Prediction and Measurement of Gypsum Solubility in the Systems

Article pubs.acs.org/IECR

Prediction and Measurement of Gypsum Solubility in the Systems CaSO4 + HMSO4 + H2SO4 + H2O (HM = Cu, Zn, Ni, Mn) at 298.15 K Wenlei Wang, Dewen Zeng,* Xia Yin, and Qiyuan Chen College of Chemistry and Chemical Engineering, Central South University, 410083, Changsha, People’s Republic of China ABSTRACT: Solubility of gypsum in the quaternary systems CaSO4−HMSO4−H2SO4−H2O (HM = Cu, Zn, Ni, Mn) are predicted up to saturated concentrations of heavy metal sulfates and to a H2SO4 concentration of 2 m by a Pitzer thermodynamic model. Experimental solubility and water activity in the subbinary and subternary systems from the literature were used for model parametrization. Then the solubility phase diagrams for the quaternary systems were predicted directly with these obtained binary and ternary model parameters. In order to verify the reliability of the predicted results, a series of solubility measurements of gypsum in these quaternary systems have been carried out at 298.15 K and the measured results were compared with the predicted ones. It was shown that the Pitzer thermodynamic model can perfectly predict the solubilities of gypsum in the quaternary systems. Meanwhile, the newly obtained experimental data were compared with limited literature data in some of the quaternary systems; good agreement was found between them. Some application examples were given based on the predicted phase diagrams.

available at 298.15 K.5−7 Experimental solubility isotherms for the ternary systems CaSO4−HMSO4−H2O (HM = Cu, Zn, Ni, Mn) are available, too.8 All the experimental data form a basis for modeling the quaternary solubility phase diagrams of these systems by a thermodynamic model. In this work, we will select a thermodynamic model to simulate the properties of the binary and ternary systems, and to predict the solubility phase diagrams of the quaternary systems in a wide concentration range. Some necessary small amount of experiments will then be carried out to check the prediction results.

1. INTRODUCTION Crystallization of calcium sulfate in hydrometallurgical processing of heavy metals (HMs), such as Cu, Zn, Ni, and Mn, harms the production process and decreases production qualities by scaling on the wall of reactors or pipelines or crystallizing along with main crystal products as impurity. To develop a new approach to avoid the harm of calcium sulfate, profound understanding of the crystallization mechanism of calcium sulfate is necessary. Generally, it is believed that the crystallization behavior of calcium sulfate is affected by crystal types, temperature, and concentrations of heavy metal sulfate and sulfuric acid. A relatively complete solubility phase diagram for the system CaSO4−HMSO4−H2SO4−H2O (HM = Cu, Zn, Ni, Mn) is desired. Solubility phase diagrams at 298.15 K provide a basis for a complete phase equilibrium analysis for the systems studied and should be considered first. The available experimental data and simulated solubility results for these quaternary systems are far from complete. Dutrizac and Kuiper1 have studied the solubility behavior of gypsum in quite typical Cu−electrolyte solutions: CaSO4−(0.0−0.8 mol·L−1) CuSO4−(1.5 mol·L−1) H2SO4− H2O and CaSO4−(0.7 mol·L−1) CuSO4−(0.0−2.2 mol·L−1) H2SO4−H2O. Dutrizac2 has also reported the solubility of gypsum in the systems CaSO4−(1.5 mol·L−1) ZnSO4−(0.0− 2.0 mol·L−1) H2SO4−H2O, CaSO4−(0.0−2.25 mol·L−1) ZnSO 4 −(0.1 mol·L − 1 ) H 2 SO 4 −H 2 O, and CaSO 4 − (1.15 mol·L−1) ZnSO4 − (0.3 mol·L−1) H2SO4−H2O. Azimi and Papangelakis3 reported the solubility of gypsum in the system CaSO4−(0.0−1.5 mol·L−1) NiSO4−(0.5 mol·L−1) H2SO4−H2O. Farrah et al.4 have reported gypsum solubility in the system CaSO4−(0, 36, 72 g of Mn2+/kg of solution) MnSO4−(0, 36, 72 g of H2SO4/kg of solution) H2SO4−H2O at temperatures higher than 303.15 K. In addition, reliable component activities and solubilities for the binary systems MSO4−H2O (M = Ca, Cu, Zn, Ni, Mn) and H2SO4−H2O are © 2012 American Chemical Society

2. METHODOLOGY 2.1. Model Selection. Recently, Azimi and Papangelakis3,9 applied a mixed solvent electrolyte (MSE) model first developed by Wang et al.10 to represent solubility phase diagrams of gypsum in the ternary systems MSO4−H 2SO4− H 2O (M = Ca, Mn) and CaSO4−HMSO4−H 2O (HM = Zn, Ni, Mn), and to predict solubility phase diagrams of the quaternary systems CaSO4−(1.5 mol·L −1) ZnSO4−(0.0− 2.0 mol·L−1) H 2SO 4−H2O, CaSO 4−(0.0−2.25 mol·L −1) ZnSO 4−(0.1 mol·L −1) H 2SO4−H 2O, and CaSO 4−(0.0−1.5 mol·L −1) NiSO 4−(0.5 mol·L −1) H 2SO 4−H 2O. In the MSE model, long-range interactions were expressed by a Pitzer− Debye−Hü c kel equation, middle-range ionic interactions were expressed by an ionic strength dependent symmetrical second-virial coefficient-type expression, and short-range interactions were expressed by a UNIQUAC model. This model is especially suitable to express molecule−molecule interactions mostly resulted from the multiple solvent Received: Revised: Accepted: Published: 5124

August 3, 2011 March 12, 2012 March 15, 2012 March 15, 2012 dx.doi.org/10.1021/ie201721m | Ind. Eng. Chem. Res. 2012, 51, 5124−5134

Industrial & Engineering Chemistry Research

Article

Table 1. Single Electrolyte Solution Pitzer Interaction Parameters at 298.15 K anion

βca(0)

βca(1)

βca(2)

