Precipitation of Ferrous Oxalate from Ferrous Ammonium Sulfate in Oxalic Acid Solution

: A kinetic study was conducted experimentally for the precipitation of ferrous oxalate. The ferrous oxalate, in the form of dihydrate (FeC 2 O 4 · 2H 2 O), was produced by the acidic dissolution of ferrous ammonium sulfate (Fe(NH 4 ) 2 (SO 4 ) 2 ) in an aqueous solution of oxalic acid, and then precipitated by nucleation and particle growth from supersaturated solution. The effect of the concentration of ferrous ammonium sulfate and oxalic acid as raw materials was investigated on the kinetics of the ferrous oxalate precipitation. Temperature was kept constant at 25 ◦ C. The surface morphology, atomic compositions, and crystal phase were characterized for the ferrous oxalate precipitate collected. As the initial concentration of ferrous ammonium sulfate increased, the initial precipitation of ferrous oxalate occurred faster. The concentration of oxalic acid did not signiﬁcantly affect the rate of precipitation of ferrous oxalate. The experimental behavior of ferrous oxalate precipitation was modeled with ﬁrst-order models of reaction kinetics.


Introduction
Radioactive materials produced in the reactor of a nuclear power plant (NPP) are deposited as corrosion oxide layers inside the primary coolant system. The corrosion oxides, deposited with radionuclides, are mainly metal oxides of iron, nickel, and chromium. It is essential to lower a radioactivity level by removing the corrosion oxides using a decontamination method before decommissioning [1,2]. Among various decontamination methods, chemical decontamination is a main technology that is capable of removing more than 95% of radionuclides generated in the primary coolant system. An extensive survey of the status and prospects of various decontamination and decommissioning technologies has recently been reported [3].
Chemical decontamination, which has been considered the most effective method so far, involves dissolving the corrosion metal oxides using redox reactions [4][5][6][7][8][9]. In order to dissolve magnetite (Fe 3 O 4 ), a typical corrosion oxide, through a reductive reaction, decontamination processes developed using oxalic acid have generated the most interest [6,7]. Recently, Lee and Oh [1] studied the temperature and concentration dependencies of chemical equilibrium for reductive dissolution of magnetite using oxalic acid. Kim et al. [2] reported kinetic experimental data on the reductive dissolution of a synthetic magnetite specimen using an aqueous oxalic acid solution.
The reaction schemes of the reductive dissolution of magnetite by oxalic acid are well known as follows [1]: Oxalic acid, a strong reducing agent, transfers electrons to Fe 3+ ions to be reduced to Fe 2+ ions. The complex formation of the dissolved ferrous ions with the oxalate according to reaction (2) produces ferrous oxalate. Ferrous oxalate exists in the form of dehydrate, as given in reaction (3). When the concentration of ferrous oxalate in the aqueous solution exceeds its solubility in water, the dissolved ferrous oxalate precipitates in the form of small particles. The precipitates thus formed are prone to be deposited inside the NPP coolant system and can be recovered with difficulty.
The purpose of this study is to investigate the kinetic behavior of the precipitation of ferrous oxalate. When Fe 3 O 4 is dissolved by oxalic acid, ferric ions (Fe 2+ ) reduced from ferrous ions (Fe 3+ ) by oxalic acid are combined with oxalate anions to form ferrous oxalate. Since the reduction reaction and crystal growth occur sequentially, the crystal growth and subsequent precipitation of ferrous oxalate occur very slowly and for a long time. This makes it difficult to observe the precipitation behavior of ferrous oxalate. As a result of searching for a material that provides the ferrous ions as a substitute for magnetite, ferrous ammonium sulfate (Fe(NH 4 ) 2 (SO 4 ) 2 ) was considered for this study. Dissolution of ferrous ammonium sulfate by oxalic acid occurs very quickly, and crystal growth and precipitation also occur rapidly, which can be considered suitable for kinetics studies. The precipitation of ferrous oxalate is performed by the chemical reaction in aqueous solution between ferrous ammonium sulfate and oxalic acid: Figure 1 shows the comparison of the chemical equilibrium calculations for two different dissolution systems: (a) the reductive dissolution of a magnetite (Fe 3 O 4 ) in an aqueous solution of oxalic acid; (b) a simple dissolution of ferrous ammonium sulfate (Fe(NH 4 ) 2 (SO 4 ) 2 ) powder in oxalic acid. The calculations were performed using Visual MINTEQ ver. 3.1 software. The profiles of the equilibrium concentrations for the two systems according to the change in the initial concentration of Fe 2+ showed many similarities in the behavior of the concentrations of Fe 2+ and ferrous oxalate complex. The pH changes for the two systems also showed similar behavior. Therefore, in this study, it was decided to use ferrous ammonium sulfate as a raw material for producing ferrous oxalate. After rapidly dissolving ferrous ammonium sulfate powder in oxalic acid, experiments for the precipitation of ferrous oxalate were carried out.
There have been many studies on the formation and precipitation of ferrous oxalate. Müller et al. [10] obtained ferrous oxalate dihydrate (α-FeC 2 O 4 ·2H 2 O) in the form of yellowbrownish single crystal precipitate by dissolving iron in sulfuric acid and reacting it with dimethyl oxalate. Li et al. [11] demonstrated ferrous oxalate precipitation by the chemical reaction between ferrous sulfate and oxalic acid and studied the nucleation and crystal growth kinetics of ferrous oxalate with a turbidity measurement, classical nucleation and particle growth theory. The nucleation rate was presented in relation to the degree of supersaturation, and the grain growth rate was presented as a function of the difference between the particle surface and bulk concentration of ferrous oxalate. Abdel-Ghafar et al. [12][13][14] studied nucleation fundamentals and morphologies of ferrous oxalate dihydrate crystals in deionized water and diluted phosphoric acid media. Ferrous sulfate heptahydrate crystals and oxalic acid were mixed in deionized water and diluted phosphoric acid. The turbidity of the mixture at different time intervals was measured and the induction time was calculated for ferrous oxalate dihydrate crystals. Xiao et al. [15] proposed a liquid-phase oxalate coprecipitation method to produce ferropericlase (Mg 0.8 Fe 0.2 O) by adding oxalic acid to a mixed solution of ferrous sulfate and magnesium chloride.
Processes 2022, 10, x FOR PEER REVIEW 3 of 11 and the induction time was calculated for ferrous oxalate dihydrate crystals. Xiao et al. [15] proposed a liquid-phase oxalate coprecipitation method to produce ferropericlase (Mg0.8Fe0.2O) by adding oxalic acid to a mixed solution of ferrous sulfate and magnesium chloride. Santawaja et al. [16] carried out dissolution experiments on iron oxide highly loaded in an oxalic acid aqueous solution. Highly acidic oxalic acid solution for dissolving the highly loaded iron oxide made it possible to produce an iron oxalates aqueous solution. Although Fe3O4 had an advantage in terms of the dissolution rate, it gave relatively low iron recovery from the solution (80~90%), which was attributed to the unavoidable formation of FeC2O4·2H2O precipitates. Ghasemi et al. [17] developed an equilibrium oxalate precipitation diagram using the solubility product data for several metal oxalates. The precipitation experiments were performed for a synthetic sulfate solution containing the metal cations selected. Selective oxalate precipitation of the metal cations including Fe 2+ was experimentally evaluated.
Many of the studies published in the aforementioned literature are mainly on the precipitation behavior from the point of nucleation and particle growth of supersaturated solution. However, this work is intended to investigate the quantitative characteristics of precipitation behavior according to concentration to control the occurrence of ferrous oxalate precipitate in the oxalic acid solution. The concentrations of ferrous ion and oxalic acid in aqueous solution were considered as experimental parameters. Temperature was kept constant at room temperature (25 °C).

