Sodium Sulfate Separation from Aqueous Alkaline Solutions via

Dec 4, 2014 - The thermodynamics and kinetics of crystallization of sodium sulfate from aqueous alkaline solutions via urea-functionalized capsules ha...
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Sodium Sulfate Separation from Aqueous Alkaline Solutions via Crystalline Urea-Functionalized Capsules: Thermodynamics and Kinetics of Crystallization Radu Custelcean,* Frederick V. Sloop, Jr., Arbin Rajbanshi, Shun Wan, and Bruce A. Moyer Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States S Supporting Information *

ABSTRACT: The thermodynamics and kinetics of crystallization of sodium sulfate with a tripodal tris-urea receptor (L1) from aqueous alkaline solutions have been measured in the 15−55 °C temperature range for a fundamental understanding of the elementary steps involved in this sulfate separation method. The use of radiolabeled Na235SO4 provided a practical way to monitor the sulfate concentration in solution by β liquid scintillation counting. Our results are consistent with a two-step crystallization mechanism, involving relatively quick dissolution of crystalline L1 followed by the rate-limiting crystallization of the Na2SO4(L1)2(H2O)4 capsules. We found that temperature exerted relatively little influence over the equilibrium sulfate concentration, which ranged between 0.004 and 0.011 M. This corresponds to 77−91% removal of sulfate from a solution containing 0.0475 M initial sulfate concentration, as found in a typical Hanford waste tank. The apparent pseudo-first-order rate constant for sulfate removal increased 20-fold from 15 to 55 °C, corresponding to an activation energy of 14.1 kcal/mol. At the highest measured temperature of 55 °C, 63% and 75% of sulfate was removed from solution within 8 and 24 h, respectively. These results indicate the capsule crystallization method is a viable approach to sulfate separation from nuclear wastes.

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INTRODUCTION Sulfate separation from highly competitive aqueous alkaline solutions is a difficult problem with relevance to the environmental cleanup of legacy nuclear wastes such as those stored at Hanford, as high concentrations of sulfate in those waste tanks have been found to interfere with the vitrification process selected for waste disposal, increase the volume of the waste forms that must be produced, and reduce their geologic performance.1 The challenge associated with this problem stems from the strongly hydrophilic nature of sulfate (ΔG°h = −1080 kJ/mol), the extreme ionic strength (>6 M) and alkalinity (pH 14) of the waste, and the high concentrations of competing anions like NO3−, NO2−, OH−, Al(OH)4−, and CO32−. We have recently developed an efficient approach to sodium sulfate separation from aqueous alkaline solutions simulating the Hanford tank waste composition (5 M NaNO3, 1−1.5 M NaOH, 0.03−0.12 M Na2SO4) based on crystallization with the tripodal tris-urea receptor L1 into urea-functionalized dimeric capsules (1) with the Na2SO4(L1)2(H2O)4 formula (Figure 1).2,3 The [SO4(L1)2]2− capsules in these crystals are interlinked by Na2(H2O)42+ cationic clusters. Encapsulation of sulfate in crystalline 1 by the formation of 12 complementary hydrogen bonds from the six urea groups lining the internal cavities of the capsules4 effectively compensates for the hydration energy lost upon removing the anion from water. Furthermore, the rigidity of the crystalline lattice allows © 2014 American Chemical Society

Figure 1. A complete separation cycle for Na2SO4 removal from alkaline sodium nitrate solutions consisting of selective encapsulation and crystallization with solid L1 into crystalline capsules 1, followed by recycling of L1 by recrystallization of 1 from water.

minimal structural distortion of the capsules, thereby preventing the accommodation of competing anions that lack shape complementarity. Since 1 is built from Na+, the most abundant cation in nuclear wastes, there is no need to add any external salts to effect the sulfate separation, which minimizes the amount of secondary wastes. The high Na+ concentration in the waste also effectively decreases the solubility of 1 through Received: November 11, 2014 Revised: December 2, 2014 Published: December 4, 2014 517

