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

Solubilidade de diferentes sais usados ​​no controle da atividade de água de alimentos

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.

Index terms:
Gravimetric method; exponential model; polynomial model; saturation; temperature.

RESUMO

Soluções salinas saturadas produzem ambientes com umidades relativas específicas utilizadas em diversas aplicações, como na determinação de isotermas de sorção de água de alimentos. No entanto, a preparação de soluções saturadas requer conhecimento de dados de solubilidade. Assim, o objetivo deste trabalho foi determinar a solubilidade de 14 sais: brometo de lítio (LiBr), cloreto de lítio (LiCl), iodeto de lítio (LiI), cloreto de magnésio (MgCl₂), iodeto de sódio (NaI), carbonato de potássio (K₂CO₃), nitrato de magnésio (Mg(NO₃)₂), brometo de sódio (NaBr), iodeto de potássio (KI), cloreto de sódio (NaCl), sulfato de amônio ((NH₄)₂SO₄), cloreto de potássio (KCl), nitrato de potássio (KNO₃) e sulfato de potássio (K₂SO₄) na faixa de temperatura de 275,15 a 363,15 K a 101,3 kPa. O aparelho para a determinação da solubilidade consiste em uma célula de vidro encamisada e um agitador magnético. Além disso, modelos empíricos polinomiais e exponenciais foram ajustados aos dados observados para determinar solubilidades de sal. A solubilidade do sal varia de 7,39 a 80,41 g de sal·(100 g de solução)^-1. Iodeto de sódio (NaI) apresentou o maior (p<0.05) solubilidade, até 343,15 K, e iodeto de lítio (LiI) até 363,15 K. Específicas umidades de equilíbrio proporcionadas pelas soluções salinas saturadas foram associadas aos dados de atividade de água. Um modelo matemático geral para determinar a solubilidade de diferentes sais não foi obtido porque os comportamentos de dissolução de cada sal são distintos. No entanto, a disponibilidade de dados de solubilidade de soluções salinas cobrindo uma ampla faixa de temperaturas é útil, pois os sais têm comportamento diferente.

Termos para indexação:
Método gravimétrico; modelo exponencial; modelo polinomial; saturação; temperatura.

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 open-access 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 MgCl₂ 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 MgCl₂ 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 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.

MATERIAL AND METHODS

Preparation of saline solutions

Saline solutions were prepared with 14 types of salts acquired from Sigma-Aldrich (St. Louis, MO, USA): LiBr, LiCl, LiI, MgCl₂, NaI, K₂CO₃, Mg(NO₃)₂, NaBr, KI, NaCl, (NH₄)₂SO₄, KCl, KNO₃, and K₂SO₄. Table 1 presents the chemical specifications.

Table 1:
Salt composition and supplier.

Chemical name	Chemical formula	Supplier	Purity (%)*	CAS number
Lithium bromide	LiBr	Sigma-Aldrich	≥ 99.9	7550-35-8
Lithium chloride	LiCl	Sigma-Aldrich	≥ 99.9	7447-41-8
Lithium iodide	LiI	Sigald (Sigma-Aldrich)	99.99	10377-51-2
Magnesium chloride	MgCl2	Sigma (Sigma-Aldrich)	99.99	7786-30-3
Sodium iodide	NaI	Sigma-Aldrich	99.99	7681-82-5
Potassium carbonate	K2CO3	Sigald (Sigma-Aldrich)	99.99	584-08-7
Magnesium nitrate	Mg(NO3)2	Sigma-Aldrich	≥ 99.99	10377-60-3
Sodium bromide	NaBr	Sigma-Aldrich	≥ 99.99	7647-15-6
Potassium iodide	KI	Sigma-Aldrich	≥ 99.99	7681-11-0
Sodium chloride	NaCl	Sigma-Aldrich	≥ 99.5	7647-14-5
Ammonium sulfate	(NH4)2SO4	Sigald (Sigma-Aldrich)	≥ 99.0	7783-20-2
Potassium chloride	KCl	Sigma-Aldrich	≥ 99.5	7447-40-7
Potassium nitrate	KNO3	Sigald (Sigma-Aldrich)	≥ 99.0	7757-79-1
Potassium sulfate	K2SO4	Sigma-Aldrich	≥ 99.99	7778-80-5

• *Purity was determined based on trace metals analysis as given by the supplier.

Distilled (Marconi, model MA078/10) and deionized water (Marconi model MA3401) was used as the solvent with an electrical conductivity of 0.113 ± 0.004 µS‧cm, thermal conductivity of 0.618 ± 0.002 W·m ⁻¹ ·K ⁻¹, and a measured specific resistance of 8.85 MΩ·cm.

