Article pubs.acs.org/JPCA
Solid/Liquid Phase Diagram of the Ammonium Sulfate/Succinic Acid/ Water System Christian S. Pearson and Keith D. Beyer* Department of Chemistry & Biochemistry, University of WisconsinLa Crosse, La Crosse, Wisconsin 54601, United States S Supporting Information *
ABSTRACT: We have studied the low-temperature phase diagram and water activities of the ammonium sulfate/succinic acid/water system using differential scanning calorimetry and infrared spectroscopy of thin films. Using the results from our experiments, we have mapped the solid/liquid ternary phase diagram, determined the water activities based on the freezing point depression, and determined the ice/ succinic acid phase boundary as well as the ternary eutectic composition and temperature. We also compared our results to the predictions of the extended AIM aerosol thermodynamics model (E-AIM) and found good agreement for the ice melting points in the ice primary phase field of this system; however, differences were found with respect to succinic acid solubility temperatures. We also compared the results of this study with those of previous studies that we have published on ammonium sulfate/dicarboxylic acid/water systems.
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INTRODUCTION Tropospheric aerosols are often composed of internal mixtures of inorganic electrolytes and organics.1−9 The inorganic fraction is made up predominantly of aqueous ammonium and sulfate ions with the molar ratio of NH4+/SO42− ranging from 1 to 2.10,11 Additionally, upper tropospheric aerosols that are composed predominantly of aqueous sulfuric acid at high concentrations have been shown to contain NH3, which partially to completely neutralizes the H2SO4 molecules.12 These particles absorb and scatter solar radiation dependent upon their phase, thus contributing to the radiation balance.13 They may also play a significant role in heterogeneous chemistry in the troposphere14 and can be found at cirrus cloud altitudes under strong convective conditions where they could serve as ice nuclei.15,16 Studies have also shown that the incorporation of organic compounds into ammonium sulfate aerosols changes their deliquescence, efflorescence, hygroscopic properties, and potentially their crystallization properties.17−21 This necessitates understanding the impact of organic substances on the phase transitions of aqueous systems that make up tropospheric aerosols. Succinic acid (C4H6O4) has been found to be among the most prevalent organic acid in the atmosphere. Kawamura et al. found concentrations in the range of 1−61 ng/m3 in Arctic aerosols, which was the highest concentration of all dicarboxylic acids that they observed.5 Very little is known about the thermodynamics of the mixed ammonium sulfate/succinic acid system in water at temperatures below 298 K. In particular, fundamental physical data is needed on this system for incorporation into atmospheric models in order to better predict atmospheric cloud properties.22,23 Data, such as the equilibrium freezing temperature of ice and the solute saturation temperature as a function of solute concentration, are among the basic parameters that need to be © XXXX American Chemical Society
experimentally determined. The binary systems of ammonium sulfate/water and succinic acid/water have been extensively studied with respect to solubilities of the solute and solid/liquid phase equilibria.24−26 With respect to solute solubilities in the ternary (NH4)2SO4/C4H6O4/H2O system, eutonic (phase boundary) concentrations have been reported at two temperatures,19,20 which represent two saturation compositions in the ternary phase diagram. To our knowledge, no ice melting points, solubility of a single solute, or the boundary between the ice/succinic acid phase stability region have been reported in the literature for the (NH4)2SO4/C4H6O4/H2O system. We present here the results of our study of the lowtemperature solid/liquid phase diagram of ammonium sulfate/ succinic acid/water and water activities using thermal analysis and infrared (IR) spectroscopy techniques. We have coupled our experimental data with our previous results for the binary systems to construct a ternary phase diagram. We also compare our results to the predictions of the extended AIM aerosol thermodynamics model (E-AIM)22,27 using the web interface.28
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EXPERIMENTAL SECTION
Sample Preparation. Ternary samples were prepared by mixing 99 wt % ACS reagent-grade (NH4)2SO4 supplied by Sigma-Aldrich and 99 wt % ACS reagent-grade C4H6O4 supplied by Acros Organics with deionized water. The concentration of all samples is known to ±0.40 wt %. Special Issue: Mario Molina Festschrift Received: July 10, 2014 Revised: November 26, 2014
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Figure 1. Ternary diagram for the (NH4)2SO4/C4H6O4/H2O system indicating concentrations studied in our lab. Data from our group for the C4H6O4/H2O binary system26 and the (NH4)2SO4/H2O binary system25 are included in the figure for completeness.
