Experimental and Modeling Study of the Thermodynamic Behavior and Solubility of the NH₄NO₃–D-Sucrose–Water Ternary System at 298.15 K

Abstract

In this study, thermodynamic properties such as water activity, osmotic coefficient, and saturation points of the aqueous mixture in the system D-Sucrose + Water + ammonium nitrate (AN) were determined at 298.15 K. The measurements were carried out on the mixtures of concentrations of NH₄NO₃ (ranging from 0.1 to 6 mol·kg⁻¹) and D-sucrose (from 0.1 to 4 mol·kg⁻¹) using our hygrometric method. Powder X-ray diffraction (XRD) and attenuated total reflection–Fourier transform infrared (ATR-FTIR) spectroscopy were used to characterize the solid phases crystallized during the supersaturation of the solution. Other thermodynamic quantities such as the solute activity coefficients, excess Gibbs energies, transfer energies, and solute solubilities were calculated using the Pitzer–Simonson–Clegg (PSC) model. The results obtained indicate that at an AN concentration lower than 1 mol·kg⁻¹, the system exhibits increasingly negative deviations from ideality, and that NH₄NO₃ promotes the salting-out effect of sucrose.

1. Introduction

Electrolytic and nonelectrolytic solutions are of great fundamental and theoretical interest in many scientific and industrial fields, including biology, pharmacy, chemistry, biochemistry, and the food industry [1,2,3,4,5]. In this study, we chose the compounds NH₄NO₃ (ammonium nitrate) and sucrose, which see high demanded in different industries. Ammonium nitrate is widely used in agriculture as a fertilizer [6], and under controlled conditions, as an explosive, and is also a reagent in chemical synthesis. Sucrose is widely employed in the food industry as a sweetener and preservative, contributing to both energy supply and microbial inhibition. Our objective in this study is to provide, for the first time, new physicochemical properties of the mixture of these two compounds in aqueous solution NH₄NO₃ + sucrose that do not exist in the literature and to deduce the influence of the properties of one on the other in this mixture which may be of great practical interest in the industrial fields mentioned above. Illustrating this relevance, Zhang et al. [6] examined the effects of ammonium nitrate and sucrose on enzyme activity (phosphoenolpyruvate carboxylase and ribulose-1,5-bisphosphate carboxylase/oxygenase), Nitrogen content and grain mass in wheat. The study concluded that the enzyme activities and the Nitrogen accumulation increased with higher C and N supplies. Grain Nitrogen concentration rose with NH₄NO₃ but decreased with sucrose.

Other authors have studied the different properties and interactions between solvent and solute in the mixture of salt_(aq) − sugar_(aq) [7,8,9,10,11,12,13,14]. However, there is no bibliographic data for the properties and saturation limits of aqueous NH₄NO_3(aq) + D-sucrose_(aq)systems.

In this context, we studied the thermodynamic properties and saturation points of the aqueous NH₄NO₃–sucrose–water system using the hygrometric method designed in our laboratory [10,14,15]. Relative humidity data for the mixtures were measured at 298.15 K for various sucrose concentrations (0.1- 0.3- 0.5- 1.0- 2.0- 3.0 and 4.0 mol·kg⁻¹) and different molalities of NH₄NO₃ (0.10, 0.50, 1.00, 2.00, 3.00, 4.00, 5.00, and 6.00 mol·kg⁻¹).

From the experimental results obtained on relative humidities, we deduced other quantities, such as the water activities and osmotic coefficients of the studied ternary system NH₄NO₃ + D-sucrose + H₂O. Other thermodynamic quantities (solute activity coefficients, excess Gibbs energies, transfer energies, and solute solubility) were calculated using the Pitzer–Simonson–Clegg model [16,17,18]. In addition, the XRPD and ATR-FTIR techniques were employed to identify the crystallized solid phases.

2. Experimental Section

Water activities were obtained from measurements of relative humidity above aqueous solutions containing non-volatile electrolytes. Experiments were performed at 298.15 K (±0.02 K) and at 0.1 MPa (±0.002 MPa).

For preparing the NaCl, NH₄NO₃, and sucrose solutions, we used anhydrous Merck and Fluka products from France (

Table 1. Descriptions of chemical materials used.

Compound	Form	Source	Fraction Purity
NaCl	Anhydrous	Fluka	≥0.995
Sucrose	Anhydrous	Panreac	≥0.990
NH4NO3	Anhydrous	Merck	≥0.995

), and deionized water (its conductivity is about 5.10⁻⁶ S.cm⁻¹). Standard uncertainties of molalities were determined using error propagation techniques with u(m) = 0.01 mol·kg⁻¹ (Appendix A).

Using a camera and diameter measurement software, an average of the hundreds of droplet diameters was determined with a relative uncertainty of approximately u_r = 0.0025. The relative uncertainty of relative humidity measurements was then deduced using error propagation (see Appendix A). Accurate measurement of relative humidity required temperature stability and thermodynamic equilibrium (which is achieved after 1 h, unlike the isopiestic method, which takes a few days). Therefore, the standard uncertainty, calculated at a confidence level of 0.68, depended on the relative humidity h_r (equivalent to a_w) level. More precisely, the standard uncertainties ranged from u(a_w) = 0.0002 for dilute solutions to u(a_w) = 0.005 for concentrated solutions (Appendix A).

Hygrometric Method

The water activity in electrolyte solutions can be evaluated by relative humidity. The relative humidity above the solution was measured using the set of devices described in Figure 1. This method of measuring relative humidity, called the hygrometric method, was designed in our laboratory and had been used for the study of thermodynamic properties of several aqueous systems of electrolytes and aqueous mixtures containing several electrolytes and it has shown its effectiveness in several publications. We provide a brief description of this method and the set of accessories used, which are illustrated in Figure 1.

Reference droplets, usually aqueous NaCl or LiCl, are sprayed onto a fine thread formed by small spiders so as not to distort the spherical shape of the drops. The thread containing the drops is fixed to a support by vacuum grease. Then, this support is placed above a small cup containing a few cubic centimeters of the solution to be studied. A digital microscope equipped with software allows the drops, with diameters of a few hundred microns, to be accurately measured. The cups are then placed in a thermostatically controlled chamber at a regulated temperature below the microscope objective, equipped with an extension on which a camera is fixed, which allows for viewing the captured image of the diameters on a computer screen. The diameters of several drops on the thread are measured several times, and their averages are determined to deduce their growth ratios (Figure 1).

