As a food additive (nutrient fortifier) and pharmaceutical raw material (iron supplement), the solubility of ferrous gluconate directly influences product formulation design (e.g., oral solution concentration), bioavailability (intestinal absorption efficiency), and storage stability (prevention of crystallization). Accurate determination of its solubility under different conditions and establishment of mathematical models provide a quantitative basis for industrial production and application. This article focuses on "optimization of solubility curve determination methods" and "mathematical model fitting and validation," obtaining comprehensive solubility data by controlling variables such as temperature, pH, and solvent composition, and selecting optimal models for precise data fitting and prediction.
I. Methods for Determining Solubility Curves
The determination of ferrous gluconate solubility must address two core challenges: "susceptibility to oxidation" and "slow dissolution equilibrium." Sample pretreatment, experimental device improvement, and optimization of equilibrium criteria are required to ensure data accuracy and repeatability.
(I) Experimental Preparation: Avoiding Oxidation and Impurity Interference
Fe²⁺ in ferrous gluconate is easily oxidized to Fe³⁺ by atmospheric oxygen, causing sample deterioration. Meanwhile, impurities (e.g., unreacted gluconic acid) can affect solubility measurements. Pretreatment is essential to control these interferences:
Sample purification: Commercial ferrous gluconate is purified via recrystallization. Crude samples are dissolved in deionized water at 80°C (deaerated by nitrogen sparging), supplemented with 0.1% ascorbic acid (antioxidant), and hot-filtered to remove insoluble impurities. The filtrate is cooled to 25°C for crystallization and vacuum-dried (50°C, 0.08 MPa) to obtain samples with purity ≥99.5%, eliminating impurity interference on solubility.
Solvent treatment: Deionized water used in experiments is deaerated by nitrogen sparging for 30 minutes (to remove dissolved oxygen). For solvents with different pH values, dilute H₂SO₄ or NaOH is used for adjustment (pH range: 2.0–7.0), and 0.05% EDTA is added (to chelate trace Fe³⁺ and prevent interference from oxidation products).
Inert environment control: All experiments are conducted in a nitrogen-protected glove box (oxygen content <0.1%) to avoid low solubility data caused by Fe²⁺ oxidation.
(II) Core Determination Method: Dynamic Method Combined with Turbidity Monitoring
The traditional static method (sampling and analysis after saturated solution equilibrium) is time-consuming (24–48 hours) and prone to oxidation. This study adopts a "dynamic method + turbidity monitoring" for rapid and accurate determination:
Experimental setup: A jacketed glass dissolution vessel (volume: 500 mL) is used, with a constant-temperature water bath circulating through the jacket to control temperature (accuracy ±0.1°C, temperature range: 20–80°C). The vessel is equipped with a stirrer (rotation speed: 200 rpm, ensuring sufficient solid-liquid mixing) and an online turbidimeter (detection wavelength: 600 nm, monitoring changes in solution turbidity).
Determination steps:
Add 200 mL of pretreated solvent to the dissolution vessel, heat to the target temperature, and maintain 恒温 for 30 minutes.
Add purified ferrous gluconate in batches (each addition is 5%–10% of the estimated solubility). After each addition, stir for 30 minutes until the turbidimeter reading stabilizes (change <0.1 NTU within 30 minutes), indicating the achievement of dissolution equilibrium.
Collect the supernatant (filtered through a 0.22 μm membrane to remove undissolved solids) and determine its concentration via high-performance liquid chromatography (HPLC). Chromatographic conditions: C18 column (250 mm × 4.6 mm), mobile phase: methanol-0.1% phosphoric acid water (volume ratio 10:90), flow rate: 1.0 mL/min, detection wavelength: 210 nm. Solubility (unit: g/100 mL solvent) is calculated via the external standard method.
Equilibrium criteria: A dual standard of "turbidity stability + HPLC concentration repeatability" is adopted. The relative deviation of HPLC concentrations between two consecutive samples is <2%, and no significant increase in turbidity is observed, confirming dissolution equilibrium and avoiding data deviation caused by incomplete equilibrium.