ring. Sample volumes were approximately 2 μL. On each side of the aluminum block, a Pyrex cell was purged with dry nitrogen gas. KBr windows were placed on the end of each cell, sealed with o-rings, and held in place by metal clamps. Heat tape was wrapped around the purge cells to prevent condensation on the KBr windows at the lowest temperatures. The sample was cooled by pouring liquid nitrogen into a circular aluminum cup attached to the top of the main cell. The cell block was warmed by resistive heaters connected to a temperature controller. Temperature was measured by a copper/constantan thermocouple placed at the edge of the ZnSe windows and connected to the temperature controller. The temperature of the cell was calibrated using HPLC-grade water and high-purity organic solvents (Aldrich), decane, octane, and acetic anhydride, of which the melting points are 243.5, 216.4, and 200.2 K, respectively.31 The IR cell temperatures are known on average to within ±1.3 K, that is, a temperature that we measured in the IR cell of a specific transition is within 1.3 K of the transition temperature that we measure (of the same transition) using the DSC. Spectra were obtained with a Bruker Tensor 37 FTIR with a DTGS detector at 4 cm−1 resolution. Each spectrum was the average of eight scans. Before spectra were taken of a sample, a background scan was obtained from a dry, purged sample cell. Samples were cooled to 205 at 3 K/min and then allowed to warm to room temperature without resistive heating; typically, this was 1 K/min or less. If the final target temperature was above room temperature, then resistive heating was applied to
Differential Scanning Calorimeter (DSC). Thermal data were obtained with both a Mettler Toledo DSC 822e with liquid nitrogen cooling and a Mettler Toledo DSC 822e cooled via an intracooler. Each DSC utilized an HSS7 sensor. Highpurity-grade nitrogen was used as a purge gas with a flow rate of 50 mL/min. The temperature reproducibility of these instruments is better than ±0.05 K. Our accuracy is estimated to be ±0.9 K with a probability of 0.94 based on a four-point temperature calibration29 using indium, HPLC-grade water, anhydrous, high-purity (99%+) octane, and anhydrous, highpurity heptane (99%+) from Aldrich, the latter three stored under nitrogen. The enthalpy/heat capacity measurement of each DSC was also calibrated using the same substances and the known enthalpy of fusion for each substance, yielding an accuracy of ±3% with a probability of 0.92. Samples were contained in 40 μL aluminum pans with crimped lids to create a seal and typically had a mass of approximately 15−25 mg. Samples were weighed before and after the experiment using a Mettler-Toledo AT20 μg balance. The average mass loss from evaporation during the experiment was less than 1%. A typical sample was cooled to 205 at 10 K/ min, held at that temperature for 5 min, and then warmed at a rate of 1 K/min to a temperature at least 5 K above the predicted melting point. IR Spectra. The sample cell used for IR spectra is similar to that described in previous literature.30 A small drop of ternary solution was placed between two ZnSe windows, which were held in the center of an aluminum block by a threaded metal B
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Figure 2. Heating portion of DSC thermograms of two (NH4)2SO4/C4H6O4 samples: blue thermogram, 10/10 wt % (NH4)2SO4/C4H6O4; red thermogram, 10/1 wt % (NH4)2SO4/C4H6O4. In both thermograms, all transitions are endothermic and represent the following from low to high temperature: (NH4)2SO4 ferroelectric phase transition at 223 K (onset of transition), ternary eutectic transition at 254 K (onset of transition), and ice melting, which completes at the peak of the thermal signal at 270.0 (red thermogram) or 269.5 K (blue thermogram). Finally, the blue thermogram shows the slow dissolution of succinic acid that completes at 309.8 K (peak of transition in thermogram).
Figure 3. IR spectra of an aqueous 10/10 wt % (NH4)2SO4/C4H6O4 sample at the temperatures as given in the legend. The black spectrum is from NIST for solid succinic acid and has been reduced by a factor of 3 to bring absorptions in line with our spectra. The sample was cooled from approximately 320 to 233 K at 10 K/min. The sample was then heated at 1 K/min until all solids dissolve. The spectra have been offset by the following absorbance units for clarity: 234 K, +0.3; 256 K, +0.5; 272 K, +0.9; 311 K, +1.1.
