Review
The apparent reversal of the Law of Mass Action in concentrated multicomponent aqueous solutions

https://doi.org/10.1016/j.molliq.2023.121470Get rights and content

Highlights

  • Solubilities of NaNO3 and NaNO2 reverse the Law of Mass Action in multicomponent solutions.

  • These occurred in multicomponent solutions without enough water to hydrate all ions.

  • The reason for this peculiar behavior is likely related to the formation of large mixed-ion clusters analogous to solid solutions.

Abstract

Although it is well known that aqueous electrolyte solutions behave non-ideally, few are so non-ideal that adding an electrolyte to a saturated solution with a common ion enhances rather than depresses solubility. Nonetheless, this apparent reversal of the Law of Mass Action (LMA) has been observed in simple nitrate solutions at high concentrations. A leading hypothesis is that ion clusters are formed and stabilized by ions having different charge densities. The present study examines this concept, in part by reviewing relevant data from multicomponent aqueous solutions containing sodium nitrate (NaNO3), sodium nitrite (NaNO2), sodium hydroxide (NaOH), and sodium aluminate (NaAl(OH)4) - the major constituents in alkaline nuclear waste. Here, NaOH and NaAl(OH)4 did not enhance the solubility of NaNO3 or NaNO2, whereas NaNO2 and NaNO3 enhanced rather than depressed the solubility of each other despite each having the sodium cation (Na+) in common.

Solutions evaluated in this study have more than 24 molal total Na+ concentration, and most have less than one mole of water per mole of ion. Thus, this reversal of the LMA occurs in solutions where there is not enough water to fully hydrate the ions, pointing to the importance of ion cluster formation. Within the composition range of the solutions analyzed here, this reversal of the LMA occurs regardless of NaAl(OH)4 and NaOH concentrations. Elevated temperatures also result in the reversal of the LMA in the subsystems NaNO2-NaNO3-H2O and NaOH-NaNO3-H2O, consistent with spectroscopic and computational studies showing enhanced interactions at higher temperatures. Although speciation in these highly concentrated electrolyte solutions is not well understood, the stabilization of ion clusters by: (i) optimizing charge density around the ions through different combinations of mixed cations and anions in solution; and (ii) high temperatures where ions experience prolonged contact, offers important clues for future research into how these species control solubility.

Introduction

Historians indicate that the Law of Mass Action (LMA) was originally developed by Guldberg and Waage in the 1860s and 1870s [1], [2], [3]. The Law is a precursor to Le Chatelier’s principle, which expressed the Law in terms of thermodynamic properties [4]. In electrolyte solutions, the Law is often translated into the “common ion effect” developed by Nernst [5]. There have been rare reports of systems that appear to disobey Le Chatellier’s principle. One of the most famous reported cases is the synthesis of ammonia (NH3) from nitrogen (N2) and hydrogen (H2) gases [6]. The focus of the present study is nitrate solutions. Alkali and ammonium nitrate solubilities have been found to behave the opposite of what the common ion effect would expect in systems with more than one cation but the nitrate ion in common [7]. The present study shows that the LMA is also violated in sodium nitrate solutions containing other anions but having Na+ in common.

Aqueous electrolyte solutions are generally thought of as being non-ideal because they do not follow Raoult’s law. Consequently, Lewis developed the concept of “activities” to describe the deviation from non-ideality in 1907 [8]. Since then, numerous empirical and semi-empirical models were developed to estimate these activities. Many modern models are being formulated to eliminate these activity coefficients, and to describe a molecular basis for this behavior by assigning some water molecules to the electrolyte, assuming that some water is adsorbed so strongly to the electrolyte that they act as part of the electrolyte [9], [10], [11].

While electrolyte solutions may behave non-ideally, some solutions are so non-ideal that their associated salt solubilities are inverse of what the LMA would predict [7], [12], [13]. For example, in alkali and ammonium nitrate (NO3) mixtures the solubility increases when the common anion nitrate is added [7], [13]. These aqueous solutions that reverse the LMA are highly concentrated. This indicates that at the molecular scale, aspects of the ion solvation process in concentrated electrolytes are still poorly understood.

In dilute to moderately concentrated solutions, the speciation of the electrolytes is generally described in terms of individual ions, ion pairs, and simple complexes [14]. In more concentrated solutions, the ions can form larger clusters [12], [15], [16], [17], [18], [19], [20], [21]. Studying these highly concentrated solutions may provide a molecular-level, thermodynamic understanding of non-ideality in concentrate electrolytes that reverse the LMA.

Many of the aqueous solutions that reverse the LMA contain nitrate (NO3) [7]. At the moment, it is not clear why reversal of the LMA is so common with nitrate solutions. It could be their tendency to form dissolved ion clusters [7]. Nitrate is an ideal candidate anion to form such clusters, (i) due to its small charge density, with partial charges on each nitrate ion below the partial charge on the oxygens in water molecules and (ii) its extremely high solubility in water [7]. Together, these properties could allow for fluctuations in the local solution density where the reversal of the LMA can occur. It is distinctly possible that reversal of the LMA will be identified in many more electrolyte systems as concentrated mixtures of other electrolytes are studied more thoroughly. For instance, reversal of the LMA has also been established for acetate solutions [12].