Ccaϕ

ref

SO42− SO42− SO42− SO42− SO42− HSO4− HSO4− HSO4− HSO4− HSO4− HSO4− SO42−

0.20 0.2358 0.1949 0.1594 0.201 0.2145 0.405 0.380 0.3559 0.360 0.2106 0.0217

2.65 2.485 2.883 2.926 2.980 2.53 4.47 4.60 4.27 4.701 0.5320 0.00

−55.7 −47.35 −32.18 −42.76 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 −0.0012 0.029 0.0406 0.0182 0.00 0.00 0.00 0.00 0.00 0.00 0.0411

Pitzer and Mayorga11 Pitzer and Mayorga11 Pitzer and Mayorga11 Reardon15 Pitzer and Mayorga11 Harvie et al.12 this work this work Reardon15 this work Reardon and Bechie13 Reardon and Bechie13

cation 2+

Ca Cu2+ Zn2+ Ni2+ Mn2+ Ca2+ Cu2+ Zn2+ Ni2+ Mn2+ H+ H+

and the anion activity coefficients γX are

components. For representation and prediction of phase diagrams of the single solvent systems CaSO 4−HMSO 4− H2SO 4−H2O (HM = Cu, Zn, Ni, Mn), a more concise Pitzer ionic interaction model may be sufficient. Earlier, Pitzer and Mayorga11 reported model parameters of the binary systems MSO 4−H 2O (M = Ca, Cu, Zn, Ni, Mn) at 298.15 K. By considering the partial dissociation reaction HSO 4− = H + + SO42−, the Pitzer model can describe the properties of the associated system H 2SO4−H 2O, too.6,12,13 Furthermore, the Pitzer model was used to represent the solubilities of the ternary systems CaSO4−H2SO 4−H2O, CuSO 4 −H 2 SO 4 −H 2 O and NiSO 4 −H 2 SO 4 −H 2 O. 12,14,15 Harvie et al.12 gave excellent solubility predictions for some quaternary systems where salt concentrations are not extremely high. Thus, the Pitzer model may be suitable to describe the titled quaternary systems in this work. Harvie and Weare16 have summarized the original Pitzer equations6,11,18,19 and given the osmotic coefficients ϕ and water activity expressions as follows: ⎛ 2 ⎜ AϕI 3/2 ϕ−1= − + ∑i mi ⎜⎝ 1 + bI1/2 +

+

+ +

∑ ∑ a a ′< a

⎞ ∑ mc ψaa ′ c)⎟⎟ ⎠ c

+ +

a a ′< a

a

∑ ∑

mc mc ′Φ′cc ′

c c ′< c

mama ′Φ′aa ′

Aϕ = (1/3)(2πN0dw/1000)1/2(e2/DkT)3/2 is one-third the Debye−Hückel limiting slope and equals 0.391 475 kg1/2·mol1/2 when T is 298.15 K;17 b is an universal empirical parameter assigned to be equal to 1.2 at 298.15 K. Coefficients BMX are functions of ionic strength (see ref 18):

(1a)

(1) (2) BMX = β(0) MX + βMX g (α1 I ) + βMX g (α2 I )

(2a)

(2) B′MX = β(1) MX g ′(α1 I ) + βMX g ′(α2 I )

(2b)

The functions g and g′ are defined by

a

mama ′ψaa ′ M + |zM|∑ ∑ mc maCca c

g (x) = 2[1 − (1 + x) exp(−x)]/x 2

(3a)

g ′(x) = −2[1 − (1 + x + x 2/2) exp(−x)]/x 2

(3b)

For 1−1 and 1−2 electrolytes, α1 = 2 and α2= 0. For 2−2 or higher valence pairs α1 = 1.4 and α2 = 12.0. In most cases, β(2) = 0 for univalent type pairs. For 2−2 electrolytes a nonzero β(2) is more common. The coefficient Z is concentration dependent:

∑ mc(2ΦMc + ∑ maψMca) ∑ ∑

a

a a ′< a

a

+

∑ ∑ mcmaB′ca + ∑ ∑ c

∑ ma(2BMa + ZCMa)

c

c

⎤ ⎡ I 2 F = −Aϕ⎢ + ln(1 + b I )⎥ ⎦ ⎣1 + b I b

The cation activity coefficients γM are

+

mc mc ′ψcc ′ X + |zX|∑ ∑ mc maCca

where

j

ln γM = zM F +

∑∑

(1c)

a w = exp( −(M H2O/1000)ϕ ∑ mj)

2

c

c c ′< c

a ϕ mama ′(Φaa ′+

∑ ma(2ΦXa + ∑ mc ψXac) a

∑ maψcc ′ a)

c c ′< c

∑ mc(2Bc X + ZCc X) c

∑ ∑ mcma(Bcaϕ + ZCca) c a

ϕ mc mc ′(Φcc ′+

∑∑

ln γX = zX 2F +

a

Z= (1b)

∑ mi|zi| i

5125

(4) dx.doi.org/10.1021/ie201721m | Ind. Eng. Chem. Res. 2012, 51, 5124−5134


Article

ϕ The parameter CMX is related to CMX by

ϕ CMX = CMX /2 |zMzX|

θijE and θijE′ are functions only of ionic strength and electrolyte pair type. In terms of these variables the unsymmetrical mixing terms are given by

(5)

θijE = (z izj/4I )[J(xij) − 1/2J(xii) − 1/2J(xjj)]

The mixing parameter Φ, which depends on ionic strength, is given the following form.19 Φij = θij + θijE(I )

θijE ′ = ∂θijE/∂I = −θijE/I + (z izj/8I 2)[xijJ ′(xij) − (1/2)xiiJ ′(xii)

(6a)

− (1/2)xjjJ ′(xjj)]

Φ′ij = θijE ′(I )

Table 2. Parameter ln K of Solid Phase in the Quaternary System CaSO4 + (Heavy Metal)SO4 + H2SO4 + H2O at 298.15 K ln K