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 363.15 K 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.

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

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.

$$S=A+BT+C{T}^2+D{T}^3+E{T}^4+F{T}^5$$ (1)

$$S={\gamma }_1+{\gamma }_2\exp \left({\gamma }_{a}T\right)$$ (2)

$$dp=\sqrt{\frac{{\displaystyle \sum {\left(S_i-\overline{S}\right)}^2}}{n-1}}$$ (3)

In Equation 1, 2 and 3, S is the solubility [g of salt‧(100 g of solution)^-1], β₁, β₂, β₃, β₄, β₅, β₆, γ₁, γ₂, and γ₃ are model parameters, T is the temperature (K), dp is sample standard deviation, S is solubility, $$\overline{S}$$ 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.

$$MRE\left(\%\right)=\left(\frac{100}{n}\right){\displaystyle {\sum }_{i=1}^n\frac{\left|Y_i-Y_i^{*}\right|}{Y_i^{*}}}$$ (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).

RESULTS AND DISCUSSION

Solubility data

The solubilities of saturated solutions of LiBr, LiCl, LiI, MgCl₂, NaI, K₂CO₃, Mg(NO₃)₂, NaBr, KI, NaCl, (NH₄)₂SO₄, KCl, KNO₃, and K₂SO₄ as a function of temperature are presented in Table 2. The solubility results ranged from 7.39 to 80.41 [g of salt·(100 g of solution)⁻¹] and are also expressed in two other units, molarity [(mol of salt‧(mol of solution)^-1] and molality [mol of salt‧(kg of water)^-1] (Tables S1 to S11 - supplementary material).

Table 2:
Saturation condition (S) of saline solutions at different temperatures (T) (mean ± standard deviation).^a

g of salt . (100 g of solution)-1

T(K)

