3.2. Supersaturation Profiles, Reactive Crystallization Images and CLD
The supersaturation as a function of time, S, was determined based on the concentration of the ions K+, Mg2+, Cl−, and SO42−. Assuming that the Mg2+ and Cl− concentrations in the solution remain constant but K+ and SO42− concentrations vary due to the formation of K2SO4(s) crystals, the concentrations of K+ and SO42− were obtained by subtracting those integrated into K2SO4(s) crystals from those entering the reaction. The molal concentrations of obtained were used to determine the activity coefficients and S, according to Equation (3).
Figure 2 shows the trajectory of S starting from the initial supersaturation
S0, images of solution/crystals captured by Crystalline PV, and the respective CLD as a function of time during the reactive crystallization of K
2SO
4 at 5 °C. The
S0 value in the reaction mixture was 5.15, showing a strong supersaturation as a precondition to initiate nucleation and growth. After an induction time of ~5 min where the reaction solution reached thermal equilibrium and became homogenized, the supersaturation decreased as a result of crystallization, reaching a minimum value of
S = 2.30 at 20 min. The Crystalline PV system detected at 1.44 and 5 min of reaction (
Figure 2a,b) embryo clouds and tiny pseudohexagonal crystals due to nucleation and growth. At the same time, after ~5 min, a low CLD in terms of crystals counted by the FBRM per s <2.5 crystals/s with a chord length of 20–30 microns and a rather unimodal CLD is determined. Once the driving force has been exhausted, after 20 min, the supersaturation remains constant and reactive crystallization is finished, which is corroborated by chemical analysis of the K
+, Mg
2+, Cl
− and SO
42− shown in
Figure S9 (SI). At ~10 min,
Figure 2c shows growing K
2SO
4 crystals, separated from each other but overlapping in some parts with defined vertices, maintaining the pseudohexagonal and orthorhombic morphology. The crystal count reached 25 crystals/s with a chord length between 30–40 microns. A few particles between 2 and 5 microns having a crystal count of 8 crystals/s also appear (
Figure 2f), thus leading to a bimodal CLD.
With the time at 20 min (
Figure 2d), the crystals grow with a considerable presence of fines whose crystal count reached 42.5 crystals/s in the size range of 30–50 microns and 15 crystals/s in the range of 2–3 microns, keeping the bimodal CLD. Finally, at 60 min (
Figure 2e), the pulp contains a considerable amount of fines that obstruct the image viewer of the Crystalline PV equipment; the crystal count reaches 70 crystals/s in the size range of 40–50 microns and 30 crystals/s in the 2–3 microns size range shown in
Figure 2f. As seen, the counts of CLD increase with time, specifying product crystals with a bimodal CLD, which is attributed to breakage, attrition by friction or collision of crystals, or crystals with the propeller blades. Thus, crystal count increased but not growth.
At a reactive crystallization temperature of 25 °C, an initial supersaturation of
S0 = 3.84 is generated (
Figure 3), which remains constant for ~10 min and then decreases slowly, reaching the final S of 2.53 at 30 min. This implies that the supersaturation was consumed in 20 min and the crystallization process was stopped.
Figure 3a,b show the presence of very tiny crystals with a crystal count <2.5 crystals/s in the chord length range of 10–40 microns (
Figure 3e). After 30 min (
Figure 3c), it is impossible to identify the crystals’ morphology due to their tiny sizes, with a crystal count of 20 crystals/s in a chord length range of 20–30 microns and 15 crystals/s with the size of 9–10 microns. After 60 min (
Figure 3d), many tiny crystals are observed with a crystal count of 30 crystals/s between 30–40 microns size and 18.5 crystals/s between 3–6 microns size. Thus, again a bimodal CLD was developed as a result of the generation of fine particles from secondary nucleation mechanisms.
