Article pubs.acs.org/jced
Determination and Modeling of Solubility for CaSO4·2H2O−NH4+−Cl−−SO42−−NO3−−H2O System Ping Tian, Pengge Ning, Hongbin Cao,* and Zhibao Li* Research Centre for Process Pollution Control, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ABSTRACT: The solubility of gypsum (CaSO4·2H2O) in ammonium solutions plays a significant role to prevent gypsum scaling on the heater and tower in the treatment of ammonium-N wastewater bearing sulfate ions by the steam stripping process. In this work solubilities of calcium sulfate dihydrate in NH4Cl, NH4NO3, and mixed NH4Cl and (NH4)2SO4 solutions up to 343.15 K were measured using the classic isothermal dissolution method. The investigated concentration (at ambient temperature) is up to 1.50 mol·dm−3 for both NH4Cl and NH4NO3. The solubility of CaSO4·2H2O was found to increase sharply with either NH4Cl or NH4NO3 concentration, whereas the temperature has a limited effect. The XRD analysis of equilibrated solids for these systems shows that CaSO4·2H2O is stable in all cases over the temperature range (298.15 to 343.15) K. The electrolyte nonrandom two-liquid (the electrolyte NRTL) model embedded in AspenPlus was applied to model the solubility of CaSO4·2H2O in the above systems. The newly obtained model parameters were used to well estimate the solubility of CaSO4·2H2O in all cases with a relative deviation of 1.52 %.
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Souheil et al.15 studied the effect of ammonia solution on the solubility of calcium sulfate dihydrate. However, there has been limited information about the solubility of CaSO4·2H2O in the NH4+−Cl−−SO42‑−NO3−−H2O system at elevated temperatures. In addition, theoretical models for the solubility of calcium sulfate in pure or mixed electrolyte solutions have been investigated by many researchers. Wang et al.16 used Pizter equation to model the gypsum solubility in MSO4 + H2SO4 + H2O (M = Cu, Zn, Ni, and Mn) systems at 298.15 K with good results. Azimi et al.17−19 successfully employed the mixed solvent electrolyte (MSE) model to predict the solubility of gypsum in multicomponent sulfate solutions, mixed chloride−sulfate solutions, and zinc processing solutions. Messnaoui et al.20 developed the electrolyte NRTL model to calculate the solubility of hemihydrate and dihydrate of calcium sulfate in the complex system Ca2+−HSO4−−SO42−− H+−H2PO4−−H3PO4−H2O at a wide range of temperatures and P2O5 concentrations. In the present study, the electrolyte NRTL model proposed by Chen et al.21 was selected to model the solubility of gypsum in the NH4+−Cl−−SO42‑−NO3−−H2O system at various temperatures and concentrations. The purpose of the present work is first to measure the solubility of calcium sulfate dihydrate in the solutions of NH4Cl, NH4NO3, and mixed NH4Cl and (NH4)2SO4 over a temperature range of (298.15 to 343.15) K and wide concentrations. Second, the electrolyte NRTL model embedded in AspenPlus has been applied to model calcium sulfate dihydrate in the above systems. New interaction parameters were obtained via regression of
INTRODUCTION Ammonium from industrial, agricultural, and domestic wastewater discharges is one of the major contributors to ecological eutrophication. Facing increasingly stringent discharge limits, much attention has been devoted to develop a new method for ammonium removal. Conventional approaches include steam stripping,1 biological treatments,2 chemical precipitation,3 ion exchange,4 and membrane processes.5 Among various methods available, steam stripping is preferred to remove ammonium from ammonia-N wastewater with high concentration more than 500 mg·L−1, such as tannery, textile, landfill leachate, and fertilizer wastewater.6 In this process, hydrated lime is applied as the pH adjuster. Ammonia is liberated by the reaction of ammonium ion with hydroxide ions in milk of hydrated lime and then stripped off the suspension by heating to about 90 to 100 °C with steam. The ammonia is finally recovered from wastewater. However, insoluble gypsum is formed when the ammonia-N wastewater contains sulfate ion as is typical. As a result, the gypsum scale leads to a blocked heat exchanger pipe and tower and reduces removal efficiency of ammonium. Therefore, the solubility determination and modeling of gypsum (CaSO4·2H2O) in ammonium solutions prove important for optimal operation of the steam stripping process. A number of works7−11 on solubility determination of CaSO4·2H2O in various media, such as ammonium sulfate solution, have been extensively studied. Sulliva,12 and Bell and Tell13 measured the solubilities of calcium sulfate dihydrate in different concentrations of ammonium sulfate at (298.15 and 323.15) K, respectively. Hill and Yanic14 investigated the solubility of calcium sulfate dihydrate at a wide range of temperatures and concentrations of ammonium sulfate. More recently, © XXXX American Chemical Society
Received: August 5, 2012 Accepted: October 24, 2012
A
dx.doi.org/10.1021/je300871p | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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experimentally determined solubility. With the new parameters, a new model was established for modeling the solubility of CaSO4·2H2O in the NH4+−Cl−−SO42‑−NO3−−H2O system, providing a thermodynamic basis for prediction of gypsum scale in the treatment of ammonium-N wastewater by the steam stripping process.