Concept of the hygrometric method:

Assuming thermodynamic equilibrium between the liquid phase of water and its vapor, the activity of water a_w is expressed by:

a_w = P_w/P_0w,

(1)

The practical identification of relative humidities (h_r) of solutions is closely associated with the a_w water activities as expressed by:

h_r = a_w,

(2)

The literature gives the physico-chemical properties for the NaCl(aq) and LiCl(aq) reference solutions. Based on the given data, we deduce the formulation between molar concentration of solutions and the relative humidity, and consequently, the variation in drop diameters of the reference solutions with the surrounding h_r.

Generally, the drop has a spherical appearance with a diameter D, and its volume V is:

V= (4/3)π(D/2)³,

(3)

The volume of the drop changes due to water evaporation from or condensing onto the solution. Consequently, the diameter of the drop increases or decreases during these processes. The growth ratio K expresses the variation in droplet diameter relative to the diameter of the same droplet measured above the reference solution at 0.84.

K = D(a_w)/D(a_ref),

(4)

where D(a_ref) and D(a_w) denote the droplet diameters above the solution at reference a_ref = 0.84 or 0.98 and at unknown a_w, respectively.

The relationship between ratio K and concentration is:

C = n/V,

(5)

where n represents the solute mole number in droplet and C denotes solute molar concentration in this droplet. Consequently, the following relationship is obtained:

K = [C(a_ref)/C(a_w)]^1/3,

(6)

where C(a_w) and C(a_ref) represent concentrations of solutions at unknown relative humidity a_w and at a_ref = 0.84 (or 0.98), respectively. The calibration procedure consists of correlating the droplet diameter D(0.84) or D(0.98) with the relative humidity. A (D(a_w)) above the studied solution is measured. The a_w is then deduced by calculating the ratio K. If the relative humidity is above 0.75, we use the NaCl reference solution. Conversely, the LiCl solution is employed for a_w below 0.75.

The saturation points of the water/D-sucrose/ammonium nitrate (NH₄NO₃) system were determined through the hygrometric technique. This approach involved gradually adding small amounts of sucrose or NH₄NO₃ to pre-prepared D-sucrose-H₂O or NH₄NO₃-H₂O until the diameter no longer varied. We characterized a solid phase using a LABXXRD-6100 Shimadzu powder X-ray diffractometer equipped with Cu radiation, operated at 40 kV and 25 mA. Diffraction patterns were recorded by scanning the samples over a 2θ range of 10° to 70°, with a scanning speed of 2.4° min⁻¹ and a step size of 0.02°.

The FT-IR-ATR spectra of the composites were collected at a resolution of 4 cm⁻¹ using a Jasco FT/IR 4600 spectrometer equipped with a Pro One type attenuated total reflectance (ATR) accessory.

3. Thermodynamic Formwork

3.1. Estimation of Thermodynamic Properties

Within the McMillan–Mayer framework, the total Gibbs free energy of a considered solution consisting of 1 kg of solvent (water, W), a molality m_N of sucrose (N), and a molality m_E of ammonium nitrate (E)–dissociating into ν_E ions–is expressed on the molality scale as [19]:

$$\begin{gathered} G\left(m_N,m_E\right)=G_W^{°}-RT\left[m_N-{\nu }_E{ m}_E\right]+{\mu }_N^{°}{m}_N+ \\ RT{m}_N\ln \left(m_N\right)+{\mu }_E^{°}{ m}_E+RT{ m}_{E}ln\left({ m}_E\right)+G^{EX}\left(m_N^2\right)+ \\ {G}^{EX}(m_E^{3/2}) + 2{\nu }_E{ m}_E{m}_N{g}_{EN}+m_N^2{g}_{NN}+ \\ 3{\nu }_E{m}_E{m}_N^2{g}_{ENN}+3{\nu }_E^2{m}_E^2{m}_N{g}_{EEN} \end{gathered}$$

(7)

where $G_W^{°}$ represents the free energy of 1 kg of pure water, ${\mu }_N^{°}$ and ${\mu }_E^{°}$ denote the standard chemical potentials of sucrose and NH₄NO₃, respectively. $G^{EX}\left(m_N^2\right)$ and $G^{EX}\left(m_E^{3/2}\right)$ correspond to the excess free energies of the binary systems sucrose–water and NH₄NO₃–water. The coefficients g_EN, g_NN, g_ENN, g_ENN, …, are the pair interaction and triplet interaction parameters. The data on the Gibbs energy of transfer of NH₄NO₃ from water to sucrose–water mixtures were used for optimization of these interaction parameters.

The free energy of transfer of NH₄NO₃ from water to sucrose–water mixtures correspond to the difference between the chemical potential of NH₄NO₃ in aqueous solutions of NH₄NO₃–sucrose–water and in pure water. Under conditions of constant temperature and pressure, this relation is expressed as:

$$\begin{array}{c}{\Delta \mathrm{G}}_{\mathrm{tr}}^E\left(\mathrm{W}\to \mathrm{W}+\mathrm{N}\right) = {\left(\mathsf{\partial }\mathrm{G}\left({\mathrm{m}}_{\mathrm{N}}{,\mathrm{m}}_{\mathrm{E}}\right)/\mathsf{\partial }{\mathrm{m}}_{\mathrm{E}}\right)}_{{\mathrm{m}}_{\mathrm{N}}} - {\left(\mathsf{\partial }\mathrm{G}\left({\mathrm{m}}_{\mathrm{E}}\right)/\mathsf{\partial }{\mathrm{m}}_{\mathrm{E}}\right)}_{{\mathrm{m}}_{\mathrm{N}}=0}\\ {=2\mathsf{\nu }}_{\mathrm{E}}{\mathrm{m}}_{\mathrm{N}}{\mathrm{g}}_{\mathrm{EN}}{ + 3\mathsf{\nu }}_{\mathrm{E}}{\mathrm{m}}_{\mathrm{N}}^2{\mathrm{g}}_{\mathrm{ENN}}{ + 6\mathsf{\nu }}_{\mathrm{E}}^2{\mathrm{m}}_{\mathrm{N}}{\mathrm{m}}_{\mathrm{E}}{\mathrm{g}}_{\mathrm{EEN}}+\dots \end{array}$$

(8)