LiBr

LiCl

LiI

MgCl2

NaI

K2CO3

Mg(NO3)2

NaBr

KI

NaCl

(NH4)2SO4

KCL

KNO3

K2SO4

275.15

58.173±0.188hB

39.704±0.134kG

58.663±0.026kB

33.601±0.067iH

61.322±0.162iA

51.496±0.351gD

38.573±1.671hG

44.965±0.128iE

56,676±0.153kC

26.527±0.057dI

41.244±0.140eF

22.148±0.535hJ

12.841±0.202jK

7.385±0.178jL

278.15

58.973±0.185gB

40.525±0.112jG

58.991±0.028jB

34.097±0.052hI

61.250±0.073iA

50.642±0.261fgD

38.868±1.557hH

45.319±0.016hE

57,035±0.074jC

26.369±0.080cdJ

42.202±0.162eF

22.733±0.550hK

14.560±0.256jL

7.776±0.188ijM

283.15

60.651±0.136fAB

43.090±0.145iF

59.554±0.042iB

34.484±0.173hI

61.317±0.118iA

51.833±0.908fgD

39.692±0.452hH

46.578±0.138gE

57,796±0.106iC

26.098±0.567cdJ

41.435±0.112eG

23.246±0.577hK

17.390±0.413iL

8.424±0.209iM

293.15

62.668±0.114eA

44.844±0.113hF

60.971±0.021hB

35.206±0.074gI

62.927±0.106hA

52.364±0.380efgD

40.956±0.038ghH

48.252±0.064fE

59,291±0.056hC

26.432±0.058cdJ

42.823±0.535deG

25.401±0.458gK

24.115±0.293hL

9.968±0.180hM

303.15

65.952±0.061dA

45.445±0.111gF

62.995±0.041gB

35.856±0.086fH

65.604±0.062gA

53.245±0.410defD

42.606±1.301fgG

49.896±0.115eE

60,541±0.597gC

26.789±0.540cdJ

43.140±1.245deG

27.361±0.024fJ

30.425±0.666gI

11.456±0.010gK

313.15

67.682±0.100cA

47.518±0.067fF

64.965±0.035fB

36.509±0.050eH

67.966±0.334fA

53.320±0.219defD

44.979±0.434efG

51.381±0.019dE

61,793±0.052fC

26.383±0.470bcdJ

44.731±1.344cdG

28.905±0.446efI

37.599±0.727fH

12.794±0.198fK

323.15

67.697±0.041cB

48.749±0.074eG

65.946±0.019eC

37.176±0.255dI

70.545±0.242eA

54.269±1.230cdeE

45.995±0.441deH

52.303±0.258cF

62,956±0.264eD

26.414±0.207bcdK

45.622±0.758bcH

30.223±0.122deJ

45.971±0.415eH

14.145±0.057eL

333.15

67.846±0.175cB

49.698±0.136dG

66.097±0.008dC

37.577±0.093dJ

72.696±0.103dA

55.108±0.408cdE

48.055±0.171cdH

52.843±0.170cF

63,945±0.254dD

26.516±0.081abcdL

46.209±0.662bcI

31.463±0.818cdK

52.159±0.200dF

15.676±0.408dM

343.15

69.813±0.018bB

51.255±0.114cF

68.936±0.006cB

38.532±0.184cH

74.150±0.012cA

56.260±0.924bcD

50.058±0.132bcF

53.345±0.076 bE

64,781±0.067cC

27.558±0.129abcJ

47.711±1.219abG

32.739±0.087bcI

56.791±0.263cD

16.569±0.044cK

353.15

69.647±0.165bC

53.098±0.147bG

80.020±0.029bA

39.558±0.190bJ

75.149±0.103bD

57.471±0.953abF

51.705±0.237bH

53.382±0.124bG

65,651±0.140bD

27.776±0.145abL

48.707±0.153ªI

33.880±0.875abK

62.991±0.718bE

17.739±0.458bM

363.15

70.59±0.198aC

54.046±0.087aF

80.414±0.069aA

40.548±0.263aH

75.542±0.055ªB

59.039±1.263aE

70.178±1.783ªC

53.854±0.113aF

66,524±0.103ªD

27.345±0.732ªJ

49.640±0.602aG

34.412±0.806ªI

66.411±1.978ªD

18.583±0.435ªK

• 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), Potassium sulfate (K₂SO₄). Means and standard deviations followed by different uppercase letters in the same row and different lowercase letters in the same column indicate significant differences according to Analysis of Variance and post-hoc Tukey’s test (α = 0.05). ^aStandard uncertainties are u(T)=0.20K, u(P)=0.10kPa, electrical conductivity u(σ)=0.004 µS.cm^-1, thermal conductivity u(λ)= 0.002 W.m⁻¹.K ⁻¹ and mass of solute u(m)=0.01g.

Among the 14 salts studied, six presented higher solubility in water: lithium iodide (LiI), sodium iodide (NaI), lithium bromide (LiBr), magnesium nitrate (Mg(NO₃)₂), potassium iodide (KI), and potassium nitrate (KNO₃). Three of them exhibited lower water solubilities, potassium sulfate (K₂SO₄), sodium chloride (NaCl), and calcium chloride (KCl). Potassium sulfate (K₂SO₄) revealed the lowest (p<0.05) water solubility when compared to other saline solutions. Sodium iodide (NaI) had the highest water solubility in the range from 275.15 to 343.15 K, and lithium iodide (LiI) from 353.15 to 363.15 K, according to the statistical analysis (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.

Figure 2:
Kosmotropic and chaotropic ions according to the Hofmeister series. Adapted from Yang (2009).

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.

Table 3:
Water activity (a_w) of different saturated saline solutions at different temperatures (T).^a

T(K)	LiBr	LiCl	LiI	MgCl2	NaI	K2CO3	Mg(NO3)2	NaBr	KI	NaCl	(NH4)2SO4	KCl	KNO3	K2SO4
275.15	0.0762	0.1124	---	0.3363	---	0.4313	0.5975	---	---	0.7556	0.8233	0.8823	0.9764	0.9865
278.15	0.0743	0.1126	0.2168	0.3360	0.4242	0.4313	0.5886	0.6351	0.7330	0.7565	0.8242	0.8767	0.99627	0.9848
283.15	0.0714	0.1129	0.2061	0.3347	0.4183	0.4314	0.5736	0.6215	0.7211	0.7567	0.8206	0.8677	0.9596	0.9818
293.15	0.0661	0.1131	0.1856	0.3307	0.3965	0.4316	0.5438	0.5914	0.6990	0.7547	0.8134	0.8511	0.9462	0.9759
303.15	0.0616	0.1128	0.1657	0.3244	0.3615	0.4317	0.5140	0.5603	0.6789	0.7509	0.8063	0.8362	0.9231	0.9700
313.15	0.0580	0.1121	0.1455	0.3160	0.3288	---	0.4842	0.5317	0.6609	0.7468	0.7991	0.8232	0.8903	0.9641
323.15	0.0553	0.1110	0.1238	0.3054	0.2921	---	0.4544	0.5093	0.6449	0.7443	0.7920	0.8120	0.8478	0.9582
333.15	0.0533	0.1095	0.0998	0.2926	0.2595	---	---	0.4966	0.6311	0.7450	---	0.8025	---	---
343.15	0.0523	0.1075	0.0723	0.2777	0.2357	---	---	0.4970	0.6193	0.7506	---	0.7949	---	---
353.15	0.0520	0.1051	---	0.2605	0.2252	---	---	0.5143	0.6097	0.7629	---	0.7890	---	---
363.15	0.0526	0.1023	---	0.2412	0.2325	---	---	---	0.6021	---	---	0.7850	---	---

• Adapted from Greenspan (1977). 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), Potassium sulfate (K₂SO₄). ^aGreenspan (1977) did not show the standard uncertainties.