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Crystallization Experiments Using Na235SO4. All crystallizations were carried out in duplicate using 5 mL of a matrix solution containing 5 M NaNO3 and 1 M NaOH, in 30 mL screw-cap Teflon tubes that were placed individually in self-sealing plastic bags for containment and mounted on clips on a rotating wheel in a temperature-controlled incubator. Na2SO4 (0.25 mmol, 0.25 mL, 1 M) containing a small amount of Na235SO4 (vide supra) was then added to the tubes. The resulting sulfate concentration (including the radiotracer) was 47.54 mM. Solid L1·2H2O (0.083 to 1.25 mmol) was subsequently added to the tubes, which were then tumbled end-overend on a rotating wheel at 35−40 rpm in a fixed temperature incubator or air box. Experiments at 15 °C were carried out in a Fisher Scientific low temperature incubator; those performed at 25 °C were accomplished in a constant-temperature air box, while those done at 30, 35, 45, and 55 °C involved the use of a Lab-Line Imperial III incubator. Periodic temperature checks typically revealed a ± 0.5 °C temperature variation over time. The duration of the experiments was 10 days to 2 weeks. Periodic subsampling involved withdrawing 100 μL of reaction supernatant. Prior to removing the subsample, the tubes were centrifuged for 10 min at 3000 rpm in a temperature-controlled Beckman Coulter Allegra 6R centrifuge in order to separate the solids from the supernatant. The subsamples were diluted with 400 μL of water before counting in scintillation vials containing 20 mL Ultima Gold scintillation cocktail each. The sulfate concentration at a given time t was determined from the counted dpm of the corresponding subsample, relative to the counted dpm of the initial solution, taking into account the natural decay of 35S from the beginning of the experiment to the time t. Dissolution of 1 Using Na235SO4. These experiments were run in duplicate, and the reported solubilities are average values of the two measurements. Crystalline 1 containing a small amount of 35SO42− was first prepared using the protocol described in the previous section, but using excess sulfate (L1/SO42− = 1.5) to ensure all L1·2H2O was converted into the sulfate complex. The mixture was stirred at 25 °C for 216 h; then it was centrifuged and the supernatant solution was removed by decantation. The resulting solid was washed with 5 mL of fresh matrix solution twice to remove the excess sulfate. Following the centrifugation and decantation of the matrix solution, the resulting solid 1 was once again mixed with 5 mL of the matrix solution, and the mixture was tumbled end-over-end on a rotating wheel at 35−40 rpm in a fixed-temperature incubator. The initial temperature was set at 25 °C, and 100 μL subsamples were withdrawn periodically to monitor the increase in sulfate concentration over time by β scintillation counting as described above. The system reached equilibrium after 167 h, as indicated by the leveling-off of the sulfate concentration in solution. The final sulfate concentration was noted; the temperature was subsequently increased to 35 °C, and the measurement was repeated to determine the equilibrium sulfate concentration at this temperature. The incubator temperature was subsequently increased to 45 °C, then 55 °C, and the process was repeated each time to obtain the corresponding solubilities after 96 and 69 h of stirring at these temperatures, respectively. L1 Solubility Measurements. All experiments were run in duplicate, and the reported solubilities are average values of the two measurements. L1·2H2O (80 mg) was added to 30 mL of deionized water in a Teflon tube, and the mixture was mechanically stirred in the incubator set at a temperature of 25 ± 0.5 °C. To monitor the kinetics of dissolution, small aliquots were periodically drawn and quickly (∼20 s) filtered using a syringe filter (Acrodisc 13CR PTFE 0.45 μm GELMAN). The resulting filtrate was diluted 40-fold with deionized water and subjected to UV−vis spectroscopic analysis (Figure S1, Supporting Information). The concentration of L1 was determined based on a calibration plot obtained from standard solutions of L1 with concentrations between 0.025 and 0.3 × 10−4 M (Figure S2, Supporting Information). The equilibrium solubility at 25 °C was measured the same way by drawing an aliquot after 48 h of stirring. The incubator temperature was subsequently increased to 35 ± 0.5 °C, and the equilibrium solubility was measured similarly after 24 h of additional stirring. The incubator temperature was subsequently increased to 45 ± 0.5 °C, then 55 ± 0.5 °C, and the process was

