Calcium carbonate and calcium sulfate precipitation, crystallization and dissolution: Evidence for the activated steps and the mechanisms from the enthalpy and entropy of activation values

Chemical Geology 381 (2014) 144–153

Contents lists available at ScienceDirect

Chemical Geology journal homepage: www.elsevier.com/locate/chemgeo

Calcium carbonate and calcium sulfate precipitation, crystallization and dissolution: Evidence for the activated steps and the mechanisms from the enthalpy and entropy of activation values Athinoula L. Petrou ⁎, Athina Terzidaki Laboratory of Inorganic Chemistry, Department of Chemistry, University of Athens, Panepistimioupolis, 15771 Athens, Greece

a r t i c l e

i n f o

Article history: Received 30 January 2014 Received in revised form 15 May 2014 Accepted 15 May 2014 Available online 22 May 2014 Editor: J. Fein Keywords: Free energy of activation Enthalpy of activation Entropy of activation Eyring–Polanyi equation Calcium carbonate Calcium sulfate

a b s t r a c t Calculation of the thermodynamic parameters Eact, ΔH≠, ΔS≠ and ΔG≠ for the precipitation, crystallization and dissolution processes of the salts CaCO3 and CaSO4, leads to very important conclusions about the activated steps and the mechanisms. The ΔG≠ values are almost the same for all the processes at the same temperature, sug2+ and SO2− gesting that the electrostatic forces between the ions Ca2+ and CO2− 3 (CaCO3) and Ca 4 (CaSO4) are the most important factors governing the above processes. The values of ΔH≠ and ΔS≠ differ but the values of ΔG≠ which refer to the overall transformations are the same and are independent of the various steps that take place as well as the mechanisms (associative, dissociative). Dehydration and aquation of the ions are revealed by the values of ΔH≠ and ΔS≠. The precipitation of the two salts may take place both by a dissociative mechanism (ΔS≠ N 0) or by an associative mechanism (ΔS≠ b 0). For processes taking place without the need for diffusion 2− −1 , whereas when diffusion of of the ions, (Ca2+, CO2− 3 , SO4 ), the free energy of activation is about 85 kJ mol −1 the ions is necessary, an additional amount of ~20 kJ mol is required. This amount is the activation energy for the diffusion. In the case of CaCO3, a wide range of values is found for ΔH≠ from −66.00 to 162.00 kJ mol−1, and for ΔS≠ from −501.00 to +248.00 J K−1 mol−1 while the ΔG≠ values cover only a small range from 75 to 90 kJ mol−1. Values of 120, 131 and 132 kJ mol−1 are reported for cases where retardation is caused due to the presence of foreign compounds. In the case of CaSO4, a wide range of values is found for ΔH≠ from 6.00 to 122.00 kJ mol−1 and for ΔS≠ from −342.00 to +117.00 J K−1 mol−1 while the ΔG≠ values fall in the narrow range from 80.00 to 89.00 kJ mol−1. A value of 126 kJ mol−1 is reported for cases where retardation is caused due to the presence of foreign compounds. The Eact values vary between −63 and 164 kJ mol−1 for CaCO3 and between 8 and 184 kJ mol−1 for CaSO4, demonstrating once again that the ΔG≠ value is more realistic, being almost the same for similar processes. The various small differences for the values of ΔG≠ arise from the different ionic strengths due to the concentration and charge of the foreign ions affecting the rate constants and thus the activation parameters. The pH also has an effect, as does the nature of the solvent. The very large and very small absolute values of ΔH≠ and ΔS≠ suggest composite reactions. Composite reactions in the precipitation, crystallization and dissolution processes are the ones where dehydration takes place (positive values of ΔH≠ and ΔS≠) followed by association of the ions (negative values of ΔH≠ and ΔS≠). The algebraic sum of the relevant ΔH≠ and ΔS≠ values gives the total value of ΔH≠ and ΔS≠. Activation energy values reported in the literature for certain cases compared to the values reported in the presence of adducts do not indicate retardation. On the contrary, they suggest acceleration of the reactions. The use of ΔG≠ instead of the Eact values is more realistic in showing the large retardation effect. The presence of salt, for example NaCl, causes retardation of the crystallization process. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Calcium carbonate (CaCO3) is an important material that occurs in the natural environment as a constituent of many biological, geological and ecological systems, while it is also involved in many industrial processes, for example in scale formation. For these reasons, precipitation, crystallization and dissolution of calcium carbonate in aqueous ⁎ Corresponding author. E-mail address: [email protected] (A.L. Petrou).

http://dx.doi.org/10.1016/j.chemgeo.2014.05.018 0009-2541/© 2014 Elsevier B.V. All rights reserved.

solutions has attracted the interest of many investigators in a wide variety of fields. Many studies have focused on the problems that are related to the mechanism of its formation, and the role that various parameters play in its formation in aqueous solutions has been studied (Koutsoukos and Kontoyannis, 1984). Thermal decomposition has also been studied by several investigators and various mechanisms have been reported (Rajeswara Rao, 1993, and refs. therein). Calcium sulfate (CaSO4) has also been intensively investigated since many aspects of its reaction mechanisms remain unanswered (Klepetsanis et al., 1999). Solution chemistry helps greatly in the

A.L. Petrou, A. Terzidaki / Chemical Geology 381 (2014) 144–153

elucidation of the reaction mechanisms of the various calcium sulfate forms (hydrates) that are formed in aqueous media. The precipitation process includes nucleation and crystal growth that are two mechanistically different steps. A knowledge of the calcium sulfate precipitation mechanism has also been very important for the effective prevention of calcium sulfate scale (Klepetsanis and Koutsoukos, 1991). A kinetic study has been conducted to measure and model the rate of calcium sulfate precipitation within porous media (Merdhah and Yassin, 2008). In this work we aim to contribute to the efforts to solve the serious problems that are related to CaCO3 and CaSO4 precipitation, crystallization and dissolution by providing values for the thermodynamic parameters in order to assist in the clarification of the corresponding mechanisms. These parameters are obtained by the treatment of literature kinetic data using the Eyring–Polanyi equation. Thus we will provide an alternative analysis of well-documented examples from the literature on calcium carbonate and calcium sulfate precipitation, crystallization and dissolution. Based on the values for enthalpy and entropy of activation (ΔH≠ and ΔS≠), we will provide evidence for the existence of dehydration and aquation (hydration) steps and we will also show that some processes of the mechanisms are composite. We will also show that in some cases (depending on the experimental conditions) the diffusion of the ions is one of the controlling factors in the activation step, adding approximately 20 kJ mol−1 to the value of the free energy of activation. From the values of the free energy of activation (ΔG≠), we draw conclusions concerning the true energy requirements of the processes. It has been shown (Petrou, 2012) that the combination of enthalpy and entropy of activation in the free energy of activation gives a more realistic value of the energy requirements of the activation step that the processes need in order to take place. The analysis has also shown that similar processes have similar ΔG≠ values (Petrou, 2012). A detailed analysis has also been presented on how the values of ΔS≠ may be used to suggest a mechanism for a process (Petrou and Economou-Eliopoulos, 2009b). Our suggestion (Petrou, 2012) of using the “corrected” energy value that is critical for geochemical processes, the ΔG≠ value, instead of the Eact value, provides a way to address unexplained or queried geochemical results, and to give solutions to existing problems: (a) Based on the Eact values authors suggest mechanisms. As we have already shown (Petrou, 2012), the Eact value is not a realistic value, i.e. it does not give the true energy requirements in geochemical processes. This implies that the mechanisms that have been proposed based on the Eact values (or the rate constants) may not be correct [Table 2, case (o)]. This problem has been solved by introducing the ΔG≠ values. (b) An explanation has also been given of why calculated activation energy values (that are related only to the enthalpy of activation values) for certain transformations deviate from the expected and observed energy requirements that characterize the processes when the entropic component is substantial. Values of Eact that are intended to explain retardation of processes indicate acceleration instead [Table 1, case (e), Table 2, case (q)]. This has also been solved by introducing ΔG≠. (c) Different values of Eact have been proposed in the literature for the various processes (precipitation, crystallization, dissolution) leading to various conclusions. However, the values of ΔG≠ are similar and point to the same conclusions. From the entropies of activation an insight into the degrees of freedom of the activated complexes can be obtained and hence information about the mechanisms of the processes may be extracted (Petrou and Economou-Eliopoulos, 2009b). 2. The Eyring or activated complex theory relation — free energy of activation The transition state or activated complex theory states that upon approach of reactant molecules some bonds start to lengthen while other bonds start to form. These changes are accompanied by energy changes and, finally, the reacting molecules achieve a specific