The triplet interaction terms can be neglected for the low-electrolyte and non-electrolyte species concentrations, and the salting coefficients are calculated from the pair interaction parameter [20]. In this present work, the salting coefficient η_s is:

$$RT{\eta }_s=2 {\upsilon }_E g_{EN}$$

(9)

where η_s is the salting constant of NH₄NO₃, expressing the phenomena of salting-out and salting-in. The Gibbs energy of transfer of NH₄NO₃ from water to mixtures of sucrose–water is calculated using the expression [21]. For the Gibbs energy of transfer for electrolyte AN (E = NH₄NO₃):

$$\begin{array}{c}\Delta G_{tr}^E\left(W\to W+N\right)={\mu }_E\left(W,E,N\right)-{\mu }_E\left(W,E\right)\\ ={\upsilon }_E RT\ln \left({\displaystyle \frac{{\gamma }_E\left(W,E,N\right)}{{\gamma }_E^0\left(W,E\right)}}\right)\end{array}$$

(10)

To calculate the excess properties and activity coefficients in the solutions of the studied binary and ternary systems, we used the PSC (Pitzer–Simonson–Clegg) model [16,17,18]. This model, using the mole-fraction scale, was developed to describe highly concentrated aqueous mixtures of ions with symmetrical charges. Within this framework, the excess Gibbs free energy is expressed as the sum of a long-range Debye–Hückel term and short-range interaction terms, allowing for the determination of both solvent and solute activity coefficients. In the present work, the PSC model is employed to calculate osmotic coefficient, activity coefficient, excess Gibbs free energy, and solubility of D-sucrose and NH₄NO₃ in the NH₄NO₃/D-sucrose/water system at 298.15 K. The PSC equations, recognized as one of the most reliable approaches for mixed electrolytes, have been successfully applied in our previous studies to reproduce the non-ideal behavior of ternary electrolyte–D-sucrose–water systems over a wide concentration range. In this model, the excess Gibbs free energy is partitioned into long-range and short-range electrostatic contributions. For the ammonium nitrate (AN)–D-sucrose (2)–water (1) system, the long-range interaction term can be expressed as:

$$\begin{gathered} {\displaystyle \frac{g_{PSC}^{ex}}{RT}}=x_1\left(x_1.W_{1.MX}+x_2.W_{2.MX}\right)+x_1^2\left(x_1.U_{1.MX}+x_2.U_{2.MX}\right)+ \\ {x}_I^2\left(x_1^2{V}_{1.MX}+x_2^2{V}_{2.MX}\right)+ \\ {x}_1{x}_2\left[W_{12}+u_{12}\left(x_1-x_2\right)+x_1(Y_{\mathrm{1,2},MX}^{\left(0\right)}+Y_{\mathrm{1,2},MX}^{\left(1\right)}{\displaystyle \frac{x_I^2}{4}})\right] \end{gathered}$$

(11)

x₁, x₂, and $x_I\left(x_I=1-x_1-x_2\right)$ represent the mole fractions of D-sucrose, water, and ions, respectively. R denotes the universal gas constant, and T is the absolute temperature. The model parameters B_MX, W₁._MX, U₁._MX, and V₁._MXwere optimized using experimental data for the single NH₄NO₃–water system, whereas the interaction parameters w₁₂ and u₁₂ were adjusted based on data from the D-sucrose–water binary system. The parameters W₂._MX, U₂._MX, and V₂._MX describe the interactions between NH₄NO₃ and D-sucrose, while $Y_{1.2.\mathrm{M}\mathrm{X}}^{\left(0\right)}$ and $Y_{1.2.\mathrm{M}\mathrm{X}}^{\left(1\right)}$ are the mixing parameters characterizing the behavior of mixtures containing both ionic and non-ionic species. The long-range Pitzer–Debye–Hückel term is expressed as:

$${\displaystyle \frac{g_{PDH}^{ex}}{RT}}=-\left({\displaystyle \frac{4A_x{I}_x}{\rho }}\right)\ln \left(1+\rho I_x^{{\displaystyle \frac{1}{2}}}\right)+({\displaystyle \frac{x_I^2}{4}})\left[B_{MX}g(\alpha I_x^{{\displaystyle \frac{1}{2}}})\right]$$

(12)

A_x is the Debye–Hückel constant, with a value of 2.917 [11]. The symbol ρ denotes the closest approach parameter, set at 14.0292 [11], and α is the standard value, typically taken as 13 [13]. B_MX represents the Pitzer interaction parameter for the MX ion pair, while I_x refers to the ionic strength $\left(I_x={\displaystyle \frac{1}{2}}\sum _{i=1}{z}_i^2{x}_i\right)$. The function ($g\left(y=\alpha \sqrt{I_x}\right)$) is:

$$g\left(y\right)={\displaystyle \frac{2}{y^2}}\left[1-\left(1+y\right)\mathrm{e}\mathrm{x}\mathrm{p}(-y)\right]$$

(13)

The differentiation of Equations (12) and (13) allows for the determination of mean activity coefficients of solutes and solvents. The water activity coefficient is given by:

$$\begin{array}{l}\ln \left({\gamma }_1\right)={\displaystyle \frac{2\cdot {\mathrm{A}}_{\mathrm{X}}\cdot {\mathrm{I}}_{\mathrm{X}}^{3/2}}{1+\mathrm{\rho }\cdot {\mathrm{I}}_{\mathrm{X}}^{1/2}}}-{\mathrm{I}}_{\mathrm{X}}^2{\mathrm{B}}_{\mathrm{M}\mathrm{X}}\exp \left(-\mathrm{\alpha }\cdot {\mathrm{I}}_{\mathrm{x}}^{1/2}\right)+{\mathrm{x}}_{\mathrm{I}}\left[\left(1-{\mathrm{x}}_1\right)\cdot {\mathrm{W}}_{1,\mathrm{M}\mathrm{X}}-{\mathrm{x}}_2\cdot {\mathrm{W}}_{2,\mathrm{M}\mathrm{X}}\right]\\ +{\mathrm{x}}_{\mathrm{I}}^2\left[\left(1-2\cdot {\mathrm{x}}_1\right)\cdot {\mathrm{U}}_{1,\mathrm{M}\mathrm{X}}-2\cdot {\mathrm{x}}_2\cdot {\mathrm{U}}_{2,\mathrm{M}\mathrm{X}}\right]+{\mathrm{x}}_{\mathrm{I}}^2\left[{\mathrm{x}}_1\left(2-3\cdot {\mathrm{x}}_1\right)\cdot {\mathrm{V}}_{1,\mathrm{M}\mathrm{X}}-3\cdot {\mathrm{x}}_2^2\cdot {\mathrm{V}}_{2,\mathrm{M}\mathrm{X}}\right]\\ +\left[2{\mathrm{x}}_2\cdot {\mathrm{I}}_{\mathrm{x}}\cdot \left(1-2\cdot {\mathrm{x}}_1\right)\cdot {\mathrm{Y}}_{1,2,\mathrm{M}\mathrm{X}}^0+\left({\displaystyle \frac{{\mathrm{x}}_{\mathrm{I}}^3}{4}}\right)\cdot {\mathrm{x}}_2\cdot \left(1-4\cdot {\mathrm{x}}_1\right)\cdot {\mathrm{Y}}_{1,2,\mathrm{M}\mathrm{X}}^1\right]\\ +{\mathrm{x}}_2\cdot \left[\left(1-{\mathrm{x}}_1\right)\cdot {\mathrm{w}}_{12}+\left(2\cdot \left({\mathrm{x}}_1-{\mathrm{x}}_2\right)\cdot \left(1-{\mathrm{x}}_1\right)+{\mathrm{x}}_2\right)\cdot {\mathrm{u}}_{12}\right]\end{array}$$

