Chemical Speciation of Environmentally Significant Metals: An IUPAC contribution to reliable and rigorous computer modelling

The question to be answered is: how does one select the most reliable values?

In contrast to Na⁺, K⁺, Ca²⁺ and Mg²⁺, which are the common cations present in most natural waters, most metal ions of environmental interest occur at ‘trace’ levels: at very low concentrations (mg dm⁻³ (ppb) range) in pristine waters and in low concentrations (mg dm⁻³ (ppm) range) in polluted waters. With the availability of very sensitive analytical techniques such as ASV, ICP and ICP-MS, measurement of the total concentrations of these ‘trace’ inorganic metal ions is easily accomplished. However, these techniques provide little, if any, information about the distribution of metal ions amongst their labile complex species.

The speciation of metal ions, viz., their distribution between soluble labile complexes and inorganic solid phases, can be calculated conveniently by computer simulation. However, the worth of such calculations is critically dependent on the equilibrium model used to define the system, the rigor of the computer modelling program and the reliability of the equilibrium constants used in the calculations. As there are a number of good, well-tested speciation modelling programs now available, reliable simulations depend on the completeness of the equilibrium model and the reliability of the equilibrium constants. The equilibrium model must include all labile species, both soluble and solid phase, that make a measureable contribution to the distribution of the metal ion. In the case of natural waters, this model will include ions such as Ca²⁺ and Mg²⁺ that will be in competition with trace metal ions for inorganic ligands such as CO₃²⁻, SO₄²⁻ and PO₄³⁻.

The equilibrium constants reported in the literature will often be derived from experiments conducted at different ionic strengths, often significantly higher than those applicable to natural waters. For a speciation simulation to be numerically reliable, the equilibrium constants must be valid for the ionic strength of the natural water of interest. This may require extrapolation or interpolation from a set of experimental values determined at different ionic strengths (typically in a 0.05 to 3.0 mol dm⁻³ medium of a supposedly non-labile electrolyte) to the value applicable to pristine fresh water (ca. 0.0015 mol dm⁻³) or a saline (seawater) medium (ca. 0.67 mol dm⁻³). Choosing the most reliable constants is a serious challenge even for experienced solution chemists. Constants will have been determined by a range of experimental methods, some less appropriate than others, by laboratories with diverse levels of expertise. Even when the experimental measurements are on a simple binary system, such as Pb²⁺ + OH⁻, the choice of different experimental pH ranges, total metal ion concentrations, or ionic strengths, or the nature of the medium (e.g., LiClO₄ vs NaClO₄ or KNO₃) [1], will lead to different species models and numerically different results. The question to be answered is: how does one select the most reliable values?

Critical evaluations of equilibrium data - the role of IUPAC

One responsibility of IUPAC is the critical evaluation of published experimental data. For equilibrium constants this includes the identification and recommendation of the most reliable values for each metal-ligand system. This is a very time-consuming process which involves the critical evaluation of experimental methods, numerical treatment of data in each publication and at all ionic strengths reported, applying clearly stated criteria to identify reliable publications and reject others, as well as the test of data reliability by establishing correlations between reliable (“accepted”) data for different ionic strengths and rejecting statistical outliers.

This process of critical evaluation of metal + ligand equilibrium constants has been applied to the complexes formed between the natural-water-dominant inorganic ligands OH⁻, Cl⁻, CO₃²⁻, SO₄²⁻ and PO₄³⁻, the proton H⁺, and the environmentally-significant heavy-metal ions Hg²⁺, Cu²⁺, Pb²⁺, Cd²⁺ and Zn²⁺, which all occur at trace levels in fresh water and sea water. The results are the outcome of IUPAC project 1999-050-1-500 and are published in a recently-completed series of IUPAC Technical Reports. [2-6]