Materials
Ferrous ammonium sulfate hexahydrate (Fe(NH4)2(SO4)2·6H2O: CAS no. 7783-85-9) with 99% purity, purchased from Samchun Chemicals (Pyeongtaek, Republic of Korea), was used as a source that provided ferrous ions. Oxalic acid dihydrate (H2C2O4·2H2O: CAS no. 6153-56-6) with 99.5% purity for dissolving ferrous ammonium sulfate was obtained from Daejung Chemicals and Metals (Siheung, Republic of Korea). In all experiments, deionized water was used to prepare aqueous solutions and analyze samples. Santawaja et al. [16] carried out dissolution experiments on iron oxide highly loaded in an oxalic acid aqueous solution. Highly acidic oxalic acid solution for dissolving the highly loaded iron oxide made it possible to produce an iron oxalates aqueous solution. Although Fe 3 O 4 had an advantage in terms of the dissolution rate, it gave relatively low iron recovery from the solution (80~90%), which was attributed to the unavoidable formation of FeC 2 O 4 ·2H 2 O precipitates. Ghasemi et al. [17] developed an equilibrium oxalate precipitation diagram using the solubility product data for several metal oxalates. The precipitation experiments were performed for a synthetic sulfate solution containing the metal cations selected. Selective oxalate precipitation of the metal cations including Fe 2+ was experimentally evaluated.
Many of the studies published in the aforementioned literature are mainly on the precipitation behavior from the point of nucleation and particle growth of supersaturated solution. However, this work is intended to investigate the quantitative characteristics of precipitation behavior according to concentration to control the occurrence of ferrous oxalate precipitate in the oxalic acid solution. The concentrations of ferrous ion and oxalic acid in aqueous solution were considered as experimental parameters. Temperature was kept constant at room temperature (25 • C).