(14)

The D-sucrose activity coefficient is expressed as

The ionic mean activity coefficient of AN in D-sucrose/Water system is:

$$\begin{array}{l}\ln \left({\mathrm{\gamma }}_2\right)={\displaystyle \frac{2\cdot {\mathrm{A}}_{\mathrm{X}}\cdot {\mathrm{I}}_{\mathrm{X}}^{3/2}}{1+\mathrm{\rho }\cdot {\mathrm{I}}_{\mathrm{X}}^{1/2}}}-{\mathrm{I}}_{\mathrm{X}}^2{\mathrm{B}}_{\mathrm{M}\mathrm{X}}\exp \left(-\mathrm{\alpha }\cdot {\mathrm{I}}_{\mathrm{x}}^{1/2}\right)+{\mathrm{x}}_{\mathrm{I}}\left[\left(1-{\mathrm{x}}_2\right)\cdot {\mathrm{W}}_{2,\mathrm{M}\mathrm{X}}-{\mathrm{x}}_1\cdot {\mathrm{W}}_{1,\mathrm{M}\mathrm{X}}\right]\\ +{\mathrm{x}}_{\mathrm{I}}^2\left[\left(1-2\cdot {\mathrm{x}}_2\right)\cdot {\mathrm{U}}_{2,\mathrm{M}\mathrm{X}}-2\cdot {\mathrm{x}}_1\cdot {\mathrm{U}}_{1,\mathrm{M}\mathrm{X}}\right]+{\mathrm{x}}_{\mathrm{I}}^2\left[{\mathrm{x}}_2\left(2-3\cdot {\mathrm{x}}_2\right)\cdot {\mathrm{V}}_{2,\mathrm{M}\mathrm{X}}-3\cdot {\mathrm{x}}_1^2\cdot {\mathrm{V}}_{1,\mathrm{M}\mathrm{X}}\right]\\ +\left[2{\mathrm{x}}_1\cdot {\mathrm{I}}_{\mathrm{x}}\cdot \left(1-2\cdot {\mathrm{x}}_2\right)\cdot {\mathrm{Y}}_{1,2,\mathrm{M}\mathrm{X}}^0+\left({\displaystyle \frac{{\mathrm{x}}_{\mathrm{I}}^3}{4}}\right)\cdot {\mathrm{x}}_1\cdot \left(1-4\cdot {\mathrm{x}}_2\right)\cdot {\mathrm{Y}}_{1,2,\mathrm{M}\mathrm{X}}^1\right]\\ +{\mathrm{x}}_1\cdot \left[\left(1-{\mathrm{x}}_2\right)\cdot {\mathrm{w}}_{12}+\left(2\cdot \left({\mathrm{x}}_1-{\mathrm{x}}_2\right)\cdot \left(1-{\mathrm{x}}_2\right)-{\mathrm{x}}_1\right)\cdot {\mathrm{u}}_{12}\right]-\left[{\mathrm{w}}_{12}+{\mathrm{u}}_{12}\right]\end{array}$$

(15)

$$\begin{array}{l}\ln \left({\mathrm{\gamma }}_{\pm }\right)=-{\mathrm{A}}_{\mathrm{X}}\left[\left({\displaystyle \frac{2}{\mathrm{\rho }}}\right)\ln \left(1+\mathrm{\rho }\cdot {\mathrm{I}}_{\mathrm{x}}^{1/2}\right)+{\displaystyle \frac{{\mathrm{I}}_{\mathrm{x}}^{1/2}\left(1-2\cdot {\mathrm{I}}_{\mathrm{x}}\right)}{1+\mathrm{\rho }\cdot {\mathrm{I}}_{\mathrm{x}}^{1/2}}}\right]\\ +\left({\displaystyle \frac{{\mathrm{I}}_{\mathrm{x}}}{2}}\right){\mathrm{B}}_{\mathrm{M}\mathrm{X}}\left[\mathrm{g}\left(\mathrm{\alpha }\cdot {\mathrm{I}}_{\mathrm{x}}^{1/2}\right)+\exp \left(-\mathrm{\alpha }\cdot {\mathrm{I}}_{\mathrm{x}}^{1/2}\right)\left(1-{\mathrm{x}}_{\mathrm{I}}\right)\right]\\ +\left(1-{\mathrm{x}}_{\mathrm{I}}\right)\left[{\mathrm{x}}_1\cdot {\mathrm{W}}_{1,\mathrm{M}\mathrm{X}}+{\mathrm{x}}_2\cdot {\mathrm{W}}_{2,\mathrm{M}\mathrm{X}}\right]+2\cdot {\mathrm{x}}_{\mathrm{I}}\left(1-{\mathrm{x}}_{\mathrm{I}}\right)\left[{\mathrm{x}}_1\cdot {\mathrm{U}}_{1,\mathrm{M}\mathrm{X}}+{\mathrm{x}}_2\cdot {\mathrm{U}}_{2,\mathrm{M}\mathrm{X}}\right]\\ +{\mathrm{x}}_{\mathrm{I}}\left(2-3\cdot {\mathrm{x}}_{\mathrm{I}}\right)\left[{\mathrm{x}}_1^2\cdot {\mathrm{V}}_{1,\mathrm{M}\mathrm{X}}+{\mathrm{x}}_2^2\cdot {\mathrm{V}}_{2,\mathrm{M}\mathrm{X}}\right]\\ +{\mathrm{x}}_1\cdot {\mathrm{x}}_2\left[\left(1-4\cdot {\mathrm{I}}_{\mathrm{x}}\right)\cdot {\mathrm{Y}}_{1,2,\mathrm{M}\mathrm{X}}^0+\left(3\cdot {\mathrm{I}}_{\mathrm{x}}^2-\cdot {\mathrm{x}}_{\mathrm{I}}^3\right)\cdot {\mathrm{Y}}_{1,2,\mathrm{M}\mathrm{X}}^1\right]\\ -{\mathrm{x}}_1\cdot {\mathrm{x}}_2\cdot \left[{\mathrm{w}}_{12}+2\cdot \left({\mathrm{x}}_1-{\mathrm{x}}_2\right)\cdot {\mathrm{u}}_{12}\right]-{\mathrm{W}}_{1,\mathrm{M}\mathrm{X}}\end{array}$$