Comparing the reactive crystallization processes of K
2SO
4 at the two temperatures of 5 and 25 °C, as expected, the initial degree of supersaturation is greater at lower temperature and vice versa. As a result, for higher initial supersaturation, de-supersaturation and induction times were shorter, and crystal growth was enhanced, leading to a defined morphology, and a higher crystal count was reached with bimodal CLD. As the crystal images provide qualitative proof of the crystallization progress, in this report, the moment data collected by the FBRM probe were considered to determine the crystallization kinetics. The supersaturation profiles for all reaction temperatures used are compiled in
Figure S10 (SI). They confirm the reaction crystallization trends discussed above.
The initial supersaturations
S0 generated by reactive crystallization in the reciprocal system are large with values of S
0 = 5.15, 4.13, 3.84, 3.54, and 3.24 at 5, 15, 25, 35, and 45 °C, respectively. In contrast, the S
0- values used in solution crystallization by cooling methods for the binary K
2SO
4-H
2O system are usually lower. For example, Bari and Pandit [
24] worked in a range of S
0 = 1.07–1.11 when cooling a saturated solution of K
2SO
4-H
2O from 60 °C to a temperature between 53–49 °C. Gougazeh et al. [
25] worked with
S ≅ 0.00913 at 50 °C and Lyczko et al. [
51] with
S0 = 1.31 at 30 °C. Mohamed et al. [
30] used an initial supersaturation of S
0 = 1.07 for a controlled cooling in a temperature range of 63.5 to 24.6 °C. Furthermore, Garside and Tavare [
52] applied S
0 = 1.09, Mullin and Gaska [
27] worked with S ≅ 1.07 at 20 °C, and Garside et al. [
53] with S = 1.15 at 30 °C. On the other hand, in reactive crystallization processes of sparingly soluble salts, the S
0 generated is much larger than for the reciprocal salt system studied in this work. Therefore, crystal nucleation and growth events occur within a few seconds of the induction time. Lu et al. [
32] report an initial supersaturation of
S0 = 1596, with an induction time of 26 s at 15 °C to crystallize Mg(OH)
2; Taguchi et al. [
31] an S
0 = 70 with an induction time of 60 s to crystallize BaSO
4, Steyer C. [
54] an
S0 = 500 to crystallize BaSO
4, and Mignon et al. [
33] values of S
0 = 771 and 960 to crystallize SrSO
4 and CaCO
3, respectively. This results from the fact that sparingly soluble salts exhibit minimal values of the thermodynamic equilibrium constant (K
SP). For example, the K
SP of BaSO
4 is 2.88 × 10
−10 (mol/kg)
2 at 25 °C [
31], compared with a K
SP of 0.0162 (mol/kg H
2O)
3 for K
2SO
4 according to the solubility data [
45].
Figure 4 presents the CLDs of K
2SO
4 crystals after 5 min and the final product after 60 min at the different reaction temperatures investigated. Usually, for an industrial mass crystallization product, a narrow and unimodal CLD, as far as possible free of fine crystals, is targeted. However, in the experiments, a unimodal CLD is only observed at the beginning after 5 min of reaction (
Figure 4a), where crystal counts are very low (1 to 4 crystals/s) with crystal sizes between 10–100 μm and fines <10 μm, which is found for all the isotherms studied. Likewise,
Figure 4b shows the CLDs of the final K
2SO
4 product with a bimodal distribution. The region of fines of size <10 μm is specified by crystal counts <2 crystals/s at 45 °C, 30 crystals/s at 5 °C, and 10–15 crystals/s for isotherms in-between. In the coarse region, the size of the crystals is 15–200 μm with crystal counts of 5 crystals/s at 45 °C, 70 crystals/s at 5 °C, and 25–35 crystals/s for isotherms between 15 and 35 °C. The bimodal distribution is attributed to the effect of secondary nucleation due to the suspension density or breakage and attrition of the crystals. The difference between
Figure 4a,b is related to uncontrolled depletion of supersaturation during isothermal reactive crystallization. Therefore, supersaturation is independent and predominant in reactive crystallization as the crystals simultaneously grow while others are born due to the motive force. As a result, the final CLD of the K
2SO
4 product is not narrow and thus not favourable for subsequent downstream processes such as filtration, drying, storage and transport, and the resistance to relative humidity as well due to the presence of fines <10 μm that can generate lumps, dust release, moisture absorption, etc.
