Solubility of different salts used in the control of the water activity of foods

ABSTRACT Saturated salt solutions produce environments with specific relative humidities used in several applications, such as determining water sorption isotherms of foods. However, the preparation of saturated solutions requires knowledge of solubility data. Thus, the objective of this work was to determine the solubility of 14 salts: lithium bromide (LiBr), lithium chloride (LiCl), lithium iodide (LiI), magnesium chloride (MgCl2), sodium iodide (NaI), potassium carbonate (K2CO3), magnesium nitrate (Mg(NO3)2), sodium bromide (NaBr), potassium iodide (KI), sodium chloride (NaCl), ammonium sulfate ((NH4)2SO4), potassium chloride (KCl), potassium nitrate (KNO3), and potassium sulfate (K2SO4) in the temperature range of 275.15 to 363.15 K at 101.3 kPa. The apparatus for the solubility determination consists of a jacketed glass cell and a magnetic stirrer. Furthermore, polynomial and exponential empirical models were fitted to the observed data to determine salt solubilities. Salt solubilities ranged from 7.39 to 80.41 g of salt·(100 g of solution)-1. Sodium iodide (NaI) presented the highest (p<0.05) solubility, up to 343.15 K, and lithium iodide (LiI) up to 363.15 K. The specific equilibrium moistures afforded by saturated saline solutions were associated with water activity data. A general mathematical model to determine the solubility of different salts was not obtained because the dissolution behaviors of each salt are distinct. However, the availability of solubility data of saline solutions covering a wide range of temperatures is helpful since the salts have different behavior.


INTRODUCTION
Solubility is a physical property of matter, defined as the maximum quantity of a given solute dissolved in a solvent at a specific temperature and pressure.
Solubility is affected by (1) the system characteristics, such as temperature, pressure, pH, and presence of compounds other than the solute and solvent.Usually, endothermic dissolution shows increased solubility with increasing temperature, which may be associated with chemical structure reorganizing and changing the entropy (Martínez;Peña;Bustamante, 2011); (2) the natures of the solute and the solvent, such as molecular mass, size, molecular structure, polarity, quantity, and energy relationship through intermolecular interactions (Bhattachar;Deschenes;Wesley, 2006;Filippa;Gasull, 2014).According to the solute content, solutions are classified as saturated (contains the maximum quantity of a solute dissolved in a solvent), unsaturated or diluted (contains less dissolved solute than its saturation concentration), and supersaturated (contains more dissolved solute than its saturation concentration).Systems under supersaturated conditions tend to be unstable.Farelo, Brachel and Offermann (1993) determined solubility data of NaCl and KCl aqueous ternary solutions from 293 K to 360 K. Pinho and Macedo (1996) described NaCl and KCl solubility data in water/methanol and water/ ethanol systems at 298.15, 323.15, and 348.15 K. Wagner et al. (1998) measured the solubility of NaCl in organic solvents and aqueous solutions of organic solvents at 298.15 K. Thus, to the best of our knowledge, the solubility values of saline solutions for several types of salts over broad temperature ranges are scarce or obsolete in openaccess literature.
Salts are used as solutes in several industrial formulations, and thus, knowledge of the solubility of different salts has many practical applications in various unit operations processes, such as crystallization, liquid-liquid extraction, and extractive or azeotropic distillation (Pinho;Macedo, 1996).The literature reported the application of saturated salt solutions to simulate environments with different relative humidities and to control the water activity of foods, as follows.For instance, Mali et al. (2005) evaluated the effect of adding plasticizers (glycerol and sorbitol) to cassava starch films on water sorption at relative humidities of 32, 58, 75, and 90%.Saturated NaCl solutions are widely used to evaluate the kinetics of water vapor sorption in biodegradable materials (Ribeiro Sanches et al., 2021).Larotonda et al. (2005) determined the water vapor permeability of Kraft paper impregnated with starch acetate under three relative humidity ranges (0 to 33%; 33 to 62%; 62 to 90%).Saline solutions of NaCl, KCl and MgCl 2 were applied in meat salting to analyze their effect on the water retention capacity and the diffusion coefficient in a food product (Bampi et al., 2016;Inguglia et al., 2017;Sanches et al., 2021;Zhang et al., 2020).Solutions of KCl and MgCl 2 are investigated as substitutes for NaCl in foods with the aim of sodium reduction.
Saline solutions are also used to obtain water sorption isotherms, described by the relationship between equilibrium moisture and food water activity under constant temperature and pressure conditions (Arslan-Tontul, 2020;Freitas et al., 2016).Knowledge and understanding of moisture sorption isotherms play a role in food science and engineering.Isotherms can help determine the shelf life of foods, estimate and predict their microbiological and chemical behavior, choose suitable packaging, and estimate and predict the physical stability of foods under known storage conditions (Leonardo Betiol et al., 2020;Polachini et al., 2016;Rosa et al., 2021;Silva et al., 2021).
The systematic method used to determine moisture sorption isotherms is the differential method, a static gravimetric method.The sample is subjected to increasing or decreasing relative humidity environments in the method, and the water content is measured after equilibration (Polachini et al., 2016).In the differential method, several relative humidity environments, under controlled conditions, are generated using different saturated salt solutions or sulfuric acid.However, sulfuric acid can promote changes in the concentration of the solution.In addition, sulfuric acid requires handling care since it is very corrosive, especially in low water activities, and solution splashes need to be avoided on the studied material.Thus, saturated salt solutions are considered most suitable for controlling the relative humidity environment because they can release or adsorb water without changing the relative humidity environment of equilibrium (Chirife;Resnik, 1984).It should be emphasized that solutions must be prepared from salt solubility data at the isotherm temperature because the solubilities of many salts vary with temperature, and the water activity of an apparent saturated solution can induce process errors.
Several saturated saline solutions perform distinctly concerning solubility due to differences in the molecular masses of salts and their behavior at the operating temperature (Martins et al., 2021;Martins et al., 2020;Ramya;Jain, 2017), highlighting the importance of evaluating the individual solubility of various types of salts.Despite the relevance of solubility for different salts, either under saturation conditions or at the solubility threshold, to obtain sorption isotherms accurately, the data are scarce and dispersed in the literature (Alberto Alves-Junior et al., 2021;Pinho;Macedo, 1996), and they were also measured at a reduced temperature range.To contribute to filling this gap and form a specific data bank for isotherms with salts commonly applied in the Ciência e Agrotecnologia, 47:e018722, 2023 food industry over a wide temperature range, the objectives of this work were (a) to investigate the solubility of 14 saturated salt solutions, LiBr, LiCl, LiI, MgCl₂, NaI, K₂CO₃, Mg(NO₃)₂, NaBr, KI, NaCl, (NH₄)₂SO₄, KCl, KNO₃, and K₂SO₄, in aqueous medium at different temperatures (275.15 to 363.15 K) to provide a solubility database of different salts to be used in the construction of sorption isotherms; (b) to adjust empirical mathematical models to the experimental solubility data to obtain predictive equations for the various salts, and (c) to show the dependence of the solubility of the aforementioned salts at 11 temperature values (275.15 K, 278.15, 283.15, 293.15, 303.15, 313.15, 323.15, 333.15, 343.15, 353.15, and 363.15 K), which comprise the most ordinary temperature conditions of storage (275.15 to 313.15 K) and drying (323.15 to 363.15 K) of foods.