(16)

The excess Gibbs free energy of the ternary water–D-sucrose–ammonium nitrate (AN) is given by:

$${\displaystyle \frac{g^{ex}}{RT}}=\sum _{i=1}{x}_i\ln \left({\gamma }_i\right)=x_1\ln \left({\gamma }_1\right)+x_2\ln \left({\gamma }_2\right)+x_I\ln \left({\gamma }_{\pm }\right)$$

(17)

The total excess Gibbs free energy $G^{ex}$ is given by:

$$G^{ex}={\sum }_i{n}_i{g}^{ex}$$

(18)

where n_i represents the number of moles of component i.

3.2. Estimation of Solubility Data

3.2.1. D-Sucrose Solubility

The D-sucrose solubility ($m_s$) in a mixture containing a salt is determined from its saturation molality ($m_s^0$) in pure water. Therefore, the equilibrium expression can be written as:

$$m_s{\gamma }_s=m_s^0{\gamma }_s^0,$$

(19)

$m_s^0$ and ${\gamma }_s^0$ represent the molality and activity coefficient of D-sucrose at the saturation point in the binary D-sucrose–water system, respectively, with their values at 298 K taken from the literature [22].$m_s$ and ${\gamma }_{\mathrm{s}}$ denote the molality and activity coefficient of D-sucrose in the studied ternary system, respectively.

3.2.2. Electrolyte Solubility

The dissolution of NH₄NO₃ in the ternary system H₂O–D-sucrose–ammonium nitrate (AN) can be represented by:

$$k_{\mathrm{s}\mathrm{p}}=m_{\mathrm{N}{\mathrm{H}}_4^{+}}{\gamma }_{\mathrm{N}{\mathrm{H}}_4^{+}}{m}_{\mathrm{N}{\mathrm{O}}_3^{-}}{\gamma }_{\mathrm{N}{\mathrm{O}}_3^{-}}=m_{\mathrm{N}{\mathrm{H}}_4{\mathrm{N}\mathrm{O}}_3}^2{\gamma }_{\pm ,\mathrm{N}{\mathrm{H}}_4{\mathrm{N}\mathrm{O}}_3}^2,$$

(20)

here ${\gamma }_{\pm \mathrm{N}{\mathrm{H}}_4\mathrm{N}{\mathrm{O}}_3}$ is the mean ionic activity coefficient of NH₄NO₃, while $m_{\mathrm{N}{\mathrm{H}}_4\mathrm{N}{\mathrm{O}}_3}$ denotes its molality. The reported value of the solubility product, k_sp, is given in our earlier work [23].

3.3. Optimization of Model Parameters

The measured data of ϕ (osmotic coefficient) and given mean ionic activity coefficient data for the binary NH₄NO₃–water and D-sucrose–water subsystems, as well as data of ternary water–D-sucrose–NH₄NO₃ system, were utilized to optimize the interaction parameters. The Marquardt algorithm [24] was applied to minimize the objective function, $S_{\varphi }$, given as:

$$S_{\varnothing }={\displaystyle \frac{1}{N_{\varnothing }-p}}{\sum }_{i=1}^{N_{\varnothing }}{({\varnothing }_i^{exp}-{\varnothing }_i^{cal})}^2+{\displaystyle \frac{1}{N_{\gamma }-p}}{\sum }_{i=1}^{N_{\gamma }}{(\ln \left({\gamma }_i^{exp}\right)-\ln \left({\gamma }_i^{cal}\right))}^2$$

(21)

Nϕ and Nγ correspond to the total number of experimental measurements employed, while p is the count of fitted parameters.

4. Results and Discussion

Experimental determinations were carried out to evaluate the a_w and ϕ of sucrose and NH₄NO₃ at various molalities. The molalities investigated for D-sucrose ranged from 0.1 to 4 mol·kg⁻¹, whereas for NH₄NO₃, the tested molalities ranged from 0.1 mol·kg⁻¹ to 6 mol·kg⁻¹. For the ϕ, the uncertainty is about u(ϕ) = 0.009.

We reported in

Table 2. The a_w (water activity) and the ϕ (osmotic coefficient) of NH₄NO₃-sucrose-H₂O from 0.2 to 4 mol·kg⁻¹ of D-sucrose for molality m_NH4NO3 of NH₄NO₃ ranging from 0.1 mol·kg⁻¹ to 6.0 mol·kg⁻¹ at 298.15 K and P = 0.1 MPa.

msucrose	mNH4NO3	aw	ϕ	msucrose	mNH4NO3	aw	ϕ
0.1	0.1	0.9949	0.946	1.0	3.0	0.9019	0.819
0.1	0.5	0.9829	0.870	1.0	4.0	0.8805	0.785
0.1	1.0	0.9691	0.830	1.0	5.0	0.8609	0.756
0.1	2.0	0.9438	0.783	1.0	6.0	0.8425	0.732
0.1	3.0	0.9209	0.750	2.0	0.1	0.9549	1.164
0.1	4.0	0.8999	0.723	2.0	0.5	0.9426	1.094
0.1	5.0	0.8804	0.700	2.0	1.0	0.9285	1.029
0.1	6.0	0.8622	0.680	2.0	2.0	0.9025	0.949
0.3	0.1	0.9912	0.981	2.0	3.0	0.8791	0.894
0.3	0.5	0.9791	0.902	2.0	4.0	0.8576	0.853
0.3	1.0	0.9652	0.855	2.0	5.0	0.8377	0.819
0.3	2.0	0.9398	0.801	2.0	6.0	0.8193	0.790
0.3	3.0	0.9168	0.765	3.0	0.1	0.9295	1.268
0.3	4.0	0.8957	0.737	3.0	0.5	0.9176	1.193
0.3	5.0	0.8761	0.713	3.0	1.0	0.9032	1.130
0.3	6.0	0.8578	0.692	3.0	2.0	0.8776	1.035
0.5	0.1	0.9873	1.014	3.0	3.0	0.8547	0.968
0.5	0.5	0.9752	0.929	3.0	4.0	0.8363	0.902
0.5	1.0	0.9613	0.876	3.0	5.0	0.8175	0.860
0.5	2.0	0.9358	0.818	3.0	6.0	0.8003	0.824
0.5	3.0	0.9126	0.781	4.0	0.1	0.9036	1.340
0.5	4.0	0.8914	0.751	4.0	0.5	0.8916	1.274
0.5	5.0	0.8718	0.725	4.0	1.0	0.8777	1.207
0.5	6.0	0.8536	0.703	4.0	2.0	0.8523	1.109
1.0	0.1	0.9772	1.067	4.0	3.0	0.8293	1.039
1.0	0.5	0.965	0.989	4.0	4.0	0.8084	0.984
1.0	1.0	0.9509	0.932	4.0	5.0	0.7889	0.940
1.0	2.0	0.9252	0.863	4.0	6.0	0.7708	0.903