In this work, the maximum K
2SO
4 crystal size obtained according to the semiquantitative analysis of CLD was between 70 and 80 µm at 5 °C, which is small compared with crystallization from pure K
2SO
4-H
2O solutions. For example, Bari and Pandit [
24] reported an average size of 286 μm via the isothermal method for low supersaturation and Bari et al. [
22] an average size of 250 μm by the cooling method. Jones et al. [
55] received an average size of 500 μm without fines using seeding and cooling, while via salting out with acetone, they obtained crystal sizes <350 μm with a greater presence of fines and agglomerates. It is concluded that reactive crystallization of K
2SO
4 from the quaternary K
+, Mg
2+, Cl
−, and SO
42−system provides smaller crystals as obtained in K
2SO
4-H
2O systems, which is due to the reaction-inherent high degree of initial local supersaturation.
3.3. Primary Nucleation Rate Bb
To determine the nucleation rate, the CLD data have been converted to CLD counts square-weighted as a function of time for each reaction isotherm. The results transformed to moment data of the order 0, 1, 2, and 3 by Equation (10) are shown in
Figures S2–S5 (SI).
In the reactive crystallization of K
2SO
4, primary nucleation (
Bb) and secondary nucleation (
B) occur, while
Bb results from the high supersaturation generated. The nucleation rate (
B) of K
2SO
4 was determined by Equation (11). B
b is related with
S0 since it has been obtained from the thermodynamic approach when considering the activities of the species K
+ and SO
42− in the multicomponent system K
+, Mg
2+/Cl
−, SO
42−//H
2O. To determine the kinetic order and rate constant parameters of
Bb, the nucleation rates obtained for each S
0 were averaged and then fitted to Equation (12) presented in
Figure 5. The fitting parameters derived are
b = 3.61 and
kb = 83.68 [#/min·kg H
2O] with a coefficient of determination R
2 = 0.89, verifying that the behaviour of
Bb is proportional to
S0.
The primary nucleation order obtained for the reactive crystallization of K
2SO
4 is lower than found for the single solute system K
2SO
4-H
2O, as reported by Bari et al. [
22], with
b = 6.5 for the isothermal method (t
ind). Nemdili et al. [
21] reported b = 4.10 and 4.68 when measuring MSZW and t
ind, respectively. Additionally, Bari and Pandit [
24] reported b = 6.5 and 5.73 when determining MSZW via the conventional method and sonocrystallization, respectively. There,
b is a physical parameter that describes the dependence of the MSZW on the cooling rate regardless of the method used. In contrast, high values for the primary nucleation order are observed in reactive crystallization kinetics of sparingly soluble salts, such as SrSO
4 and CaCO
3 with
b = 36.0 and 12.0, respectively, reported by Mignon et al. [
33]. In this report, the empirical value of
b = 3.61 for the reactive crystallization of K
2SO
4 has no relation to the MSZW but classifies into the range established by the value of the primary nucleation order for inorganic compounds obtained by cooling, which, as a general rule, are found between 0.98 and 8.3 [
23].
3.4. Secondary Nucleation Rate B
The profiles of the nucleation rates B during reactive crystallization of K
2SO
4 at different temperatures are shown in
Figure 6. At 5 °C (with
S0 = 5.15), B decreases from a maximum of 2.68 × 10
6 (#/min·kgH
2O) at 3 min to a minimum of 8.35 × 10
5 (#/min·kgH
2O) at 20 min, which implies the consumption of supersaturation due to spontaneous nucleation. The decrease in B is attributed to the presence of crystals within the solution since the growth of crystals consumes the supersaturation, the concentration resulting from the suspension density is higher, which is also observed for the 15 °C isotherms. However, at 25 °C (with
S0 = 3.84) B starts with 7.7 × 10
4 (#/min·kgH
2O) at 10 min reaching a maximum of 8 × 10
5 (#/min·kgH
2O) at ~30 min of crystallization. Clearly B increases, with the increase being slight and attributed to slow crystal growth consuming less supersaturation. The concentration resulting from the suspension density is lower, a behaviour also seen for the 35 and 45 °C isotherms. Therefore, it is concluded that the greater S
0, the greater is B, and it is depleted in less time than with less S
0. This statement agrees with the report by Bari and Pandit [
24], also referring to reactive crystallization.
