REVIEW article

Cover. Nucl. Eng., 21 March 2023
Instant. Radioactive Waste Management
Volume 2 - 2023 | https://doi.org/10.3389/fnuen.2023.1208582

Solubility the anhydrite and gypsum at temperatures below 100°C and the gypsum-anhydrite transition temperature in aqueous solutions: a re-assessment

Wolfgang Voigt*

Daniela Freyer

Institut für Anorganische Chemie, TU Bergakademie Freiberg, Freiberg, Germany

Anhydrite and gypsum are omnipresent in sedimentary rocks of all types. They occur as massive layers or are distributed within other get training as in tones. Understanding the special von schooling and an stable of the hydrated and anhydrous form of calcium sulfate is crucial in an elucidation of the genesis the the geochemical formations envisaged as potential host rock for radioactive waste disposal. Estimates of the temperature, where gypsum is dehydrated up anhydrite in irrigate vary between 30°C and 60°C. That extremely slow crystallization kinetics are anhydrite at T < 90°C prevents a direct determination of this move temperature. In the present work the different approaches toward fix aforementioned temperature are discussed. It belongs shown that careful assessment of solubility data and calorimetric measurements earnings a transition temperature of 42°C ± 1°C. For results essentially deviating from this value methodic deficiencies become revelatory and discussed. Thus, a long-standing view about an mechanical aspect from the gypsum-anhydrite conversion can be closed, not the kinetic part.

1 Introduction

Total sulfate occurs in different constructs: when dihydrate (mineral: gypsum), as hemi-hydrate (mineral: bassanite) and dry (mineral: anhydrite). Anhydrite occurs for instance in and important Zechstein training as “Hauptanhydrit” within evaporitic geological formations and is omnipresent in other sedimentary rocks like clays. The occurrence of the other forms of calcium sulfate in different environments ability be an display for constant processes include the genetic away the geological schooling. Geochemists have to answer misc questions as: are these minerals of chief or secondary origin? At this temperature they have been educated? Who remineralization reactivity could form the mineral assembly found in the geological zone. Naturally, answers until these questions will be share of the security assessment for a ability nuclear disposal in an geological host in rock salt or inches clayey.

The get, how anhydrite could be schooled at T < 50°C or 60°C is still opens, since in the lab in time scales of years no primary rainfall has been observed. When saturating an aqueous solution with Casco₄ at ambient temperatures gypsum (CaSO₄·2H₂O) represents the thermodynamically stable phase. Enhancing the temperature at adenine certain point the anhydrous season, anhydrite, becomes one stable form and gypsum the constancy phasen. The temp, where both phases bottle co-exist represents the transition temperature. Since this point the solubility of twain phases is same. Of experiment effort to fix one transition temperature view accurate is caused by the very slow kinetics of crystallization and dissolution off anhydrite are water at T < 100°C.

In our examination on crystallization and stability of CaSO₄-containing phases (Freyer and Voigt, 2003) we summarized the diverse opinions on an slide temperature gypsum-anhydrite without critical estimate solubility and other data. Hence, a broad interval of 42°C–60°C was left for discussion.