CaSO4·2H2O CuSO4·5H2O ZnSO4·7H2O ZnSO4·6H2O ZnSO4·1H2O NiSO4·7H2O NiSO4·6H2O MnSO4·1H2O

−10.597609 −6.067564 −4.2220 −3.80270 −1.4080 −5.1260 −5.0084 −2.7525

solubility data for parameter determination 20

Hulett and Allen, Partridge and White Foote26 Copeland and Short29 Copeland and Short29 Copeland and Short29 Reardon15 Reardon15 Taylor30

(7b)

θijE and θijE′ are zero when zi = zj. The functions J(xij) and J′(xij) are determined by

(6b)

solid phase

(7a)

J(xij) = xij/[4 + C1xijC2 exp(C3xijC4)]

(8a)

J ′(xij) = ∂J(xij)/∂xij

(8b)

21

with C1 = 4.581, C2 = 0.7237, C3 = 0.0120, and C4 = 0.528. The variables xij for cations i and j are calculated by

xij = 6z izjA ϕI1/2

(9)

To calculate solubility isotherms in ternary and quaternary systems, the solubility product KMSO4·nH2O (M = Ca, Cu, Zn, Ni, Mn)

Figure 1. Comparison of calculated and experimental solubility isotherms in the system MSO4−H2SO4−H2O (M = Ca, Cu, Zn, Mn) at 298.15 K: dashed lines, calculated values by binary parameters only; solid lines, calculated values with binary and mixing parameters. Symbols, experimental values: (a) ■, Marshall and Jones;23 ○, Cameron and Breazeale;24 △, Zdanovskii and Vlasov;25 (b) ■, Foote;26 □, Bell and Taber;27 (c) ■, □, ⊞, Copeland and Short;29 (d) ■, Taylor.30 5126

dx.doi.org/10.1021/ie201721m | Ind. Eng. Chem. Res. 2012, 51, 5124−5134


Article

H2SO4− = H+ + HSO42− is partially completed with a dissociation constant K2:

should be determined at first in corresponding binary systems by the following equilibrium at saturation point: MSO4 ·nH2O = M2 + + SO4 2 − + nH2O

K2 =

K MSO4 ·nH2O = a M2 +aSO 2 −a H2On 4 = m M2 +mSO 2 −(γ M2 +γSO 2 −a H2On) 4 4 (10)

In sulfuric acid solution, the first order dissociation equilibrium H 2SO 4 = H + + HSO 4− is considered as complete, and the second order dissociation equilibrium Table 3. Common-Ion Pitzer Interaction Parameter Values for Cations 2+

Ca Ca2+ Ca2+ Ca2+ Ca2+ H+ H+ H+ H+

c′

θcc′

ψcc′SO42−

ψcc′HSO4−

ref

+

0.044 0.001 0.004 0.01 0.00 −0.023 0.007 0.00 −0.01

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

this work this work this work this work this work this work this work Reardon15 this work

H Cu2+ Zn2+ Ni2+ Mn2+ Cu2+ Zn2+ Ni2+ Mn2+

4 a HSO4−

=

(mH+ γ H+)(mSO 2 −γSO 2 −) 4

4

mHSO4−γHSO − 4

(11)

2.2. Binary Parameter Determination. 2.2.1. CaSO4− H2O System. Binary parameters for CaSO4, listed in Table 1, are directly taken from Pitzer and Mayorga.11 Using the binary parameters, the solubility product ln KCaSO4·2H2O for gypsum was determined by the solubility data of Hulett and Allen20 and Partridge and White21 (see Table 2). 2.2.2. H2SO4 + H2O. Pitzer and Roy6 have accurately fit water activity data for the H2SO4−H2O system incorporating species HSO4− in the dissociation equilibrium HSO4− = H+ + SO42−, with the familiar dissociation constant K = 0.0105 at 298.15 K. In their parameter determination, no unsymmetrical electrolyte term (eqs 7a and 7b) was considered. Harvie et al.12 and Reardon and Bechie13 reevaluated the parameters by introducing the unsymmetrical electrolyte term. Both of their parameters are generally consistent at 298.15 K. Hovey et al.22 described the system H2SO4−H2O more accurately, but with eight parameters at 298.15 K only, difficulties might be encountered when we extrapolate the model to higher temperatures. Considering that the set of Pitzer parameters given by Reardon and Bechie13 with only four parameters is suitable for higher temperatures, this set of parameters was selected in this work, as shown in Table 1. 2.2.3. HMSO4 + H2O (HM = Cu, Zn, Ni, Mn). Pitzer and Mayorga11 have given the binary parameters for CuSO4, ZnSO4, MnSO4, and NiSO4. Later, Reardon15 reevaluated the

= (m M2 + γ M2 +)(mSO 2 −γSO 2 −)a H2On 4 4

c

a H+aSO 2 −

Figure 2. Comparison of calculated and experimental solubility data for gypsum in HMSO4 (HM = Cu, Zn, Ni, Mn) solutions at 298.15 K: dashed lines, calculated values by binary parameters only; solid lines, calculated values with binary and mixing parameters; ■, experimental values.8 5127



Article

Figure 3. Predicted solubility isotherms of gypsum in the system CaSO4−HMSO4−H2SO4−H2O (HM = Cu, Zn, Ni, Mn) at 298.15 K: grid surface, predicted.

parameters for the system NiSO4−H2O and made them valid at higher temperatures up to 363.15 K. Both are generally consistent at 298.15 K, and the latter’s values were chosen for our purpose. All selected parameters are listed in Table 1, and values of the solubility product ln KHMSO4·nH2O (HM = Cu, Zn, Ni, Mn) are listed in Table 2. 2.3. Ternary Parameter Determination. 2.3.1. MSO4 + H2SO4 + H2O (M = Ca, Cu, Zn, Ni, Mn). Using parameters determined from binary systems, we predicted solubility isotherms in the systems MSO4−H2SO4−H2O (M = Ca, Cu, Zn, Mn) for solids that can also precipitate in binary solutions, as shown by the dashed lines in Figure 1. All predicted isotherms deviate from experimental data largely. The main reason may come from the interaction between M2+ and HSO4− or H+, which were not represented in each binary system.