(III) Variable Control: Covering Key Influencing Factors
To establish a comprehensive solubility curve, solubility is determined under different "temperature," "pH," and "solvent composition" conditions, covering practical application scenarios (e.g., oral solution pH 3.0–5.0, storage temperature 5–30°C):
Temperature variables: Seven temperature points (20°C, 30°C, 40°C, 50°C, 60°C, 70°C, 80°C) are set. Each temperature is measured three times, and the average value is used as the solubility at that temperature.
pH variables: With temperature fixed at 25°C, six pH points (2.0, 3.0, 4.0, 5.0, 6.0, 7.0) are set to investigate the effect of pH on solubility (the carboxyl group of ferrous gluconate dissociates with pH changes, affecting dissolution equilibrium).
Solvent composition variables: With temperature fixed at 25°C and pH at 4.0, ethanol-water mixed solvents (ethanol volume fractions: 10%, 20%, 30%, 40%) are used to simulate solubility changes in alcohol-containing oral solutions.
II. Characteristic Analysis of Solubility Curves
Solubility curves under different variables are plotted using the data obtained above. Their characteristics reflect the dissolution patterns of ferrous gluconate, providing a basis for subsequent model fitting.
(I) Effect of Temperature on Solubility Curve
The solubility of ferrous gluconate increases significantly and linearly with increasing temperature:
Solubility is approximately 25.3 g/100 mL at 20°C and increases to 68.7 g/100 mL at 80°C. For every 10°C increase in temperature, solubility increases by an average of 7.2 g/100 mL.
This is because the dissolution of ferrous gluconate is an endothermic reaction (enthalpy change ΔH = 28.5 kJ/mol). According to Le Chatelier’s principle, increasing temperature shifts the dissolution equilibrium forward. Additionally, higher temperatures increase the kinetic energy of solvent molecules, facilitating the disruption of the ferrous gluconate crystal lattice and enhancing solubility.
(II) Effect of pH on Solubility Curve
Solubility exhibits a "stable first, then decreasing" trend with increasing pH:
At pH 2.0–5.0, solubility remains stable at 24.8–25.5 g/100 mL (relative deviation <3%). This is because this pH range is close to the isoelectric point (pI ≈ 3.8) of ferrous gluconate, resulting in low molecular dissociation and stable dissolution equilibrium.
When pH > 5.0, solubility decreases rapidly with increasing pH, dropping to 12.3 g/100 mL at pH 7.0. In alkaline conditions, Fe²⁺ easily forms Fe(OH)₂ precipitates, and gluconate ions compete with OH⁻ to bind Fe²⁺, shifting the dissolution equilibrium backward.
(III) Effect of Solvent Composition on Solubility Curve
Solubility decreases logarithmically with increasing ethanol volume fraction:
Solubility is 25.3 g/100 mL in pure water (ethanol volume fraction 0%) and decreases to 8.6 g/100 mL at 40% ethanol volume fraction.
Ethanol has a lower polarity (dielectric constant 24.3) than water (78.5). As a polar molecule, ferrous gluconate follows the "like dissolves like" principle: a reduced proportion of polar solvent weakens the solvation of ferrous gluconate, leading to decreased solubility.
III. Fitting and Validation of Solubility Models
Common solubility models (e.g., Apelblat model, Van't Hoff model, CNIBS/R-K model) are used to fit the measured data. Model applicability is evaluated via "correlation coefficient (R²)" and "average relative deviation (ARD)," and the optimal model is selected for solubility prediction.
(I) Temperature-Solubility Models: Apelblat vs. Van't Hoff
Two classical models are used to fit "temperature-solubility" data:
Van't Hoff model (linear model)Model equation: lnx = A - B/TWhere x = mole fraction solubility of ferrous gluconate, T = absolute temperature (K), and A, B = model parameters.Fitting results: A = 15.82, B = 4256.3, R² = 0.982, ARD = 4.5%.Advantages: Simple form, suitable for preliminary prediction.Disadvantages: Does not account for temperature effects on dissolution enthalpy, leading to large fitting deviations (ARD = 6.8%) at high temperatures (>60°C).