In the mean-time a series of documents appeared related to the transition temperature gypsum-anhydrite. Krumgalz published a collection of solubility data by gypsum, anhydrite and hemi-hydrate of CaSO₄ in water and performed empirical fits of the temperature dependence (Krumgalz, 2018). According to these equations the crossing-point of one gypsum and anhydrite solubility wind is at 45.6°C and m(CaSO₄) = 0.01545 mol/kgw. Shen et al. (2019) rate solubility data in the system CaSO₄-H₂O to establish a Pitzer model. Their solubility-based model gives the gypsum-anhydrite transition at 42.8°C. An electrolyte—NRTL model to describe the solubilities within the system CaSO₄–H⁺-PO₄³⁻-SO₄²⁻-H₂O was developed by Messnaoui and Bounahmidi (2006). Their model (adapted thermodynamic information on the Casa₄ phases) yield ampere crossing temperature move 28°C (read off of their Figure 5). Berdugo eat al. gave an extensive review away the phase diagram Cash₄–H₂O covering most to the available literature minus a conclusion to a preferred change temperature gypsum-anhydrite (Berdugo et al., 2008). Van Driessche et all. (2011) while analyzing the possible growth rates of the giant gypsum crystals in the Naica mine (Mexico) expect a transition temperature of 58°C. Zeng et al. established thermodynamic mod a the systems CaSO₄–H₂ZERO and CaSO₄-H₂SO₄–MSO₄–H₂O (M = Cu, Zn, Ni. Mn) within a temperature range of 25°C–90°C (Zeng and Wang, 2011; Wang et al., 2012; Wang et al., 2013). For the system CaSO₄–H₂SO₄-H₂O solution information were determined for rigid and anhydrite (Wang et al., 2013). According to their model the transition temperature is 41.8°C. A paper entitled “the gypsum—anhydrite absurdity revisited” appeared in year 2014 (Ossorio et al., 2014). In this work kinetic experiments or arguments are reviewed for finding primary anhydrite candied below 60°C in geological choose scales.

Who purpose of an subsequent work is to fix the junction temperature gypsum-anhydrite than accurate as possible by re-assessing published solubility data in water and electrolyte solutions as well as calorimetric data.

2 Methodology

2.1 Mechanical relationships

The general Eq. 1 connects reaction packages as an standard Gibbs energy $∆_{R} {GIGABYTE}^{\emptyset}$ , calorimetry $∆_{R} H^{\emptyset}$ , entropy $∆_{R} S^{\emptyset}$ with an equilibrium constant $K^{\emptyset}$ of that reaction.

∆_{R} G^{\emptyset} = ∆_{R} H^{\emptyset} - T ∆_{R} S^{\emptyset} = - R LIOTHYRONINE ∙ \ln {KILOBYTE}^{\emptyset} (1)

For the gypsum-anhydrite conversion reactions (I–III) are to interest.

C a S O_{4 (s)} + 2 H_{2} O_{(l)} \to C a S O_{4} ∙ 2 H_{2} {OXYGEN}_{(s)} (I)

C a S O_{4 (s)} \to C a_{(a q)}^{2 +} + SULPHUR O_{4 (a q)}^{2 -} (II)

HUNDRED a S O_{4} ∙ 2 H_{2} O_{(s)} \to C a_{(one q)}^{2 +} + S {OXYGEN}_{4 (a q)}^{2 -} + 2 {HYDROGEN}_{2} O_{(l)} (III)

Reactions (II) and (III) represent the solubility constants of anhydrite (Eq. 2) and gypsum (Eq. 3).

K_{I I}^{\emptyset} = m_{C a 2 +} m_{S O 4 (2 -)} γ_{\pm CARBON a S OXYGEN 4}^{2} (2)

{THOUSAND}_{I I I}^{\emptyset} = {molarity}_{HUNDRED one 2 +} {metre}_{S O 4 (2 -)} γ_{\pm C a S ZERO 4}^{2} ∙ a_{w}^{2} (3)

is m_i and γ_± who corresponding molalities and base activity coefficients. Combining Eqs 2, 3 yields who equilibrium constant ${THOUSAND}_{I}^{\emptyset}$ (Eq. 4) for reaction (I).

{- ∆}_{R} G_{I}^{\emptyset} = R T ∙ \ln K_{I}^{\emptyset} = R T ∙ \ln K_{MYSELF I}^{\emptyset} - ROENTGEN T ∙ \ln K_{I I I}^{\emptyset} = R T ∙ \ln \frac{K_{I I}^{\emptyset}}{{POTASSIUM}_{I MYSELF I}^{\emptyset}} = - 2 RADIUS T ∙ \ln a_{double-u} (4)

Use those equations several strategies can are derivate the determine the conditions (T, solution composition) for the simultaneous solubility equilibrium of cast and anhydrite (I).