145

arrangement before they can be transformed into the products of the reaction. The specific, transient, arrangement that possesses a definite energy is known as the transition state. The “transition state” or “activated complex” theory postulates that the reaction proceeds through formation of an “activated complex” that is in equilibrium with the reactants (Petrou and Economou-Eliopoulos, 2009b; Petrou, 2012), and the rate constant is given by:   ≠ k ¼ κðRT=NhÞ exp −ΔG =RT :

ð1Þ

The transmission coefficient κ is generally close to unity and may be ignored (Espenson, 1981). ΔG≠ is the Gibbs free energy of activation, h is Planck's constant, R is the Universal gas constant and N is the Avogadro's number. The term RT/Nh is independent of the nature of the reactants and, at a given temperature, the rate of any reaction is determined by ΔG≠. By applying the thermodynamic relationship ≠

ΔG

≠

≠

¼ ΔH −TΔS :

ð2Þ

Eq. (1) can be expressed in terms of the activation enthalpy, ΔΗ≠, and the activation entropy, ΔS≠, thus:     ≠ ≠ k ¼ κðRT=NhÞ exp ΔS =R exp −ΔH =RT :

ð3Þ

The above Eq. (3) is the general form of the Eyring equation or Activated Complex Theory equation, which is also known as Eyring–Polanyi equation in chemical kinetics. It relates the reaction rate constant to temperature and its linear form is:     ≠ ≠ ln ðk=TÞ ¼ − ΔΗ =R ð1=TÞ þ ln ðκR=NhÞ þ ΔS =R :

ð4Þ

This linear form is usually used for the suggestion of a mechanism of a certain reaction in the following way: the reaction is performed at various temperatures and the reaction rate constant is measured. The plot of ln (k/T) versus 1/T gives a straight line with slope − ΔH≠/R from which the Enthalpy of Activation is derived and with intercept ln(κR/Nh) + ΔS≠/R from which the Entropy of Activation is calculated. The term ln (κR/Nh) has a known constant value 23.76. The calculated value of the Entropy of Activation suggests an Associative mechanism when ΔS≠ is negative, a Dissociative mechanism when ΔS≠ is positive, an Interchange mechanism when ΔS≠ is equal to zero (when the rate constants refer to replacement reactions) (Petrou and EconomouEliopoulos, 2009b). Calculation of ΔG≠ is possible for the appropriate reaction temperatures according to the Eq. (2). 3. Diffusion-controlled reactions Reactions in solution in which every collision of the reacting molecules leads to products are called diffusion-controlled reactions. Their rates are limited only by diffusion that has activation energy values ranging from 10 to 20 kJ mol−1. The rate-constants for such (second order) reactions range from 109 to 1010 M−1 s−1 and are dependent on the nature of the solvent (Katakis and Gordon, 1987). Alkattan et al. (1998), have reported an apparent activation energy for diffusion of 19 ± 4 kJ mol−1 which is somewhat higher than the 13.2 kJ mol−1 obtained by Oelkers and Helgeson (1988) for the apparent activation energy of HCl diffusion. The differences between these results were assigned to the hydrodynamics of the different experimental setups used to obtain the rates (Alkattan et al., 1998).

146

A.L. Petrou, A. Terzidaki / Chemical Geology 381 (2014) 144–153

4. Application of the Eyring–Polanyi equation to calcium carbonate and calcium sulfate precipitation, crystallization and dissolution processes We have applied the Eyring–Polanyi equation to literature data and have calculated ΔH≠, which is related to the activation energy Eact (Petrou and Economou-Eliopoulos, 2009a) by the equation ≠

ΔH ¼ Eact –RT;

ΔS≠, which is related to A of the Arrhenius equation, and ΔG≠, which combines ΔH≠ and ΔS≠ (ΔG≠ = ΔH≠ − TΔS≠, Eq. (2)). It has been shown that similar processes have similar ΔG≠ values (at the same temperatures) but may have different enthalpic and entropic contributions (Petrou, 2012). We will present and compare these activation parameters (along with the Eact) that have been calculated from data reported in the literature for precipitation, crystallization and dissolution of CaCO3 (Table 1) and CaSO4 (Table 2).

ð5ÞTable 1

Kinetic data (k, T) and calculated thermodynamic parameters (Eact, ΔH≠, ΔS≠, ΔG≠) for precipitation, crystallization and dissolution of calcium carbonate (CaCO3). T (K) 1. Precipitation in aqueous solutions Case (d)

Case (e)

Case (e*)

Case (f)

2. Crystallization in aqueous solutions Case (g)

Case (h)

Case (i)

Case (j), kRS

Case (j), kRM Case (k), calcite crystallization

Case (k), calcite nucleation (from induction times)

3. Dissolution in aqueous solutions Case (l)

Case (m)

Case (n) Carrara marble

Case (n) Iceland spar

Case (o), strained

Case (o), normal

298.15 308.15 318.15 283 298 313 278 298 310 335.7 318.7 302.3

lnk(a)

−1 E(b) act kJ mol

ΔH≠(c) kJ mol−1

ΔS≠(c) J K−1 mol−1

ΔG≠(c) kJ mol−1

−5.12 −4.446 −1.485 −5.265 −3.932 −2.318 −5.10 −4.78 −4.483 −15.61 −16.76 −17.91

142.2(c) 155(d)

139.6

177.8

84.8 at 308 K

72.1(c) 71.2(e)

69.7

−42.5

82.8

13.52(c)

11.09

−246.9

87.13

58.1(c) 46(f)

55.43

−210.4

120.2 at 308 K

57.04(c) 57.1(g)

54.5

−66.4

75 at 308 K

43.5(c) 43.1 ± 3.8(h)

41.0

−135.3

82.7 at 308 K

46.7(c) 28.9(c) 46 ± 4(i)

44.2 26.5

−120.3 −181.9

81.3 82.5

163.9(c)

161.4

247.6

85.1

−63.03(c)

−65.52

−501.2

88.86

73.6(c) 66 ± 2(k)

71

40.78

58.44

73.7(c) 73 ± 10(k)

71.3

−59.75

89.7

34.7(c) 35.1(l)

32.2

−233.2

104.0 at 308 K

20.22(c) –(m)

17.5

−207.5

81.4 at 308 K

59.1(c) 54 ± 4(n)

56.5

−88.9

83.9 at 308 K

45.14(c) 46 ± 4(n)

42.5

−145.5

87.3 at 308 K

−388.7

130.84

284.4 294.7 298 306.8 315.5 284 293.5 302.1 312.7 298 283 313 298 298 300.5 306 293 298 306 301 312,5 323 283 293 298

−1.715 −0.759 −0.58 0.223 0.621 −4.211 −3.70 −3.158 −2.532 −3.139 −3.758 −1.966 −2.871 −5.952 −5.298 −4.2 −4.001 −4.343 −5.09 6 7 8 −7.97 −6.84 −6.67

278 293 303 313 323 298 323 353 298 314 328 335 298 314 328 335 276 298 353 276 298 353

−12.786 −11.564 −11.418 −10.82 −10.68 −2.659 −1.833 −1.386 −4.075 −2.779 −1.871 −1.431 −5.167 −4.382 −3.59 −3.137 −22.384 −21.59 −21.011 −22.76 −22.00 −21.19

13.72(c) 11.12

−383.6 16.1(c)