(0) (1) Harvie et al.12 evaluated the parameters, βCa−HSO , βCa−HSO , 4 4 and θCa−H by the solubility data of the system CaSO4−H2SO4− H2O.23 Since the parameters for H2SO4 used in this work are slightly different from those given by Harvie et al.,12 we kept 12 (1) the parameters of β(0) Ca−HSO4 and β Ca−HSO4 given by Harvie et al. and adjusted the parameter θCa−H slightly (see Tables 1 and 3). The calculated results were plotted in a solid line comparing with experimental solubility data of this work and the literature in Figure 1a.23−25 Baes et al.14 have reported interaction parameters between Cu2+ and HSO4− for the ternary system CuSO4−H2SO4−H2O based on the set of binary parameters for H2SO4−H2O reported by Hovey et al.22 at 298.15 K, and found that at least 13 parameters are needed for the ternary system. Far more than 13 parameters will be needed for representation of the properties of the quaternary system CaSO4−CuSO4−H2SO4−H2O. (1) We noted that eight parameters, i.e., β(0) H−HSO4, β H−HSO4,

5128



Article

Table 5. Solubility of Gypsum in the System CaSO4 + ZnSO4 + H2SO4 + H2O at 298.15 K composition (mol·kg−1)

Figure 4. Analysis strategy of ICP used in this work.

Table 4. Solubility of Gypsum in the System CaSO4 + CuSO4 + H2SO4 + H2O at 298.15 K composition (mol·kg−1)

a

H2SO4

CuSO4

CaSO4

0.2 0.2 0.2 0.2 0.2 0.2a 0.5 0.5 0.5 0.5 0.5a 1.0 1.0 1.0 1.0 1.0 1.0a 1.5 1.5 1.5 1.5a 2.0 2.0 2.0 2.0a

0.0498 0.15 0.4977 1.0009 1.2998 1.39a 0.25 0.5009 0.7498 0.9999 1.328a 0.2498 0.4998 0.4999 0.7502 0.9998 1.208a 0.2499 0.4997 0.7503 1.076a 0.2493 0.5 0.7493 0.945a

0.01686 0.01612 0.01532 0.01576 0.01501 0.0152 0.01854 0.01741 0.01677 0.01530 0.01454 0.01895 0.01748 0.01716 0.01617 0.01431 0.01315 0.01746 0.01636 0.01433 0.01170 0.01522 0.01354 0.01179 0.01035

a

H2SO4

ZnSO4

CaSO4

0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2a 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5a 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0a 1.5 1.5 1.5 1.5 1.5a 2.0 2.0 2.0 2.0 2.0a

0.2505 0.4989 1.0125 1.5111 2.0019 2.5231 3.0432 3.534a 0.2511 0.402 0.9678 1.5010 2.1 2.4965 3.0238 3.403a 0.2498 0.5 0.5017 0.9783 1.0 1.3421 1.75 2.4633 3.211a 0.5022 0.9998 1.5 2.0321 3.056a 0.4999 1.0 1.5001 1.9997 2.937a

0.01538 0.01554 0.01580 0.01444 0.01253 0.01008 0.00796 0.00619 0.01778 0.01736 0.01580 0.01344 0.01023 0.00871 0.00625 0.00530 0.0187 0.01714 0.01689 0.01391 0.01393 0.01190 0.01029 0.00726 0.00412 0.01503 0.01201 0.00933 0.00688 0.00308 0.01352 0.01028 0.00769 0.00555 0.00219

Solid phase: ZnSO4·7H2O and CaSO4·2H2O.

(1) parameters β(0) Cu−HSO4, β Cu−HSO4, and θCu−H by fitting to solubility data of the system CuSO4−H2SO4−H2O reported by Foote26 and Bell and Taber.27 The new obtained parameters β(0) Cu−HSO4, β(1) Cu−HSO4, and θCu−H are listed in Tables 1 and 3. Thus, four parameters were saved for the ternary system CuSO4−H2SO4− H2O. The calculated isotherm for CuSO4·5H2O (solid line in Figure 1b) represents satisfactorily the experimental data.26,27 For parameter evaluation, we constructed an objective function as

Solid phase: CuSO4·5H2O and CaSO4·2H2O.

Min = (1) ϕ CϕH−HSO4, β(0) H−SO4, β H−SO4, C H−SO4, θHSO4−SO4, and ψH−HSO4−SO4, were employed for the binary system H2SO4−H2O;22 however, Reardon and Bechie13 reported that only four parameters, i.e., (1) (0) ϕ β(0) H−HSO4, β H−HSO4, β H−SO4, and C H−SO4, are sufficient to represent the properties of the binary system H2SO4−H2O. For the sake of simplicity, we took the set of parameters for the binary system H2SO4−H2O reported by Reardon and Bechie,13 where the parameter CϕH−HSO4, β(1) H−HSO 4 , θHSO 4 −SO 4 , and ψH−HSO4−SO4 were set to be zero, and reevaluated the mixing

∑ ∑ (ln Q j , i − ln Kj)2 j i∈j

where j denotes all concerned solid phases, i is the solubility points for the phase j, Kj is the solubility product of the solid phase j, and Qj,i is the activity product at point i for the solid j. By adjusting the parameters, one can calculate activities of each component, as well as the ln Q values, and consequently obtain a series of values of the objection function. The optimal set of parameters, which leads to a minimal value of the objection function, is thus obtained. 5129



Article

Table 6. Solubility of Gypsum in the System CaSO4 + NiSO4 + H2SO4 + H2O at 298.15 K

Table 7. Solubility of Gypsum in the System CaSO4 + MnSO4 + H2SO4 + H2O at 298.15 K

composition (mol·kg−1) H2SO4

NiSO4

CaSO4

H2SO4

MnSO4

CaSO4

0.2 0.2 0.2 0.2 0.2 0.2 0.2a 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5a 1.0 1.0 1.0 1.0 1.0 1.0b 1.5 1.5 1.5 1.5 1.5b 2.0a 2.0 2.0 2.0 2.0 2.0b