In AspenPlus, an empirical equation was employed to calculate the solubility product constant (KSP) below ln KSP = A +
■
Gm*E = Gm*E,PDH + Gm*E,lc
(3)
Taking the appropriate derivative, the activity coefficient of the mixed electrolyte system can be expressed as follows: ln γi* = ln γi*PDH + ln γi*lc
(4)
The excess Gibbs free energy expression for long-range ion− ion interactions represented by the Pitzer−Debye−Hückel model is given by ⎛ 1000 ⎞1/2 ⎛ 4AφIx ⎞ Gm*E,PDH 1/2 = − (∑ x k )⎜ ⎟ ⎜ ⎟ ln(1 + ρIx ) RT ⎝ MB ⎠ ⎝ ρ ⎠ k (5)
Taking the appropriate derivative of eq 5, an expression for the activity coefficient can be determined ⎛ 1000 ⎞1/2 ⎡⎛ 2Zi2 ⎞ Z 2I1/2 − 2Ix3/2 ⎤ ⎥ ⎟ ln(1 + ρIx1/2) + i x ln γi*PDH = − ⎜ ⎟ Aφ⎢⎜ ⎢ ρ M ⎝ B ⎠ 1 + ρIx1/2 ⎥⎦ ⎠ ⎣⎝
(6)
The local interaction contribution is accounted for by the NRTL theory with the basic assumption that the nonideal entropy of mixing is negligible compared to the heat of mixing. In the mixed electrolyte systems the excess Gibbs energy expression is Gm*E,lc = RT
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THERMODYNAMIC MODELING FRAMWORK Chemical Equilibria. The solubility equilibrium of CaSO4·2H2O in NH4+−SO42‑−Cl−−NO3− solutions can be described by following dissolution reaction:
∑ XB B
×
×
2−
CaSO4 ·2H 2O(s) = Ca (aq) + SO4 (aq) + 2H 2O(l)
The solubility product constant, KSP, for CaSO4·2H2O is expressed as K sp = aCa 2+aSO4 2‐aH2O2 = mCa 2+mSO4 2‐γ±2·a H2O2
(2)
where A, B, C, and D are empirical parameters and already exist in the databank of AspenPlus in this work. Electrolyte NRTL Model for Mixed Electrolyte Systems. To model solubilities of calcium sulfate dihydrate in NH4+− SO42‑−Cl−−NO3−−H2O system, it is significant to precisely calculate the activity coefficient of ions in the saturated solutions. The electrolyte NRTL model, originally proposed by Chen et al.21 for the mixed electrolyte systems over the entire range of electrolyte concentrations, is a versatile thermodynamic model to compute the activity coefficient. This model is based on two fundamental assumptions, one for like-ion repulsion assumption and the other for local electroneutrality assumption. The excess Gibbs energy expression contains two contributions: (i) a contribution for the long-range ion−ion interactions represented by the Pitzer−Debye−Hückel model, and (ii) another contribution for the local interactions represented by the non-random two liquid (NRTL) theory. The electrolyte NRTL model is described by the following excess Gibbs free energy expression:
EXPERIMENTAL SECTION Materials. The chemicals used in this work include calcium sulfate dihydrate (mass fraction purity ≥ 99 %), ammonium sulfate (mass fraction purity ≥ 99.5 %), ammonium chloride (mass fraction purity ≥ 99.5 %), and ammonium nitrate (mass fraction purity ≥ 99.0 %). All reagents above were purchased from Sinopharm Chemical Reagent Co. Ltd. and were directly used without further purification. All solutions used in this study were prepared by dissolving the specified chemicals in double deionized water (conductivity < 0.1 μS·cm−1). Apparatus and Procedure. The experimental approach used in the present work is the isothermal dissolution method that has been discussed in detail in the previous literature.22 The experiments were carried out in a 500-mL glass bottle equipped with a magnetic stirrer and sealed with a rubber stopper. A water bath was used to maintain the system temperature. First, 300 mL of the electrolyte solution with known composition was added into the bottle and preheated to a fixed temperature at a constant stirring rate in the water bath. Then, excess solid (4g) was added to the solution in a flash. The temperature was kept constant within 0.1 K. The standard equilibration time used was 24 h, which was adopted by many researchers.24,25 After the solid− liquid equilibrium was attained, stirring was stopped to allow solids to settle. The supernatant solution was taken off and immediately filtered through a 0.22 μm membrane filter. The clear filtrate was moved into a 25-mL volumetric flask kept in the same water bath for measuring the density of the saturated solution. The measured densities were uncertain to 0.0001 g·cm−3. The content of Ca was determined by titration with EDTA using calconcarboxylic acid as an indicator. The solid phase was filtered and washed with double distilled water 3 times and with ethanol 2 times, dried at 333.15 K for 24 h, and finally subjected to XRD (X’Pert PRO MPD PANalytical Netherlands) analysis to determine whether the solid phase had been altered by phase transformation. Reproducibility. To assess the accuracy and reproducibility of the apparatus and procedure adopted above, the solubility of CaSO4·2H2O in pure water was determined in this work and compared with the values reported in the literature.25 The result showed that the experimental values agreed well with the published solubility data. The overall average absolute deviation was only ± 0.00025 mol·kg−1 with a relative deviation of 0.5 %. It is concluded the apparatus and procedure were reliable to measure the experimental solubility in this work.