also monitoring temperature. Identifying the precise temperature of phase transitions using IR spectroscopy alone can be very difficult because changes in IR spectra as a function of temperature/phase can be very subtle. Thus, we rely on the DSC experiments for accurate phase transition temperatures and the IR experiments for identification of phases. Therefore, to identify the presence of a particular phase that undergoes a transition to another phase (such as melting of a specific solid), one would observe an endothermic or exothermic transition in the DSC thermogram at the transition temperature and a change in the IR spectra at a similar temperature within a
increase temperature at about 1 K/min. Our spectra compare well for ice,32 ammonium sulfate,33 and succinic acid.33 Experimental Protocol. All samples at each concentration studied were run in both DSC and IR experiments. The DSC technique provides accurate and precise temperature and enthalpy data for phase transitions. Therefore, all temperatures reported here are from DSC experiments. However, the identity of solids that may be present cannot be uniquely identified from the DSC results; therefore, IR experiments are utilized to identify the solids/liquids/ions that may be present utilizing specific IR absorption bands, as stated above, while C
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reasonable temperature range (typically no greater than ±2 K of the DSC temperature).
either solid or aqueous forms. In the NIST spectrum, the solid has absorption bands at 1198 and 800 cm−1, which are indicated by vertical dotted lines in Figure 3. We also observed a small absorption band at 1238 cm−1 (marked by a vertical dotted line in Figure 3) that is present when succinic acid is dissolved in solution but is absent when it is in solid form. Given these spectral features and the known absorptions of (NH4)2SO4 and water in solid and solution,33,35 the state of each species can be determined in the IR spectra. Referring to Figure 3, we observe that at the start of the experiment (294 K), the solution is mostly liquid, but some C4H6O4 has already precipitated, as indicated by very small absorption bands beginning to appear at 1198 and 800 cm−1, while the band at 1238 cm−1 is still clearly present. The presence of succinic acid solid at this temperature is expected because in DSC experiments (blue thermogram in Figure 2), we determined the saturation temperature with respect to succinic acid to be 309.8 K. The sample was then cooled to 234 K (yellow spectrum), where it is seen that ice (very broad peak centered at 709 cm−1 narrows and shifts to a center at 831 cm−1), solid (NH4)2SO4 (NH4+ peak at 1450 cm−1 sharpens and shifts to 1412 cm−1; SO42− at 1101 cm−1 shifts to 1086 cm−1), and solid C4H6O4 are clearly present, and there appears to be no trace of solution. As the sample is warmed, the ternary eutectic temperature is passed, and at 256 K (green spectrum), the (NH4)2SO4 has dissolved with some C4H6O4 and water to form a solution at the ternary eutectic concentration. However, ice is still present as well as solid C4H6O4, as seen by the characteristic features in the spectrum. As the sample is warmed, ice slowly melts along with some dissolution of C4H6O4 along the phase boundary until the final melting of ice at 272 K (purple spectrum). Upon continued heating, the last C4H6O4 dissolves at 311 K (orange spectrum). Thus, the IR data are used to identify which solids are undergoing transition at the temperatures determined in the DSC experiments, and we find good agreement between the transition temperatures in the DSC experiment (blue thermogram in Figure 2) and the IR experiment. Phase Diagram. We fit the final melting/dissolution temperatures from the DSC experiments to polynomial equations as a function of C4H6O4 concentration (while holding the (NH4)2SO4 concentration constant. The polynomial fits are of the form
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RESULTS (NH4)2SO4/C4H6O4/H2O Data. The (NH4)2SO4/H2O and C4H6O4/H2O binary phase diagrams have been studied previously by our group,25,26 and those data are incorporated into our figures for analysis of the ternary system. Figure 1 shows the concentrations studied utilizing DSC and FTIR techniques. Samples at all concentrations appeared to completely freeze, as indicated by two (binary samples) or three (ternary samples) melting transitions in DSC and IR experiments. For ternary samples with very low [C4H6O4] (less that 2.1 wt %), which we determined to be in the ice primary phase region (ice melts last), only two endotherms were observed upon heating. These endotherms correspond to (1) the dissolution of (NH4)2SO4, dissolution of some C4H6O4, and the melting of some ice to form a ternary eutectic solution and (2) the slow melting of ice upon further heating. An example of these