Once the nuclei appear, they become stable crystals and grow over time. However, nucleation persists assisted by crystals constituted as suspension density, supersaturation decreases to a low level, and it is there that secondary nucleation occurs (B). Therefore, secondary nucleation is often dependent on suspension density (MT) and supersaturation (S). Furthermore, growth (G) is also a function of S. Then, the relationship of B with G and MT describes the secondary nucleation rate of K2SO4 in the reactive crystallization process with time and is given by Equation (13). The parameters KR, i, and j are estimated by adjusting the experimental data of G and MT with time using multiple linear regression to obtain the secondary nucleation rate calculated (Bcal) for each So.
The results of
Bexp and
Bcal are shown in
Figure 6. A good correlation of secondary nucleation with G and M
T is observed for most of the isotherms. The
Bexp and
Bcal values have practically the same tendencies, superimposed, at 5, 15, 25 and 45 °C (
S0 = 5.15, 4.15, 3.84 and 3.24), with a coefficient of determination of R
2 = 0.976, 0.997, 0.998, and 0.979, respectively, and a slightly lower correlation for the 35 °C isotherm (
S0 = 3.54), with R
2 = 0.943.
The empirical parameters
KR,
i, and
j obtained for each reaction isotherm are compiled in
Table S6 (SI). From the results, it can be concluded that B depends on the density of the suspension, whose values of
j are between 0.20 and 0.80. However,
i has values of 1.18, 0.63 and 0.1 for the 5, 15, and 25–45 °C isotherms, which is attributed to the fact that B depends on G implied by the supersaturation, whose value of
i is greater than
j for isotherms of 5 and 15 °C. For the 25–45 °C isotherms,
i is less than
j, suggesting little dependence on B for G. On the other hand, the K
R values show irregular behaviour, as seen in the trends of B in
Figure 6.
To finally evaluate secondary nucleation via Equation (13), the
G and
MT values for different
S0 (
Figure 6) were fitted to the following Equation:
This general description of secondary nucleation in the reactive crystallization process of K
2SO
4 leads to a relatively low coefficient of determination R
2 = 0.11. Therefore it is difficult to attribute the dependence of
B to the suspension density or crystal growth rate, whose values of
i and
j are 0.75 and 0.71, respectively, and thus, both are close to unity [
20]. For the crystallization processes in the single solute K
2SO
4-H
2O system via cooling and seeding, Mohamed et al. [
30] reported
i = 0.9 and
j = 0.57 and concluded that
B depends on S and M
T.
The presence of K
2SO
4(s) in the reactive crystallization solution contributes to nucleation so that the exponents
i and
j take on characteristic values. However, the primary nucleation order (b) depends solely on the degree of supersaturation and the method of detecting the appearance of nuclei, so the nucleation order is greater than the secondary one. Bari et al. [
22] reported the dependence of secondary nucleation order (b2) on supersaturation and M
T. They found b2 = 2.25 and b = 6.5 for the K
2SO
4-H
2O system, obtained by the isothermal method and, as evident, b2 <b. Taguchi et al. [
31] observed in the reactive crystallization process of BaSO
4, when mixing two equimolar solutions of BaCl
2 and Na
2SO
4 at 25 °C, that secondary nucleation is influenced by the stirring speed (N
s), M
T and S, whose exponents are 0.98, 0.84 and 1.72, respectively, with a multiple correlation coefficient of 0.61. The K
R parameter implies the dependence of temperature, hydrodynamics, presence of impurities and the properties of the established crystals. Thus, the K
R data obtained for each reactive crystallization isotherm of K
2SO
4 is used to estimate the secondary nucleation activation energy in the following.
3.5. Crystal Growth Rate of K2SO4
The crystal growth rate (G) of K
2SO
4 was simultaneously determined from the square weighted CLD data, according to Equation (14).