the common ion effect, thereby increasing the sulfate removal yield. Finally, L1 can be easily recovered by recrystallization of 1 from water, taking advantage of the lower aqueous solubility of the ligand relative to 1 in the absence of excess Na+.2 Interest in the potential application of the simple cycle shown in Figure 1 for sulfate separation from nuclear wastes has raised fundamental questions regarding the crystallization thermodynamics and kinetics. The main limitation of this sulfate separation method has been the slow rate of crystallization, requiring about 4 days to complete at room temperature. We also observed a decrease in the sulfate crystallization yield in the presence of some waste components like aluminate.3 Thus, it became apparent that we needed a more quantitative understanding of solubility and rates of crystallization and dissolution for the crystalline phases involved, as well as of the effects of different variables such as temperature, solution composition, and crystal size and morphology. Along this line, we set out to investigate the kinetics and thermodynamics of crystallization of 1 from solid L1 for deeper molecular-level understanding, which can then aid in identifying the optimal conditions for efficient and quick sulfate removal from highly alkaline sodium nitrate solutions as found in nuclear wastes.

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EXPERIMENTAL SECTION

All reagents utilized were of commercial grade and used as received. The L1 ligand (1,1′,1″-(nitrilotris(ethane-2,1-diyl))tris(3-(pyridin-3yl)urea)) was synthesized according to previously published procedures2 and recrystallized from water/MeOH prior to use. Powder X-ray diffraction (PXRD) confirmed that the crystalline ligand was in its dihydrated form (L1·2H2O). Na235SO4 was purchased from PerkinElmer, and its specific activity was 1494 Ci/mmol, with an as-received concentration of 2 mCi 35S per mL of water. Liquid Scintillation Counting. The 35S radiolabel requires that samples be counted using liquid scintillation. All counting was performed using a Packard Tri-Carb 2500TR liquid scintillation analyzer. The high ionic strength, charge, and presence of alkali in the analyzed solutions could impede the formation of a necessary stable microemulsion and cause phase instability due to their known tendency to coalesce and potentially generate chemiluminescence in the scintillation cocktail. To minimize those effects, the 0.1 mL samples withdrawn from the crystallization mixtures were diluted with the addition of 0.4 mL of water prior to their introduction into 20 mL of Ultima Gold scintillation cocktail (PerkinElmer). Standard 20 mL polyethylene scintillation vials were used for the counting procedure. Diluting all samples 1:4 with water, using a large scintillation cocktail to sample ratio, and dark-adapting the samples for 30−60 min prior to their counting served to mitigate most of the potential interferences in the samples being counted. The counter was normalized each day by running 14C and 3H standards as a check on efficiency and further checked with a background standard prior to cueing any experimental samples. Assuming a maximum of 99.9% removal of the radiolabeled Na235SO4 from solution over the course of the crystallization experiments, and keeping in mind that scintillation counter efficiency and sensitivity requires 300−500 disintegrations per minute (dpm) to get statistically reasonable counts above background, there needs to be 500 000 dpm of 35S per 100 μL (sample size) of the starting reaction, which would equal 27.5 × 106 dpm 35S-radiolabeled Na2SO4 added to each reaction at the onset of the experiment. Since S-35 has an 87.4day half-life, a decay chart (Table S1, Supporting Information) was used to calculate the remaining activity of stock over time and appropriately adjust the volume necessary to transfer the requisite starting counts of 27.5 × 106 dpm. This amounted to between 7 and 24 μL of Na235SO4 solution added to the 5 mL of solution used in each crystallization experiment. 518