transitions is shown in the red thermogram in Figure 2 for a sample with [(NH4)2SO4] = 10 wt % and [C4H6O4] = 1 wt %. For this sample (and all samples with total concentration in the ice primary phase field), the dissolution of succinic acid should occur over a range of temperatures along the ice/succinic acid phase boundary. Given the small amount of C4H6O4 present and the slow dissolution as temperature increases, we would expect the thermal signal to be very small, and in fact, we conclude that it is too small to be detected in our DSC thermograms. Likewise, shifts in the IR spectra would be too small to be detected for these low concentrations of C4H6O4, which agrees with our observations. However, were succinic acid not to have crystallized, then some solution would remain at the lowest temperatures, and instead of a sharp endotherm in the DSC thermogram at the ternary eutectic, we would observe a slow dissolution of (NH4)2SO4 as the temperature increases, resulting in a long “tail” to the (NH4)2SO4 dissolution endotherm. This is not what we observed. We observed a sharp endothermic transition in all thermograms regardless of concentration for samples that have three dissolution/melting transitions (blue thermogram in Figure 2) and for those in the ice primary phase field where only two were discernible, as described above. The complete set of experimental final melting/dissolution points for ternary samples is given in Table S1 in the Supporting Information (throughout, we will refer to the transition H2O(s) → H2O(l) as “melting” and the transitions (NH 4 ) 2 SO 4 (s) → (NH4)2SO4(aq) and C4H6O4(s) → C4H6O4(aq) as “dissolution”). We utilized FTIR spectroscopy to identify the solids that formed and the order of melting/dissolution in our samples. Figure 3 shows a series of IR spectra in the fingerprint region for a 10/10 wt % (NH4)2SO4/C4H6O4 sample from a typical experiment where the sample is cooled to induce crystallization and then warmed to observe the melting or dissolution of each solid. In the experiment shown in Figure 3, the sample is placed on the IR windows above room temperature. However, by the time the first spectrum is acquired, the sample has reached room temperature, which in this experiment was 294.2 K (red spectrum in figure), and some precipitation of C4H6O4 is seen. We have included an IR spectrum of solid succinic acid from the NIST Standard Reference Database34 (black spectrum in figure) for comparison to our spectra. We utilized three unique absorption bands for succinic acid to detect its presence in
T = A 2 X2 + A1X + A 0
(1)
where T is the melting/dissolution temperature in Kelvin and X is the wt % of C4H6O4. The polynomial fits reproduced our final melting/dissolution temperatures to an average difference of ±0.34 K in the ice primary phase field, which is within our experimental error, and to an average difference of ±1.5 K in the succinic acid primary phase field. Nearly all samples studied were composed of ≤10 wt % succinic acid. Thus, the larger error in the final melts in the succinic primary phase field is due to the weaker signals that were seen for the succinic acid dissolution transitions in the thermograms (see Figure 2 for an example at 10 wt % C4H6O4.) Coefficient values for the parametrizations are given in Table 1 along with the concentration ranges for which the equations are valid. Typical plots of this analysis are given in Figure 4. Referring to the figure, it is seen for isothermal conditions that increasing the concentration of (NH4)2SO4 decreases the solubility of C4H6O4 or a “salting out” effect of (NH4)2SO4 on C4H6O4. To illustrate this at a single temperature (298 K), we calculated D
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Table 1. Melting/Dissolution Temperature Polynomial Coefficients from Equation 1a [(NH4)2SO4] 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 40
A2
A1
A0
Ice Primary Phase Field −0.2545 273.0 −0.1435 272.2 −0.1061 270.4 1.3853 268.2 0.0780 266.4 0.1528 263.7 −0.3411 262.0 −0.1272 0.3733 257.8 Succinic Acid Primary Phase Field −0.166 6.151 260.4 −0.3796 9.217 254.3 −0.5592 −11.36 251.6 −0.4615 10.28 256.2 −0.9985 −15.16 249.5 −1.465 19.28 245.2 −1.465 19.40 249.8 −1.549 20.11 252.5 −2.484 23.81 255.2
Table 2. Concentration of Liquid (wt %) That Is in Equilibrium with Two Solids at the Temperature Indicateda
range [C4H6O4]b
[(NH4)2SO4]
[C5H8O4]
[H2O]
temp (K)
solids in equilibrium
0.0 5.00 10.00 15.00 20.00 25.00 30.00 35.00 39.95
2.08 2.10 1.80 1.46 1.22 1.06 0.65 0.28 0.00
97.92 92.91 88.20 83.54 78.78 73.95 69.35 64.73 60.05
272.5 271.9 270.2 270.2 266.5 263.9 261.8 257.9 254.7
ice/C4H6O4 ice/C4H6O4 ice/C4H6O4 ice/C4H6O4 ice/C4H6O4 ice/C4H6O4 ice/C4H6O4 ice/C4H6O4 ice/(NH4)2SO4
0−PB 0−PB 0−PB 0−PB 0−PB 0−PB 0−PB 0−PB a
PB−15 PB−10 PB−10 PB−10 PB−7 PB−7 PB−7 PB−7 PB−4
Described as a “phase boundary” in the text.