Determination of salt solubility data
Salt solubility was determined in triplicate according to the methodology described by Martins et al. (2021) for the 14 studied salts at 11 temperature values (275.15 K, 278.15, 283.15, 293.15, 303.15, 313.15, 323.15, 333.15, 343.15, 353.15, and 363.15K with a variation of ± 0.20 K).This temperature range simulates the conditions of storage (275.15 to 313.15 k) and drying (323.15 to 363.15 K) that are commonly used to determine water sorption isotherms of foods.
The experimental apparatus includes a glass cell, a thermocouple, an ultrathermostatic bath (Marconi, model MA-184), a stirrer, and a data acquisition system, as depicted in Figure 1.
The glass cell of 50 mL capacity is equipped with a water-circulating jacket to ensure an isothermal system.The cell contains two lateral inlets, one for solute feeding in the system and the other for taking samples and a top opening sealed with a Teflon stopper to prevent evaporation.The type K thermocouple (MT-455, Minipa, USA) was placed upon the sealed device in the center of the cell.The saturated solution prepared with 50 mL of deionized water was filled into the glass cell and magnetic stirrer to ensure homogeneity.The temperature was measured using a data acquisition system connected to a thermocouple.After isothermal condition attainment, the solute was inserted through the lateral entrance of the glass cell in small quantities until the formation of a precipitate, ensuring the saturation of the solution.Next, the saline solution was stirred for 50 h and then allowed to settle for 24 h to ensure solution saturation (Bensouissi;Roge;Mathlouthi, 2010).The experiment was carried out at atmospheric pressure.
The solubility was gravimetrically determined after soluble solids quantification on an analytical balance accurate to 0.01 g (AUX220, Shimadzu, Japan).Three aliquots of approximately 10 mL of the supernatant solution were removed from the cell top with the help of a syringe to avoid carrying the precipitate.Then, the samples were placed on glass plates and dried in a vacuum oven (model TE-395, Tecnal, Brazil) at 353.15 K until constant mass.

Mathematical Modeling
Empirical mathematical models were adjusted to the observed solubility data as a function of temperature ranging from 275.15 to 363.15 K, aiming at predicting solubility over this temperature range.The models used were polynomial (first-to fifth-degree) Equation 1 and exponential Equation 2 similar to the one used by Martins et al. (2021).The sample standard deviation of the experimental data was calculated Equation 3. OriginPro 8.0 software (OriginLab Corporation, Northampton, MA, USA) was applied to solve the nonlinear mathematical regressions.(1) In Equation 1, 2 and 3, S is the solubility [g of salt‧(100 g of solution) -1 ], β 1 , β 2 , β 3 , β 4 , β 5 , β 6 , γ 1 , γ 2 , and γ 3 are model parameters, T is the temperature (K), dp is sample standard deviation, S is solubility, S is average solubility and n is number of samples.
The evaluation criteria to determine the best fitted model were the adjusted coefficient of determination (R adj 2 ) and the mean relative error (MRE) Equation 4.
In Equation 4, Y i and are the predicted and observed values, respectively, and n is the number of experiments.