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repeated to obtain the corresponding solubilities after 24 h of stirring at each of these temperatures (these filtrates were diluted 100-fold before the UV−vis analysis). A separate, similar experiment was run in order to measure the solubility of L1 at 15 ± 0.5 °C, using a lowtemperature incubator instead. An alternative method used to measure L1 solubility was by gravimetric analysis. This approach was particularly useful for solubility measurements in solutions containing high concentrations of salts (e.g., matrix solution containing 5 M NaNO3 and 1 M NaOH) that interfered with the UV−vis analysis. These gravimetric measurements were carried out in duplicate, and the reported solubilities are average values of the two measurements. L1·2H2O (100 mg) was carefully weighed out in a 200 mL glass jar, and 100 mL of either deionized water or the matrix solution of interest was added to it. The mixture was stirred at room temperature for 3 days over a water bath equipped with a thermometer, which read a temperature of 20 ± 1 °C throughout the experiment. At the end of the stirring period, the solution was filtered using a vacuum-dried filter paper that was preweighed several times until its weight remained constant. For the experiments involving concentrated matrix solutions, the precipitate was briefly washed with a small amount of deionized water to wash off any matrix salts sticking to the filter paper. The filter paper along with the collected solid were dried in a vacuum oven and weighed out several times until the weight remained constant. PXRD analysis confirmed that the collected solid at the end of the experiment was still L1·2H2O, and thus no phase change occurred.

Accordingly, the total concentration of sulfate in solution is the sum of free and complexed sulfate, that is [SO42−]T = [SO42−] + [L1· SO42−]. The use of radiolabeled Na235SO4 provided a simple way to monitor the total sulfate concentration in solution by β liquid scintillation counting (see Experimental Section for details). All crystallization experiments were performed with 5 mL of a matrix solution containing 5 M NaNO3 and 1 M NaOH. To this solution was added 0.25 mmol of Na2SO4 (0.25 mL, 1 M) containing a small amount of Na235SO4, so that the total initial sulfate concentration was 47.54 mM. Solid L1·2H2O was then added, and the mixture was stirred at constant temperature, monitoring the amount of sulfate left in solution by periodically withdrawing small subsamples and determining the sulfate concentration by β scintillation counting. An initial series of crystallization experiments was set up at 25 °C to test the viability of our method and whether the system behaves as expected according to eq 3. Thus, the initial sulfate amount was kept constant at 0.25 mmol in all the experiments, while the amount of solid L1·2H2O added was varied from 0 (control experiment) to 1.25 mmol, corresponding to L1/SO42− molar ratios ranging from 0 to 5. The proportion of sulfate remaining in solution in each experiment was plotted against time, as shown in Figure 2a. The amount of crystallized sulfate leveled off after about 4 days in all of the runs, indicating attainment of the equilibrium. These results are consistent with our previous observation, indicating that it takes about 4 days to completely convert solid L1·2H2O into 1 under these conditions.2 Furthermore, as shown in Figure 2b, the

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RESULTS AND DISCUSSION Thermodynamics of Crystallization. Our preliminary studies indicated that addition of crystalline L1·2H2O to an aqueous solution containing 5 M NaNO3, 1 M NaOH, and 0.044 M Na2SO4 resulted in crystallization of 1 in 90% yield over the course of 4 days at room temperature.2 The slow rate of formation of crystalline 1, and its completely different crystal packing from the starting L1·2H2O, suggest a solvent-mediated mechanism involving dissolution of L1·2H2O (eq 1) followed by crystallization of 1 (eq 2). Equation 3 represents the overall reaction with the corresponding equilibrium constant K3, valid when both solid phases are present simultaneously. This condition would be expected when L1 is present in molar excess relative to sulfate (L1/SO4 2− > 2). Since the crystallization solution contains a large excess of sodium cations, [Na+] can be considered constant, and the value of K3 can then be simply determined from the measured sulfate concentration at equilibrium and the corresponding activity coefficient (γ). L1·2H 2O(s) ⇆ L1(aq) + 2H 2O