2+
B + C ln T + DT T
∑j XjGjB ∑k XkGkB
⎛
+
∑j XjGjc , a ′ cτjc , a ′ c ∑k XkGkc , a ′ c
Xa ⎞ ⎟⎟ ⎝ ∑a ″ Xa ″ ⎠
∑ Xc ∑ ⎜⎜ c
a′
⎛
+
Xc ′ ⎞ ⎟⎟ ⎝ ∑c ″ Xc ″ ⎠
∑ Xa ∑ ⎜⎜ a
c′
∑j XjGja , c ′ aτja , c ′ a ∑k XkGka , c ′ a
(7)
In the electrolyte NRTL model, the local composition activity coefficient contains three parts as described below: The activity coefficient equation for molecular components is given by
(1) B
dx.doi.org/10.1021/je300871p | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data ln γBlc =
∑j XjGj Bτj B
+
∑k XkGk B
∑ B′
Article
∑ XG τ ⎞ XB ′G BB ′ ⎛ ⎜⎜τBB ′ − k k kB ′ kB ′ ⎟⎟ ∑k XkGkB ′ ⎝ ∑k XkGkB ′ ⎠
τB,ca = C B,ca +
⎛ X ⎞ XcG Bc , a ′ c ⎛ ⎞ ∑ XG τ a′ ⎟ ⎜⎜τBc , a ′ c − k k kc , a ′ c kc , a ′ c ⎟⎟ + ∑ ∑ ⎜⎜ ⎟ ∑k XkGkc , a ′ c ⎠ c a ′ ⎝ ∑a ″ Xa ″ ⎠ ∑k Xk Gkc , a ′ c ⎝ ⎞ ∑ XG τ Xc ′ ⎞ XaG Ba , c ′ a ⎛ ⎟⎟ ⎜⎜τBa , c ′ a − k k ka , c ′ a ka , c ′ a ⎟⎟ ∑k XkGka , c ′ a ⎠ ⎝ ∑c ″ Xc ″ ⎠ ∑k XkGka , c ′ a ⎝
∑ ∑ ⎜⎜ a
c′
T
⎡ (T − T ) ⎛ T ⎞⎤ + E B,ca⎢ r + ln⎜ ⎟⎥ ⎢⎣ T ⎝ Tr ⎠⎥⎦
τc ′ a,c ″ a = Cc ′ a,c ″ a +
Dc ′ a,c ″ a T
⎡ (T − T ) ⎛ T ⎞⎤ + Ec ′ a,c ″ a⎢ r + ln⎜ ⎟⎥ ⎢⎣ T ⎝ Tr ⎠⎥⎦
(16)
(8)
The activity coefficient equation for cations is given by 1 ln γc*lc = Zc
τca ′ ,ca ″ = Cca ′ ,ca ″ +
⎛
Xa ′ ⎞ ∑k XkGkc , a ′ cτkc , a ′ c ⎟⎟ ⎝ ∑a ″ Xa ″ ⎠ ∑k XkGkc , a ′ c
∑ ⎜⎜ a′
+∑ B
To model the solubility of CaSO4·2H2O in Cl−−NO3−H2O system, three adjustable parameters C, D, and E in eqs 14−17 need to be calculated over the whole range of temperature to obtain each interaction energy parameter τ. Compilation and Reduction of Experimental Data. In AspenPlus, the mole fraction xi is used in all calculation process. Therefore, molality mi needs to be conversion via the following relation: mi xi = n ∑ j vjmj + 55.508 (18)
Xc ′ ⎞ XaGca , c ′ a ⎟⎟ ⎝ ∑c ″ Xc ″ ⎠ ∑k XkGka , c ′ a
∑ ∑ ⎜⎜ c′
⎛ ∑ XkGka , c ′ aτka , c ′ a ⎞ ⎟⎟ × ⎜⎜τca , c ′ a − k ∑k XkGka , c ′ a ⎠ ⎝
(9)
The activity coefficient equation for anions is given by
Based on the maximum-likelihood principle,26 the general objective function was used to optimize the solubility data as follows:
⎛ X ⎞ ∑ XkGk a, c ′ aτk a, c ′ a 1 c′ ⎟⎟ k ln γa*lc = ∑ ⎜⎜ ∑ ∑k XkGk a, c ′ a Za X c′ ⎝ c″ c″ ⎠ +∑ B
2 ⎡ ⎛ exp ⎛ P exp − P cal ⎞2 Ti − Tical ⎞ i ⎢ ⎟⎟ + w2⎜⎜ i ⎟⎟ OBF = min ∑ w1⎜⎜ ⎢ σ σ ⎝ ⎠ ⎝ ⎠ T P i ⎣
∑ XG τ ⎞ XBGaB ⎛ ⎜⎜τaB − k k kB kB ⎟⎟ ∑k XkGkB ⎝ ∑k XkGkB ⎠ ⎛
+
Xa ′ ⎞ XcGac , a ′ c ⎟⎟ ⎝ ∑a ″ Xa ″ ⎠ ∑k XkGkc , a ′ c
∑ ∑ ⎜⎜ c
a′
⎛ ∑ XkGkc , a ′ cτkc , a ′ c ⎞ ⎟⎟ × ⎜⎜τac , a ′ c − k ∑k XkGkc , a ′ c ⎠ ⎝
■
αcB =
∑a XaGca ,B ∑a ′ Xa ′ ∑a Xaαca,B ∑a ′ Xa ′
, GaB =
, αaB =
∑c XcGca,B ∑c ′ Xc ′
,
∑c Xcαca,B ∑c ′ Xc ′
Gka,c ′ a = e−τka,c′aα
(11) (12)
τBa,ca = τaB − τca,B + τB,ca , τBa,ac = τcB − τca,B + τB,ca , τca,c ′ a = −τc ′ a,ca , τca,ca ′ = −τca ′ ,ca
(13)
The electrolyte NRTL parameters are the nonrandomness factors α and the energy parameters τ of the local composition term. In practice, the value of α usually is 0.2 for molecule−electrolyte and electrolyte−electrolyte, and the energy parameters τ are written as a function of temperature as follows. Electrolyte−molecule pair parameters: τca,B = Cca,B +
Dca,B T
⎡ (T − T ) ⎛ T ⎞⎤ + Eca,B⎢ r + ln⎜ ⎟⎥ ⎢⎣ T ⎝ Tr ⎠⎥⎦
⎛ x exp − x cal ⎞2 ⎤ i ⎟⎟ ⎥ + w3⎜⎜ i σx ⎝ ⎠ ⎥⎦
(19)
RESULTS AND DISCUSSION Solubility of CaSO4·2H2O in NH4Cl Solutions. Calcium sulfate dihydrate solubilities in ammonium chloride solutions were measured from (298.15 to 343.15) K. The investigated concentration of ammonium chloride is from (0.0 to 1.5) mol·dm−3 at room temperature. The results of experiment are summarized in Table 1 and graphically in Figure 1. The experimental solubility of CaSO4·2H2O increases sharply with an increase NH4Cl concentration but has been slightly affected by temperature. The XRD analysis of equilibrated solid phases is shown in Figure 5 and Table 4, indicating CaSO4·2H2O to be stable in NH4Cl solutions at the temperature range of (298.15 to 343.15) K. For modeling the system of CaSO4·2H2O−NH4Cl−H2O by the electrolyte NRTL embedded in AspenPlus, eight energy parameters τ for both electrolyte−H2O and electrolyte−electrolyte need to be determined. The interaction parameters for electrolyte− H2O were retained in the AspenPlus’s default database. The binary parameters τ (Ca 2 + ,SO 4 2− )−(Ca 2+ ,Cl − ) and τ (Ca 2 + ,Cl − )−(Ca 2+ ,SO 4 2 − ) , τ(Ca2+,SO42−)−(NH42+,SO42−), and τ(NH42+,SO42−)−(Ca2+,SO42−) were regressed with the solubility data measured by Li22 and Hill,14 respectively. The other parameters were regressed with the solubility values determined in this work. The regressed model parameters were tabulated in Table 5. The calculated results for the solubilities of CaSO4·2H2O in NH4Cl solutions with these new parameters are shown in Figure 1, indicating that ENRTL model can well
