the solution. Different dissolution rates at different pH levels are also reported by several other studies [17; 18]. Although, when the pH value is continuously adjusted and kept to low values, the dissolution of minerals progresses to completion [9; 10]. The pH value is not the only parameter that affects the dissolution of mineral phases. Several studies report different ion mobilities depending on the phases being dissolved. [PERSON] et al. [19] shows how Ca and Si are the most leached elements from BOF slags, due to the high solubility of larnite. On the other hand, Mg and Al show very low mobilities since they are associated with Fe-bearing phases with very low solubilities. However, [PERSON] et al. [9] report high solubility levels of Mg and Al, as well as a varying dissolution of Si depending on the material tested. Moreover, [PERSON] et al. [20] show an increased dissolution of Mg when the amount of dissolved Ca is low, while the dissolved Al content seems to increase the more Ca is being dissolved. Therefore, there seems to be no consensus regarding an independent leaching behavior of single elements. In fact, the aforementioned studies affirm that the dissolution of the mineral phases determines the solubilities of the elements leached in the solution [9; 19; 20]. Overall, all the studies agree that Ca is the most mobile element, and most Ca-bearing minerals found in metallurgical slags are at least partially soluble in water. In addition, different dissolved elements modify the pH value in different ways [17; 18]. The theoretical chemical equilibria of the most common and abundant elements in steel-making slags are listed in the following equations:  
\[\text{CaO}(\mathbf{s})+2\text{H}^{+}\ \rightarrow\ \text{Ca}^{2+}+\text{H}_{2}\text{O} \tag{1}\]\[\text{MgO(s)}+2\text{H}^{+} \rightarrow \text{Mg}^{2+}+\text{H}_{2}\text{O} \tag{2}\] \[\text{Al}_{2}\text{O}_{3}\text{(s)}+6\text{H}^{+} \rightarrow 2\text{Al}^{3+}+3\text{H}_{2}\text{O}\] (3) \[\text{Al}^{3+}+3\text{H}_{2}\text{O} \rightarrow \text{Al(OH)}_{3}\text{ (s) }+\text{ 3H}^{+}\] (4) \[\text{Al(OH)}_{3}\text{(s)}+\text{H}_{2}\text{O} \rightarrow \text{Al(OH)}_{4}^{-}+\text{H}^{+}\] (5) \[\text{SiO}_{2}\text{(s)}+2\text{H}_{2}\text{O} \rightarrow \text{Si(OH)}_{4}\text{(aq)}\] (6) \[\text{Si(OH)}_{4}\text{ (aq) }\rightarrow \text{SiO(OH)}_{3}^{-}+\text{H}^{+} \tag{7}\]  
As is it possible to notice from Equations (1) and (2), Ca and Mg present the same chemistry: the oxides dissociate in a bivalent proton and a water molecule. This reaction raises the pH value of the solution by removing dissolved protons. However, the chemistry of Al and Si is more complex. Al oxides dissolves by consuming 6 protons forming 2 trivalent Al ions and 3 water molecules. In addition, Al is involved in two more reactions which both generate a proton as shown in Equations (4) and (5). Si also forms a proton when the hydrated form of its oxide dissociates in aqueous media. Pourbaix diagrams have been used in previous studies to determine the favored species as a function of the pH value [17]. The diagrams are calculated using FactSage 6.1, according to a study made by [PERSON] at al. [21].By analyzing the graphs is it possible to notice that silic acid does not dissociate until very high levels of pH. Therefore, it does not contribute negatively to the increase of pH of the solution.