13.5

131.6

A.L. Petrou, A. Terzidaki / Chemical Geology 381 (2014) 144–153

4.1. Processes involving CaCO3 4.1.1. Precipitation of CaCO3 in aqueous solutions Calcium carbonate is encountered in several polymorphic crystalline phases including its hexa and monohydrate forms, vaterite, aragonite and calcite (Dalas and Koutsoukos, 1990). These differ in solubility and they demonstrate sensitivity to temperature, pH and the presence of foreign ions or compounds. The precipitation of calcium carbonate in aqueous solutions depends on solution supersaturation, and it has been studied at supersaturations sufficient for spontaneous precipitation (Koutsoukos and Kontoyannis, 1984). This implies that the activation energy for the diffusion of ions is not needed. The diffusion activation energy is about 10–20 kJ mol−1 (Katakis and Gordon, 1987). According to the authors, the high values of the apparent activation energies, 155 kJ mol−1, estimated from kinetic data of precipitation, suggest a surface-controlled mechanism [see Table 1, case (d)]. Calculating Eact, ΔH≠, ΔS≠, and ΔG≠ from the data of the above work we find that both ΔH≠ and ΔS≠ are positive. ΔG≠ has the value 84.8 kJ mol−1 at 308 K. The positive value of ΔS≠ suggests a dissociative mechanism. This can be explained by release of water molecules from the ionic [Ca2+(aq), CO32−(aq)]* environment in order to form the precipitate [* the symbol (aq) means aquated, i.e. hydrated]. The high value of ΔH≠ suggests that a large amount of energy is needed at the activation step (reactants to transition state step) in order to break the bonds that exist between the ions and the water molecules of the coordination sphere of the ions. The breaking of bonds requires energy while the formation of bonds releases energy. Thus dehydration is an endothermic main step in the “reactants-transition state process” and governs the ΔH≠ and ΔS≠ values for the precipitation. The combination of the ions to form the electrostatic “bond” is an exothermic process and results in negative ΔH0 and ΔS0. Under the conditions of precipitation described in case (d), the governing activation step is the dehydration of the ions as indicated by the positive values of ΔH≠ and ΔS≠. Hydration of the ions should result in −ΔH≠ and −ΔS≠ values. In case (e) the heterogeneous precipitation of aragonite from dilute solutions is reported (Romanek et al., 2011). In the above study, the rate was calculated directly by the mass of solid precipitated per unit time, taking into consideration the change in surface area over the course of the run. In the same work in Table 4, there are data for rate constants from published data in artificial and natural sea water studies, which are also included in Table 1 [case (e*)]. The association of the ions in case (e) may be governing the activated step since ΔS≠ has an overall negative value (−42.5 J K−1 mol−1). The ΔG≠ is 82.8 kJ mol−1 (as expected). In case (e*) some exothermic equilibria preceding the ratedetermining step must be taking place (studies in artificial and natural sea water) lowering the value of ΔH≠ [from 69.7 in case e to 11.09 kJ mol− 1 in case (e*)]. The value of ΔS≠ is more negative [−42.5 in case (e) vs. − 246.9 J K−1 mol−1 in case (e*)] suggesting a more organized structure in the transition state. The presence of foreign

147

ions is most probably causing these effects causing also retardation of the reactions [ΔG≠ 82.8 kJ mol− 1 in case (e) and 87.13 kJ mol−1 in case (e*)]. The higher value of ΔG≠ in case (e*) implies slower process, the ionic strength playing its retarding role on the rate constants and thus the ΔG≠. For the precipitation reaction of vaterite in aqueous solutions, an apparent activation energy of 46 kJ mol−1 was obtained [case (f)] (Xyla et al., 1991). According to the authors, the precipitation, took place via a polynuclear mechanism. The presence of EHDP (ethane-1hydroxyethylideno-1,2-di-phosphonic acid) had a strong retardation effect both on the induction times and on the subsequent rates of precipitation (Koutsoukos and Kontoyannis, 1984). Retardation implies higher free energy of activation and this explains the higher ΔG≠ value (120 kJ mol−1) compared to approximately 80 kJ mol−1 expected for the precipitation of CaCO3 or 100 kJ mol−1 expected for the precipitation that includes also diffusion of species (~20 kJ mol−1, activation energy for the diffusion). The activation energy of 46 kJ mol−1 [case (f)] compared to 155 kJ mol−1 [case (d)] does not indicate the retardation caused by EHDP. On the contrary, it implies acceleration of the reaction and it is thus once again shown that the use of ΔG≠ instead of Eact is more realistic (Petrou, 2012) and corroborates the large retardation effect (120.2 kJ mol−1 vs. 84.8 kJ mol−1). Data for the calculation of the thermodynamic parameters, Eact, ΔH≠, ΔS≠, ΔG≠, were taken from Fig. 7 of the above work [case (f)]. 4.1.2. Crystallization of CaCO3 in aqueous solutions Crystallization can be categorized into the processes nucleation and growth. Nucleation refers to the process of critical nucleus formation and growth is the augmentation of those critical nuclei. Growth may be a dominant process if the saturation level is not enough to overcome the energy barrier for nucleation. When there are small concentrations of crystals present, nucleation and growth both take place simultaneously (spontaneous or homogenous crystallization). The spontaneous crystallization process does not allow a reliable kinetic analysis to be made since the implied assumption that homogeneous nucleation takes place is doubtful (Nancollas and Purdie, 1968): nucleation is likely to occur on impurity particles which offer available sites for crystal growth. During spontaneous crystallization both the total number and size distribution of the particles vary. All the above explain the variation of the ΔG≠ values that we have calculated for the crystallization processes for both CaCO3 and CaSO4. Studying the kinetics of crystal growth of vaterite (CaCO3) in aqueous solution [case (g)], Kralj et al. (1990) reported a value of 57.1 kJ mol−1 for the activation energy. This, according to the authors, means that the rate-determining mechanism is the release of water molecules from the calcium ions as they “jump” into lattice positions. Our calculations [Table 1, case (g)] based on the data of this work suggest that a composite reaction is taking place since the absolute value of ΔS≠ is small. This composite reaction may consist of: a) the

Notes to Table 1: (a) Experimental data in units of T in K and of k in: s−1 (cases d, f, k), nm s−1 (case g), M−1 s−1/mg seed l−1 (case h), M−1 s−1/mg seed/100 ml (case i), s−1 cm−2 (case l), mol m−2 s−1 (case m), cm s−1 (case n), μmol m−2 s−1 (case e), l2 s−1 mol−1 cm−2 (case j, kRS), l2 s−1 mol−1 mg−1(case j, kRM), mol cm−2 s−1 (case o). (b) Calculated values. (c) This work. (d) Koutsoukos and Kontoyannis, 1984. (e) Romanek et al., 2011. (f) Xyla et al., 1991. (g) Kralj et al., 1990. (h) Wiechers et al., 1975. (i) Nancollas and Reddy, 1971. (j) Hasson et al., 2010. (k) Rodriguez-Blanco et al., 2011. (l) Sjoberg, 1976. (m) Alkattan et al., 1998. (n) Sjoberg and Rickard, 1984. (o) Schott et al., 1989.

148

A.L. Petrou, A. Terzidaki / Chemical Geology 381 (2014) 144–153

dehydration of the ions, which results in the increase of the degrees of freedom and follows a dissociative mechanism with positive values of ΔS≠ and ΔH≠ and b) the accommodation of the ions into lattice positions which means loss of degrees of freedom and follows an associative mechanism with negative values of ΔS≠ and ΔH≠. The algebraic sum of

the ΔS≠ values (for explanation see below) gives a small overall negative result. The ΔH≠ value being also the algebraic sum of the ΔH≠ values of the two processes also has a small value. This value is obviously smaller than the value due to dehydration only [see case (d)]. This means that, in this case, the association of the ions in the lattice happens

Table 2 Kinetic data (k, T) and calculated thermodynamic parameters (Eact, ΔH≠, ΔS≠, ΔG≠) for precipitation, crystallization and dissolution of calcium sulfate (CaSO4). lnk(a)

−1 E(b) act kJ mol

ΔH≠(c) kJ mol−1

1. Precipitation in aqueous solutions Case (d) 293 303 318 333 Case (e) 303 313 323 333 Case (f) 298 308 313 Case (g) 352.6 311.43 298 Case (h) 363 343 323 Case (i) 322.58 303.03 294.12

−6.624 −4.634 −2.534 −0.394 −4.094 −3.401 −2.639 −2.303 −12.3 −11.2 −10.66 −11.354 −11.864 −12.284 −2.6 −2.9 −3.1 −5.113 −5.310 −5.436

124.3(c) 184 ± 2(d)

121.7

2. Crystallization in aqueous solutions Case (j) 347.8 346.6 344.8 Case (k) 288 298 303 308 318 Case (l) 298 323 343 363 Case (m) 318.5 307.7 288.2 Case (n) 328 318 308 298 Case (o) 303 323 343 363 1 303 Case (p) Without polyacrylates 313 323 2 303 Case (p) 313 With polyacrylates 323 Case (q) 303.03 322.58 344.82 370.37 Case (r) 333 343 353 363