0.09 0.2497 0.7491 1.5 2.0234 2.4992 2.582a 0.1189 0.1484 0.2569 0.5043 0.7359 0.9997 1.4999 1.7502 2.2512 2.444a 0.2505 0.4999 1.0 1.5 2.0021 2.228b 0.2507 0.5 1.0 1.45 1.7502b 2.026a 0.2497 0.5 0.9996 1.4 1.842b

0.01554 0.01496 0.01510 0.01438 0.01161 0.00931 0.00915 0.01816 0.01788 0.01735 0.01681 0.01671 0.01538 0.01358 0.01203 0.00934 0.00868 0.01812 0.01651 0.01366 0.01159 0.00952 0.00802 0.01718 0.01566 0.01236 0.01058 0.00964 0.00749 0.01510 0.01351 0.01089 0.00883 0.00701

0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2a 0.5 0.5 0.5 0.5 0.5 0.5a 1.0 1.0 1.0 1.0 1.0 1.0 1.0a 1.5 1.5 1.5 1.5 1.5 1.5a 2.0 2.0 2.0 2.0 2.0a

0.009 0.249 0.249 0.7491 1.4755 2.2503 3.2387 4.084a 0.2502 0.5010 1.2506 1.9998 3.0012 3.818a 0.2503 0.5 1.5 1.5 2.2502 3.0 3.405a 0.2497 0.9077 1.4846 1.9912 2.5090 3.027a 0.5008 0.9999 1.4989 2.0 2.682a

0.01661 0.01547 0.01546 0.01554 0.01422 0.01141 0.00782 0.00480 0.01743 0.01683 0.01461 0.01143 0.00735 0.00470 0.01835 0.01707 0.01212 0.01210 0.00917 0.00651 0.00490 0.01748 0.01356 0.01112 0.00901 0.00750 0.00502 0.01386 0.01139 0.00903 0.00751 0.00522

Solid phase: NiSO4·7H2O and CaSO4·2H2 O. NiSO4·6H2O and CaSO4·2H2O.

a

composition (mol·kg−1)

b

a

Solid phase: MnSO4·1H2O and CaSO4·2H2O.

(1) parameters β(0) Mn−HSO4, β Mn−HSO4, and θMn−H, which are listed in Tables 1 and 3. 2.3.2. CaSO4 + HMSO4 + H2O (HM = Cu, Zn, Ni, Mn). No simulations have been done by the Pitzer model for these system. As we discussed previously,31 solubility isotherms for these sytems measured by Wollmann and Vogit8 should be the most reliable data. In this work, we predicted at first the solubility isotherms of gypsum in these systems, obtaining the predicted dashed lines in Figure 2, which are in good agreement with the experimental data,8 especially for the system CaSO4 + MnSO4 + H2O. For obtaining a better model representation of the solubility isotherms, the mixing parameters θCa−M (M = Cu, Zn, Ni) were introduced to fit the experimental data and are listed in Table 3. Consequently, the calculated solid lines in Figure 2 with the mixing parameters is improved slightly.

Solid phase:

Guerra and Beatetti28 reported ternary model parameters for the system ZnSO4−H2SO4−H2O at 298.15 K, but their parameters are limited to the concentration range 0−2.5 mol·kg−1 ZnSO4 + 0−2.0 mol·kg−1 H2SO4, which may be not suitable for saturated solution. In this case, we refitted the ternary model parameters to the experimental solubility data given by Copeland and Short,29 obtaining the parameters (1) β(0) Zn−HSO4, β Zn−HSO4, and θZn−H as listed in Tables 1 and 3. The calculated solubility isotherms for the solid phases ZnSO4·nH2O (n = 1, 6, 7) agree well with the experimental data (Figure 1c).29 Reardon15 applied the Pitzer model to represent the solubility properties of the system NiSO4−H2SO4−H2O in a wide temperature range from 273.15 to 363.15 K. Their parameters for the ternary system and its subbinary system were accepted for our calculation without any change. The Pitzer model has not been applied to simulate the solubility of the system MnSO4−H2SO4−H2O. By fitting to experimental solubility data, 30 we obtained the model

3. SOLUBILITY PREDICTION OF THE QUATERNARY SYSTEMS CaSO4 + HMSO4 + H2SO4 + H2O (HM = Cu, Zn, Ni, Mn) Solubility phase diagrams of gypsum in the quaternary systems CaSO4−HMSO4−H2SO4−H2O (HM = Cu, Zn, Ni, Mn) at 298.15 K were predicted with the binary and mixing parameters listed in Tables 1 and 3. As is illustrated in Figure 3, the 5130



Article

Figure 5. Comparison of predicted and experimental solubility data of gypsum in the system CaSO4−HMSO4−H2SO4−H2O (HM = Cu, Zn, Ni, Mn) at 298.15 K: all lines, calculated values; symbols, experimental values in this work.

influence of the concentrations of heavy metal sulfates and sulfuric acid on solubilities of gypsum is very remarkable. In the HMSO4−H2SO4−H2O (HM = Cu, Zn, Ni, Mn) solutions at 298.15 K, the largest solubility area of gypsum locates at mH2SO4= 1 mol·kg−1 and mHMSO4= 0 mol·kg−1 (HM = Cu, Zn, Ni, Mn). When the sulfuric acid concentration is lower than 0.5 mol·kg−1, the solubility of gypsum decreases at first, increases after a minimum point, and then decreases after a maximum point, with heavy metal sulfate concentration increasing. When sulfuric acid concentration is higher than 0.5 mol·kg−1, solubilities of gypsum decrease monotonically with the increase of heavy metal sulfate concentration.