(10)
Other quantities are defined below GcB =
T
⎡ (T − T ) ⎛ T ⎞⎤ + Eca ′ ,ca ″⎢ r + ln⎜ ⎟⎥ ⎢⎣ T ⎝ Tr ⎠⎥⎦ (17)
∑ XG τ ⎞ XBGcB ⎛ ⎜⎜τcB − k k kB kB ⎟⎟ ∑k XkGkB ⎝ ∑k XkGkB ⎠
a
Dca ′ ,ca ″
NH4+−SO42−−
⎛
+
(15)
Electrolyte−electrolyte pair parameters:
⎛
+
DB,ca
(14) C
dx.doi.org/10.1021/je300871p | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 1. Solubility of CaSO4 (1) as Dihydrate in NH4Cl(2)−H2O Systems (Equilibration Time: 24 h) solubility as CaSO4 in different units
solution parameters M2 mol·dm
ρs
m2 −3
mol·kg
−1
0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.1000 1.2000 1.3000 1.4000 1.5000
0.0000 0.0502 0.1007 0.1513 0.2021 0.2531 0.3043 0.4079 0.5118 0.6164 0.7219 0.8282 0.9354 1.0434 1.1503 1.2598 1.3702 1.4816 1.5938
0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.1000 1.2000 1.3000 1.4000 1.5000
0.0000 0.0502 0.1007 0.1513 0.2021 0.2531 0.3043 0.4079 0.5118 0.6164 0.7219 0.8282 0.9354 1.0434 1.1503 1.2598 1.3702 1.4816 1.5938
g·cm
M1 −3
298.15 K 0.9973 1.0006 1.0093 1.0038 1.0075 1.0083 1.0152 1.0161 1.0212 1.0212 1.0117 1.0154 1.0150 1.0188 1.0204 1.0211 1.0227 1.0247 1.0258 308.15 K 1.0041 0.9971 1.0014 0.9996 1.0029 1.0007 1.0036 1.0167 1.0162 1.0189 1.0125 1.0189 1.0186 1.0261 1.0194 1.0185 1.0205 1.0219 1.0256
M2
m1 −3
mol·dm
mol·kg
solubility as CaSO4 in different units
solution parameters
−1
mol·dm
ρs
m2 −3
mol·kg
−1
0.0151 0.0199 0.0233 0.0261 0.0284 0.0306 0.0326 0.0361 0.0390 0.0416 0.0438 0.0463 0.0487 0.0501 0.0526 0.0546 0.0551 0.0561 0.0575
0.0151 0.0200 0.0232 0.0263 0.0286 0.0309 0.0328 0.0364 0.0394 0.0423 0.0452 0.0479 0.0507 0.0523 0.0551 0.0574 0.0583 0.0595 0.0613
0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.1000 1.2000 1.3000 1.4000 1.5000
0.0000 0.0502 0.1007 0.1513 0.2021 0.2531 0.3043 0.4079 0.5118 0.6164 0.7219 0.8282 0.9354 1.0434 1.1503 1.2598 1.3702 1.4816 1.5938
0.0156 0.0202 0.0236 0.0262 0.0288 0.0310 0.0330 0.0365 0.0399 0.0424 0.0450 0.0475 0.0493 0.0509 0.0528 0.0546 0.0558 0.0570 0.0585
0.0155 0.0204 0.0238 0.0265 0.0291 0.0315 0.0336 0.0369 0.0406 0.0432 0.0464 0.0489 0.0511 0.0527 0.0554 0.0576 0.0592 0.0607 0.0624
0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.1000 1.2000 1.3000 1.4000 1.5000
0.0000 0.0502 0.1007 0.1513 0.2021 0.2531 0.3043 0.4079 0.5118 0.6164 0.7219 0.8282 0.9354 1.0434 1.1503 1.2598 1.3702 1.4816 1.5938
g·cm
M1 −3
323.15 K 0.9995 0.9919 0.9966 0.9955 0.9994 0.9973 1.0018 1.0062 1.0141 1.0137 1.0145 1.0089 1.0147 1.0157 1.0185 1.0168 1.0198 1.0219 1.0293 343.15 K 0.9947 0.9941 0.9957 0.9900 0.9943 0.9944 0.9962 0.9986 0.9946 0.9978 0.9980 1.0017 1.0013 1.0030 1.0040 1.0056 1.0069 1.0044 1.0077
mol·dm
m1 −3
mol·kg−1
0.0154 0.0201 0.0234 0.0261 0.0287 0.0307 0.0328 0.0365 0.0398 0.0423 0.0449 0.0473 0.0492 0.0508 0.0524 0.0536 0.0558 0.0565 0.0583
0.0154 0.0203 0.0237 0.0265 0.0291 0.0313 0.0334 0.0372 0.0405 0.0434 0.0462 0.0493 0.0513 0.0531 0.0550 0.0567 0.0592 0.0601 0.0619
0.0146 0.0192 0.0225 0.0250 0.0277 0.0300 0.0322 0.0354 0.0389 0.0416 0.0443 0.0463 0.0486 0.0508 0.0519 0.0533 0.0555 0.0561 0.0580
0.0147 0.0194 0.0228 0.0256 0.0283 0.0307 0.0327 0.0363 0.0404 0.0433 0.0464 0.0486 0.0513 0.0538 0.0553 0.0570 0.0596 0.0607 0.0630
For the CaSO4·2H2O−NH4NO3−H2O system, another six new model parameters need to be obtained via regressing the experimental solubility data. Newly regressed model parameters are shown in Table 5 and the regressed solubility values for the solubility of CaSO4·2H2O in NH4NO3−H2O system are depicted in Figure 2. The results demonstrate that the effect of NH4NO3 concentration and temperature on the solubility of CaSO4·2H2O could be well represented with the ARD of 0.90 % as shown in Figure 3. Solubility of CaSO4·2H 2O in the Mixed NH 4Cl− (NH4)2SO4 Solutions. The solubilities of calcium sulfate dihydrate in the mixed NH4Cl and (NH4)2SO4 (0.50 mol·dm−3) solutions are shown in Table 3 and also presented graphically in Figure 4. The concentration of NH4Cl investigated is in the range