−7.497 −7.55 −7.619 −4.656 −3.663 −3.211 −2.885 −2.083 −2.425 −1.099 1.204 2.303 −3.75 −4.1 −4.8 −2.554 −3.321 −4.181 −5.053 −13.332 −11.190 −10.131 −9.302 −2.557 −1.799 −1.012 −2.601 −1.752 −0.933 −19.625 −19.113 −18.644 −18.015 −2.55 −2.23 −1.92 −1.52

40.33(c) 65.2(j)

T (K)

III Dissolution in aqueous solutions Case (s)

283 288 293 298 303

− 4.358 −4.160 −3.808 −3.381 −3.182

ΔS≠(c) J K−1 mol−1 116.7

ΔG≠(c) kJ mol−1 85.8 at 308 K

51.62(c) 51–71(e)⁎

49

84.6(c) 84.30(f)

81.9

−72.2

14.2(c) –(g)

11.5

−307.8

106 at 308 K

12.12(c) 30(h)

9.3

−242.63

84.03 at 308 K

8.84(c) 30–50(i)

6.274

−268.45

88.96

37.4

−200.7

99 at 308 K

64.75(c) 62.8 ± 2(k)

62.2

−66.7

82.8 at 308 K

68.1(c) 52.6(l)⁎

65.41

−47.5

80.04 at 308 K

26.4(c) 26.9–30.7(m) Average = 28.9 39(c) 66.9 ± 6.3(n)

23.9

−201.36

85.92 at 308 K

36.5

−157.9

85.12 at 308 K

60.68(c) 62.8(o)

57.93

−162.25

107.9 at 308 K

62.79(c)

60.2

−67.63

81.03 at 308 K

67.832(c) 64.9(p2)

65.23

−51.28

81.03 at 308 K

22.015(c) 13.76–23.14(q)

20.39

−341.45

125.56 at 308 K

33.9(c) 34 ± 2(r)

31.05

−173.83

84.59

44.6(c) 41.8 ± 6.3(s)

42.2

−132

82.9 at 308 K

−117

(p1)

85.02 at 308 K

104.1 at 308 K

A.L. Petrou, A. Terzidaki / Chemical Geology 381 (2014) 144–153

during the activation step, whereas in the case of precipitation [case (d)] only dehydration occurs during the activation step. The ΔG≠ is approximately 75 kJ mol−1 at 308 K. Thus, dehydration, being an endothermic process, and crystal formation i.e. formation of (electrostatic) bonds, being an exothermic process, both take place during the “reactants-transition state step” process resulting in values of ΔH≠ and ΔS≠ smaller than those found for the case where only dehydration occurs during the “reactants-transition state step” process [precipitation, case (d)]. Reddy and Nancollas (1971), reporting on the kinetics of crystallization of calcium carbonate, state that the activation energy is relatively high, 46.0 kJ mol−1, and that the crystallization rate is independent of the stirring speed. Wiechers et al. (1975, case (h)) suggest that the crystallization process conforms to the model for Ca2+ removal proposed by Reddy and Nancollas (1971). The removal rate constant, k, is temperature dependent according to the Arrhenius relationship with Eact = 43.1 ± 3.8 kJ mol− 1. The high activation energy and other kinetic parameters support the hypothesis that the crystallization process is surface controlled. Nancollas and Reddy (1971), in case (i) point out that the activation energy for crystal growth of calcite is 46.0 ± 4.2 kJ mol−1, thus supporting the proposed surface-controlled mechanism for crystal growth. This value is considerably larger than the 17.6 kJ mol−1 to be expected for a diffusion controlled reaction (Howard et al., 1960), again pointing to the proposed interfacially controlled mechanism for calcium carbonate crystal growth. The assumptions made of homogeneous nucleation and of simultaneous nucleation and growth are, however, open to considerable criticism (Nancollas et al., 1964). Data from Table 1 of the above work [case (i)] led us to calculate ΔH≠1 = 44.2 kJ mol− 1, ΔH≠2 = 26.5 kJ mol− 1, ΔS≠1 = − 120.3 J K− 1 mol− 1, ΔS≠2 = − 181.92 J K− 1 mol− 1, ΔG≠1 = 81.3 kJ mol−1 at 308 K, ΔG≠2 = 82.5 kJ mol−1 at 308 K. The subscripts 1 and 2 refer to data that differ only according to mg seed crystal/ 100 ml, the stirring rate (rpm) being the same. A novel electrochemical system developed in case (j) (Hasson et al., 2010) enables drastic reduction in the electrode area requirement by directing the precipitation of calcium carbonate to occur in a seeds crystallization vessel rather than on the cathode. Kinetic coefficients reported in the literature are of two types: fundamental coefficients kRS based on the actual crystallization area and coefficients kRM based on seeds concentration. Literature values of the above kinetic coefficients kRS and kRM are taken from Table 1 of case (j). The values of the two different kinetic coefficients result, as expected, in similar values of ΔG≠ (85.1 vs. 88.86 kJ mol−1 from kRS and kRM, respectively) but the values of ΔH≠ and ΔS≠ are completely different implying completely different

149

processes and thus mechanisms. The ΔH≠ and ΔS≠ values resulting from kRS are positive, but those resulting from kRM are negative. Certainly the values from both coefficients suggest composite processes. The first include endothermic processes whereas the second include exothermic ones which govern the total procedures. The very negative value of ΔS≠ from kRM suggests a great degree of organization in all the processes including the transition state step. In case (k) a study of amorphous calcium carbonate ACC crystallization to calcite via vaterite is presented (Rodriguez-Blanco et al., 2011). According to the authors, the crystallization process occurs in two stages: firstly the particles of ACC rapidly dehydrate and crystallize to form individual particles of vaterite; secondly the vaterite transforms to calcite via a dissolution and reprecipitation mechanism with the reaction rate controlled by the surface area of calcite. The Ecryst value for calcite growth is found by the authors to be 66 ± 2 kJ mol−1. Several other authors have derived activation energies for seeded calcite growth ranging from ~39 to ~70 kJ mol−1. The fact that our calculated value of ΔG≠ is 58.4 kJ mol− 1 for calcite crystallization, i.e., smaller than the value found (by us) in all other cases (~80 kJ mol−1), is easily explained by the fact that in this crystallization process only the ions are present in the solution. All other ions that are presCa2+ and CO2− 3 ent in all the other cases are absent in this case. In this case the vaterite transforms to calcite via dissolution and reprecipitation. It has been found that retardation is caused due to the presence of foreign compounds. In this case there are no foreign compounds. So, the crystallization process should be faster than in all other cases. This implies a smaller free energy of activation and this is actually happening. The value of 58.44 kJ mol− 1 is the smallest value which can be found for calcite crystallization. In the other cases of Table 1, Na2CO3 and CaCl2 are the sources for CO23 − and Ca2 +, respectively, whereas in case k, CaCO3 was the source of both ions. The rest of the ions that are present contribute in the ionic strength of the solutions which affects the values of the rate constants and hence the Eact, ΔH≠, ΔS≠ and ΔG≠ values making the rate slower and hence the ΔG≠ bigger. In this case ΔS≠ is positive (40.78 J K−1 mol−1) in agreement with the dehydration process that the authors suggest based on other kind of scientific findings. The rate determining step is governed by the dehydration step resulting in positive values of ΔS≠. The contribution of dehydration only, results in larger values of ΔS≠ [Table 1, case (d) and Table 2 case (d)]. The kinetic data that are derived from induction times (calcite nucleation) result in negative ΔS≠ and a value for ΔG≠ of 89.7 kJ mol−1. One could argue that the dissolution process in general does not involve foreign compounds, so should the ΔG≠ values be smaller? The smaller value is ~60 kJ mol−1 (case (k), calcite crystallization). The free energy for dissolution is found to be ~80 kJ mol−1 (Tables 1,2). The diffusion activation

Notes to Table 2: (a) Experimental data in units of T in K and of k in: s−1 (cases d, e, f, h, i,k, l, m, s), M−1 s−1 (cases g, k, p), μm/s wt%2 (case j), l mm mol−2 s−1 (case n), mol/cm2 s (case o), mol m−2 s−1 (case q), l mol−1 s−1 (case r). Case e*: for the supersaturation range between 2.5 and 11. Case l*: activation energy for the nucleation of calcium sulfate dihydrate in 3 m NaCl solutions. The activation energy for case l was obtained using the induction time, tind. (b) Calculated values. (c) This work. (d) Klepetsanis and Koutsoukos, 1991. (e) Alimi et al., 2003. (f) Merdhah and Yassin, 2008. (g) Klepetsanis et al., 1999. (h) Lancia et al., 1999. (i) Prisciandaro et al., 2013. (j) Jamialahmadi and Muller-Steinhagen, 2000. (k) Liu and Nancollas, 1970. (l) He et al., 1994. (m) Prisciandaro et al., 2003. (n) Liu and Nancollas, 1973. (o) Smith and Sweett, 1971. (p)1 and (p)2 Amjad and Masler, 1985. (q) Yehia et al., 2011. (r) Cetin et al., 2001. (s) Liu and Nancollas, 1971.