Equation 1 was solved at each respective concentration of (NH4)2SO4 for specific temperatures (260, 265 K, etc.) to determine the concentration of C4H6O4 and thus construct isotherms on the ternary phase diagram. Figure 5 shows the portion of the (NH4)2SO4/C4H6O4/H2O phase diagram covered by the concentrations that we studied with the calculated isotherms (colored lines in the figure with corresponding temperatures indicated on the plot). It should be noted that the data used to construct Figure 5 are not continuous but rather are at specific concentration intervals, every 1 wt % or less, as shown in Figure 1. Therefore, the temperature contours are smoothed interpolations between data points and are only valid on the order of ±1 wt % for a given temperature. Ternary Eutectic. The ternary eutectic is an invariant point where all three solids are in equilibrium with the liquid phase and is the lowest temperature at which liquid can exist in equilibrium; therefore, all solid/liquid equilibrium points on the diagram are at higher temperature. The ternary eutectic also falls at the intersection of the ice/C4H6O4, ice/(NH4)2SO4, and (NH4)2SO4/C4H6O4 phase boundaries and occurs at the lowest temperature along these boundaries. The average ternary eutectic temperature of all ternary samples studied in DSC experiments was 254.24 ± 0.67 K. To aid in determining the
[(NH4)2SO4] and [C4H6O4] are in wt %. b“PB” indicates the phase boundary concentration as given in Table 2 for each respective concentration of (NH4)2SO4.
a
the solubility of C4H6O4 at each (NH4)2SO4 concentration that we studied using our fits to the data. We then plotted the solubility of C4H6O4 as a function of (NH4)2SO4 concentration and found the relationship to be linear (see Figure S1, Supporting Information). We also used the fits to our data to determine the ice/C4H6O4 phase boundary for (NH4)2SO4 concentrations up to and including 35 wt %. The equations on both sides of the phase boundary were solved simultaneously for the temperature and concentration where both solids and a liquid were in coexistence. These values are given in Table 2. For completeness, the ice/(NH4)2SO4 binary eutectic25 is included in Table 2.
Figure 4. Final melting points of ice and succinic acid dissolution at constant [(NH4)2SO4] as given in the legend. Curves are fits to the data as given by eq 1 with parameters in Table 1 E
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Figure 5. Portion of the solid/liquid phase diagram of the (NH4)2SO4/C4H6O4/H2O system ([H2O] > 50 wt %, [(NH4)2SO4] < 50 wt %, [C4H6O4] < 50 wt %, top portion of Figure 1) showing melting/dissolution point isotherms and phase boundaries (see the text for details); colored solid lines are calculated isotherms at temperatures in Kelvin as indicated on the figure, and the solid black curve is the phase boundary between ice and succinic acid from fits to the melting point curves as given in the text. At [(NH4)2SO4] > 39 wt %, the solid black curve represents the ice/ (NH4)2SO4 phase boundary. Red and blue solid circles correspond to the concentrations of the two thermograms in Figure 2 and are color coded to match the thermogram colors. Two eutonic points (point of saturation of (NH4)2SO4 and C4H6O4) from Brooks et al.19 are given on the figure: square, 297 K; triangle, 277 K. The single eutonic point of Wise et al.20 at 298 K is coincident with the concentration of the eutonic point of Brooks et al. at 297 K (triangle on the figure). The dashed black line is the predicted phase boundary between the (NH4)2SO4 and C4H6O4 primary phase fields from the data of Brooks et al. The intersection of the solid black line, and the dashed black line is the predicted concentration of the ternary eutectic.