The temperature range studied includes the industrial conditions used for drying and storing most food systems, enabling obtaining food sorption isotherms. These isotherms, in turn, are used to solve problems in food engineering and food science, such as in the storage of industrial waste, such as papaya seed (Rosa et al., 2021), melon seed (Mallek-Ayadi; Bahloul; Kechaou, 2020), cassava bagasse (Polachini et al., 2016), and products such as cooked ham (Barretto et al., 2018), chia seed (Arslan-Tontul, 2020), pork liver (Sánchez-Torres et al., 2021), wheat malt (Silva et al., 2021) and dry-cured ham (Leonardo Betiol et al., 2020).

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.

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

Parameters	LiBr	LiCl	LiI	MgCl2	NaI	K2CO3	Mg(NO3)2	NaBr	KI	NaCl	(NH4)2SO4	KCl	KNO3	K2SO4
A	-7148.21714	-6941.75942	372632.36617	-342.63757	1162.73816	66.95652	-12.24708	-135.55158	-22.46057	79143.0481	85.65506	-220.90708	1524.59032	-14.49529
B	87.32071	85.36493	-5833.17375	3.51641	-10.92939	-0.1668	0.1815	1.07486	0.42096	-1272.0714	-0.35914	1.86361	-16.00393	-0.1067
C	-0.39731	-0.39129	36.40708	-0.01104	0.03554	3.95071·10-4	-	-0.00153	-4.85213·10-4	8.1631	7.20504·10-4	-0.00473	0.05445	0.00109
D	8.0481·10-4	7.96698·10-4	-0.11323	1.17331·10-5	-3.7685·10-5	-	-	-	-	-0.0261	-	4.2254·10-6	-5.90784·10-5	-1.489·10-6
E	-6.11704·10-7	-6.07027·10-7	1.7546·10-4	-	-	-	-	-	-	4.1732·10-5	-	-	-	-
F	-	-	-1.08375·10-7	-	-	-	-	-	-	-2.6594·10-8	-	-	-	-
R 2	0.9734	0.9915	0.9094	0.9966	0.9990	0.9378	0.9871	0.9993	0.9996	0.9127	0.9804	0.9995	0.9994	0.99991
MRE	0.7508	0.5646	1.9283	0.2258	0.3341	0.5744	2.8770	0.3044	0.0730	0.6130	0.9755	0.0589	1.2492	0.5169

• 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), Potassium sulfate (K₂SO₄).

Figure 3:
Salt solubility (S) at different temperatures (T). Points: solubility mean values. Vertical bars: standard deviations. Lines: best-fitted model. Saturated aqueous solutions of LiBr, LiCl, LiI, MgCl₂, NaI, K₂CO₃, Mg(NO₃)₂, NaB, KI, NaCl, (NH₄)₂SO₄, KCl, KNO₃, and K₂SO₄.

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.

Solubility data for saturated saline solutions are not easily found in the literature and are helpful in isotherm studies, analysis of evaporation mechanisms (Kuznetsov et al., 2018), preparation of activated charcoal (Yuliusman et al., 2020), meat salting processes (Cárcel et al., 2007), and in the project and design of equipment such as a water absorption machine of single-stage lithium bromide (LiBr) (Florides et al., 2003).

CONCLUSIONS

Solubility and water activity data of saline solutions are useful for determining food sorption isotherms. The LiI revealed the highest solubility in aqueous solutions, and K₂SO₄ had the lowest solubility. The salts showed dependence and differentiated behavior in the temperature range studied. Furthermore, the water activity of saline solutions decreases with increasing temperature. A general mathematical model was not proposed to predict solubility data, as each salt had specific characteristics, making the solubility database essential.

ACKNOWLEDGMENTS

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. The authors are also grateful to the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brazil) for funding the productivity grants of J. Telis-Romero (308567/2017-0).

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Publication Dates

• Publication in this collection
  10 July 2023
• Date of issue
  2023

History

• Received
  15 Dec 2022
• Accepted
  05 Apr 2023