150

A.L. Petrou, A. Terzidaki / Chemical Geology 381 (2014) 144–153

2− energy is needed for the separation of the ions (Ca2+, CO2− 3 , SO4 ) and this has a value of ~ 20 kJ mol− 1 increasing the 60 kJ mol−1 value to ~80 kJ mol−1 (as found). So the value of ~60 kJ mol−1 is the free energy of activation in the absence of foreign ions.

4.1.3. Dissolution of CaCO3 in aqueous solutions Sjoberg (1976) describes a fundamental equation for calcite dissolution kinetics. He reports an apparent activation energy for the reaction between 5 and 50 °C of 35.1 kJ mol−1 [case (l)]. The relatively high activation energy indicates, according to the author, that the reaction is mainly chemically- rather than diffusion-controlled. Nancollas and Reddy (1971) determined an activation energy of 46 ± 4.2 kJ mol−1 for the precipitation reaction and concluded that the rate-determining step is a surface-controlled rather than transport-controlled precipitation. For a diffusion-controlled reaction, according to Burkin (1966), the expected activation energy is about 16.7 kJ mol−1. From the data of the above work [case (l)] we calculate Eact = 34.67 kJ mol−1, ΔH≠ = 32.19 kJ mol−1, ΔS≠ = −233.2 J K−1 mol−1, ΔG≠ = 104.0 kJ mol−1 at 308 K. Alkattan et al. (1998) reported an experimental study of calcite and limestone dissolution rates as a function of pH from −1 to 3 (aqueous HCl solutions) and temperature from 25 to 80 °C [case (m)]. Dissolution rates were determined for single calcite crystals, limestone sand and compressed calcite powders. The corresponding rates of the three different sample types were identical. Apparent rate constants and H+ diffusion coefficients were reported. According to the authors, the apparent activation energy of 19 kJ mol−1, is somewhat higher than the 13.2 kJ mol−1 obtained by Oelkers and Helgeson (1988), for the apparent activation energy of HCl diffusion. Our calculations give a dissolution value for ΔG≠ 81.4 kJ mol−1 [Table 1, case (m)]. Sjoberg and Rickard (1984) found an activation energy 54 ± 4 kJ mol−1 for Carrara marble and 46 ± 4 kJ mol−1 for Iceland spar, determined at pH 8.4 in 0.7 M KCl solutions [cases (n)]. Our calculations give ΔG≠ values 83.9 kJ mol−1 for Carrara marble and 87.3 kJ mol−1 for Iceland spar. From the data of the work of Sjoberg (1976) and Alkattan et al. (1998) we calculate negative values for ΔS≠ that suggest that the associative mechanisms are predominant. The large absolute value generally suggests a composite reaction or process (Petrou, 2012). The enthalpy of activation for the total (composite) transformation is equal to the algebraic sum of the various enthalpies that accompany all the steps involved in the composite process. This algebraic sum may obviously be positive, zero or negative depending on the absolute values of the various enthalpies that are involved. The same applies for the entropy of activation. Hydration-aquation (formation of bonds) is an exothermic process (ΔH0 is negative) and this is the reason that the ΔH≠ for this decomposition (dissolution) is so small. Hydration-aquation follows an associative mechanism (loss of degrees of freedom, increase of organization) and thus the value of ΔS≠ is negative. The total ΔS≠ is the sum of a negative value for the aquation of the cations, a negative value for the aquation of the anions and a positive value for the dissociation of the salt (dissociative mechanism), i.e. the separation of the calcium and the carbonate ions (increase of degrees of freedom, loss of organization). In case (o) dissolution kinetics data of strained calcite are presented (Schott et al., 1989). It is reported that interface-limited dissolution of minerals occurs non-uniformly with preferential attack at sites of excess surface energy such as dislocation, edges, point defects, and microfractures. Strained crystals are predicted to show higher dissolution rates due to the increased internal energy associated with dislocations and due to enhanced nucleation of dissolution pits at dislocation outcrops on the surface. Using calcite strained to different degrees, the authors have observed a measurable rate enhancement relative to unstrained crystals at temperatures from 3 to 80 °C. The authors used large, single crystals of calcite for which surface area and rate should be directly

related. From Fig. 4 of case (o) we take data for comparison of the rates of dissolution of normal (non-strained) calcite and calcite strained to a dislocation density of 0.5 × 109–1.0 × 109 cm−2 as a function of pH at 3, 25 and 80 °C. The data were taken for pH = 5.5. Our calculations prove that the ΔG≠ values are similar (130.8 vs. 131.6 kJ mol−1). The values of ΔG≠ suggest retardation in comparison with the other cases of Table 1 and this may be attributed to the increased ionic strength due to KCl and HCl present in the solution. The very negative ΔS≠ suggests a great degree of organization in the transition state compared to the reactants. The values of ΔH≠ are very low suggesting composite reactions. Similar effect of the ionic strength, that is retardation, is observed in cases: Table 1 case (f) and Table 2 case (q). 4.2. Processes involving CaSO4 4.2.1. Precipitation of CaSO4 in aqueous solutions An understanding of the mechanism of CaSO4 formation in aqueous solutions where precipitation takes place spontaneously due to high supersaturation is of great importance for the control of undesirable scale deposits. The time period that elapses between the attainment of supersaturation and the appearance of the first crystals is called the induction time (He et al., 1994). An empirical relationship similar to the Arrhenius equation (temperature dependence of the rate constant) was suggested (Liu and Nancollas, 1975) for the effect of temperature on induction period. For the spontaneous precipitation of calcium sulfate dihydrate at conditions of sustained supersaturation, an apparent activation energy of 184 ± 2 kJ mol−1 [Table 2, case (d)] has been reported (Klepetsanis and Koutsoukos, 1991). The kinetic analysis according to the Arrhenius equation yielded a high activation energy value indicative, according to the authors, of surface-controlled mechanisms. According also to the authors, calcium sulfate dihydrate is formed in aqueous supersaturated solutions by a polynuclear mechanism. Using the kinetic data of the above work, we have calculated Eact, ΔH≠, ΔS≠ and ΔG≠ [Table 2, case (d)]. The ΔH≠ and the ΔS≠ values are positive suggesting a dissociative mechanism, i.e. going from the reactants to the transition state the number of the various species increases. This may mean that water molecules are released from the ionic environments of Ca2+(aq), and SO42 −(aq) in order to form the precipitate. ΔG≠ has the value 85.8 kJ mol−1 at 308 K [Table 2 case (d)]. Due to the supersaturation conditions the diffusion activation energy of ~20 kJ mol−1 is obviously not needed. This value of ΔG≠ is comparable with the value of 84.8 kJ mol− 1 at 308 K for calcium carbonate precipitation [Table 1, case (d)]. The high value of ΔH≠ suggests that a large amount of energy is needed in order to break the bonds that exist between the ions and the water molecules in the coordination sphere of the ions. Thus dehydration of the ions is a main step in the “reactants-transition state” process and is the main component of the ΔH≠ and the ΔS≠ values. Hydration of the ions should result in −ΔH≠ and −ΔS≠ values. Alimi et al. (2003) studying the kinetics of the precipitation of calcium sulfate dihydrate in a desalination unit, reported an activation energy value of 51.047 kJ mol−1 [Table 2, case (e)]. Using data from the above work we calculate Eact = 51.62 kJ mol−1, ΔH≠ = 49 kJ mol−1, ΔS≠ = −117 J K−1 mol−1, ΔG≠ = 85.02 kJ mol−1 at 308 K. The negative value of ΔS≠ suggests an associative mechanism, i.e. going from the reactants to the transition state the number of the various species decreases. This may suggest that the water molecules are released from the ionic environments [Ca 2 +(aq) , and SO 4 2 −(aq)] before the slow rate-determining step. The combination of the positive and negative ions leading to negative ΔS≠ i.e. to decrease of the number of the various species [decrease of the degrees of freedom], is the rate-determining step. In a laboratory study and a prediction of calcium sulfate at highsalinity formation water (Merdhah et. al., 2008) the activation energy is found to be 84.30 kJ mol−1. Calculating ΔH≠, ΔS≠ and ΔG≠ from the data of this work [Table 2, case (f)], we find that ΔS≠ is negative, as