concentration of the ternary eutectic point, we plotted the two data points from Brooks et al.19 in Figure 5 for (NH4)2SO4/ C4H6O4 saturation at 297 and 277 K. These points must lie on the (NH4)2SO4/C4H6O4 phase boundary, and thus, we connected them with a dashed line in Figure 5 as a simple linear fit and extended that line to the ice/C4H6O4 phase boundary that we determined (black curve in Figure 5). All of our samples studied at 40 wt % (NH4)2SO4, which were ≥1 wt % C4H6O4, as well as all samples studied at 42.5 wt % (NH4)2SO4, which were ≥2 wt % C4H6O4, were clearly in the succinic acid primary phase field as indicated by succinic acid final melt in the IR. This is in agreement with the data of Brooks et al. and the phase boundary line in Figure 5 connecting their points. It is seen that the intersection of our phase boundaries for ice/C4H6O4 and ice/(NH4)2SO4 and that of Brooks et al. for (NH4)2SO4/C4H6O4 occurs at 39 ± 0.5 wt % (NH4)2SO4 and 0.5 ± 0.3 wt % C4H6O4. Thus, we take this to be the concentration of the ternary eutectic. Water Activities. In a multicomponent system, the freezing point depression can be used to determine solvent activities via the equation36
ln a1 = −
∫T
f
Tf*
ΔHfus RT 2
dT
(2)
where a1 is the activity of water at Tf, ΔHfus is the molar enthalpy of fusion of ice, R = 0.008314 kJ mol−1 K−1, Tf is the depressed melting point, and T*f is the melting point of pure water. To a first approximation, the enthalpy of fusion can be considered constant as a function of temperature over a small temperature range; if this is done, the error in the calculated value of the water activity is less than 2% for the temperature range that we studied. However, for highest accuracy, the temperature dependence of ΔHfus should be accounted for. Therefore, ΔHfus needs to be expressed in terms of temperature so that the integral in eq 2 can be solved. We fit the values for ΔHfus of ice given in the Smithsonian Meteorological Tables37 for temperatures at 273.15 K and below to a second-order polynomial ΔHfus = −(2.330 × 10−4)T 2 + 0.1622T − 20.92
(3)
where T is in Kelvin and ΔHfus is in kJ/mol. Substituting eq 3 into eq 2 and integrating yields F
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Figure 6. Water activity coefficients as a function of [(NH4)2SO4] for C4H6O4 concentrations in the water primary phase field of the (NH4)2SO4/ C4H6O4/H2O ternary system. The solid line is a fit to all data with the equation given in the text. The fit to the model predictions of Koop and Zobrist38 is given by the black dashed line.
⎛ T* ⎞ 1⎡ ln a1 = − ⎢ −2.33 × 10−4(Tf* − Tf ) + 0.1622 ln⎜ f ⎟ R ⎢⎣ ⎝ Tf ⎠ ⎛ 1 1 ⎞⎤ + 20.92⎜ − ⎟⎥ Tf ⎠⎥⎦ ⎝ Tf*
using eq 7 by Koop and Zobrist by +0.003, with the greatest difference being +0.009. We have used the water activities predicted by Koop and Zobrist to calculate water activity coefficients at our experimental concentrations. The results are given in Figure 6. The best fit to the Koop and Zobrist predictions was also a second-order polynomial. At [(NH4)2SO4] < 25 wt %, the differences between our experiment-based activity coefficients and those predicted by the model are less than 0.004. At higher (NH 4 ) 2 SO 4 concentrations (>25 wt %), the difference in activity coefficients become larger but is no greater than 0.012, with the model-predicted activity coefficients tending toward lower values than ours. This seems counterintuitive as higher ionic solute concentration should lead to a less ideal solution, as our results show. Changing the C4H6O4 concentration has no impact on the agreement between model predictions and our results, again likely because the succinic acid concentrations are so low. Comparison to the E-AIM. We have compared our experimentally determined final melting (ice) and dissolution (succinic acid, ammonium sulfate) points with those predicted by the E-AIM22,27 using the web interface version (http:// www.aim.env.uea.ac.uk/aim/aim.php).28 Model II of the EAIM allows prediction of physical properties in systems containing one or more of the following in water: organics, H+, NH4+, SO42−, NO3−. Thus, this model was used for ammonium sulfate. For succinic acid, we used the UNIFACbased model with the Peng et al.39 parameters. Literature solubility data for succinic acid in water24,40 was used to constrain the model. First, a value for the enthalpy of dissociation for succinic acid at 298 K was entered (3.186 kJ/ mol41). Then, using the “Aqueous Solution and Liquid Mixture Calculation”, we entered the literature solubility (as molality) and temperatures in the range of 273−323 K and calculated the succinic acid molality (taking acid dissociation into account) and activity coefficients. These values were then used to calculate succinic acid activities (molality-based). The equili-