K1 = [L1]

(1)

2L1(aq) + 2Na +(aq) + SO4 2 −(aq) + 4H 2O ⇆ Na 2SO4 (L1)2 (H 2O)4(s)

K2 =

1/γ 3[L1]2 [Na +]2 [SO4 2 −]

(2)

2L1· 2H 2O(s) + 2Na +(aq) + SO4 2 −(aq) ⇆ Na 2SO4 (L1)2 (H 2O)4(s) K3 = K12K 2 = 1/γ 3[Na +]2 [SO4 2 −]

(3)

Another potentially relevant reaction is the complexation of sulfate by L1 in solution, according to eq 4: L1(aq) +

SO4 2 −(aq)

⇆

Figure 2. (a) Proportion of sulfate remaining in solution as a function of time and L1/SO42− molar ratio for crystallization of 1 at 25 °C. (b) Plot of the fraction of sulfate remaining in solution at equilibrium vs L1/SO42− molar ratio. All sulfate concentrations are corrected to take into account the natural decay of 35S.

L1·SO4 2 −(aq)

K4 = [L1· SO4 2 −]/[L1][SO4 2 −]

(4) 519

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proportion of sulfate left in solution at equilibrium decreases proportionally with the increase of the L1·2H2O added, reaching about 12% for the stoichiometric L1/SO42− molar ratio of 2; adding excess L1·2H2O did not result in a further increase in the amount of sulfate removed. A series of analogous experiments was also run in parallel, but with no Na235SO4 added, and the final crystalline solids were filtered and analyzed by PXRD, which confirmed that L1·2H2O and 1 were the only crystalline phases observed throughout the experiments. Thus, all these observations are consistent with a clean conversion of crystalline L1·2H2O into crystalline 1, according to eq 3. To investigate the effect of temperature on crystallization of 1, we next ran a series of experiments at five different temperatures between 15 and 55 °C, with starting L1/SO42− molar ratios of 3 (50% molar excess L1). The plots of total sulfate concentrations as a function of time for the five different temperatures are shown in Figure 3, and the equilibrium sulfate concentrations with the corresponding apparent equilibrium constants are listed in Table 1.

Figure 4. Van’t Hoff plot for crystallization of 1 in the 15−55 °C temperature range.

factors may contribute to the observed temperature dependence of Kapp. First, the crystals of L1·2H2O or 1 could undergo a phase transition around 35 °C. Ex situ PXRD measurements of crystalline L1·2H2O or 1 that have been stirred for 3 days at 55 °C in an alkaline sodium nitrate solution with a composition similar to that of the matrix solution used in the 35S experiments failed to identify any new crystalline phases (Figure S3, Supporting Information). However, we cannot completely rule out a phase transition, particularly if it involved a transient structure that could not be captured ex situ, or an amorphous phase that could not be observed by PXRD. Second, salting-out effects of the matrix components are expected to increase nonlinearly with temperature,5 which could change the relative solubilities of the crystalline phases involved. Finally, the degree of sulfate complexation by L1 in solution (eq 4) could change significantly with temperature, thereby causing the observed inflection in Kapp as a result of a switch in the controlling reaction (see Supporting Information for the full thermodynamic analysis of this case). To gain additional insight into the thermodynamics of sulfate crystallization, we studied the dissolution of L1·2H2O in water as a function of temperature. Besides its relevance to crystallization of 1 as the first step of the overall process (eq 1), solubility measurements of L1·2H2O are also important in the context of ligand recovery for an efficient and sustainable sulfate separation from nuclear wastes. The ligand solubility in pure water was most conveniently measured by UV−vis spectroscopy. The measured solubility values showed a monotonous increase with temperature in the range of 15 to 55 °C (Table 2). The van’t Hoff plot (Figure 5) of −R ln K1 vs 1/T is fairly linear (R2 = 0.97), and its slope corresponds to an enthalpy of dissolution (ΔHdiss) of 8.5 ± 0.2 kcal/mol. Additional dissolution measurements of L1·2H2O were done in order to assess the effect of solution composition on L1 solubility. We were particularly interested in determining ligand solubility in solutions with compositions similar to those of