The reference solution is sodium chloride. Standard uncertainty of molality is u(m) = 0.01 mol·kg⁻¹ and temperature is u(T) = 0.02 K. The relative standard uncertainty of water activity is u(a_w) = 0.0005 for a_w > 0.95 and u(a_w) = 0.002 for a_w < 0.95, and for the osmotic coefficient ϕ is u(ϕ) = 0.0055.

the experimental data of ϕ and a_w. Figure 2 illustrates the water activity versus the square root of ionic strength for the concentrations of D-sucrose. For all D-sucrose contents, water activity decreases with increasing molality. This behavior is commonly observed in aqueous solutions of non-volatile electrolytes. The addition of NH₄NO₃ to the D-sucrose–water system significantly influences its thermodynamic properties. These changes result from the specific interactions between water and D-sucrose, NH₄NO₃ and water, and NH₄NO₃ and D-sucrose, as well as from the ternary interactions among all three components. This implies that the presence of NH₄NO₃ substantially disrupts the hydration structure of the sugar solution. These interactions are governed by the hydration degree of each species, which directly affects the system’s activity.

Figure 3 represents the osmotic coefficients derived from activities of water measurements for the studied Water–D-sucrose–ammonium nitrate (AN) system. The graph indicated that, at constant NH₄NO₃ concentration, this coefficient increased with rising D-sucrose content. However, the curves do not follow a uniform trend as a function of sucrose molality. Additionally, a slight decrease in the osmotic coefficient was observed with increasing NH₄NO₃ concentration.

The activities of water a_w were correlated with the ECA equation (Appendix B) [25], the Lin et al. correlation (Appendix C) [26], and the Lietzke and Stoughton (LS II) equation (Appendix D) [27,28]. The thermodynamic data used to optimize the parameters of ECA and Lin et al. equations were taken from Robinson and Stokes [26] for the binary water–D-sucrose system and from this work and data reported in the literature [29,30] for the water–NH₄NO₃ system. Our experimental data for the ternary system were then employed to determine the mixing coefficients of the Lin et al. and ECA equations. For the ECA correlation, λ = 0.00438 (mol·kg⁻¹)⁻² and δ = 0.000758 (mol·kg⁻¹)⁻³, while for the Lin et al. equation, C₁₂ = 0.0000418. The calculated $a_w$ and ϕ using the ECA and Lin et al. equations show good agreement with the experimental data. In contrast, predictions obtained using the LS II exhibit significant deviations from the measured values. This discrepancy is attributed to the inherent limitation of the LS model, which treats the behavior of the mixture as a simple sum of the behavior of its individual components, thereby neglecting specific interactions present in the ternary system.

To calculate the parameters of the PSC model for the water–sucrose–NH₄NO₃ system, the sum of squared deviations between calculated and experimental osmotic coefficients was minimized. The ionic parameters B_MX, W₁,_MX, U₁,_MX, and V₁,_MX were determined from experimental data on osmotic coefficients (ϕ) and mean ionic activity coefficients (γ _{± AN}) for the water–NH₄NO₃ system [15]. For the water–D-sucrose system, the Margules parameters w₁₂ and u₁₂ were taken from the data in Robinson et al. [21]. The W₂,_MX, U₂,_MX, V₂,_MX, Y ⁽⁰⁾₁,₂,_MX, and Y⁽¹⁾₁,₂,_MX were obtained from measured ϕ in this study. In

Table 3. Binary parameters of the model for NH₄NO₃-H₂O, D-sucrose–H₂O and ternary parameters for H₄NO₃-D-sucrose–H₂O at 298 K and P = 0.1 MPa.

NH4NO3-H2O	mmax (mol·kg−1)	BMX	U1MX	V1MX	W1MX	SDϕ × 03	SDγ × 103
	7.405	−9.9030	−0.7388	0.3779	0.2568	3.397 a	1.65 a
Sucrose–H2O	mmax (mol·kg−1)	w12	u12			SDφ × 102	SDγ × 102
	6.00	−11.013	1.753			1.2124	2.0183
NH4NO3–sucrose-H2O	N a	UNMX	VNMX	WNMX	Y0MNMX	Y1MNMX	SD × 103
	57	2.306	0	−7.317	3.006	0	1.003

^a The number of data points. The SD values are standard deviation of the fit.

, these parameters are given with their standard deviations.

The standard deviations show that a_w and ϕ are more reliable for the sucrose–water and NH₄NO₃–water systems. Our goal is to determine the optimized parameters of the model for the studied system. The results revealed important details about the interactions between different substances of the solution.

The developed model was applied to determine activity coefficients of NH₄NO₃ and sucrose, as well as the excess Gibbs free energy, in the ternary H₂O–sucrose–ammonium nitrate. The corresponding results are presented in

Table 4. Mean activity coefficients γ _± of NH₄NO₃ (aq). Activity coefficients of D-sucrose and excess Gibbs energy (J·mol⁻¹) of NH₄NO₃-D-sucrose (aq) at the temperature 298.15 K and P = 0.1 MPa.