(primary grade, purity >0.999 in mass fraction, China National Pharmaceutical Industry Co. Ltd.) with H2SO4 and crystallized several times. Doubly distilled water (S < 1.2 × 10−4 S·m−1) was used. 4.2. Experimental Apparatus. The equilibrium experiments were carried out in a water bath (Lauda E219, Germany) with temperature stability up to ±0.01 K. The temperature was determined by means of a calibrated glass thermometer (Miller & Weber, Inc., USA) with an accuracy of ±0.01 K. A Sartorius BS224S balance was used for weighing with an error of ±0.1 mg. Inductively coupled plasma optical emission spectroscopy (ICP-OES; 5300DV, Perkin-Elmer, USA) was used for the Ca2+ analysis. 4.3. Experimental Procedure. As described in our previous work,31 binary stock aqueous solutions of each heavy metal sulfate and sulfuric acid were prepared with the chemical agents described above, whose contents were determined by precipitating SO 42− by BaCl2 solution, respectively. Calculated amounts of stock solutions of a heavy metal sulfate and sulfuric acid were weighed and added in a weighed Erlenmeyer flask, forming a mixture solution. The objective contents of sulfuric acid and heavy metal sulfate in the mixture solution were reached by diluting or by evaporizing. Then a certain amount of gypsum was added into the mixture solution in the flask, which was placed in a water bath at 298.15 K for about 120 h. The mixture solution was stirred by a magnetic stirrer driven by a motor outside the water bath. At the end of each experiment, the solution was kept unstirred for 8 h and then the superlayer clear solution was taken out into a weighed vacuum tube. The Ca2+ content in the superlayer clear solution was analyzed by ICP-OES. By ICP analysis, four portions with

4. EXPERIMENTAL SECTION To check the reliability of our predicted results, a limited number of experimental measurements have been carried out. 4.1. Chemical Agents. The electrolyte solutions of CuSO4, ZnSO4, and MnSO4 were prepared by dissolving electrolytic copper (grade A, purity >0.9999 in mass fraction, Hubei Daye Non Ferrous Metals Co., Ltd.), electrolytic zinc (grade 0#, purity >0.9999 in mass fraction, Zhuzhou Smelter Group Co., Ltd.), and electrolytic manganese (purity >0.997 in mass fraction, Kingray New Materials Science & Technology Co. Ltd.) with H2O2 (analytical reagent (A.R.), China National Pharmaceutical Industry Co. Ltd.) and H2SO4 (A.R., purity >0.999 in mass fraction, China National Pharmaceutical Industry Co. Ltd.), respectively. The prepared CuSO4, ZnSO4, and MnSO4 solutions and the NiSO4 solution prepared by analytically pure agents were condensed and crystallized four times to produce the chemical agents CuSO4·5H2O, ZnSO4·6H2O, NiSO4·H2O, and MnSO4·H2O. CaSO4·2H2O was prepared by dissolving CaCO3 5131



Article

controlled within 2% in most cases, and that for SO42− can be controlled within 0.1%. 4.4. Experimental Results. The measured solubility data of gypsum in the systems CaSO4 + HMSO4 + H2SO4 + H2O (HM = Cu, Zn, Ni, Mn) at 298.15 K are presented in Tables 4−7.

Table 8. Comparison of Predicted and Experimental Solubility Data Given by Mutalala et al.32 and Dutrizac and Kuiper1 of Gypsum in the System CaSO4−CuSO4−H2SO4− H2O at 298.15 K CaSO4 (mol·kg−1) H2SO4 (mol·kg−1)

CuSO4 (mol·kg−1)

exptl

pred

deviationa

0.202 0.405 0.608 0.832 1.050 1.384 1.491 1.600 1.726 1.960 0.489 0.992 1.045 1.616 1.674

0.705 0.709 0.709 0.728 0.735 0.807 0.746 0.640 0.755 0.762 0.172 0.175 0.330 0.515 0.689

0.01505b 0.01532b 0.01565b 0.01540b 0.01497b 0.01579b 0.01369b 0.01374b 0.01264b 0.01190b 0.01822c 0.01851c 0.01638c 0.01476c 0.01373c

0.01611 0.01675 0.01688 0.01647 0.01577 0.01392 0.01386 0.01410 0.01272 0.01164 0.01845 0.01934 0.01839 0.01492 0.01341

7.04 9.33 7.86 6.95 5.34 −11.84 1.24 2.62 0.63 −2.18 1.26 4.48 12.27 1.08 −2.33

5. COMPARISON AND DISCUSSION In Figure 5 is the comparison of our experimental data (symbols) with predicted values (lines). It can be observed that the predicted results are in good agreement with the newly obtained experimental solubility data for gypsum. The average relative deviations between experimental and predicted ones in the systems CaSO4−HMSO4−H2SO4−H2O (HM = Cu, Zn, Ni, Mn) are 2.0, 3.7, 3.3, and 3.6%, respectively. Table 10. Comparison of Predicted and Experimental Solubility Data Given by Azimi and Papangelakis3 of Gypsum in the System CaSO4−ZnSO4−H2SO4−H2O at 298.15 Ka CaSO4 (mol·kg−1)

Relative deviation = (experimental value − predicted value)/ experimental value × 100%. bMutalala et al.32 cDutrizac and Kuiper.1 a

Table 9. Comparison of Predicted and Experimental Data Given by Dutrizac2 of Gypsum Solubility in the System CaSO4−ZnSO4−H2SO4−H2O at 298.15 K CaSO4 (mol·kg ) ZnSO4 (mol·kg−1)

exptl

pred

deviationa

0.099 0.200 0.310 0.403 0.613 0.825 1.043 1.241 1.483 1.696 1.957

1.488 1.499 1.548 1.513 1.533 1.547 1.565 1.551 1.589 1.590 1.631

0.01290 0.01278 0.01302 0.01226 0.01150 0.01043 0.00966 0.00913 0.00848 0.00755 0.00645

0.01442 0.01422 0.01378 0.01367 0.01293 0.01209 0.01118 0.01052 0.00948 0.00880 0.00787

11.78 11.27 5.84 11.50 12.43 15.92 15.73 15.22 11.79 16.56 22.02

NiSO4 (mol·kg−1)

exptl

pred

deviationb

0.512 0.515 0.512 0.513 0.524

0.102 0.258 0.512 1.026 1.571

0.01842 0.01711 0.01698 0.01519 0.01372

0.01862 0.01820 0.01756 0.01587 0.01322

1.08 6.37 3.41 4.47 −3.64

a All of the available literature data in mol·kg−1 are converted from the originally reported data in mol·L−1. bRelative deviation = (experimental value − predicted value)/experimental value × 100%.