Figure 3. Evolution of sulfate concentration during crystallization of 1 from L1·2H2O at various temperatures, as monitored by 35S β scintillation counting. The initial solution composition was 5 M NaNO3, 1 M NaOH, and 0.0475 M Na2SO4, and the starting L1/ SO42− molar ratio was 3:1. All sulfate concentrations are corrected to take into account the natural decay of 35S.

Table 1. Total Sulfate Concentrations at Equilibrium ([SO42−]T) and Apparent Equilibrium Constants (Kapp) for Crystallization of 1 from L1·2H2O in the 15−55 °C Temperature Range T (°C) 15 25 35 45 55

% SO42− removed 77.0 86.7 90.7 90.0 88.9

± ± ± ± ±

2 2 1 1 1

[SO42−]T (M)

Kappa

± ± ± ± ±

2.54 4.40 6.29 5.85 5.27

0.011 0.006 0.0044 0.0048 0.0053

0.001 0.001 0.0005 0.0005 0.0005

Table 2. Solubility of L1 in Water (K1) in the 15−55 °C Temperature Range, Measured by UV-Vis Spectroscopy

a

Kapp = 1/[Na+]2[SO42−]T. See Supporting Information for the relationship between Kapp and K3.

Evidently, the equilibrium sulfate concentration does not follow a monotonous trend with temperature. Instead, it decreases from 15 to 35 °C, followed by a slight increase from 35 to 55 °C. As a result, the van’t Hoff plot of −R ln Kapp vs 1/ T shows a change in slope at 35 °C (Figure 4). A number of 520

T (°C)

K1 (M)

15 20 25 35 45 55

0.00057(2) 0.00065(1) 0.00073(1) 0.00111(1) 0.00197(3) 0.00346(11) dx.doi.org/10.1021/cg501656s | Cryst. Growth Des. 2015, 15, 517−522

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Figure 5. Van’t Hoff plot for dissolution of L1·2H2O in water in the 15−55 °C temperature range.

Figure 6. Comparison of the kinetics of L1·2H2O dissolution in water (blue circles) and of sulfate removal by crystallization of 1 from a solution of 5 M NaNO3, 1 M NaOH, and 0.0475 M Na2SO4 in the presence of L1 at an initial L1/SO42− mole ratio of 3 (red squares). Both measurements were done at 25 °C.

nuclear wastes, a necessary step toward developing an efficient sulfate crystallization process from these wastes. As UV−vis spectroscopy proved impractical for investigating these solutions due to their high salt concentration, we opted for gravimetric analysis for these solubility measurements. By this method, the measured solubility of L1 in pure water at 20 °C was 0.00072(1) M, comparable to the analogous value of 0.00065(1) M found by UV−vis spectroscopy (see Table 2). By comparison, at 0.00036(1) M, the gravimetrically measured solubility of L1 in the matrix solution of 5 M NaNO3 and 1 M NaOH was only half as much. This suggests minimal interaction between L1 and the salt components of the matrix solution, which instead have a salting-out effect on the ligand. Solubility of L1 in a similar matrix solution, which additionally contained 0.57 M aluminate, was even lower at 0.00025(1) M. This refutes the notion that aluminate binding by L1 is responsible for the previously reported decrease in sulfate crystallization yield in the presence of this anion.3 Finally, the increased L1 solubility of 0.00125(1) M, measured in a 0.03 M aqueous Na2SO4 solution, suggests significant sulfate binding by L1 under these conditions (eq 4), which needs to be taken into account when optimizing ligand recovery. Unlike the solubility of L1·2H2O, which displayed relatively strong temperature dependence, the solubility of 1 was found to be relatively insensitive to temperature. Dissolution of crystalline 1 (spiked with 35SO42−) in the matrix solution of 5 M NaNO3 and 1 M NaOH was monitored by β scintillation counting (see Experimental Section for details). The measured equilibrium sulfate concentrations varied only slightly with temperature (Table S2, Supporting Information), indicating that dissolution of 1 is essentially thermoneutral. Kinetics of Crystallization. According to eqs 1−3, sulfate removal from solution by crystallization of 1 involves two steps: dissolution of L1·2H2O (eq 1) and formation of crystalline 1 (eq 2). The latter can also be considered a two-step process, consisting of nucleation and subsequent crystal growth of 1. Any of these steps could be rate limiting and thus could determine the overall rate of sulfate removal from solution. Figure 6 compares the kinetics of L1·2H2O dissolution in water, with the kinetics of sulfate removal from the 5 M NaNO3 + 1 M NaOH matrix solution by crystallization of 1. Clearly, the rate of L1·2H2O dissolution is much higher than the rate of sulfate removal, suggesting the formation of crystalline 1 is the rate-limiting step. The rate of sulfate removal by crystallization of 1 can be expressed as