represent the effect of temperature and NH4Cl concentration on the solubility of CaSO4·2H2O. The average relative deviations (ARD) between experimental and calculated values are 1.94 % as presented in Figure 3. Solubility of CaSO4·2H2O in NH4NO3 Solutions. The measured solubilities of calcium sulfate dihydrate in various NH4NO3 solutions from (298.15 to 343.15) K are given in Table 2 and depicted in Figure 2. Figure 2 reveals the augment of NH4NO3 concentration from (0.0 to 1.50) mol·dm−3 leads to a rapid increase of the dihydrate solubility while the effect of temperature on the solubility is not evident. The XRD results tabulated in Table 4 show the solid phase is stable in the NH4NO3−H2O system over the whole temperature range. D
dx.doi.org/10.1021/je300871p | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 1. Molality solubility of CaSO4 against molality of NH4Cl solution at different temperatures. Points, experimental data in this work:●, 298.15 K; red triangle, 308.15 K; green triangle, 323.15 K; blue square, 343.15 K; lines, calculated results.
Figure 2. Molality solubility of CaSO4 against molality of NH4NO3 solution at different temperatures. Points, experimental data in this work: ●, 298.15 K; red triangle, 308.15 K; green triangle, 323.15 K; blue square, 343.15 K; lines, calculated results.
of (0.0 to 1.5) mol·dm−3 and temperature range up to 343.15 K. As demonstrated in Table 3 and Figure 3, the solubility of dihydrate consistently increases with increasing NH4Cl concentration and temperature. These results show that the presence of (NH4)2SO4 in NH4Cl solutions markedly decreases the dihydrate solubility several times by common ion effect in
comparison with the values in NH4Cl solutions. Furthermore, the larger effect of temperature on dihydrate solubility in this mixture system was also caused by the addition of (NH4)2SO4.14 The XRD results as shown in Table 4 demonstrate that CaSO4·2H2O is stable in the mixed solutions over a temperature range of (298.15 to 343.15) K.
Table 2. Solubility of CaSO4 (1) as Dihydrate in NH4NO3(2)−H2O Systems (Equilibration Time: 24 h) solubility as CaSO4 in different units
solution parameters M2 mol·dm
ρs
m2 −3
mol·kg
−1
0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.2000 1.5000
0.0000 0.1007 0.2025 0.3053 0.4093 0.5145 0.6207 0.7282 0.8369 0.9468 1.0580 1.2842 1.6338
0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.2000 1.5000
0.0000 0.1007 0.2025 0.3053 0.4093 0.5145 0.6207 0.7282 0.8369 0.9468 1.0580 1.2842 1.6338
g·cm
M1 −3
298.15 K 0.9973 1.0019 1.0066 1.0104 1.0134 1.0150 1.0257 1.0239 1.0274 1.0327 1.0346 1.0408 1.0494 308.15 K 1.0041 1.0023 1.0025 1.0080 1.0105 1.0125 1.0203 1.0204 1.0252 1.0309 1.0318 1.0434 1.0495
M2
m1 −3
mol·dm
mol·kg
solubility as CaSO4 in different units
solution parameters
−1
mol·dm
ρs
m2 −3
mol·kg
−1
0.0151 0.0236 0.0288 0.0329 0.0373 0.0408 0.0439 0.0467 0.0492 0.0519 0.0541 0.0580 0.0635
0.0151 0.0238 0.0291 0.0335 0.0382 0.0420 0.0451 0.0485 0.0513 0.0543 0.0569 0.0617 0.0685
0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.2000 1.5000
0.0000 0.1007 0.2025 0.3053 0.4093 0.5145 0.6207 0.7282 0.8369 0.9468 1.0580 1.2842 1.6338
0.0156 0.0237 0.0293 0.0335 0.0375 0.0410 0.0440 0.0471 0.0493 0.0519 0.0542 0.0580 0.0635
0.0155 0.0239 0.0298 0.0342 0.0385 0.0424 0.0455 0.0490 0.0515 0.0544 0.0572 0.0615 0.0685
0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.2000 1.5000
0.0000 0.1007 0.2025 0.3053 0.4093 0.5145 0.6207 0.7282 0.8369 0.9468 1.0580 1.2842 1.6338
E
g·cm
M1 −3
323.15 K 0.9967 0.9968 1.0042 1.0040 1.0078 1.0127 1.0177 1.0206 1.0224 1.0254 1.0303 1.0380 1.0380 343.15 K 0.9947 0.9872 0.9955 0.9935 0.9987 0.9987 1.0079 1.0058 1.0125 1.0159 1.0158 1.0268 1.0340
mol·dm
m1 −3
mol·kg−1
0.0154 0.0234 0.0296 0.0333 0.0373 0.0405 0.0435 0.0464 0.0489 0.0511 0.0533 0.0571 0.0631
0.0155 0.0237 0.0300 0.0341 0.0384 0.0418 0.0451 0.0484 0.0512 0.0539 0.0564 0.0608 0.0687
0.0146 0.0224 0.0289 0.0326 0.0358 0.0396 0.0424 0.0456 0.0476 0.0495 0.0513 0.0554 0.0606
0.0147 0.0230 0.0296 0.0337 0.0371 0.0415 0.0444 0.0482 0.0504 0.0526 0.0550 0.0596 0.0663
dx.doi.org/10.1021/je300871p | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Figure 3. Relative deviation w % = 100·{m(exp) − m(cal)}/m(exp) of the experimental molality solubility m of CaSO4 in different ammonium solution from the value obtained from electrolyte NRTL model calculation as a function of temperature T. Orange circle, NH4Cl−H2O; blue ×, NH4Cl-(NH4)2SO4−H2O; green square, NH4NO3−H2O.
