MSE middle-range ion interaction parameters in this study.

<p>MSE middle-range ion interaction parameters in this study.</p

Normalized Ni K-edge XANES spectra of nickel complexes as a function of concentration (thin lines).

<p>Baseline-removed pre-edges are shown as a function of concentration in inset for clarity. Thick lines are the calculated (convoluted) XANES spectra for Ni aqueous species using fully hydrated regular (re.) and distorted (dis., DFT optimized), as well as [NiCl(H₂O)₅]²⁺ (ADF., DFT optimized) octahedral configuration models from literature [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119805#pone.0119805.ref005" target="_blank">5</a>].</p

Distribution of Ni(II) species in NiCl₂-H₂O (a, b), and NiCl₂-MgCl₂-H₂O (c) solutions and average number of ligand in the first shell of Ni²⁺ as a function of NiCl₂ solution concentration.

<p>In (a) and (c), the distributions of species are calculated with the formation constant and MSE parameters determined in this study (all lines); in (b), the distributions of species was calculated for NiCl₂ solutions using the model and parameters from literature [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119805#pone.0119805.ref010" target="_blank">10</a>]; In (a), the calculated average numbers of ligands in the first shell of Ni²⁺ are compared with the number of ligands extracted by EXAFS (Cl ligand, empty circles with error bar; O ligand, triangles with error bar) and XRD [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119805#pone.0119805.ref021" target="_blank">21</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119805#pone.0119805.ref025" target="_blank">25</a>] (Cl ligand, filled circles) analysis are shown for comparison; and (b) the result using the model and parameters from literature [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119805#pone.0119805.ref010" target="_blank">10</a>].</p

Comparison of experimental and calculated mean activity coefficient for NiCl₂ solution at room temperature.

<p>The line is calculated ones using the method of this work; the dash line represents the calculated results using the method from literature [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119805#pone.0119805.ref010" target="_blank">10</a>]; the circle are literature values [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119805#pone.0119805.ref063" target="_blank">63</a>]. The dot line of inset is the mean stoichiometric activity coefficient, namely, without considering effect of complexes in system, with the parameters derived in present model.</p

Previous studies on aqueous Ni(II) halide complexes in aqueous solutions.

<p>* m is molality and M is molarity.</p><p>^a Complex geometries: O_h: octahedral; T_d: tetrahedral.</p><p>Previous studies on aqueous Ni(II) halide complexes in aqueous solutions.</p

Calculated solubility isotherms (solid line by MSE model in this work and dashed line by Pitzer model) compared with experimental values (symbols: ■, MgCl₂∙6H₂O; ◪, MgCl₂∙6H₂O + NiCl₂∙4H₂O; □, NiCl₂∙4H₂O; ◨, NiCl₂∙4H₂O + NiCl₂∙6H₂O; ◫, NiCl₂∙6H₂O, data from literature [64]) at room temperature.

<p>Calculated solubility isotherms (solid line by MSE model in this work and dashed line by Pitzer model) compared with experimental values (symbols: ■, MgCl₂∙6H₂O; ◪, MgCl₂∙6H₂O + NiCl₂∙4H₂O; □, NiCl₂∙4H₂O; ◨, NiCl₂∙4H₂O + NiCl₂∙6H₂O; ◫, NiCl₂∙6H₂O, data from literature [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119805#pone.0119805.ref064" target="_blank">64</a>]) at room temperature.</p

The distribution maps of analysis error of XAS spectra for 2 mol∙kg^-1 (a) and 5.05 mol∙kg^-1 (b) NiCl₂ solution as a function of number of Cl ligands.

<p>The gray area represents 90% confidence level.</p

Principal component analysis results for NiCl₂-H₂O and Ni-MgCl₂-H₂O system in 350–550 nm and 580–850 nm absorbance bands, respectively.

<p>The circle is calculated by 100 ×</p><p></p><p></p><p></p><p></p><p></p><p></p><p></p><p></p><p><mo stretchy="false">(</mo></p><p><mi>x</mi></p><p>calc</p><p></p><mo>−</mo><p><mi>x</mi></p><p>meas</p><p></p><mo stretchy="false">)</mo><p></p><mn>2</mn><p></p><p></p><p></p><p><mi>x</mi></p><p>meas</p><p></p><p></p><p></p><p></p><p></p><p></p><p></p><p></p>, where <i>x</i>^calc and <i>x</i>^meas are the model and observed value, respectively. The gray area stands for the level of experimental error of 0.2%-0.5%.<p></p

Comparison experimental and predicted water activity for NiCl₂ solution at room temperature.

<p>The line is predicted one in this work and the dot line represents the prediction one without considering effect of complexes in system, corresponding to the dot line in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119805#pone.0119805.g009" target="_blank">Fig 9</a>; the circles are literature values [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119805#pone.0119805.ref063" target="_blank">63</a>].</p

The solubility product of solid phase in MSE and Pitzer model and the formation constant of NiCl⁺ and [NiCl₂]⁰ species determined in this study.

<p>The association constant of [HCl]⁰ aqueous species used in the calculation is also listed.</p><p>Uncertainty limits are given in parentheses.</p><p>* The solubility products were converted from mole fraction-scale in the literatures to molality-scale.</p><p>^£ Value was calculated by Pitzer−Simonson−Clegg (PSC) model [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119805#pone.0119805.ref046" target="_blank">46</a>].</p><p>^§ Values were calculated by HSC software (H = enthalpy, S = entropy, C = heat capacity) in literature [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119805#pone.0119805.ref048" target="_blank">48</a>].</p><p>^¶ The activity coefficient model assumed <i>γ</i>_ion = <i>γ</i>_<i>±</i>,_ion.</p><p>The solubility product of solid phase in MSE and Pitzer model and the formation constant of NiCl⁺ and [NiCl₂]⁰ species determined in this study.</p