msucrose/mol·kg−1	mNH4NO3/mol·kg−1	γ ± NH4NO3	γsucrose	GE/RT	msucrose/mol·kg−1	mNH4NO3/mol·kg−1	γNH4NO3	γsucrose	GE/RT
0.10	0.10	0.751	0.783	−0.038	1.00	0.10	0.774	0.927	0.073
0.10	0.50	0.586	0.662	−0.373	1.00	0.50	0.605	0.783	−0.224
0.10	1.00	0.504	0.620	−0.959	1.00	1.00	0.520	0.731	−0.763
0.10	2.00	0.419	0.598	−2.416	1.00	2.00	0.432	0.699	−2.128
0.10	3.00	0.368	0.601	−4.112	1.00	3.00	0.379	0.699	−3.734
0.10	4.00	0.332	0.614	−5.974	1.00	4.00	0.341	0.710	−5.510
0.10	5.00	0.304	0.633	−7.964	1.00	5.00	0.312	0.728	−7.416
0.10	6.00	0.281	0.655	−10.058	1.00	6.00	0.289	0.750	−9.429
0.30	0.10	0.756	0.813	−0.027	2.00	0.10	0.799	1.114	0.388
0.30	0.50	0.590	0.687	−0.354	2.00	0.50	0.624	0.939	0.130
0.30	1.00	0.508	0.643	−0.929	2.00	1.00	0.537	0.873	−0.360
0.30	2.00	0.422	0.619	−2.366	2.00	2.00	0.445	0.831	−1.630
0.30	3.00	0.371	0.621	−4.041	2.00	3.00	0.390	0.825	−3.143
0.30	4.00	0.334	0.634	−5.883	2.00	4.00	0.351	0.833	−4.829
0.30	5.00	0.306	0.653	−7.854	2.00	5.00	0.321	0.848	−6.648
0.30	6.00	0.283	0.675	−9.929	2.00	6.00	0.296	0.869	−8.577
0.50	0.10	0.761	0.844	−0.009	4.00	0.10	0.841	1.589	1.607
0.50	0.50	0.594	0.713	−0.327	4.00	0.50	0.658	1.333	1.418
0.50	1.00	0.512	0.667	−0.892	4.00	1.00	0.566	1.232	1.013
0.50	2.00	0.425	0.641	−2.307	4.00	2.00	0.469	1.157	−0.087
0.50	3.00	0.373	0.643	−3.963	4.00	3.00	0.411	1.134	−1.436
0.50	4.00	0.336	0.655	−5.785	4.00	4.00	0.369	1.132	−2.962
0.50	5.00	0.307	0.674	−7.737	4.00	5.00	0.336	1.140	−4.627
0.50	6.00	0.285	0.696	−9.795	4.00	6.00	0.310	1.156	−6.405

, while the graphical representations are shown in Figure 4, Figure 5 and Figure 6.

Figure 4 shows the variation in activity coefficient of ammonium nitrate (AN) in the ternary solution. The curves followed a clear pattern influenced by ion–ion interactions, ion–water molecules hydration, and water molecules–sucrose molecules interactions. In solutions with a high AN concentration and molality of sucrose inferior to 1 mol·kg⁻¹, the ammonium nitrate activity coefficients are very close to that in pure aqueous NH₄NO₃. However, when the D-sucrose concentration exceeds 1 mol·kg⁻¹, the activity coefficient γ_(NH4NO3) decreases as ammonium nitrate concentration increases but shows a slight increase with higher D-sucrose levels. This behavior results from different interactions between ions and molecules of sucrose, and those between molecules of water and molecules of sucrose, which together affect the solution’s thermodynamics.

Figure 5 illustrates the variation in the activity coefficient of sucrose. All curves exhibit a similar trend, depending on the amounts of D-sucrose and ammonium nitrate. The data show that the activity coefficient of sucrose in the ternary solutions is higher than in pure aqueous sucrose solutions, indicating that NH₄NO₃ strongly affects the sucrose activity coefficient and induces a salting-out effect. Moreover, as ammonium nitrate concentration increases, both sucrose activity coefficient and the salting-out effect become more pronounced. The results obtained show that the thermodynamic properties of sucrose are affected by the addition of the salt NH₄NO₃. This is due to different types of interactions such as binary water–sucrose, electrolyte–water and electrolyte–sucrose interactions, as well as ternary interactions between NH₄NO₃ ions, sucrose molecules, and water molecules. Table 4 shows that the addition of NH₄NO₃ to sugar solutions disrupts the hydration structure of the solution with respect to sugar. These interactions are affected by the degree of hydration of each component and, consequently, by the activity coefficient. As the NH₄NO₃ concentration increases, the activity coefficient of sugar in mixed solution decreases, passes through a minimum at about 3 mol·kg⁻¹ of NH₄NO₃, and then increases with the amount of NH₄NO₃ in aqueous solution, all of which were observed at different molalities of sucrose. This behavior of the activity coefficient in the mixture may be due to the ion–solvent and sugar–solvent interactions by hydration and the ion–sugar molecule interaction. Thus, the effect of short-range ion–solvent interactions is important in the low concentration region, and similarly for ion–sucrose in high concentrations. Indeed, the negative deviation from ideality was observed for the salt concentration inferior to 3 mol·kg⁻¹; at this molality, the deviation is greater and the interaction is also greater between the species in solution by hydration. At a molality above 3 mol·kg⁻¹, the activity coefficients of sucrose in the aqueous solution increase along with the increase in its molality and salt concentration, resulting in the phenomenon of salting-out and a decrease in its hydration. This illustrates the important influence of the electrolyte on sucrose.

The values of _G^E/RT g^E were determined across the entire range of molalities studied for NH₄NO₃ and sucrose using the parameters of Equations (14) to (18). Table 4 presents the calculated _G^E/RT g^E for the water–sucrose–AN system at different sucrose concentrations. The results show similar overall trends: as the concentration of D-sucrose increases, the excess Gibbs free energy also increases, suggesting stronger interactions between sucrose molecules and the other system components. Conversely, as ionic strength increases, the excess Gibbs free energy decreases, indicating that ions weaken the interactions of sucrose with other species in the solution. These observations are consistent with the obtained data (Figure 6).

Figure 7 presents the calculated Transfer Gibbs Energies of NH₄NO₃ from water to mixed water–sucrose mixtures at various molalities of sucrose. The data show that this parameter increases with sucrose concentration, indicating that the presence of sucrose makes the transfer progressively less favorable and less spontaneous. For a given sucrose molality, ΔG^tr remains constant across different NH₄NO₃ concentrations, reflecting that once equilibrium is established, the hydration environment of NH₄⁺ and NO₃⁻ ions is not significantly altered by additional salt.

This behavior arises because ammonium and nitrate ions primarily hydrate through electrostatic interactions with water, while sucrose interacts via dipole–dipole interactions and hydrogen bonding. Although sucrose reduces the availability of bulk water, compensating solute–solvent interactions maintain a dynamic equilibrium. Overall, these results highlight that increasing sucrose content destabilizes ammonium nitrate dissolution by reducing its thermodynamic spontaneity.