Figure 4. Molality solubility of CaSO4 against molality of mixed NH4Cl−(NH4) 2SO4 solution at different temperatures. Points, experimental data in this work: ●, 298.15 K; red triangle, 308.15 K; green triangle, 323.15 K; blue square, 343.15 K; lines, predicted results.
Table 3. Solubility of CaSO4 (1) as Dihydrate in NH4Cl(2)−(NH4)2SO4 (3) −H2O Systems (Equilibration Time: 24 h) solubility as CaSO4 in different units
solution parameters M2 mol·dm
m2 −3
mol·kg
ρs
M3 −1
0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.1000 1.3000 1.5000
0.0000 0.0516 0.1035 0.1555 0.2078 0.2603 0.3130 0.4191 0.5262 0.6341 0.7430 0.8528 0.9636 1.0754 1.1881 1.4166 1.6492
0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.1000 1.3000 1.5000
0.0000 0.0516 0.1035 0.1555 0.2078 0.2603 0.3130 0.4191 0.5262 0.6341 0.7430 0.8528 0.9636 1.0754 1.1881 1.4166 1.6492
mol·dm
−3
298.15 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 308.15 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000
g·cm
M1 −3
K 1.0318 1.0354 1.0346 1.0380 1.0354 1.0420 1.0344 1.0494 1.0550 1.0529 1.0550 1.0514 1.0520 1.0500 1.0507 1.0534 1.0615 K 1.0304 1.0333 1.0325 1.0363 1.0357 1.0389 1.0316 1.0439 1.0524 1.0501 1.0526 1.0451 1.0505 1.0472 1.0481 1.0495 1.0631
mol·dm
M2
m1 −3
mol·kg
solubility as CaSO4 in different units
solution parameters
−1
mol·dm
m2 −3
mol·kg
0.0147 0.0149 0.0151 0.0154 0.0155 0.0157 0.0159 0.0161 0.0165 0.0166 0.0169 0.0170 0.0172 0.0174 0.0171 0.0175 0.0180
0.0153 0.0154 0.0157 0.0160 0.0162 0.0164 0.0167 0.0168 0.0173 0.0175 0.0178 0.0181 0.0184 0.0188 0.0185 0.0191 0.0197
0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.1000 1.3000 1.5000
0.0000 0.0516 0.1035 0.1555 0.2078 0.2603 0.3130 0.4191 0.5262 0.6341 0.7430 0.8528 0.9636 1.0754 1.1881 1.4166 1.6492
0.0153 0.0155 0.0158 0.0159 0.0160 0.0162 0.0163 0.0165 0.0169 0.0171 0.0173 0.0174 0.0177 0.0179 0.0180 0.0181 0.0185
0.0158 0.0161 0.0165 0.0166 0.0167 0.0169 0.0172 0.0173 0.0177 0.0181 0.0183 0.0187 0.0190 0.0193 0.0195 0.0198 0.0202
0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.1000 1.3000 1.5000
0.0000 0.0516 0.1035 0.1555 0.2078 0.2603 0.3130 0.4191 0.5262 0.6341 0.7430 0.8528 0.9636 1.0754 1.1881 1.4166 1.6492
F
ρs
M3 −1
mol·dm
−3
323.15 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 343.15 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000
g·cm
M1 −3
K 1.0256 1.0292 1.0280 1.0308 1.0280 1.0280 1.0345 1.0388 1.0471 1.0463 1.0475 1.0396 1.0454 1.0428 1.0433 1.0457 1.0586 K 1.0180 1.0195 1.0222 1.0206 1.0208 1.0261 1.0262 1.0333 1.0293 1.0300 1.0304 1.0324 1.0328 1.0358 1.0359 1.0342 1.0351
mol·dm
m1 −3
mol·kg−1
0.0158 0.0161 0.0162 0.0164 0.0167 0.0169 0.0171 0.0173 0.0175 0.0177 0.0179 0.0182 0.0183 0.0185 0.0185 0.0185 0.0190
0.0165 0.0168 0.0170 0.0172 0.0176 0.0179 0.0180 0.0182 0.0184 0.0187 0.0190 0.0196 0.0197 0.0200 0.0201 0.0204 0.0209
0.0169 0.0169 0.0171 0.0172 0.0175 0.0178 0.0179 0.0181 0.0183 0.0187 0.0191 0.0192 0.0193 0.0195 0.0195 0.0195 0.0200
0.0178 0.0178 0.0180 0.0182 0.0185 0.0188 0.0190 0.0192 0.0195 0.0201 0.0206 0.0208 0.0210 0.0213 0.0214 0.0217 0.0224
dx.doi.org/10.1021/je300871p | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
The solubility of CaSO4·2H2O in the mixed NH4Cl− (NH4)2SO4 solutions was predicted with the newly regressed parameters in Table 5. The predicted solubilities are depicted in Figure 4. The results demonstrate that the predicted values are in good agreement with experimental data with the total ARD of 0.28 % as shown in Figure 3. All results serve as a validation of the newly established model for its good performance in making CaSO4·2H2O solubility predictions well.