−d[SO4 2 −]/dt = nkcryst([L1] − [L1]eq )2 ([Na +] − [Na +]eq )2 ([SO4 2 −] − [SO4 2 −]eq )

(5)

in which kcryst represents the rate constant for crystallization of 1 and n is the number of active growth sites.6,7 Since Na+ is present in large excess in solution, its concentration can be considered constant. Following the induction period (vide infra), the concentration of L1 can also be considered constant, as the dissolved ligand is continually replenished from crystalline L1·2H2O at a rate that exceeds its consumption. As a result, the kinetics of sulfate removal are reduced to pseudo first-order in sulfate concentration according to eq 6, in which k′ is the apparent first-order rate constant. −d[SO4 2 −]/dt = k′([SO4 2 −] − [SO4 2 −]eq )

(6)

This equation, however, does not apply to the very early stage of crystallization of 1. In most crystallization experiments, we observed an induction period during which the decrease in sulfate concentration in solution was negligible. Its length varied with the crystallization conditions and was particularly sensitive to temperature, decreasing from about 20 h at 15 °C to just a few minutes at 55 °C. We surmise that the observed induction period corresponds to the necessary time for the solution to become saturated in L1 and allow nucleation of 1. Since the sulfate concentration changed only marginally during the induction period, our data do not allow for a more quantitative analysis of this early stage of crystallization, and our kinetic study is limited to the crystal growth phase corresponding to the bulk removal of sulfate from solution. As expected, the kinetics of sulfate removal are first order with respect to sulfate concentration (Figure 7), with an apparent rate constant k′ of 0.050(16) h−1 at 25 °C. The obtained rate constant is relatively insensitive to experimental variables such as the starting L1/SO42− molar ratio (3 vs 2), the particle size for the initial L1·2H2O crystals (fine polycrystalline precipitate vs large single crystals), or the initial presence or absence of crystal seeds of 1 (Figures S4−S6, Supporting Information). The crystallization data from the other four temperatures could also be fitted to first-order kinetics (Figures S7−S10, Supporting Information), though at the highest two temperatures of 45 and 55 °C the fit was only good up to about 50− 55% conversion, beyond which the rates of crystallization 521

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crystallization of 1, which could be probed by molecular dynamics simulations10 in the future. From a practical perspective, these results provide the basis for identifying the optimal conditions for efficient and quick sulfate removal from Hanford wastes by crystallization of 1. One drawback associated with this approach is the relatively slow crystallization rate of 1, requiring about 4 days to complete at room temperature. However, the significant increase in the sulfate crystallization rate with temperature, observed in the current study, can be exploited to reduce the amount of time required to remove the bulk of sulfate from the waste. Specifically, there is a 20-fold increase in the sulfate crystallization rate constant from 15 to 55 °C. Furthermore, the induction period for nucleation and crystallization of 1 shortens drastically with the increase in temperature. As a result, at 35 °C, 85% of sulfate was removed within 24 h. At the highest measured temperature of 55 °C, 63% of sulfate was removed from solution within 8 h. Such separation times are within practical bounds, making crystallization of 1 a potentially viable approach for sulfate separation from Hanford wastes.