−1

H2SO4 (mol·kg−1)

H2SO4 (mol·kg−1)

There were also scattered solubility data of gypsum in the system CaSO4−HMSO4−H2SO4−H2O (HM = Cu, Zn, Ni) reported by other authors,1−3,32 who gave results in the unit of molarity, as well as the corresponding density of solution. We converted the results into the unit of molality, and calculated the solubilities of gypsum for comparison, as shown in Tables 8−10. In the system CaSO4−CuSO4−H2SO4−H2O at 298.15 K, our predicted results agree better with those reported by Dutrizac and Kuiper1 than with those reported by Mutalala et al.32 The average relative deviation between these experimental and our predicted results is about 5%. We noted that the equilibrium time taken in the experiments Mutalala et al.32 and Dutrizac and Kuiper1 was 48 or 6 h, which may be a little too short according to our experience.31 In the system CaSO4− (1.5 mol·L−1) ZnSO4−H2SO4−H2O the experimental solubility data reported by Dutrizac2 are generally lower than we predicted by about 13.6%. In the system CaSO4−NiSO4− (0.5 mol·L−1) H2SO4−H2O the solubility data given by Azimi and Papangelakis3 agree with our results quite well, with an average relative deviation about 3.8%, within the reported experimental accuracy of 5%.

Relative deviation = (experimental value − predicted value)/ experimental value × 100%. a

equal mass amounts of solution were sampled into four flasks, respectively. Then different amounts of known CaCl2 standard solution were added to three of the four solutions, respectively, and then the four solutions were diluted by doubly distilled water to an equal total mass amount of solution. The Ca2+ contents of the four well-mixed solutions were analyzed by ICP-OES. The Ca2+ content in the initial sample solution, in which no CaCl2 standard solution was added, was determined by prolonging the analyzed line to zero amount of the detected ICP signal. The analysis strategy is outlined in Figure 4. To ensure high analysis accuracy of Ca2+ content, the Ca2+ amount in the standard solution added to the initial sample solution was always kept compatible with that in in the sample solution. The measured results in each analysis run, as shown by the line in Figure 4, possess a correlation coefficient larger than 0.9999 in every time. The analysis error for Ca2+ can be

6. CONCLUSIONS We simulated the solubility of gypsum in the binary and ternary systems MSO4−H2O (M = Ca, Cu, Zn, Ni, Mn), MSO4− H2SO4−H2O (M = Ca, Cu, Zn, Ni, Mn), and CaSO4− HMSO4−H2O (HM = Cu, Zn, Ni, Mn) at 298.15 K with a Pitzer model in its simple form, and we predicted the solubility of gypsum in the quaternary systems CaSO4−HMSO4− H2SO4−H2O (HM = Cu, Zn, Ni, Mn) at 298.15 K. Necessary 5132



Article

θijE′ = derivative of θijE ψijk = observable third order interaction coefficient for each cation−cation−anion or anion−anion−cation triplet ϕ = osmotic coefficient of the aqueous solution Φ = equation for θij Φ′ = derivative of Φ ψ = observable third order interaction coefficient for triple ion interaction

experiments have been carried out to check the reliability of the model prediction. Comparisons showed that the Pitzer model in its simple form can sufficiently predict the solubility behavior of gypsum in the quaternary system. Based on the parametrized model, relatively complete solubility diagrams of gypsum in the quaternary systems have been constructed. The predicted results provide a profound understanding on how the solubility of gypsum is comprehensively affected by H2SO4 and HMSO4 (HM = Cu, Zn, Ni, Mn) concentrations.

■

Subscripts

AUTHOR INFORMATION

■

Corresponding Author

*E-mail: [email protected]. Tel.: +86 13618496806. Fax: +86 731 88879616.

M, c, and c′ = symbols denoting cations X, a, and a′ = symbols denoting anions

REFERENCES

(1) Dutrizac, J. E.; Kuiper, A. The solubility of calcium sulphate in simulated copper sulphate electrorefining solutions. Hydrometallurgy 2008, 92, 54. (2) Dutrizac, J. E. Calcium sulphate solubilities in simulated zinc processing solutions. Hydrometallurgy 2002, 65, 109. (3) Azimi, G.; Papangelakis, V. G. Thermodynamic modeling and experimental measurement of calcium sulfate in complex aqueous solutions. Fluid Phase Equilib. 2010, 290, 88. (4) Farrah, H. E.; Geoffrey, A.; Lawrance, E.; Wanless, E. J. Solubility of calcium sulfate salts in acidic manganese sulfate solution from 30 to 105 °C. Hydrometallurgy 2007, 86, 13. (5) Robinson, R. A.; Stokes, R. H. Eletrolyte Solutions, 2nd ed., 5th rev impression; Butterworth: London, 1970. (6) Pitzer, K. S.; Roy, R. N. Thermodynamics of Eletrolytes. 7. Sulfuric Acid. J. Am. Soc. Chem. 1977, 99, 4930. (7) Linke, W. F.; Seidell, A. Solubilities of Inorganic and Metal Organic Compounds; American Chemical Society: Washington, DC, 1965. (8) Wollmann, G.; Vogit, 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. (9) Azimi, G.; Papangelakis, V. G. The solubility of gypsum and anhydrite in simulated laterite pressure acid leach solutions up to 250 °C. Hydrometallurgy 2010, 102, 1. (10) Wang, P.; Anderko, A.; Young, R. D. A speciation-based model for mixed-solvent electrolyte systems. Fluid Phase Equilib. 2002, 203, 141. (11) Pitzer, K. S.; Mayorga, G. Thermodynamics of electrolytes. III. Activity and osmotic coefficients for 2−2 electrolytes. J. Solution Chem. 1974, 3, 539. (12) Harvie, C. E.; Møller, N.; Weare, J. H. The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3CO3-CO2-H2O system to high ionic strengths at 25 °C. Geochim. Cosmochim. Acta 1984, 48, 723. (13) Reardon, E. J.; Bechie, R. D. Modelling chemical equilibrium of acid-drainage: The FeSO4-H2SO4-H2O system. Geochim. Cosmochim. Acta 1987, 51, 2355. (14) Baes, C. F. Jr.; Reardon, E. J.; Moyer, B. A. Ion Interaction Model Applied to the CuSO4-H2SO4-H2O System at 25 °C. J. Phys. Chem. 1993, 97, 12343. (15) Reardon, E. J. Ion interaction model applied to equilibrium in the NiSO4-H2SO4-H2O system. J. Phys. Chem. 1989, 93, 4630. (16) Harvie, C. E.; Weare, J. H. The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-Cl-SO4-H2O system from zero to high concentration at 25 °C. Geochim. Cosmochim. Acta 1980, 44, 981. (17) Silvester, L. F.; Pitzer, K. S. Thermodynamics of Electrolytes. 8. High-Temperature Properties, Including Enthalpy and Heat Capacity, with Application to Sodium Chloride. J. Phys. Chem. 1977, 81, 1822. (18) Pitzer, K. S. Thermodynamics of Electrolytes. I. Theoretical Basis and General Equations. J. Phys. Chem. 1973, 77, 268. (19) Pitzer, K. S. Thermodynamics of Electrolytes V: Effects of higher order electrostatic terms. J. Solution Chem. 1975, 4, 249. (20) Hulett, G. A.; Allen, L. E. The solubility of gypsum. J. Am. Chem. Soc. 1902, 24, 667.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was financially supported by the National Nature Science Foundation of China under Contract Nos. 21176261 and 51134007 and the Nature Science Foundation of Hunan Province under Contract No. 11JJ2011.