(4)
We have determined the water activities of our solutions using eq 4 at Tf for each concentration in the ice primary phase field. In our analysis, we also included binary C4H6O4/H2O and (NH4)2SO4/H2O solutions that we have previously studied.25,26 From the respective calculated activities, water activity coefficients (γ1) were calculated using a γ1 = 1 x1 (5) with x1 being the mole fraction of water for each system. The results are given in Table S1 (Supporting Information) and plotted in Figure 6. It is seen that throughout the range of concentrations studied here, the activity coefficients differ from unity by at most 0.068, with the average deviation being 0.034. In all cases for ternary samples, the activity coefficients were greater than 1. This was also the case for (NH4)2SO4/H2O binary solutions. As expected, the deviation of the water activity coefficient from unity increased with increasing (NH4)2SO4 concentration but was not dependent on the C 4 H 6 O 4 concentration, which is very low in the ice primary phase field. As seen in Figure 6, the relationship between the water activity coefficient and [(NH4)2SO4] is nearly linear with a best-fit equation of γ1 = −1.15 × 10−5W 2 + 2.11 × 10−3W + 1.00
(6)
where W represents the [(NH4)2SO4] in wt %. We have compared our calculated water activities to those predicted by Koop and Zobrist38 based on water and ice vapor pressure measurements and find good agreement. Our calculated water activities for those samples where ice is the final melting phase differ on average from the values calculated G
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in our experiments and determined the predicted final melting/ dissolution points. The results of our analysis are given in Figure 8 for several constant succinic acid concentrations. Excellent agreement is seen between our experimental data and the model predictions in the ice primary phase region. The only exception is for 2 wt % C4H6O4, where the E-AIM predicts the phase boundary between ice and succinic acid to be at a lower (NH4)2SO4 concentration than we observe. For all C4H6O4 concentrations that we studied of 1 wt % or larger, the E-AIM predicts lower succinic acid solubility temperatures than we observed. It must be noted the E-AIM does not allow for or include “salting out” or “salting in” effects. Therefore, the observation that E-AIM does not predict the salting out effect of (NH4)2SO4 on succinic acid that we observe in our measurements is as expected. Clegg and Seinfeld23 used a Pitzer molality-based model applied to the (NH4)2SO4/C4H6O4/H2O system and were able to reproduce the eutonic composition at 297 K reported by Brooks et al.19 with a moderate level of accuracy (0.058 mole fraction of succinic acid predicted by the model versus 0.04 mole fraction of succinic acid measured by Brooks et al.) The Clegg and Seinfeld model does incorporate parameters that account for salting in and salting out effects, and thus, their predictions are consistent with our experimental results. The comparison of the E-AIM predictions to our experimental results shows that the salting out effect is important in this and similar ternary systems and must be accounted for in models. Comparison of Dicarboxylic Acid/(NH4)2SO4/H2O Systems. We have studied five dicarboxylic acid/(NH4)2SO4/H2O ternary systems in our lab: C3H4O4/(NH4)2SO4/H2O,43 C4H4O4/(NH4)2SO4/H2O,44 C4H6O5/(NH4)2SO4/H2O,45 C5H8O4/(NH4)2SO4/H2O,46 and C4H6O4/(NH4)2SO4/H2O studied in this paper. Table 3 summarizes some of the key physical properties that we measured in these systems. As shown in the table, the concentration of both ammonium sulfate and the respective organic acid is lower at the ternary eutectic than it is for the respective aqueous binary system eutectic points. Also, when studying the ice/organic acid phase boundaries in each of the respective ternary systems, in all cases but two (succinic and glutaric), the equilibrium concentration of the organic acid was less than that at the organic acid/ice eutectic. For the C4H6O4/(NH4)2SO4/H2O and C5H8O4/ (NH4)2SO4/H2O systems, the equilibrium concentration of the organic acid at the phase boundary increases slightly for ammonium sulfate concentration of 5 wt %; however, at higher ammonium sulfate concentrations, the organic acid concentration decreases below the respective organic acid/water binary system eutectic concentration. Thus, addition of ammonium sulfate to the respective aqueous organic acid systems causes the respective organic acid to be less soluble at the temperature of coexistence with ice (salting out effect.) Similarly, the concentration of ammonium sulfate at the ice/ ammonium sulfate phase boundary decreases as temperature decreases to the ternary eutectic point. Thus, the addition of the respective organic acids that we studied to aqueous ammonium sulfate decreases the ammonium sulfate solubility at the ice/ammonium sulfate phase boundary. For C5H8O4/ (NH4)2SO4/H2O and C4H6O4/(NH4)2SO4/H2O systems, the temperature of the ternary eutectic is very near or at the temperature of the (NH4)2SO4/H2O eutectic temperature of 254 K. This is reflected in the observation that the organic acid concentration at the ternary eutectic is very small in both of these systems. Comparing the five systems, as the concen-