A.L. Petrou, A. Terzidaki / Chemical Geology 381 (2014) 144–153

previously, suggesting an associative mechanism. The negative value of ΔS≠ suggests that going from the reactants to the transition state the number of particles overall decreases and that the combination of the positive and negative ions [Ca2+, SO2− 4 ] may be the rate-determining step. The release of water molecules from the aquated ions [Ca2+(aq) and SO42−(aq)] (resulting in an increase in ΔS≠) may have taken place in a faster preceding step. The high-salinity formation water applied in this experiment may have played a role in attracting the water of solvation and thus accelerating the release of water molecules in a step prior to the rate-determining step of the precipitation process. ΔG≠ has the value 104.14 kJ mol−1 at 308 K [Table 2, case (f)] which suggests that the diffusion activation energy (~20 kJ mol−1) is needed (~85 + ~20 kJ mol−1). According to the authors, a temperature rise from 40 to 90 °C causes a decrease of CaSO4 solubility, that is, the solubility of CaSO4 is overall an exothermic process. This implies that the heat of aquation of the ions Ca2+ and SO2− 4 , which is a process that releases heat, is greater than the heat needed for separating the ions Ca2+ and SO2− 4 , i.e. the breaking of the lattice of the salt (CaSO4) which is an endothermic process. In a study of the role of temperature in the spontaneous precipitation of calcium sulfate dihydrate in supersaturated solutions (Klepetsanis et al., 1999), the authors maintain that surface diffusion is the mechanism according to which the growth units are integrated into the active sites of the supercritical nuclei. According to our calculations [Table 2, case (g)], diffusion is actually taking place as revealed by the value of ΔG≠, 106 kJ mol−1 (~80 + ~20 kJ mol−1 due to diffusion). The ΔH≠, ΔS≠ and ΔG≠ values were estimated by the application of the Eyring equation on the data of the above work (Table 2). ΔH≠ has a very small absolute value, 11.5 kJ mol−1, due to a composite, possibly exothermic, process with negative ΔH0, that precedes the activated step. ΔS≠ is negative with very large absolute value (−307.8 J K−1 mol−1) implying again a composite process. The negative ΔS≠ value suggests an associative mechanism which would mean that considerable organization occurs at the transition state. ΔG≠ is 106.0 kJ mol−1 at 308 K. The hydration may be the exothermic step that results in a negative component in the enthalpic term, thus decreasing its absolute value, and also in a negative component in the entropic term, thus increasing its absolute value. The organization may be due to the association of the ions (calcium and sulfate) along with water molecules (dihydrate salt). Thus the composite process may be: a) the association of the ions, Ca2+ and SO2− 4 , and b) the association of water molecules to form the dihydrated salt (hydration). The dehydration process (release of water molecules from the coordination sphere of the ions) clearly does not occur at the transition step since it would lead to a positive contribution to ΔS≠, increasing thus its very negative value to a less negative one, and also to a positive contribution to ΔH≠, increasing its very low positive value. The ΔG≠ value of case (f) (104.1 kJ mol−1) is comparable with the ≠ ΔG value of case (g), (10 kJ mol−1), though their ΔS≠ values differ by a factor of about 4.3 (− 72 versus − 308 J K−1 mol−1) and their ΔH≠ values differ by a factor of about 7.12 (81.9 versus 11.5 kJ mol−1). The value for ΔG≠ is the same in both cases, as expected (Petrou, 2012), since the same reaction is taking place. In case (h), the dependence of the induction period (tind) on temperature made it possible to evaluate Eact as 30 kJ mol−1 (Lancia et al., 1999). Our calculations, based on the data of this work [case (h)], gave a very small value for ΔH≠ (9.3 kJ mol− 1) and a very negative value for ΔS≠ (− 242.6 J K− 1 mol− 1). The ΔG≠ value is 84.03 kJ mol−1 at 308 K (Table 2). Prisciandaro et al. (2013) studied gypsum precipitation in industrial equipment and made a comparison of different additives. We found ΔG≠ values 88.96 kJ mol−1 for gypsum precipitation without additives [Table 2, case (i)]. Again the ΔH≠ value was very small (6.3 kJ mol−1) and the ΔS≠ value very negative (−268.45 J K−1 mol−1). The three cases (g), (h), (i) bear very small ΔH≠ values, very negative ΔS≠ values and the ΔG≠ values are 106 kJ mol− 1 for case

151

(g), 84 kJ mol−1 for case (h) and 89 kJ mol−1 for case (i). This indicates that, for the three cases (g), (h) and (i), similar mechanisms must be taking place with the only difference being that for case (g) the diffusion of the ions is needed which adds an amount of ~ 20 kJ mol−1 to the activation energy. 4.2.2. Crystallization of CaSO4 in aqueous solutions Jamialahmadi and Muller-Steinhagen (2000, case (j)), reporting on the crystallization of calcium sulfate dihydrate from phosphoric acid, state that the effect of temperature on the growth rate constant follows an Arrhenius relationship with an activation energy of 65.2 kJ mol−1. From the Arrhenius plot of growth rate constant we get data from which we calculate ΔH≠ = 37.4 kJ mol− 1, ΔS≠ = −200.72 J K−1 mol−1 and ΔG≠ = 99 kJ mol−1 at 308 K [Table 2, case (j)]. The negative ΔS≠ value suggests an associative mechanism and its large absolute value suggests a composite process (see previous cases). Liu and Nancollas (1970), studied the kinetics of crystal growth of calcium sulfate dihydrate [case (k)] and reported an activation energy value for the surface controlled crystal growth of 62.8 ± 2 kJ mol−1. The authors declare that this value is appreciably larger than the value 18.8 kJ mol− 1 (Howard et al., 1960) to be expected on the basis of pure mass transport control. Using data from the above work we calculate Eact = 64.75 kJ mol− 1, ΔH≠ = 62.24 kJ mol− 1, ΔS≠ = −66.7 J K−1 mol−1, ΔG≠ = 82.78 kJ mol−1 at 308 K. The nucleation kinetics of calcium sulfate dihydrate in NaCl solutions up to 6 m and 90 °C was studied by He et al. (1994, case (l)). Using data from the above work at 25, 50, 70, 90 °C, NaCl 3.0 m, CaSO4 (aq) 180.0 mm and the corresponding induction times (in s), we calculated ΔG≠ = 80.04 kJ mol−1. Rate constants were calculated from induction times. Prisciandaro et al. (2003, case (m)) propose that citric acid has a strong retarding effect towards gypsum nucleation. Several values for the interfacial tension and activation energy have been estimated as a function of citric acid concentration and of temperature. The average of the activation energy values reported by the authors is 28.9 kJ mol− 1. The values with the above average are comparable with respect to that previously found in the absence of any additives (Eact = 30 kJ mol − 1 , Lancia et al., 1999). Thus we could say that there is no actual retarding effect. On the other hand, our calculations reveal that ΔG ≠ is 85.92 kJ mol− 1 , ΔH≠ = 23.9 kJ mol − 1 , ΔS≠ =− 201.36 J K − 1 mol− 1 , implying an associative mechanism and a composite reaction. The ΔG≠ value does not suggest strong retardation. Studying the linear crystallization and the induction-period of the growth of calcium sulfate dihydrate crystals, Liu and Nancollas (1973) reported that the linear crystallization of well-formed crystals of calcium sulfate dihydrate from supersaturated solutions needs the activation energy of 66.9 ± 6.3 kJ mol− 1 for the fast-growing faces. Using data from this work we find ΔG≠ = 85.12 kJ mol−1 at 308 K. Smith and Sweett (1971, case (o)), studying the crystallization of calcium sulfate dihydrate (CaSO4·2H2O) reported that the value of the rate constant indicated that the rate-controlling step was dehydration of calcium ions. This suggests a positive value for ΔS≠ and a dissociative mechanism. However, the value of ΔS≠ is found to be negative [Table 2, case (o)] suggesting an associative process. The ΔG≠ value is 107.9 at 308 K implying that diffusion of the ions is taking place in the ratedetermining step. Amjad and Masler (1985, case (p)) suggest that their results indicate that the crystallization of CaSO4·2H2O in the presence of polyacrylates is preceded by an induction period. Crystal growth of CaSO4·2H2O proceeds with a rate close to that in pure supersaturated solution. The authors report an activation energy of 64.9 kJ mol−1 for the polymer containing solution which is in excellent agreement, according to the authors, with the Eact value reported for the CaSO4·2H2O seeded growth in the presence of phosphonates (Liu et al., 1975). Our results show that