Table 5. The parameters of interaction relating to the Gibbs energies of transfer of NH₄NO₃ from H₂O to mixed H₂O + D-sucrose and the salting constants η_s at the temperature 298.15 K.

gEN J.kg.mol−2	gEEN J.kg.mol−3	gENN J.kg.mol−3	R2%	ηs
137.89	−7.73561	−5.93842	99.99	0.2225

presents the pair and triplet interaction parameters, along with the salting constant. In this work, we assume that the g_EEN and g_ENN terms are negligible at low solute molalities, and therefore, the salting coefficients are obtained from the pair interaction parameter, g_EN. This approximation is supported by the small fitted values of triplet terms g_ENN (−5.94 J·kg²·mol⁻³) and g_EEN (−7.73 J·kg²·mol⁻³)—compared to the significantly larger value of the pair interaction parameter g_EN g_EN (137.89 J·kg·mol⁻²). This clear disparity shows that the contribution of the triplet terms is negligible at low concentrations of sucrose and NH₄NO₃.

The positive sucrose–NH₄NO₃ interaction values indicate a repulsive effect, demonstrating that NH₄NO₃ induces salting-out of sucrose. Similar behavior has been reported in the literature for sucrose–NaCl [10,11], sucrose–MgCl₂ [13], and sucrose–CaCl₂ [13]. In contrast, KCl exhibits a weak attractive interaction with sucrose, resulting in less pronounced salting-out [14].

The saturation limit of the components in the studied solution is obtained using our hygrometric method described above. Once the solution reaches saturation, both the relative humidity and solute concentration in liquid phase remain constant [12,15]. To identify the solid phases formed, ATR-FTIR spectroscopy and powder X-Ray diffraction (PXRD) analyses were performed. The PXRD patterns of the crystals are shown in Figure 8, while the ATR-FTIR spectra are presented in Figure 9.

As shown in Figure 8a, PXRD analyses of solids crystallized from supersaturated sucrose–water and from water/D-sucrose/AN mixtures at high sucrose concentrations yielded identical diffraction patterns. The PXRD profile of crystalline sucrose (Figure 8a) is in excellent agreement with reference data reported in the literature. Figure 8b presents the PXRD patterns of crystals obtained from supersaturated water/D-sucrose/AN solutions with high ammonium nitrate content. These results confirm that a dry AN crystal is formed during the crystallization of ammonium nitrate, both from pure aqueous solutions and from supersaturated ammonium nitrate–sucrose–water systems at elevated AN concentration. Figure 9 shows the ATR-FTIR spectra of solids recovered from the super-saturated mixtures of ammonium nitrate, sucrose, and water, alongside the spectra of the pure sucrose and the pure ammonium nitrate crystallized from water for comparison.

Figure 10 shows the variation in water activity in the NH₄NO₃–sucrose–H₂O system versus sucrose molality, with a fixed NH₄NO₃ concentration set at 18.7 mol·kg⁻¹. In this Figure, it is observed that water activity remains stable once the saturation limit is reached. The approximate value of this limit, extracted from Figure 10, is around 6.15 mol·kg⁻¹, corresponding to the solubility of sucrose inthe NH₄NO₃–sucrose–H₂O system containing 18.7 mol·kg⁻¹ of NH₄NO₃. The same methodology was applied to determine the sucrose solubility at different NH₄NO₃ molalities and the solubility of NH₄NO₃ at different molalities of sucrose (see Figure 11).

The experimental saturated aqueous solutions of mixed water, sucrose, and NH₄NO₃ are presented in

Table 6. The measured solubility in the NH₄NO₃–sucrose–H₂O system at 298.15 K and P = 0.1 MPa.

msucrose (mol·kg−1)	Solubility of NH4NO3 (mol·kg−1)	Uncertainty	Crystalline Solid
0.00	26.955	0.527	NH4NO3(S)
2.50	25.040	0.415	NH4NO3(S)
2.80	24.828	0.634	NH4NO3(S)
3.10	24.620	0.293	NH4NO3(S)
3.40	24.416	0.591	NH4NO3(S)
Solubility of sucrose (mol·kg−1)	mNH4NO3 (mol·kg−1)	Uncertainty	Crystalline Solid
5.98	0.200	0.120	Sucrose(S)
4.19	18.700	0.108	Sucrose(S)
6.00	0.000	0.152	Sucrose(S)

and also are shown in Figure 12. These results demonstrate good agreement between the measurement values and those calculated by Equations (19) and (20) and the PSC model with a standard deviation of σ_s = 0.02. The same Figure shows that the solubility of sucrose in the NH₄NO₃–sucrose–H₂O decreases slightly as the salt content increases. Also, the solubility of NH₄NO₃ decreases as the concentration of sucrose increases. The literature gives the solubility value for only binary solutions of NH₄NO₃ + H₂O as 25.3 mol·kg⁻¹ and that of sugar + H₂O as 6.2 mol·kg⁻¹. Comparing our experimental results with those in the literature for binary solutions, we observed that RMSE = 1.65 for ammonium nitrate and RMSE = 0.22 for sugar. For the ternary solutions NH₄NO₃ + sucrose + H₂O, there was no data in the literature on the solubility of this ternary and this present study is the first instance that the solubility curve of the mixture NH₄NO₃ + Sugar + H₂O was obtained. The estimate of the experimental error of the solubility of the aqueous ternary mixture of sugar and ammonium nitrate is about 0.4 mol·kg⁻¹ for NH₄NO₃ and 0.12 mol·kg⁻¹ for sugar.

5. Conclusions

The hygrometric technique was employed to measure the thermodynamic properties and saturation points of the ternary NH₄NO₃/D-sucrose/water system at 298.15 K, over a wide range of ammonium nitrate and sucrose concentrations. The measured water activities allow for obtaining osmotic coefficient values ϕ. The solubilities of NH₄NO₃ and D-sucrose were determined over a wide range of NH₄NO₃ and sugar molalities. The solid characterization was carried out using X-ray powder diffraction and spectroscopic analyses.

The unknown parameters of the Pitzer–Simonson–Clegg (PSC) model for the single systems NH₄NO₃–water and sucrose–water were optimized using the osmotic and activity coefficient data reported in the literature, as well as those measured in the present study. The mixed model parameters were further optimized based on the ϕ-data obtained via experiments in the present study. The PSC thermodynamic model was then applied to calculate the activity coefficients and solubilities of sucrose and ammonium nitrate, the free energy of transfer of NH₄NO₃ from water to the water–sucrose mixture, and the excess Gibbs free energy of the D-sucrose-NH₄NO₃ mixture. The resulting data on the free energy of transfer were used to estimate the salting coefficient. The results indicate that the system exhibits increasingly negative deviations from ideality, and that NH₄NO₃ enhances the salting-out effect of sucrose.