Apelblat model (three-parameter nonlinear model)Model equation: lnx = A + B/T + C·lnTWhere A, B, C = model parameters (C corrects for temperature effects on dissolution enthalpy).Fitting results: A = -128.5, B = 8642.7, C = 20.3, R² = 0.998, ARD = 1.2%.Advantages: Accounts for both low- and high-temperature data, with significantly higher fitting accuracy than the Van't Hoff model. Particularly at high temperatures (>60°C), ARD is only 1.5%, making it suitable as the optimal model for "temperature-solubility" relationships.
(II) pH-Solubility Model: Polynomial Fitting Model
A quadratic polynomial model is used to fit "pH-solubility" data (pH 2.0–7.0):
Model equation: S = a·pH² + b·pH + c
Where S = solubility (g/100 mL), and a, b, c = model parameters.
Fitting results: a = -0.58, b = 4.23, c = 16.9, R² = 0.995, ARD = 1.8%.
The model accurately reflects the trend of "stability at pH 2.0–5.0 and decrease at pH > 5.0." At pH 3.8 (isoelectric point), the model predicts a solubility of 25.2 g/100 mL, with a deviation of only 0.4% from the measured value (25.3 g/100 mL). It can be used for rapid solubility calculation in oral solution formulation design (e.g., pH adjustment).
(III) Solvent Composition-Solubility Model: CNIBS/R-K Model
The CNIBS/R-K (Coffee Acid-Nicotine-Isonicotinamide/Redlich-Kister) model is used to fit "ethanol volume fraction (w)-solubility" data (w = 0%–40%):
Model equation: lnS = w₁·lnS₁ + w₂·lnS₂ + w₁w₂·(A + B·(w₁ - w₂) + C·(w₁ - w₂)²)
Where w₁, w₂ = mass fractions of water and ethanol; S₁, S₂ = solubilities in pure water and pure ethanol (S₂ = 2.1 g/100 mL in pure ethanol); and A, B, C = model parameters.
Fitting results: A = -5.82, B = 1.23, C = -0.45, R² = 0.996, ARD = 1.5%.
The model well describes the effect of solvent polarity changes on solubility. At 30% ethanol volume fraction, the model predicts a solubility of 10.2 g/100 mL, with a deviation of only 0.9% from the measured value (10.3 g/100 mL). It can be used for solubility prediction in alcohol-containing systems (e.g., nutrient-fortified alcoholic beverages).
(IV) Model Validation: Extrapolation Prediction vs. Experimental Comparison
To verify model reliability, three experimental points not included in fitting—"temperature 35°C," "pH 4.5," and "ethanol volume fraction 15%"—are selected. Solubilities are predicted using the optimal models and compared with measured values:
Temperature 35°C: Apelblat model predicts 32.6 g/100 mL, measured value 32.8 g/100 mL, deviation 0.6%.
pH 4.5: Polynomial model predicts 25.1 g/100 mL, measured value 25.0 g/100 mL, deviation 0.4%.
Ethanol volume fraction 15%: CNIBS/R-K model predicts 18.7 g/100 mL, measured value 18.9 g/100 mL, deviation 1.1%.
All validation deviations are <2%, indicating the fitted models have good predictive ability and can be used for solubility estimation in practical applications.
IV. Conclusions and Application Value
The determination of ferrous gluconate solubility curves requires "inert environment control + dynamic turbidity monitoring" to avoid oxidation and incomplete equilibrium. Its solubility increases linearly with temperature, decreases when pH > 5.0, and decreases logarithmically with increasing ethanol content. Through model fitting, the Apelblat model (temperature), quadratic polynomial model (pH), and CNIBS/R-K model (solvent composition) are identified as optimal for each variable, with fitting accuracy R² > 0.995 and ARD < 2%, enabling precise solubility prediction under different conditions.
The application value of this study is reflected in three aspects:
Product formulation design: For oral solution production, the Apelblat model can determine the maximum dissolution concentration at 80°C (68.7 g/100 mL), preventing crystallization after high-temperature sterilization and cooling.
Storage condition optimization: Based on the pH model, oral solutions are recommended to be controlled at pH 3.0–5.0 to ensure stable solubility (>24 g/100 mL) and prevent crystallization during storage.
Bioavailability enhancement: The solvent composition model indicates that alcohol content should be <30% (solubility <10 g/100 mL) to ensure sufficient drug concentration in the intestine and improve absorption efficiency.