brium constant (K) can be related to the enthalpy of dissolution (ΔHdissol) by42 d(ln K ) d
1 T
()
=−
ΔHdissol R
(7)
where T is the Kelvin temperature. Thus, if ln K is plotted versus 1/T, then the slope is given by −ΔHdissol/R. For the dissolution of succinic acid, we have the reaction C4 H6O4 (s) ⇄ C4 H6O4 (aq)
(8)
and the equilibrium constant is simply equal to the succinic acid activity. Thus, we used the calculated activities of succinic acid from the E-AIM at the literature solubility temperatures and plotted ln K versus 1/T. This plot is given as Figure S2 (Supporting Information), and an excellent linear fit is achieved yielding ΔHdissol = 28.89 kJ/mol. The fit was also used to calculate the value of the equilibrium constant at 298 K, yielding a value of 0.6616 (molality scale). These values were entered into the model on the “Organic Compound Properties” page for succinic acid. We then ran the model using the “Parametric, varying temperature” calculation to check if the EAIM would accurately predict the solubility of succinic acid in water. Fixed liquid water was selected, and amounts of succinic acid were entered corresponding to the literature solubilities. The results are given in Figure 7 along with the literature
Figure 7. Succinic acid/water binary phase diagram with solubility data from the literature and the predictions of the E-AIM as discussed in the text. Red symbols are from experimental work as given in Beyer et al.:26 circles, ice melting points; squares succinic acid solubility; triangles, eutectic transitions. Blue symbols are solubility data from the literature: square, Stephen and Stephen24 Table 1179; diamond, Stephen and Stephen Table24 1180; circle, Apelblat and Manzurola;40 cross, Brooks et al.;19 triangle, Marcolli et al.21 Solid black curves are fits to all experimental data. The dashed curve is the predicted succinic acid solubility using E-AIM.
data24,40 and our results previously published.26 Excellent agreement is seen with the literature data, with our previously published solubilities at slightly higher temperatures at the low end of succinic acid concentrations. This is likely due to interference between dissolution and eutectic signals in the DSC and the very small value for ΔHdissol, as discussed earlier in the Results section. We then input the amounts of (NH4)2SO4, C4H6O4, and H2O in the model to match the concentrations that we studied H
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Figure 8. Ice and succinic acid solubility temperatures as a function of (NH4)2SO4 concentration for the following succinic acid concentrations: (a) 0.5, (b) 1, (c) 2, (d) 3, (e) 4, (f) 5, and (g) 7 wt %. Symbols in each panel are as follows: circle, experimental ice melting point; square, experimental succinic acid solubility point; ×, E-AIM predicts that (NH4)2SO4 will precipitate at this point instead of succinic acid. Dashed lines are the E-AIM prediction of ice melting. Solid curves are the E-AIM prediction of the succinic acid solubility. I
dx.doi.org/10.1021/jp506902q | J. Phys. Chem. A XXXX, XXX, XXX−XXX
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Table 3. Summary of Physical Data for Several Aqueous Binary and Corresponding Dicarboxylic Acid/(NH4)2SO4/H2O Systems
highly concentrated in solute and viscous. This resulting solution may have had a high barrier to either nucleation or crystal growth. In the case of C4H6O5/(NH4)2SO4/H2O, we never observed a ternary concentration at which all three solids formed. At most, two solids formed (either ice/solid C4H6O5 or ice/solid (NH4)2SO4), and for most concentrations, only one solid formed (ice).45 This leads to the conclusion that the C4H6O5/NH4+/SO42− interactions are favorable in solution, leading to a very low ternary eutectic temperature. This may not be surprising for C4H6O5 given that it has three OH bonds and two CO bonds (more than the other dicarboxylic acids that we studied), which would lead to strong interactions with water and NH4+/SO42− ions.
tration of organic acid increases at the ternary eutectic, the temperature of the ternary eutectic also decreases (see Table 3, 251 K for maleic acid with a ternary eutectic concentration of 10 wt % and