Statistical Analysis
Solubility results are presented as the mean values ± standard deviation of three replicates.Data were analyzed statistically using analysis of variance (ANOVA), and mean values were compared by Tukey's test (p< 0.05).
Literature reports mostly address salt solubilities in aqueous and alcoholic media (Pinho;Macedo, 1996;Wagner et al., 1998) under salt restriction (Farelo;Brachel and Offermann 1993;Pinho;Macedo, 2005) and often refer to the salts NaCl, NaBr, and KCl.The observed solubility data differ from those found by Pinho and Macedo (2005) by a maximum of 5.0% for the salts NaBr, NaCl and KCl.However, comparison among solubility results should be done with caution due to the low similarity between temperature and solvent conditions used in the tests.
Intermolecular interactions between water molecules affect salt solubility.If ion-dipole interactions between the water molecules and the salt ions are, on average, stronger than electrostatic attraction between the salt ions, salt dissociation occurs (Bensouissi;Roge;Mathlouthi, 2010).On the other hand, solubilization considerably increases the total configurational entropy in the system.It is related to the number of alternatives that the available energy can be distributed among the particles contained in a given system.When the total configurational entropy is high, it tends to increase the solubility of the salt in water (Fisicaro et al., 2008;Graeser et al., 2010).
In addition, solubility can be explained by the Law of Matching Water Affinities theory, which is associated with Hofmeister's effects.Figure 2 shows the classification of the Hofmeister series ions as kosmotropic or chaotropic following the hydration degree.). a Greenspan (1977) did not show the standard uncertainties.
Kosmotropic ions exhibited a strong bond with water and a high degree of hydration (Yang, 2009); chaotropic ions presented weakly bound with water and a low degree of hydration.The ion size also influences their interaction with water molecules.Larger ions have loosely bound water molecules around them, and the smaller ions have an inverse behavior (Kunz;Neueder, 2009).
Temperature changes affected solubility, as observed in Table 2. Solubility increased (p<0.05) with increasing temperature for all saturated saline solutions, corroborating the behavior reported by Pinho and Macedo (2005).High temperatures are a consequence of the higher kinetic energy of the molecules and ions.We also verified that the temperature increase promoted great stability in solubility for salts, with low solubilities, and large modifications in solubility for salts with higher solubilities.The amount of solute can also influence the solubility; the larger the amount of solute is, the greater the changes in hydrogen interactions of water molecules.The literature pointed out that some solute characteristics could explain the high solute solubility in water, such as low molecular mass, less complex chemical structures, and resistance to chemical reactions.Thus, solvent-mixed solutions are used to enhance solute solubility (Demirbas, 2004;Martínez;Peña;Bustamante, 2011).
The salt amounts to prepare 100 g of the saturated aqueous solution of the 14 studied types of salts are presented in Table 2. Greenspan (1977) presents data on equilibrium relative humidity for several saturated saline solutions.The division of these values by 100 results in the water activity data.Consequently, environments for isothermal experiments can be formed with safety from the solubility (Table 2) and water activity (Table 3) data.Thus, we present a list of salts used to determine moisture sorption isotherms of foods over a wide temperature range (275.15 to 363.15 K), including 11 temperature values.Yang (2009).

Mathematical modeling
Linear, second-order to fifth-order polynomial, and exponential mathematical models were fitted with experimental data.These types of models are considered simple and easy to apply in calculations involving unit operations.Thus, they are frequently applied in thermophysical property studies of food systems, such as concentrated grape juice (Evangelista et al., 2020), Malay rose apple pulp (Fontan, 2018), and aqueous solutions of sodium chloride (Carvalho et al., 2015), sucrose-maltitol (Martins et al., 2021), and isomaltulose (Do Carmo et al., 2022).
A general mathematical model to predict the solubility of all saline solutions was not obtained due to the different salt behavior and performance on the temperature increase; thus, five mathematical models are proposed to represent the solubility behavior of the tested salts.
The parameters and the adjustments of the best polynomial model for each salt (R adj 2 ≥ 0.9094 and RMSE ≤ 2.8770) are shown in Table 4.The fit of the other models to the experimental data is available in the supplementary material (Table S15).The graphical representation of the data with the best-fitted model is presented in Figure 3.
For LiI and NaCl solutions, the mathematical models exhibited poor representation of the experimental data; therefore, the solubility values for both types of salts can be determined using the observed values in Table 2. Linear interpolation can be applied if necessary.

Figure 1 :
Figure 1: Apparatus used to determine the solubility of different salts in water.Adapted from Martins et al. (2021).

Table 4 :
Fitting parameters of the fifth-degree polynomial model to describe the solubility (S) of saturated salt solutions.

Table 1 :
Salt composition and supplier.
*Purity was determined based on trace metals analysis as given by the supplier.