Figure 7 shows the growth rate of K
2SO
4 crystals as a function of time during the reactive crystallization process for different S
0. At 5 °C (with S
0 = 5.15), G starts with a value of 231.06 μm/min determined at 4.01 min and reaches a minimum value of 4.94 μm/min after 20 min. The decrease in G is caused by the decrease in supersaturation due to crystallization. At 25 °C (with S
0 = 3.84), G has an initial value of 101.5 μm/min and decreases over time to 5.30 μm/min at ≈30 min.
As seen in
Figure 7, the crystal growth rate is low due to the predominance of 0th. moment values (μ
0) according to Equation (14). It is estimated that the nuclei are in a metastable state; therefore, the decrease in supersaturation is slight. Then, G becomes predominant, and S decreases.
As expected, the initial growth rates in the K
2SO
4 reactive crystallization are significantly higher than observed in the binary K
2SO
4-H
2O system. Bari and Pandit [
24] reported a G of 8.82 μm/min at 49 °C studying K
2SO
4 growth by microscopy. Mohamed et al. [
30] reported a maximum growth rate of 6 μm/min at 40 °C with seeding, based on population balance data measured in the multichannel Coulter Counter. Mullin and Gaska [
27] reported single K
2SO
4 crystal growth rates of 4.68 and 5.16 μm/min for faces 100 and 001 at 20 °C, respectively. In the present report, a maximum growth rate of 231 μm/min was observed at 5 °C for the reciprocal quaternary system K
+, Mg
2+/Cl
−, SO
42−/H
2O using the FBRM probe in situ, without the need to take samples and without seeding.
With the G data for different degrees of S
0, the empirical fit parameters were determined according to Equation (15). As shown in
Figure 7, the growth rates steadily decreased from an initial maximum to a minimum for all isotherms. However, for reaction isotherms 35 and 45 °C, G increased at the beginning and then diminished to the minimum due to depletion of supersaturation. Thus, the crystals grew, as seen in
Figure 2a–c. To correlate G as a function of
S0, the G values of each isotherm were averaged to estimate the empirical parameters
kg and
g.
Figure 8 shows the correlation and adjustment of G versus S
0, obtaining a value of
g = 4.64 and
kg = 0.028 (μm/min) with a coefficient of determination of R
2 = 0.761.
In reactive crystallization, the high supersaturation promotes both nucleation and crystal growth, leading to a fast [
31] and relatively uncontrolled decrease in supersaturation. Thus,
g is much higher due to the higher growth rate that implies higher
S0. However, in reactive crystallization processes for sparingly soluble salts, Taguchi et al. [
31] correlated the G of BaSO
4 with the stirring speed (N) and
S0. They mention that the influence of N implies the occurrence of growth controlled by diffusion, while the order with respect to S
0 indicates that both diffusion and surface reaction exert some influence on growth rates. Tavare and Gaikar [
47] correlated the growth rate of salicylic acid crystals with solution concentration and stirring speed. They report that due to the complexity of determining supersaturation, S was omitted in the correlation. Therefore, the adjusting exponents of both the concentrations of salicylic acid and the agitation speed prevented the attribution of any mechanism of influence on growth.
In this report, the value of g = 4.64 is strongly influenced by the initial supersaturation. When
S0 is higher for 5, 15, and 25 °C, a higher crystal growth rate is promoted. However, the growth rate is much lower for
S0 at 35 and 45 °C. Therefore, when adjusting G vs.
S0 (obtained for 5–45 °C) to an empirical Equation, the slope is greater than those known for the K
2SO
4-H
2O systems attributable to growth mechanisms. Thus, for future studies, it is proposed to develop a strategy that allows determining the growth mechanism of K
2SO
4, taking advantage of the generation of supersaturation by reaction and the initial presence of fine crystals so that a cubic cooling profile can be used to control supersaturation. As a result, a fairly narrow CSD and acceptable average crystal size [
56,
57] would be feasible.
On the other hand, there are numerous reports for the K
2SO
4-H
2O system for the isolated determination of the growth mechanisms in crystallization processes with low supersaturation controlled by a cooling technique. In these works, generally, the mechanism that controls the growth of K
2SO
4 is diffusion [
21,
25,
26,
27].