152

A.L. Petrou, A. Terzidaki / Chemical Geology 381 (2014) 144–153

polyacrylates do not affect the activation parameters, the ΔG≠ being 81.03 kJ mol−1 in both cases, i.e. without and with polyacrylates. The values of ΔS≠ and ΔH≠ differ slightly (Table 2). Yehia et al. (2011, case (q)) studied the effects of some parameters affecting the crystallization rate of calcium sulfate dihydrate in sodium chloride solution at different supersaturation, pH = 3, ionic strength I = 0.5 M and at 20–80 °C, and they reported that the rate of crystallization was found to depend on the stirring rate, suggesting a diffusion mechanism. In addition, the presence of Mg2+ or Al3+ retarded the rate of crystallization to an extent proportional to the amounts present. Furthermore, the retardation effect was enhanced as the supersaturation decreased. The presence of sodium chloride decreases the supersaturation and enhances the retardation. This explains the value of ΔG≠ that we found, namely 125.6 kJ mol−1 (in the absence of additives). Thus, the presence of NaCl caused an increase in ΔG≠, i.e. a decrease of k (retardaattract each tion). This agrees with the fact that the ions Ca2+ and SO2− 4 other with Coulombic forces and the presence of Na+, Cl− among them decreases the attractive forces and consequently decreases the rate constant, thus increasing ΔG≠. The effect of the presence of the ions Na+, Cl−, that is the effect of the ionic strength on the rate constant, is expressed by various equations (Katakis and Gordon, 1987). However, the reported values of Eact, 13.76–23.14 kJ mol−1, do not support retardation. On the contrary, they suggest acceleration of the reaction (small Eact values suggest large values for rate constants) [for the values of Eact of the CaSO4 crystallization see Table 2, column Eact]. In case (r) the kinetics of gypsum formation and growth during the dissolution of colemanite in sulfuric acid is presented (Cetin et al., 2001). After the fast dissolution reaction of colemanite in aqueous sulfuric acid, the nucleation of the gypsum crystals first occurs from the supersaturated solution and then the crystals grow on these nuclei. The authors report an activation energy of 34 ± 2 kJ mol−1 for the crystal growth of gypsum. Our calculated value of ΔG≠ is 84.59 kJ mol−1 as expected. The ΔS≠ is negative as expected and the ΔH≠ is 31.05 kJ mol−1. 4.2.3. Dissolution of CaSO4 in aqueous solutions The kinetics of dissolution of calcium sulfate dihydrate crystals in subsaturated solutions of the salt was studied at various temperatures and there was a suggestion of film diffusion as the rate-controlling step (Liu and Nancollas, 1971, case (s)). The activation energy was found to be 41.84 ± 6.3 kJ mol−1. This value, according to the authors, is larger than the value 18.8 kJ mol− 1 to be expected on the basis of pure mass transport control. Although much of the evidence points to film diffusion as being the rate-controlling step, the authors support that it is not possible to exclude the possibility of a more complicated mechanism due to the relatively large activation energy. Our calculations based on data of the above work give: Eact = 44.6 kJ mol− 1, ΔH≠ = 42.2 kJ mol− 1, ΔS≠ = − 132 J K− 1 mol− 1, ΔG≠ = 82.9 kJ mol− 1 at 308 K. The negative value of ΔS≠ suggests that the transition state is more organized than the reactants. 5. Conclusions The calculation of the thermodynamic parameters Eact, ΔH≠, ΔS≠ and ΔG≠ of the precipitation, crystallization and dissolution processes for the salts CaCO3 and CaSO4, has demonstrated once again that, for geochemical processes, the critical factor is ΔG≠ and not Eact (Petrou, 2012). The values of the above thermodynamic parameters lead to the following conclusions: • The ΔG≠ values are almost the same for CaCO3 and CaSO4 precipitation, crystallization and dissolution at the same temperature. This suggests that the electrostatic forces between the ions Ca2+ and CO2− 3 (CaCO3) and Ca2 + and SO24 − (CaSO4) are important and that they govern the above processes. • The precipitation of the two salts may take place both by a dissociative mechanism, ΔS≠ N 0 [cases (d) of Tables 1 and 2, case (k) for calcite

crystallization, case (j) for kRS coefficient] and by an associative mechanism, ΔS≠ b 0 [all the other cases, Tables 1 and 2]. The ΔG≠ values are approximately the same whereas the values of ΔH≠ and ΔS≠ are different. The fact that the ΔG≠ values are almost the same for cases (d) of Tables 1 and 2, suggests that the rate-determining step is the same and this must be the dehydration of CaCO3 and CaSO4. The positive values of ΔS≠ suggest dissociative mechanisms and actually this is the mechanism when water molecules are released from the coordination spheres of the cations [Ca2 +aq] and anions [CO32 −(aq) and SO42 −(aq)]. This dehydration process involves breaking of bonds and demands energy that is revealed as large values for ΔH≠. In all the other cases, ΔS≠ is negative implying an associative mechanism, i.e. increased order in the transition state. • When a process takes place without the need for diffusion of the ions, the free energy of activation is about 85 kJ mol− 1 whereas when there is a need for diffusion of the ions an additional amount of ~ 20 kJ mol− 1 is required. This amount is the activation energy for the diffusion. Thus, in total, ~ 100 kJ mol− 1 is needed for these processes. • In the case of CaCO3, a very wide range is found for the values for ΔH≠ (−66.00–162.00 kJ mol−1) and ΔS≠ (−501.00 to +248.00 J K−1 mol−1) while the ΔG≠ values cover a narrow range (75–90 kJmol−1). An additional amount of +20 kJmol−1 is needed when diffusion of the ions takes place. Values of 120, 131 and 132 kJ mol−1 are observed for cases [case (f), cases (o), Table 1] where retardation is caused due to the presence of foreign compounds. • Similarly, in the case of CaSO4, a very wide range is found for the values for ΔH≠ (6.00–122.00 kJ mol−1) and ΔS≠ (−342.00 to +117.00 J K−1 mol−1), while a narrow range is found for the ΔG≠ values (80.00–89.00 kJ mol−1). There is an additional amount of +20 kJ mol−1 for processes that include diffusion of the ions. A value of 126 kJ mol−1 is observed for one case [case (q), Table 2] where retardation is caused due to the presence of foreign compounds. • The Eact values vary between −63 and 164 kJ mol−1 for CaCO3 and between 8 and 184 kJ mol−1 for CaSO4, demonstrating once more that the ΔG≠ value is a more realistic parameter, being almost the same for similar processes. • The various small differences that appear in the values of ΔG≠ are due to differences in ionic strength (the concentration and charge of the foreign ions) that affect the rate constants and thus the activation parameters. The pH also has an effect, as does also the nature of the solvent. • The large absolute values of ΔH≠ and ΔS≠ reveal composite reactions. A composite reaction is, for example, one for which dehydration takes place (positive values of ΔH≠ and ΔS ≠) followed by association of the ions (negative values of ΔH≠ and ΔS≠). The algebraic sum of the values is the total value of ΔH≠ and ΔS≠. • Acceleration/retardation. The activation energy value of 46 kJ mol−1 for case (f) compared to the value of 155 kJ mol−1 for case (d) does not indicate retardation caused by EHDP, but, on the contrary, implies acceleration of the reaction. However, the use of ΔG≠ instead of Eact has been shown to be more realistic (Petrou, 2012), indicating here the large retardation effect. ΔG≠ for case (f) is 120.2 kJ mol−1 and for case (d) is 84.8 kJ mol−1. The larger value of ΔG≠ suggests a slower reaction. Also, in case (q), the values of Eact reported by the authors do not justify retardation, but, on the contrary, suggest acceleration of the reaction since small Eact values suggest large values of rate constants. Again the use of ΔG≠ instead of Eact explains the retardation [20 vs. 126 kJ mol−1, case (q)]. • The addition of salt, for example NaCl, causes retardation of the crystallization process [case (q)]. The ΔS≠ value, (− 341.45 J K−1 mol−1) suggests a very organized transition state. This is due to the attraction and Ca2+, respectively. of Na+ and Cl− to SO2− 4