This review of the IUPAC Technical Reports presents examples of speciation diagrams, viz., plots of metal ion distribution as a function of pH. For brevity the examples and tables are limited to the speciation of Zn^II in natural waters. Comprehensive examples for each metal ion for binary systems and natural waters are given in the respective Technical Reports. These diagrams are calculated from the stability constants K_n or β_p,q,r for each ligand-metal combination. In addition to the experimental equilibrium constants, values of the standard state (zero ionic strength) constants, K_n° or β_p,q,r°, are also reported. These standard state constants are obtained by extrapolation of the accepted experimental values at finite ionic strengths using the Brønsted–Guggenheim–Scatchard Specific Ion-Interaction Theory (SIT), [7] which represents a reasonable trade-off between theoretical rigor and numerical simplicity.

For the general reaction of a metal ion M with a ligand L (omitting charges except for H⁺):

pM + qL + rH₂O ⇌ M_pL_q(OH)_r + rH⁺

the SIT relationship between the standard equilibrium constant β_p,q,r° and that determined in an ionic

medium of ionic strength I_m (molality scale), β_p,q,r is:

log₁₀β_p,q,r − Δz²D − rlog₁₀a(H₂O) =

log₁₀β_p,q,r° − ΔεI_m (1)

in which Δz² = (pz_M + qz_L – r)² + r – p(z_M)² – q(z_L)². The value of the constant D is defined by the SIT activity coefficient relationship on the molality scale for a single ion i:

log₁₀ γ_m(i) = − z_i²A√I_m (1 + a_jB√ I_m)^⁻1 + Σ_k ε(i,k) m_k

= − z_i²D + Σ_k ε(i,k) m_k(2)

in which k represents the electrolyte ions N⁺ or X^⁻, ε(i,k) is the aqueous SIT coefficient for short-range interactions between ions i and k, and Δε is the reaction SIT coefficient given by:

Δε = ε(complex, N⁺ or X⁻) + rε (H⁺,X⁻) − pε (Mⁿ⁺,X⁻)

− qε (L^m−, N⁺)

A is the Debye–Hückel limiting slope (0.509 mol^−1/2 kg^1/2 at 25 °C) and a_jB = 1.5. [7] Equation 1 is used to determine log₁₀β_p,q,r° values as the intercept of the extrapolation of a suite of accepted log₁₀β_p,q,r values. To view all of these extrapolations and a more rigorous treatment, the reader is referred to the IUPAC Technical Reports. [2-6] These reports include all log₁₀β_p,q,r° or log₁₀K_n° and Δε values determined in this IUPAC project.

Speciation calculations

The availability of equilibrium constants and their ionic strength dependencies allows the modelling of metal ion speciation in natural water systems. Figures 1 and 2 present examples for Zn^II in natural waters. In fresh water the ionic strength is low, which will cause only small changes in the formation constants from values at I_c (or I_m) = 0. However, in a sea water system the changes become more pronounced. This is evident from the data presented in Table 1, which contains calculated log₁₀K_n or log₁₀β_p,q,r values for species found to contribute significantly to the speciation of Zn^II in fresh and sea water systems. The speciation calculations were achieved using WinSGW (www.WinSGW.se). This program incorporates the SIT functions and generates the ionic-strength-corrected values of log₁₀β_p,q,r for each datum in the calculation.

Example: a multicomponent freshwater system

Figure 1 illustrates the speciation diagram for Zn^II in fresh water (I_c = 0.0015 mol dm^⁻3) in equilibrium with air having a CO₂ fugacity of 10^⁻1.5 kPa. The total concentration of Zn^II was set to 1 nmol dm^⁻3 and the total concentrations of the inorganic anions were those typically found in fresh water [8]: [Cl⁻]_T = 0.23 mmol dm^⁻3, [SO₄^2⁻]_T = 0.42 mmol dm^⁻3 and [HPO₄^2⁻]_T = 0.7 µmol dm^⁻3. The pH was allowed to vary between 6.0 and 9.0. In this range the ionic strength varies from ca. I_c = 0.0015 mol dm^⁻3 at pH = 7, to 0.007 mol dm^⁻3 at pH = 9 due to the increase in [HCO₃^⁻] and [CO₃^2⁻] at constant f(CO₂). The impact on the stability constant values caused by this change in I_c was accounted for in the calculation. This calculation also includes the competing reactions between Mg²⁺ and Ca²⁺ and the ligands (not shown). [9] Figure 1 shows that the predominant species are Zn²⁺ (pH ≤ 8.4) and ZnCO₃(aq) (pH ≥ 8.4), and that hydroxido- complexes

(Zn_p(OH)_q^{(2p – q)+}) make only a minor contribution (< 10 %).