3.6. Crystal Suspension Density MT
The variation of the suspension density with respect to time was determined by Equation (16), with the results presented in
Figure S11 (SI). However, the absolute suspension density was identified via empirical Equation (17) to relate the amount by weight of crystals obtained gravimetrically at the end of reactive crystallization. The results allowed estimating the amount of potassium and sulfate ions in the solution during the reaction to later be used to determine the supersaturation profile.
In
Figure 9, the absolute suspension densities at different reactive crystallization isotherms are shown as a function of time. At 5 °C (
S0 = 5.15), the suspension density increased linearly from 6.84 g of K
2SO
4/kg H
2O at 6 min to 108.45 g of K
2SO
4/kg H
2O at the end of the reactive crystallization at 20 min. At 25 °C (
S0 = 3.84), an increase in M
T from 3.95 g of K
2SO
4/kg H
2O at 10 min to 56.68 g of K
2SO
4/kg H
2O at the end of the reactive crystallization at 30 min is obtained. Thus, the higher
S0, the higher the suspension density reached in less time. The final M
T for the isotherms at 15, 35 and 45 °C, with the respective
S0 of 4.13, 3.54 and 3.24, were 67.41, 47.03 and 21.29 g of K
2SO
4/kg H
2O, respectively.
The suspension density (
MT) targeted by crystallization is limited by the solubility, and the S
0 reached in the system under study. It depends on the crystallization method and is further affected by the morphology and size distribution of the crystals, filtration demands, and the cocrystallization of an undesired compound. Mohamed et al. [
30] reported an M
T between 58 and 95 (g of K
2SO
4 crystals/kg H
2O) by cooling from 63.5 to 24.6 °C, and 75 (g of K
2SO
4 crystals/kg H
2O) at 40 °C for a K
2SO
4-H
2O solution with seeding. In this report of reactive crystallization, a maximum
MT of 108.45 g of K
2SO
4/kg H
2O at 5 °C was obtained and was limited by the potential cocrystallization of another compound from the reciprocal salt pair.
The product yield was estimated based on the suspension density data at the end of the reactive crystallization process. For the 5, 15, 25, 35, and 45 °C isotherms, the yields achieved were 72.6%, 45.2%, 37.9%, 31.5%, and 14.3% of K
2SO
4, respectively. As expected, the higher the
S0 in the system, the higher the yield and the less reactive crystallization time is required. The yield was determined by relating the amount of K
2SO
4 obtained experimentally with that calculated by stoichiometry. The mass balances of the reactive crystallization experiments established from the suspension density and the solute concentration (as obtained by Equations (17) and (18)) are depicted in
Figure S12 (SI). While the solute concentration decreases, the suspension density increases due to the consumption of supersaturation by crystallization.
The solid K
2SO
4 obtained at 5 °C represents a solid concentration of 11 wt/wt% in the pulp, which is highly favourable for process monitoring by FBRM, as recommended by Senaputra et al. [
58], who recommend a pulp concentration not greater than 20 wt/wt%.
3.7. Activation Energy E
As mentioned above, the dependence of the secondary nucleation rate constant
KR on the absolute temperature enables estimating the secondary nucleation activation energy
E via the Arrhenius Equation (20). The results for the reactive crystallization process studied are presented in
Figure 10, specifying the secondary nucleation activation energy as
E = 69.83 kJ∙mol
−1. However, to obtain
E, the
KR values were considered as a function of the temperature that best fit. In addition, the Excel solver has been used under the restrictions of
j ≥ 1 for the isotherms of 5, 15, and 25 °C, also to
i ≥ 1.5 and 0.12 for the isotherms of 35 and 45 °C, respectively, which improves the determination coefficient (R
2 = 0.92) in the activation energy estimation. As seen in
Figure 10, the secondary nucleation activation energy is higher in the 5–25 °C segment due to the higher S
0 promoting secondary nucleation, while S
0 is lower in the 25–45 °C range with the consequence of a lower E.