Table 4. Stability of CaSO4·2H2O in Investigated Systems system
M/mol·dm−3
T/K
NH4Cl−H2O
298.15
NH4Cl−H2O
308.15
NH4Cl−H2O
323.15
NH4Cl−H2O
343.15
NH4Cl−(NH4)2SO4−H2O
298.15
NH4Cl−(NH4)2SO4−H2O
308.15
NH4Cl−(NH4)2SO4−H2O
323.15
NH4Cl−(NH4)2SO4−H2O
343.15
NH4NO3−H2O
298.15
NH4NO3−H2O
308.15
NH4NO3−H2O
323.15
NH4NO3−H2O
343.15
0.0 to 1.5 (NH4Cl) 0.0 to 1.5 (NH4Cl) 0.0 to 1.5 (NH4Cl) 0.0 to 1.5 (NH4Cl) 0.0 to 1.5 (NH4Cl) 0.0 to 1.5 (NH4Cl) 0.0 to 1.5 (NH4Cl) 0.0 to 1.5 (NH4Cl) 0.0 to 1.5 (NH4NO3) 0.0 to 1.5 (NH4NO3) 0.0 to 1.5 (NH4NO3) 0.0 to 1.5 (NH4NO3)
t/h
equilibrated solid phase(s)
24
CaSO4·2H2O
24
CaSO4·2H2O
24
CaSO4·2H2O
24
CaSO4·2H2O
24
CaSO4·2H2O
24
CaSO4·2H2O
24
CaSO4·2H2O
24
CaSO4·2H2O
24
CaSO4·2H2O
24
CaSO4·2H2O
24
CaSO4·2H2O
24
CaSO4·2H2O
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CONCLUSIONS The solubility of calcium sulfate dihydrate in NH4Cl, NH4NO3, and mixed NH4Cl and (NH4)2SO 4 solutions has been determined over the temperature range (298.15 to 343.15) K. The solubility of dihydrate in all cases increases rapidly with increasing either NH4Cl or NH4NO3 concentrations from (0.0 to 1.5) mol·dm−3. The solubility of CaSO4·2H2O enhances with an increase of temperature up to 343.15 K in the mixed solutions of NH4Cl and (NH4)2SO4 but does not significantly vary in the other solutions. The addition of (NH4)2SO4 in NH4Cl solutions makes the solubility of CaSO4·2H2O decrease sharply due to the common ion effect. The XRD results indicate CaSO4·2H2O is stable in all systems investigated. New parameters in the electrolyte NRTL model were obtained via regressing the CaSO4·2H2O solubility measured in single electrolyte solutions. With these parameters, a new electrolyte NRTL model was established to predict the solubility of calcium sulfate dihydrate in the NH4+−Cl−−SO42‑−NO3−− H2O system well as a function of temperature and concentration. As a result, this model provides a thermodynamic basis for predicting the gypsum scale in steam stripping of ammonium-N wastewater.
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AUTHOR INFORMATION
Corresponding Author
*Tel./Fax: +86-10-82544844 or +86-10-62551557. E-mail:
[email protected] or
[email protected]. Funding
The authors are grateful to the financial support from the Water Pollution Control and Management Project of China (2008ZX07529−004), and the Integration Projects of Industry, Education and Research of Guangdong Province of China (2011A090100022).
Figure 5. XRD patterns of equilibrated calcium sulfate in 1.5 mol/L NH4Cl solution. , 298.15 K; red line, 308.15 K; green line, 323.15 K; blue line, 343.15 K. △ are the characteristic peaks of CaSO4·2H2O.