Example: a multicomponent seawater system

In a sea water system high concentrations of chloride (545 mmol dm^⁻3) and sulphate (28 mmol dm^⁻3) significantly affect the speciation. [8] This is illustrated in Figure 2, which shows the speciation for Zn^II in a sea water medium (I_c = 0.67 mol dm^⁻3), a calculation including carbonato- and sulfato- complexes of Mg²⁺ and Ca²⁺. It was assumed that [Zn^II]_T = 1 nmol dm^⁻3. Similar to the fresh water system, the species Zn²⁺ and ZnCO₃(aq) predominate. However, due to the competing formation of chlorido- and sulphato- complexes, the concentration of Zn²⁺ is now ca. 55% of [Zn]_T at sea water pH (ca. 8.2), in contrast to ca. 94 % of [Zn]_T at the pH of fresh water (ca. 6.5). Similarly, the formation of ZnCO₃(aq) is also suppressed and this does not become the predominant species until pH ≥ 8.7.

IUPAC Recommended values of critical equilibrium constants

For a full set of the critically evaluated Recommended or Provisional equilibrium data the reader is referred to the published Technical Reports. [2-6] To illustrate the scope of the data currently available, Table 2 presents the evaluated stability constants, reaction ion interaction coefficients (Δε) and, where available, the reaction enthalpy change for formation of soluble Zn^II complexes with the common environmental inorganic ligands. For the sake of brevity the reactions for nine heterogeneous reactions are omitted from this Table. The reader is referred to the Technical Report. [6]

Comments

As a result of this project, the environmental chemist wishing to model inorganic complexation of the important trace metal ions in natural waters now has easy access to the most reliable stability constant values currently available for the relevant equilibria and applicable ionic strengths. An outcome from the critical evaluations [2-6] is that a lack of detailed high-quality data for many of the metal + ligand systems has been identified. This is particularly true for the M²⁺ + PO₄^3⁻ systems for which no values could be recommended at I_m = 0 mol dm^⁻3. Reliable data in several of the systems M²⁺ + CO₃^2⁻ (e.g. M = Cd, Pb, Zn) were also missing at finite ionic strengths, as too were data for some of the systems M²⁺ + SO₄^2⁻. It has been possible to evaluate very few enthalpy values, let alone recommend them, which means that a rigorous thermodynamic modelling of the chemical speciation at temperatures other than 25 °C is still not possible. Further, the absence of reliable thermodynamic data for metal complexes with relevant organic ligands (e.g. humic substances) remains the major challenge to the modelling of complexation in natural water systems. In this domain there is an urgent need for additional critical evaluations.

Kipton J. Powell is an Emeritus Professor at University of Canterbury (Christchurch). Paul L. Brown is Principal Advisor, Mineral Waste Management at Rio Tinto Technology and Innovation (Bundoora). Robert H. Byrne is Distinguished University Professor in Seawater Physical Chemistry at the University of South Florida (St. Petersburg). Tamas Gajda is at University of Szeged (Szeged). Glenn Hefter is Professor of Chemistry at Murdoch University. Ann-Kathrin Leuz is Section Head at the Swiss Federal Nuclear Safety Inspectorate (Brugg). Staffan Sjöberg is Professor Emeritus in Chemistry at Umeå University. Hans Wanner is Director General of the Swiss Federal Nuclear Safety Inspectorate (Brugg).