Characterization and Analysis
The precipitate sample collected from the aqueous solution was dried at 100 • C for about four hours using a muffle furnace. The surface morphology and atomic composition of the precipitate samples were analyzed using a field emission scanning electron microscope (FE-SEM) (Jeol model JSM-7610F Plus) equipped with an energy-dispersive X-ray spectroscope (EDS). For the FE-SEM analysis, platinum coating was applied to the precipitate sample and the accelerating voltage used for imaging was 15 kV. When measuring the atomic composition, an area-scan method was used. The crystal structure and phase of the precipitate sample were identified with X-ray diffraction (XRD) (Bruker model D2 PHASER XE-T) using a Cu-Kα radiation source (λ = 1.54184 Å). The step size was 0.01 • , the scan speed was 2.25 • ·min −1 , and the counting time for each step was 0.2 s. The slit widths were set as follows: Soller slit of 0.04 radian, divergence slit of 1 mm, and matching anti-scatter slit of 3 mm. The diffractograms were recorded from 10 • to 60 • , and matched to reference data in the JCPDS database. The concentration of total Fe dissolved in the solution samples collected during the kinetic experiments of precipitation was determined by an inductively coupled plasma mass spectrometer (ICP-MS) (Perkin Elmer model NexION 2000), which had a detection limit of 1.5 ng·L −1 or less for 56 Fe element.    Figure 3 shows the FE-SEM images for the ferrous oxalate precipitate obtained from our experiments. It can be seen that the ferrous oxalate precipitate is rod-or pillar-shaped. As the initial concentration of ferrous ammonium sulfate increased, the volume and crosssectional area of the precipitate particles increased due to the particle growth.  The experimental procedure is briefly described below. After setting an experimental condition first, the amounts of ferrous ammonium sulfate, oxalic acid, and deionized water were quantified by using precision balances (AND model HM-300 with ±0.1 mg accuracy and AND model GX-1003A with ±1 mg accuracy). After putting the prepared oxalic acid solution and ferrous ammonium sulfate solution into the reactor, the reflux condenser was connected. The temperature of the reactor was set by using a stirring mantle (Misung Scientific model MS-DMSDB634, Yangju, Republic of Korea) and was controlled within ±1 • C. The solution was stirred at a constant rate of 300 rpm during the reaction.

Characteristics of Precipitate
During the kinetic precipitation reaction experiment, samples were taken at fixed time intervals. After taking a sample using a syringe coupled with a submicron filter (Hyundai Micro, Seoul, Republic of Korea) of 0.2 µm polyvinylidene fluoride, it was immediately placed in a 15 mL centrifuge conical tube made of polypropylene (Hyundai Micro, Seoul, Republic of Korea) and diluted to a concentration of 1 mmol·L −1 or less to prevent further precipitation reaction. After separating the solid from the diluted solution using a centrifuge (ALLforLAB model ACF-10, Seoul, Republic of Korea), the supernatant was collected with a filter syringe. The reaction proceeded for a total time of 240 min to obtain kinetic data on the precipitation. As a final step, the concentration of the total Fe present in the sampled solution was determined by the ICP-MS analysis. Table 1 gives the experimental conditions for the precipitation reaction of ferrous oxalate from the ferrous ammonium sulfate in the oxalic acid aqueous solution. The amount of the ferrous ion (Fe 2+ ) varied depending on the change of the concentration of ferrous ammonium sulfate introduced into the reactor. The behavior of precipitated ferrous oxalate was observed by changing the concentrations of oxalic acid. The temperature of the precipitation reaction was kept constant at 25 • C.  Figure 3 shows the FE-SEM images for the ferrous oxalate precipitate obtained from our experiments. It can be seen that the ferrous oxalate precipitate is rod-or pillar-shaped. As the initial concentration of ferrous ammonium sulfate increased, the volume and crosssectional area of the precipitate particles increased due to the particle growth. Figure 4 shows the EDS analysis for the precipitate sample, in which the presence of Fe, C and O is indicated. According to the EDS analysis, the precipitate sample turned out to be a material with the chemical formula of Fe 1.00 C 1.93 O 4.47 . Considering the error of analysis, it can be said that this material gives a chemical formula very close to that of ferrous oxalate (FeC 2 O 4 ).