■

NOMENCLATURE ai = activity of species i Aϕ = one-third the Debye−Hückel limiting slope, 0.391 475 kg1/2. mol1/2 b = parameter in Pitzer’s equations with an fixed value of 1.2 BMX = observable second order interaction coefficient for neutral electrolyte MX (M = cation, X = anion) B′MX = derivation of BMX with respect to ionic strength C1, C2, C3, C4 = constant parameters for J(x) and J′(x) ϕ CMX = third order interaction coefficient for neutral electrolyte MX CMX = quantity CϕMX/2(|zMzX|)1/2 dw = density of water D = static dielectric constant of water e = dielectric constant F = sum of Debye−Hückel terms G = Gibbs free energy I = ionic strength, mol·kg−1 J(x) = function used to describe higher order electrical interaction terms in Pitzer’s equations J′(x) = derivative of J(x) with respect to x k = electric conductivity K = thermodynamic equilibrium constant m = molality concentration, mol·kg−1 n = number of water molecules in aqueous solute species N0 = Avogadro constant, 6.022 × 1023 mol−1 R = ideal gas constant, 8.314 J·mol−1·K−1 T = temperature, K WH2O = molecular weight of water, 18.0152 g·mol−1 Xij = general algebraic variable z = subscript denoting charge of solute species ϕ Z = coefficient for CMX a1, a2 = parameters appearing in Pitzer’s equation (1) (2) β(0) MX, β MX, β MX = observable second order interaction coefficient parameters for neutral electrolyte MX γi = activity coefficient of solute species θij = observable second order interaction coefficient for cation−cation pair or anion−anion pair θij E = electrostatic part of θij 5133



Article

(21) Partridge, E. P.; White, A. H. The solubility of calcium sulfate from 0 to 200°C. J. Am. Chem. Soc. 1929, 51, 360. (22) Hovey, J. K.; Pitzer, K. S.; Rard, J. A. Thermodynamics of NaSO4(aq) at temperatures T from 273 K to 373 K and of {(1-y)H2SO4 + yNa2SO4}(aq) at T = 298.15 K. J. Chem. Thermodyn. 1993, 25, 173. (23) Marshall, W. L.; Jones, E. V. Second dissociation constant of sulfuric acid from 25 to 350 °C evaluated from solubilities of calcium sulfate in sulfuric acid solutions. J. Phys. Chem. 1966, 70, 4028. (24) Cameron, F. K.; Breazeale, J. F. Solubility of calcium sulphate in aqueous solutions of sulphuric acid. J. Phys. Chem. 1903, 7, 571. (25) Zdanovskii, A. B.; Vlasov, G. A. Solubility of the various modifications of calcium sulfate in H2SO4 solutions at 25 °C. Russ. J. Inorg. Chem. 1968, 13, 1415. (26) Foote, H. W. A method of determining the hydrates formed by a salt. J. Am. Chem. Soc. 1915, 37, 288. (27) Bell, J .M.; Taber, W. C. The three-component systemCuO,SO3,H2O-at 25 °C. J. Phys. Chem. 1908, 12, 171. (28) Guerra, E.; Bestetti, M. Physicochemical Properties of ZnSO4H2SO4-H2O Electrolytes of Relevance to Zinc Electrowinning. J. Chem. Eng. Data 2006, 51, 1491. (29) Copeland, L. C.; Short, O. A. Studies of the ternary systems ZnSO4-H2SO4-H2O from −5 to 70 °C and ZnO-SO3-H2O at 25 °C. J. Am. Chem. Soc. 1940, 62, 3285. (30) Taylor, D. The system manganese sulfate-sulfuric acid-water. J. Chem. Soc. 1952, 2370. (31) Zeng, D.; Wang, W. Solubility phenomena involving CaSO4 in hydrometallurgical process concerning heavy metals. Pure Appl. Chem. 2011, 83, 1045. (32) Mutalala, B. K.; Umetsu, Y.; Tozawa, K. Solubility of calcium sulfate in acidic copper sulfate solutions over the temperature range of 298 to 333 K. Mater. Trans. 1989, 30, 394.

5134


Prediction and Measurement of Gypsum Solubility in the Systems

Recommend Documents