Table 5. Binary Electrolyte NRTL Interaction Parameters for CaSO4·2H2O−NH4+−Cl−−SO42‑−H2O Systems component i
component j
C
D
E
αij
Ca2+, Cl− Ca2+, SO42‑ Ca2+, SO42‑ NH4+, SO42‑ Ca2+, Cl− NH4+, Cl− NH4+, SO42‑ NH4+, Cl− Ca2+, NO3− NH4+,NO3− NH4+,NO3− NH4+, SO42‑ Ca2+, SO42‑ Ca2+, NO3−
Ca2+, SO42‑ Ca2+, Cl− NH4+, SO42‑ Ca2+, SO42‑ NH4+, Cl− Ca2+, Cl− NH4+, Cl− NH4+, SO42‑ NH4+,NO3− Ca2+, NO3− NH4+, SO42‑ NH4+,NO3− Ca2+, NO3− Ca2+, SO42‑
24.880 10.843 −222.584 −334.834 4.947 −14.354 −174.621 68.627 2.333 10.538 −11.371 2.411 3.036 0.745
−7038.651 −5064.776 1.243 × 105 1.780 × 105 −475.074 −3643.420 −9.273 × 104 −4.027 × 104 343.556 4782.935 −2225.450 369.046 318.112 −467.156
−147.306 −183.619 2327.965 2936.728 3947.915 23.501 −5325.207 −728.970 527.853 −8233.773 −11642.534 522.345 6206.467 14148.089
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
G
dx.doi.org/10.1021/je300871p | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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Notes
(7) Farrah, H. E.; Lawrance, G. A.; Wanless, E. J. Solubility of calcium sulfate salts in acidic manganese sulfate solutions from 30 to 105 °C. Hydrometallurgy 2007, 86, 13−21. (8) Kumar, A.; Shukla, J.; Dangar, Y.; Mohandas, V. P. Effect of MgCl2 on the solubility of CaSO4· 2H2O in the aqueous NaCl system and physicochemical solution properties at 35 °C. J. Chem. Eng. Data 2010, 55, 1675−1678. (9) Wu, X.; He, W.; Guan, B.; Wu, Z. Solubility of calcium sulfate dihydrate in Ca Mg K chloride salt solution in the range of (348.15 to 371.15) K. J. Chem. Eng. Data 2010, 55, 2100−2107. (10) Li, Z.; Demopoulos, G. P. Effect of NaCl, MgCl2, FeCl2, FeCl3, and AlCl3 on solubility of CaSO4 phases in aqueous HCl or HCl−CaCl2 solutions at 298 to 353 K. J. Chem. Eng. Data 2006, 51, 569−576. (11) Wollmann, G.; Voigt, W. Solubility of gypsum in MSO4 solutions (M = Mg, Mn, Co, Ni, Cu, Zn) at 298.15 and 313.15 K. J. Chem. Eng. Data 2008, 53, 1375−1380. (12) Sulliva, E. C. Calcium sulphate in ammonium sulphate solution. J. Am. Chem. Soc. 1905, 27, 529−539. (13) Bell, J. M.; Taber, W. C. The solubility of gyspsum in solution of ammonium sulphate. J. Phys. Chem. 1906, 10, 119−122. (14) Hill, E.; Yanic, N. S. Ternary systems. XX. calcium sulfate, ammonium sulfate and water. J. Am. Chem. Soc. 1935, 57, 645−651. (15) Souheil, B.; Ahmed, H. H.; Ridha, R.; Adel, M. Solubility study of sodium, potassium and calcium sulfates and chlorides, in ammonia. Russ. J. Inorg. Chem. 2011, 56, 991−998. (16) Wang, W.; Zeng, D.; Yin, X.; Chen, Q. Prediction and measurement of gypsum solubility in the systems CaSO4 + HMSO4 +H2SO4 +H2O (HM = Cu, Zn, Ni, Mn) at 298.15 K. Ind. Eng. Chem. Res. 2012, 51, 5124−5134. (17) Azimi, G.; Papangelakis, V. G.; Dutrizac, J. E. Modelling of calcium sulphate solubility in concentrated multi-component sulphate solutions. Fluid Phase Equilib. 2007, 260, 300−315. (18) Azimi, G.; Papangelakis, V. G.; Dutrizac, J. E. Development of an MSE-based chemical model for the solubility of calcium sulphate in mixed chloride−sulphate solutions. Fluid Phase Equilib. 2008, 266, 172− 186. (19) Azimi, G.; Papangelakis, V. G.; Dutrizac, J. E. Development of a chemical model for the solubility of calcium sulphate in zinc processing solutions. Can. Metall. Q. 2010, 49, 01−08. (20) Messnaoui, B.; Bounahmidi, T. On the modeling of calcium sulfate solubility in aqueous solutions. Fluid Phase Equilib. 2006, 2, 117− 127. (21) Chen, C. C. Representation of solid−liquid equilibrium of aqueous electrolyte systems with the electrolyte NRTL model. Fluid Phase Equilib. 1986, 27, 457−474. (22) Li, Z.; Demopoulos, G. P. Solubility of CaSO4 phases in aqueous HCl−CaCl2 solutions from 283 to 353 K. J. Chem. Eng. Data 2005, 50, 1971−1982. (23) Dutrizac, J. E.; Kuiper, A. The solubility of calcium sulphate in simulated nickel sulphate−chloride processing solutions. Hydrometallurgy 2006, 82, 13−31. (24) Tanji, K. K. Solubility of gypsum in aqueous electrolytes as affected by ion association and ionic strengths up to 0.15M and at 25 °C. Environ. Sci. Technol. 1969, 3, 656−661. (25) Lide, D. R. CRC handbook of chemistry and physics, 89th ed.; CRC Press/Taylor and Francis: Boca Raton, FL, 2008. (26) Aspen property system: physical property methods and models 11.1. aspentech; Aspentech: Burlington, MA, 2001; pp 405−435.
The authors declare no competing financial interest.
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NOMENCLATURE KSP solubility product constant a activity A, B, C, and D empirical parameters γi activity coefficient of ion i γ± mean activity coefficient γ*i unsymmetrical activity coefficient of ionic species mi molality of species i (mol·kg−1 H2O) G molar Gibbs energy changes of the solid (J·mol−1) R universal gas constant (J·mol−1·K−1) T absolute temperature (K) Tr reference temperature (298.15 K) MB molecular weight of the solvent (g·mol−1) the Debye−Hückel parameter Aφ ρ “closest approach” parameter, 14.9 Zi charge number of ion i Ix ionic strength (mole fraction scale) X valid mole fraction τ interaction energy parameter α NRTL nonrandomness factor parameter C, D, and E three adjustable parameters νi stoichiometric number of an ion i xi mole fraction of species i σ the standard deviations P the pressure of system (kPa) Subscripts and Superscripts
E * PDH lc a, a′, a″ B, B′ c, c′, c″ ca i, j, and k exp cal
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excess property unsymmetrical Pitzer−Debye−Hückel local composition anion solvent cation electrolyte (cation−anion) any species (a, c, or B) experimental data calculated data
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dx.doi.org/10.1021/je300871p | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