Effect of the Concentration of Ferrous Ammonium Sulfate and Oxalic Acid on the Kinetics of Ferrous Oxalate Precipitation
A kinetic study of the precipitation of ferrous oxalate was conducted with the experimental conditions of Table 1. The main experimental variables were the concentration of both ferrous ammonium sulfate and oxalic acid. During the precipitation reaction, samples of about 1 mL were taken from the reaction solution at preset reaction times, and the residual Fe content in the solution (based on concentration) was analyzed. Figure 6 shows the residual concentration of ferrous ions (C Fe 2+ ) as the precipitation rate of ferrous oxalate changes according to the initial concentration of ferrous oxalate. The concentration of ferrous ammonium sulfate (C FAS ) varied at 2, 8, and 16 mmol·L −1 . The concentration of oxalic acid (C OA ) and the reaction temperature were fixed at 60 mmol·L −1 and 25 • C, respectively. Four experiments were performed under each experimental condition, and the experimental point at each reaction time is the average of the concentration values for the four experiments. In addition, the error bar showing the standard deviation for each concentration was also inserted. Noticeable changes in kinetics were observed with the change of C FAS . When C FAS was 16 mmol·L −1 , the concentration of ferrous ions remaining in the reaction solution dropped sharply at the beginning of the reaction, and after that, the rate of decrease was gradually reduced and the concentration reached about 1.5 mmol·L −1 , which approached the solubility of ferrous oxalate (0.097 g of FeC 2 O 4 ·2H 2 O/100 mL at 25 • C; data obtained from reference [18]). This shows that the precipitation reaction of ferrous oxalate occurred very rapidly at the beginning of the reaction. Additionally, as the solubility of ferrous oxalate was reached, the precipitation reaction no longer occurred.
A kinetic study of the precipitation of ferrous oxalate was conducted with the experimental conditions of Table 1. The main experimental variables were the concentration of both ferrous ammonium sulfate and oxalic acid. During the precipitation reaction, samples of about 1 mL were taken from the reaction solution at preset reaction times, and the residual Fe content in the solution (based on concentration) was analyzed. Figure 6 shows the residual concentration of ferrous ions ( 2+ ) as the precipitation rate of ferrous oxalate changes according to the initial concentration of ferrous oxalate. The concentration of ferrous ammonium sulfate ( ) varied at 2, 8, and 16 mmol·L⁻ 1 . The concentration of oxalic acid ( ) and the reaction temperature were fixed at 60 mmol·L⁻ 1 and 25 °C, respectively. Four experiments were performed under each experimental condition, and the experimental point at each reaction time is the average of the concentration values for the four experiments. In addition, the error bar showing the standard deviation for each concentration was also inserted. Noticeable changes in kinetics were observed with the change of . When was 16 mmol·L⁻ 1 , the concentration of ferrous ions remaining in the reaction solution dropped sharply at the beginning of the reaction, and after that, the rate of decrease was gradually reduced and the concentration reached about 1.5 mmol·L⁻ 1 , which approached the solubility of ferrous oxalate (0.097 g of FeC2O4·2H2O/100 mL at 25 °C; data obtained from reference [18]). This shows that the precipitation reaction of ferrous oxalate occurred very rapidly at the beginning of the reaction. Additionally, as the solubility of ferrous oxalate was reached, the precipitation reaction no longer occurred.    Figure 7 shows the experimental kinetic data of ferrous oxalate precipitation according to the change of oxalic acid concentration at 25 • C. It gives the residual concentration of ferrous ions remaining in the solution without precipitation as the reaction proceeded. Note that the oxalic acid concentration (C OA ) varied at 40, 60, and 80 mmol·L −1 , while the concentration of ferrous ammonium sulfate (C FAS ) was fixed at 16 mmol·L −1 . Figure 7 represents the effect of oxalic acid concentration on the precipitation rate of ferrous oxalate. It can be seen that the precipitation behavior (the change in the precipitation rate) of ferrous oxalate in the oxalic acid concentration range set in our experiments is almost similar. That is, the concentration of oxalic acid did not significantly affect the precipitation behavior of ferrous oxalate. concentration of ferrous ammonium sulfate ( ) was fixed at 16 mmol·L⁻ 1 . Figure 7 represents the effect of oxalic acid concentration on the precipitation rate of ferrous oxalate. It can be seen that the precipitation behavior (the change in the precipitation rate) of ferrous oxalate in the oxalic acid concentration range set in our experiments is almost similar. That is, the concentration of oxalic acid did not significantly affect the precipitation behavior of ferrous oxalate.