Figure 7. First-order fit for the kinetics of sulfate removal by crystallization of 1 from a solution of 5 M NaNO3, 1 M NaOH, and 0.0475 M Na2SO4 at 25 °C, using a starting L1/SO42− molar ratio of 3.

slowed down. The reason for this behavior remains uncertain but is possibly related to the increase in the equilibrium sulfate concentration observed at these higher temperatures; the resulting lower degree of sulfate supersaturation may trigger a change in the mechanism of crystallization as observed in some minerals.8 The obtained rate constants increased with temperature in the measuring range of 15−55 °C, and the corresponding Arrhenius plot is linear (Figure 8), yielding an activation energy (Ea) of 14.1 ± 0.5 kcal/mol.

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ASSOCIATED CONTENT

S Supporting Information *

Additional thermodynamic, kinetic, and PXRD data and analysis, UV−vis calibration data, and 35S decay chart. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was sponsored by the Office of Technology Innovation and Development, Office of Environmental Management, U.S. Department of Energy.

Figure 8. Arrhenius plot for crystallization of 1 in the 15−55 °C temperature range.

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REFERENCES

(1) Moyer, B. A.; Custelcean, R.; Hay, B. P.; Sessler, J. L.; BowmanJames, K.; Day, V. W.; Kang, S.-O. Inorg. Chem. 2013, 52, 3473. (2) Rajbanshi, A.; Moyer, B. A.; Custelcean, R. Cryst. Growth. Des. 2011, 11, 2702. (3) Rajbanshi, A.; Moyer, B. A.; Custelcean, R. Sep. Sci. Technol. 2012, 47, 2145. (4) Custelcean, R. Chem. Commun. 2013, 49, 2173. (5) Il’in, K. K.; Cherkasov, D. G.; Kurskii, V. F. Russ. J. Inorg. Chem. 2011, 56, 1670. (6) Liu, S.-T.; Nancollas, G. H. J. Cryst. Growth 1970, 6, 281. (7) Nancollas, G. H. Adv. Colloid Interface Sci. 1979, 215. (8) Stack, A. G. Greenhouse Gas Sci. Technol. 2014, 1. (9) Zhang, J.; Nancollas, G. H. J. Cryst. Growth 1992, 118, 287. (10) Stack, A. G.; Raiteri, P.; Gale, J. D. J. Am. Chem. Soc. 2012, 134, 11.

CONCLUSION The thermodynamics and kinetics of crystallization of Na2SO4(L1)2(H2O)4 capsules (1) from aqueous alkaline solutions and crystalline L1·2H2O have been measured in the 15−55 °C temperature range, by using radiolabeled Na235SO4 and monitoring the sulfate concentration in solution by β scintillation counting. Our data are consistent with a two-step crystallization mechanism, involving quick dissolution of crystalline L1·2H2O followed by the rate-limiting growth of the Na2SO4(L1)2(H2O)4 crystals. The equilibrium sulfate concentration varied slightly with temperature, ranging between 0.004 and 0.011 M, with the lowest value observed at 35 °C and corresponding to 91% sulfate removal. The rates of sulfate removal from solution displayed pseudo-first-order kinetics with respect to sulfate concentration, with the obtained rate constants in the 15−55 °C temperature range obeying the Arrhenius law and corresponding to an activation energy of 14.1 ± 0.5 kcal/mol. This activation energy is comparable with the Ea of 15 kcal/mol observed for crystallization of calcium sulfate dihydrate,6 where sulfate dehydration and adsorption on the crystal surface was proposed as the rate-determining step.9 It is plausible that the same process may control the 522

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