In general, the secondary nucleation activation energy of 69.83 kJ∙mol
−1 obtained for the reactive crystallization process of K
2SO
4 obeys the principle of positivity. However, it is believed that the activation energy for reactive crystallization primary nucleation of K
2SO
4 would be much lower due to the rate K
2SO
4 nucleated from a crystal-free solution. As there are no similar works, they cannot yet be compared with other values related to the reactive crystallization kinetics of soluble salts. However, for reference, Luo et al. [
23] reported the activation energy of primary nucleation for cooling crystallization in the K
2SO
4-H
2O system to be 33.99 kJ∙mol
−1, much less than obtained for the secondary nucleation of K
2SO
4 by reactive crystallization in this work. On the other hand, for reactive crystallization of a poorly soluble salt, Lu et al. [
32] reported a nucleation activation energy of 73.049 kJ∙mol
−1 for Mg(OH)
2. As seen, when nucleation depends only on supersaturation, the activation energy of primary nucleation is much lower, implying that nucleation is faster than obtained in the present report, where the activation energy of secondary nucleation depends on the density of suspension.
3.8. K2SO4 Product Quality
The crystals of K
2SO
4 obtained as a final product in the reactive crystallization experiments were subjected to X-ray diffraction analysis to be compared with the reagents K
2SO
4, KCl, and MgSO
4 and synthesized picromerite. The diffractograms are compiled in
Figure 11. In addition, the product crystals were analyzed regarding the presence of Magnesium as an impurity by ion chromatography. As a result, only very small contents of 0.51, 0.11, and 0.01 wt% of Magnesium were detected in the products of reaction temperatures 5, 15, and 25, 35, and 45 °C, respectively. The X-ray patterns in
Figure 11 and the low residual Mg amounts in the crystals prove that the K
2SO
4 obtained is of high quality. The diffractogram obtained for the K
2SO
4 product at 5 °C exhibits several intense peaks that correspond to the patterns of K
2SO
4 and picromerite, verifying the somewhat higher Mg content in the respective product. K
2SO
4 is the majority phase, and no other crystalline phase is present, considering a detection limit of XRPD <1%. The presence of picromerite peaks might be attributed to mother liquor occluded between the K
2SO
4 crystals which, after filtration, crystallizes as picromerite when drying. In this work, the washing process of the K
2SO
4 product was omitted. Of course, when including washing after solid–liquid separation, a further increase of purity is possible but at the expense of yield. The washing process is essential to improve the quality of K
2SO
4, as accomplished in the crystallization process of K
2SO
4 from the KCl
(s) picromerite
(s)-H
2O system reported by Fezei et al. [
12,
13,
14,
15].
It is important to mention the presence of the eutectic point in the system, which allows deriving the lowest feasible crystallization temperature. In this sense, despite the reactive crystallization of K
2SO
4 from the multicomponent system K
+, Mg
2+/Cl
−, SO
42−//H
2O, the remaining solution still contains salts like MgSO
4(aq), KCl
(aq), and MgCl
2(aq) that could provide more K
2SO
4 at reaction temperatures below 5 °C. The eutectic points of the salts with solubilities are 7.29 g of K
2SO
4/100 g of saturated solution at −1.9 °C, 19 g of MgSO
4/100 g of saturated solution at −3.9 °C, 19.87 g of KCl/100 g of saturated solution at −10.8 °C, and 21.0 g of MgCl
2/100 g of saturated solution at −33.6 °C [
45].
Based on the quality of the K
2SO
4 obtained by reactive crystallization at 5 °C and the eutectic points mentioned above, they allow working at reactive crystallization temperatures below 5 °C. In addition, this enables generating higher S
0 to improve the process performance since the eutectic point of K
2SO
4 is −1.9 °C, and it is estimated that this temperature is even much lower in the presence of K
+, Mg
2+, Cl
−, and SO
42− ions. In this regard, Song et al. [
59] mention that the solubility of the precipitating compound in a reactive crystallization process increases in the presence of ions in the system; for example, for CaSO
4, the solubility increases in the presence of Cl
−, H
+, Ca
2+, and SO
42− ions at 60 °C.