Sodium nitrate is a major electrolyte in alkaline nuclear waste in the United States (US). This waste, created from actinide production at U.S. Department of Energy (US DOE) sites such as Savannah River and Hanford, contains significant quantities of NO3, nitrite (NO2), aluminate (Al(OH)4), and hydroxide (OH). Sodium ions (Na+) are the most prevalent cations in the waste liquids [22], [23]. These wastes are so concentrated that even highly soluble salts like sodium nitrate (NaNO3) have precipitated [24]. In addition to these major components, the waste contains significant quantities of fluoride (F), carbonate (CO32–), phosphate (PO43), sulfate (SO42), chloride (Cl), and dozens of organic constituents [22], [23]. This liquid waste, currently stored in underground tanks will pumped to a waste treatment plant where it will be transformed into a vitrified waste form for disposal [22]. Understanding how and under what conditions these concentrated nitrate-rich electrolytes exhibit LMA reversal could help optimize processing efficiency.

To better understand waste chemistry, Reynolds evaluated the solubilities of 13 salts in aqueous solutions of NaNO3, sodium nitrite (NaNO2), sodium chloride (NaCl), and sodium hydroxide (NaOH), and found that there are consistent trends in solubility [25]. Specifically, the solubility of every Na+-bearing salt was higher in NaNO3 solutions than NaOH solutions at the same total Na+ molality. A direct contrast to expectations from the LMA, addition of NaNO3 to a saturated Na+-bearing salt solution did not result in any meaningful salt precipitation in some cases [25].

The present study reviews the solubility of salts in simulated Hanford nuclear waste published in several reports written for the United States Government [26], [27], [28], as well as literature that gives a greater chemical context to those studies. In the following discussion, these government reports are denoted as the Herting studies. Though not widely disseminated, these studies have immense importance to understanding non-ideality in concentrated electrolyte solutions. They are among the few places demonstrating that the LMA can be reversed in highly concentrated multicomponent solutions. They may provide clues to the cause of the extreme non-ideality exhibited by aqueous electrolyte solutions containing NO3.

Section snippets

Solubility of Na+ salts in mixed anion solutions

Before looking at data that reverse the LMA, we start with more common solubility behavior that follows the LMA. Fig. 1 shows the solubility of NaNO3 in aqueous solutions of NaOH or NaNO2 at 25° C. The solubility of NaNO3 is different in NaOH solutions than NaNO2 solutions, a difference that is captured in thermodynamic solubility models using empirical interaction coefficients [31]. Despite the difference in solubility as a function of background electrolyte, the direction of the effect is as

Ion cluster formation and stabilization

By placing these observations of LMA reversal in nitrate-rich systems in the context of a broader class of electrolyte systems exhibiting similar phenomenology, possible underlying causes can be explored. The competition of ions for limited water molecules for solvation is particularly central. Lyashchenko concluded that the LMA was reversed in the potassium acetate-cobalt acetate-water (KCH3COO-Co(CH3COO)2-H2O) system when the ions started to aggregate into ion clusters rather than stay

Conclusions

Here, taking advantage of solubility studies conducted by Herting and coworkers on salts in alkaline nuclear waste simulants, the phenomenon of apparent reversal of the LMA in concentrated aqueous electrolytes has been reviewed. These reports highlight conditions for nitrate-rich systems where solubilities behave exactly opposite to what is predicted by the LMA. Several subsystems also reverse the LMA at temperatures 100 °C or greater, but not at lower temperatures. From our analysis, the

Perspectives on future work

Several questions about why these salt solubilities appear to reverse the LMA remain. The main hypothesis that solubility behavior is linked to the stability of solution clusters comes primarily from analogy to solid solutions, but also from conceptual support from molecular scale investigations of the temperature effect on ion-ion interactions. More data is needed to establish a molecular basis for this phenomenon, such as the direct confirmation of ion-clusters that contain both NO2 and NO3.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

The authors are thankful to Dan Herting for laboratory work used in this study, his backing for this review of his work, and his insight on anomalous solubilities in Hanford waste. ETN, STM, CIP and KMR acknowledge support from IDREAM (Interfacial Dynamics in Radioactive Environments and Materials), an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Science. IDREAM is led by Pacific Northwest National Laboratory (PNNL), which is a

References (82)

  • H.L. Le Chatelier

    A general statement of the laws of chemical equilibrium

    Comptes Rendus

    (1884)
  • W. Nernst

    Ueber gegenseitige beeinflussung der löslichkeit von salzen

    Z. Phys. Chem.

    (1889)
  • M.J. Uline et al.

    The ammonia synthesis reaction: An exception to the Le Chatelier principle and effects of nonideality

    J. Chem. Educ.

    (2006)
  • J.G. Reynolds

    Solubilities in aqueous nitrate solutions that reverse the Law of Mass Action

    Phys. Chem. Chem. Phys.

