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