A.L. Petrou, A. Terzidaki / Chemical Geology 381 (2014) 144–153

Acknowledgments Many thanks are due to all the authors that are included in the list of references, who, with their valuable data, the high-level scientific work both in experiments and in explanations, have given us significant assistance in providing additional evidence concerning the activated steps and the mechanisms for precipitation, crystallization and dissolution of CaCO3 and CaSO4. We thank Pauline Zannia for her assistance. We also thank the University of Athens for the financial support of this work. References Alimi, F., Elfil, H., Gadri, A., 2003. Kinetics of the precipitation of calcium sulfate dihydrate in a desalination unit. Desalination 157, 9–16. Alkattan, M., Oelkers, E.H., Dandurand, J.-L., Schott, J., 1998. An experimental study of calcite and limestone dissolution rates as a function of pH from −1 to 3 and temperature from 25 to 80 °C. Chem. Geol. 151, 199–214. Amjad, Z., Masler III, W.F., 1985. The inhibition of calcium sulfate dihydrate crystal growth by polyacrylates and the influence of molecular weight. Corrosion 85 (paper number 357). Burkin, A.R., 1966. The Chemistry of Hydrometallurgical Processes. E. & F. N. Spon, (158 pp.). Cetin, E., Eroglou, I., Ozkar, S., 2001. Kinetics of gypsum formation and growth during the dissolution of colemanite in sulfuric acid. J. Cryst. Growth 231, 559–567. Dalas, E., Koutsoukos, P.G., 1990. Calcium carbonate scale formation and prevention in a flow-through system at various temperatures. Desalination 78, 403–416. Espenson, J.H., 1981. Chemical Kinetics and Reaction Mechanisms. McGraw-Hill, New York. Hasson, D., Sidorenko, G., Semiat, R., 2010. Calcium carbonate hardness removal by a novelelectrochemical seeds system. Desalination. http://dx.doi.org/10.1016/j.desal. 2010.06.036. He, S., Oddo, J.E., Thomson, M.B., 1994. The nucleation kinetics of calcium sulfate dihydrate in NaCl solutions up to 6 m and 90 °C. J. Colloid Interface Sci. 162, 297–303. Howard, J.R., Nancollas, G.H., Purdie, N., 1960. Trans. Faraday Soc. 56, 278. Jamialahmadi, M., Muller-Steinhagen, H., 2000. Crystallization of calcium sulfate dihydrate from phosphoric acid. Dev. Chem. Eng. Miner. Process. 8 (5/6), 587–604. Katakis, D., Gordon, G., 1987. Mechanisms of Inorganic Reactions. Wiley-Interscience, New York. Klepetsanis, P.G., Koutsoukos, P.G., 1991. Spontaneous precipitation of calcium sulfate at conditions of sustained supersaturation. J. Colloid Interface Sci. 143 (2), 299–308. Klepetsanis, P.G., Dalas, E., Koutsoukos, P.G., 1999. Role of temperature in the spontaneous precipitation of calcium sulfate dihydrate. Langmuir 15, 1534–1540. Koutsoukos, P.G., Kontoyannis, C.G., 1984. Precipitation of calcium carbonate in aqueous solutions. J. Chem. Soc. Faraday Trans. 1 (80), 1181–1192. Kralj, D., Brecevic, L., Nielsen, A.E., 1990. Vaterite growth and dissolution in aqueous solution I. Kinetics of crystal growth. J. Cryst. Growth 104, 793–800. Lancia, A., Musmarra, D., Prisciandaro, M., 1999. Measuring induction period for calcium sulfate dihydrate precipitation. AIChE J. 45 (2), 390–397. Liu, S.-T., Nancollas, G.H., 1970. The kinetics of crystal growth of calcium sulfate dihydrate. J. Cryst. Growth 6, 281–289.

153

Liu, S.-T., Nancollas, G.H., 1971. The kinetics of dissolution of calcium sulfate dihydrate. J. Inorg. Nucl. Chem. 33, 2311–2316. Liu, S.-T., Nancollas, G.H., 1973. Linear crystallization and induction-period studies of the growth of calcium sulphate dihydrate crystals. Talanta 20, 211–216. Liu, S.-T., Nancollas, G.H., 1975. A kinetic and morphological study of the seeded growth of calcium sulfate dihydrate in the presence of additives. J. Colloid Interface Sci. 52, 593. Merdhah, A.B..B., Yassin, A.A.M., 2008. Laboratory study and prediction of calcium sulphate at high-salinity formation water. Open Petr. Eng. J. 1, 62–73. Nancollas, G.H., Purdie, N., 1964. Q. Rev. (Lond.) 28, 1. Nancollas, G.H., Purdie, N., 1968. The kinetics of crystal growth. Q. Rev. (Lond.) 28, 1–20. Nancollas, G.H., Reddy, M.M., 1971. The crystallization of calcium carbonate II. Calcite growth mechanism. J. Colloid Interface Sci. 37, 824–830. Oelkers, E.H., Helgeson, H.C., 1988. Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: aqueous tracer diffusion coefficients of ions to 1000 °C and 5 kb. Geochim. Cosmochim. Acta 52, 63–85. Petrou, A.L., 2012. The free energy of activation as the critical factor in geochemical processes. Chem. Geol. 308–309, 50–59. Petrou, A.L., Economou-Eliopoulos, M., 2009a. The activation energy values estimated by the Arrhenius equation as a controlling factor of platinum-group mineral formation. Geochim. Cosmochim. Acta 73, 1625–1636. Petrou, A.L., Economou-Eliopoulos, M., 2009b. Platinum-group mineral formation: evidence of an interchange process from the entropy of activation values. Geochim. Cosmochim. Acta 73, 5635–5645. Prisciandaro, M., Lancia, A., Musmarra, D., 2003. The retarding effect of citric acid on calcium sulfate nucleation kinetics. Ind. Eng. Chem. Res. 42, 6647–6652. Prisciandaro, M., Amedeo, L., Mazziotti di Celso, G., Musmarra, D., 2013. Antiscalants for gypsum precipitation in industrial equipments: comparison among different additives. Chem. Eng. Trans. 32, 2137–2142. Rajeswara Rao, T., 1993. Kinetic parameters for decomposition of calcium carbonate. Can. J. Chem. Eng. 71, 481–484. Reddy, M.M., Nancollas, G.H., 1971. The crystallization of calcium carbonate: I.isotopic exchange and kinetics. J. Colloid Interface Sci. 36, 166. Rodriguez-Blanco, J.D., Shaw, S., Benning, L.G., 2011. The kinetics and mechanisms of amorphous calcium carbonate (ACC) crystallisation to calcite, via Vaterite. Nanoscale 3, 265. Romanek, C.S., Morse, J.W., Grossman, E.L., 2011. Aragonite kinetics in dilute solutions. Aquat. Geochem.. http://dx.doi.org/10.1007/s10498-011-9127-2. Schott, J., Brantley, S., Crerar, D., Guy, C., Borcsik, M., Willaime, C., 1989. Dissolution kinetics of strained calcite. Geochim. Cosmochim. Acta 53, 373–382. Sjoberg, E.L., 1976. A fundamental equation for calcite dissolution kinetics. Geochim. Cosmochim. Acta 40, 441–447. Sjoberg, E.L., Rickard, D.T., 1984. Temperature dependence of calcite dissolution kinetics between 1 and 62 °C at pH 2.7 to 8.4 in aqueous solutions. Geochim. Cosmochim. Acta 48, 485–493. Smith, B.R., Sweett, F., 1971. The crystallization of calcium sulfate dihydrate. J. Colloid Interface Sci. 37 (3), 612–618. Wiechers, H.N.S., Sturrock, P., Marais, G.V.R., 1975. Calcium carbonate crystallization kinetics. Water Res. 9, 835–845. Xyla, A.G., Giannimaras, E.K., Koutsoukos, P.G., 1991. The precipitation of calcium carbonate in aqueous solutions. Colloids Surf. 53, 241–255. Yehia, N.S., Ali, M.M., Kandil, K.M., El-Maddawy, M.M., 2011. Effects of some parameters affecting the crystallization rate of calcium sulfate dihydrate in sodium chloride solution. J. Am. Sci. 7 (6), 635–643.