Modeling of Ferrous Oxalate Precipitation Behavior
The supersaturated aqueous ferrous oxalate solution precipitates until the ferrous oxalate concentration reaches the solubility in aqueous phase. Therefore, the precipitation behavior of supersaturated ferrous oxalate can be simulated with a model for decreasing the residual Fe 2+ concentration. Two models for the residual Fe 2+ concentration change were adopted in this work. Model 1 is a simple first-order reaction model proportional to the residual Fe 2+ concentration, and model 2 is a model in which a reaction rate constant changes during the reaction. The residual Fe 2+ concentration in the solution as a function of time is defined as follows: where Fe 2+ ( ) is the residual Fe 2+ concentration in the reaction solution and FeC 2 O 4 * is a solubility of ferrous oxalate that is a function of oxalic acid concentration and temperature.

Modeling of Ferrous Oxalate Precipitation Behavior
The supersaturated aqueous ferrous oxalate solution precipitates until the ferrous oxalate concentration reaches the solubility in aqueous phase. Therefore, the precipitation behavior of supersaturated ferrous oxalate can be simulated with a model for decreasing the residual Fe 2+ concentration. Two models for the residual Fe 2+ concentration change were adopted in this work. Model 1 is a simple first-order reaction model proportional to the residual Fe 2+ concentration, and model 2 is a model in which a reaction rate constant changes during the reaction. The residual Fe 2+ concentration in the solution as a function of time is defined as follows: where C Fe 2+ (t) is the residual Fe 2+ concentration in the reaction solution and C * FeC 2 O 4 is a solubility of ferrous oxalate that is a function of oxalic acid concentration and temperature.
The model 1 can be expressed as follows: with an initial condition of C Fe 2+ (0) = C 0,Fe 2+ − C * FeC 2 O 4 . In Equation (6), k is a first-order reaction constant. Solving Equation (6) gives the following solution: Meanwhile, model 2 can be expressed as follows: Processes 2022, 10, 2420 9 of 11 where k f and k s are reaction constants for the two-parameter model. Solving Equation (8) gives the following solution: In Equation (7), the first-order reaction constant, h, represents the half-life time of the initial Fe 2+ concentration, C 0,Fe 2+ . Additionally, h f and h s in Equation (9) represent the halflife times of (1 − w)C 0,Fe 2+ subject to a fast precipitation fraction and wC 0,Fe 2+ subject to a slow precipitation fraction, respectively. The model parameters (h, h f , h s ) were obtained by minimizing the sum of the square value (F) of the difference between the experimental value and the model calculation value as shown below: Here, w, a weighting factor, was selected as a value that minimizes the root mean square error (RMSE) by arbitrarily setting 0.1, 0.2, 0.3, and 0.4.
The experimental results of the ferrous oxalate precipitation behavior in Figure 6 were simulated by the model Equations (7) and (9), and the results are summarized in Table 2. From the above results, it can be seen that both the model constants are the same, except when the initial concentration is low close to the solubility, so that both can be simulated by the simple first-order model Equation (7).  Figure 8 shows the comparison between the experimental results and the modeling results for the ferrous oxalate precipitation. From the modeling results, it can be seen that the precipitation behavior for most of the supersaturated ferrous oxalate solution can be expressed as the first-order reaction formula such as model 1. However, the initial concentration of 1.5 mmol·L −1 was very close to the solubility, so it was a very small precipitate that was difficult to measure the change in concentration in. In addition, since the coefficient of determination of the model equation approaches 99%, this firstorder reaction model equation was considered to be able to simulate the ferrous oxalate precipitation behavior very accurately. Processes 2022, 10, x FOR PEER REVIEW 10 of 11

Conclusions
Through an experimental kinetic study on the ferrous oxalate precipitation depending on the concentrations of both oxalic acid and ferrous ammonium sulfate, the following conclusions were obtained in the experimental range: a. The higher the initial ferrous concentration, the faster precipitation, due to the more precipitate particles which supplied particle growth sites. b. The change in oxalic acid concentration did not significantly affect the precipitation rate. c. The ferrous oxalate precipitation behavior could be modeled with a first-order response of the residual ferrous concentration.

Conflicts of Interest:
The authors declare no conflicts of interest.

Conclusions
Through an experimental kinetic study on the ferrous oxalate precipitation depending on the concentrations of both oxalic acid and ferrous ammonium sulfate, the following conclusions were obtained in the experimental range: a.
The higher the initial ferrous concentration, the faster precipitation, due to the more precipitate particles which supplied particle growth sites. b.
The change in oxalic acid concentration did not significantly affect the precipitation rate. c.
The ferrous oxalate precipitation behavior could be modeled with a first-order response of the residual ferrous concentration.