    (2021)
  • G.N. Lewis

    Outlines of a new system of thermodynamic chemistry

    Proc. Am. Acad. Arts Sci.

    (1907)
  • R. Heyrovska. A reappraisal of Arrhenius’ theory of partial dissociation of electrolytes. In: Electrochemistry Past and...
  • A.S. Wexler

    Raoult was right after all

    ACS Omega

    (2019)
  • A.A. Zavitsas

    Quest to demystify water: Ideal solution behaviors are obtained by adhering to the equilibrium mass action law

    J. Phys. Chem. B

    (2019)
  • A. Wrobel-Kaszanek et al.

    Equilibrium study in the KNO3 + NH4NO3 + H2O system at temperatures from 283.15 to 323.15 K

    J. Chem. Eng. Data

    (2019)
  • P.M. May et al.

    Thermodynamic modeling of aqueous systems: Current status

    J. Chem. Eng. Data

    (2017)
  • H. Bian et al.

    Ion clustering in aqueous solutions proved with vibrational energy transfer

    Proc. National Acad. Sci.

    (2011)
  • S.A. Hassan

    Morphology of ion clusters in aqueous electrolytes

    Phys. Rev. E

    (2008)
  • M. Hellström et al.

    Concentration-dependent proton transfer mechanisms in aqueous NaOH solutions: from acceptor-driven to donor-driven and back

    J. Phys. Chem. Lett.

    (2016)
  • M. Hellstrom et al.

    Structure of aqueous NaOH solutions: Insights from neural-network based molecular dynamics simulations

    Phys. Chem. Chem. Phys.

    (2017)
  • W.J. Xie et al.

    Ion pairing in alkali nitrate electrolyte solutions

    J. Phys. Chem B

    (2016)
  • H.A. Colburn et al.

    A history of Hanford tank waste, implications for waste treatment, and disposal

    Environ. Prog. Sustain. Energy

    (2021)
  • R. C. P. Hill, J.G. Reynolds, P.L. Rutland. A Comparison of Hanford and Savannah River Site High-Level Wastes....
  • R.W. Warrant et al.

    Characterization of the solids waste in the Hanford waste tanks using a combination of XRD, SEM and PLM

    Adv. X-Ray Anal.

    (2003)
  • J.G. Reynolds

    Salt solubilities in aqueous solutions of NaNO3, NaNO2, NaCl, and NaOH: A Hofmeister-like series for understanding alkaline nuclear waste

    ACS Omega

    (2018)
  • D.A. Reynolds et al.

    Solubilities of sodium nitrate, sodium nitrite, and sodium aluminate in simulated nuclear waste. RHO-RE-ST-14-P. Rockwell International. Richland

    WA.

    (1984)
  • D.L. Herting et al.

    Solubility Phase Diagram – Final Report

    (1983)
  • D.L. Herting, R. M. Cleavenger, Extended Solubility Phase Diagram. Report number 65453-84-152. Rockwell Hanford...
  • H. Šimková et al.

    The solubility of electrolytes. III. The quaternary system sodium nitrate-sodium nitrite-sodium chloride-water

    Collect. Czech. Chem. Commun.

    (1959)
  • V.F. Plekhotkin et al.

    The NaNO2-NaOH-H2O and NaNO3-NaOH-H2O systems

    Russ. J. Inorg. Chem.

    (1970)
  • J.G. Reynolds et al.

    A Pitzer interaction model for the NaNO3-NaNO2-NaOH-H2O system from 0°C to 100°C

    Ind. Eng. Chem. Res.

    (2015)
  • J. Eysseltova et al.

    IUPAC-NIST solubility data series. 89. Alkali metal nitrates. Part 2. Sodium nitrate

    J. Phys. Chem. Ref. Data

    (2017)
  • V.R. Fricke et al.

    Untersuchungen uber die Ggeichgewichte in der system Al2O3-Na2O-H2O und Al2O3-K2O-H2O

    Z. Anorg. Allg. Chem.

    (1930)
  • M. Weinberger et al.

    Die kristallstruktur des natriumoxohydroxoaluminathydrates Na2[Al2O3(OH)2]· 1,5H2O

    Z. Anorg. Allg. Chem.

    (1995)
  • M. Weinberger et al.

    Nonanatrium-his(hexahydroxoaluminat)- trihydroxid-hexahydrat (Na9[Al(OH)6] (OH)3 · 6H2O) – cristallstruktur, NMR-spektroskopie und thermisches verhalten

    Z. Anorg. Allg. Chem.

    (1996)
  • V. Zabel et al.

    Nonasodium bis(hexahydroxoaluminate) trihydroxide hexahydrate

    Acta Cryst. Sect. C.

    (1996)
  • D.L. Herting et al.

    Conversion of coarse gibbsite remaining in Hanford nuclear waste tank heels to solid sodium aluminate [NaAl (OH)4*1.5H2O]

    Ind. Eng. Chem. Res.

    (2014)
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