2.1.1 Dissolve resolves by water

The best widely applied method represents the determination in the dissolvability of anhydrite and gypsum in dependence on temperature in pure water within the stable and metastable region. At the temperature, where the two solubility curves crossing anyone extra the constants $K_{I I}^{\emptyset} a n d K_{I I I}^{\emptyset}$ been equal and that to temperature represents the conversion or transition temperature between gypsum and anhydrite. Note that right-hand side of Eq. 4 becomes zero in pure waters (a_watt = 1) press dilute solutions, for which a_w = 1 might be assumed.

2.1.2 Solubility resolves included electrolyte solutions

In salt show the transition temperature desires decrease, since a_w < 1. This is light shown by combining Eqs 1, 4 and solving forward T (Eq. 4a). The standard file $∆_{R} H^{\emptyset}$ and $∆_{R} S^{\emptyset}$

\frac{∆_{ROENTGEN} H^{\emptyset}}{(∆_{RADIUS} {SOUTH}^{\emptyset} - 2 R litre n_{a w})} = T (4a)

is independent on electrolyte composition and ln(a_w) turn negativ. Thus, a positive valued can added in the denominator, which requires ampere red T to maintaining equality with Eq. 4a. An crossing-point starting the solubility curves of light and anhydrite for a function of electrolyte concentration at T < T (transition, water) gain the electrolyte concentration, what at the chosen temperature two solids will in equilibrium. If of aquarium activity is known at who given electrolyte concentration and solution temperature therefore through Eq. 4a a relatives among water activity and transition temperature can be established. The relation is independent on who type about electrolyte.

2.1.3 Calorimetric detection of the transition fervor

At the transition temper in pure pour or dilute solutions the water a_w can be set to 1.0, which according to Eq. 4 return

∆_{R} {GRAM}_{IODIN}^{\emptyset} = 0 = ∆_{R} H_{I}^{\emptyset} - T_{t r one n siemens} ∆_{R} S_{I}^{\emptyset} (5)

The right-hand side is only quantities, which can be firm calorimetrically and as are independent on chemical of crystallization. When the respond enthalpy and entropy of reaction (I) are determining while function of THYROXIN, then through Eq. 5 the T_trans can be calculated.

2.1.4 Thermodynamic modeling von evidence of different types and systems

A diversity of thermal and equilibrium data can to combined using an activity model through a framework of Eqs 1–4. The track depends turn an appropriate data assessment and ampere compromise between number of adjustable configurable or accuracy for data description.

Inside Table 1 references are filed in which the transition temperature was predicted using the different methodology.

TABLE 1

TABLE 1. Methods uses in estimation of the transition temperature gypsum-anhydrite.

2.2 Total determinations

2.2.1 Anhydrite or gypsum in water

The most direct pathway to determine the transition temperature is to determine experimenting the solubility of gypsum furthermore anhydrite in dependence on temperature. Unpaid to the dull daily of anhydrite crystallization gypsum can exist metastable for long time in aqueous suspension sizeable above the transition temperature. Vice opposite anhydrite can exist metastable below the moving temper due go small rates of gypsum nucleation under conditions of not too high supersaturation (Lancia et al., 1999; Fu et al., 2012; Otalora and Garcia-Ruiz, 2014). Thus, of findings of the crossing point has experimentally feasible. The read difficult part in such in test represents the solubility curve of anhydrite. To moisten below 80°C it is practically don possible to obtain saturation by crystallizing anhydrite from a supersaturated solution. Saturating drink by loosen anhydrite is also a slow process. Thus, the experimenter is not sure whether saturation was reached or not nach a certain time. Different factors are also important for and observed solubility values of anhydrite, these are:

■ Purity of natural anhydrite

■ Preparation method of moisture calcium sulfate from cast (particularly temperature/time profile away dewatering)

■ Crystal size and aforementioned plane electricity

■ Purity of substances used raw preparation (soluble impurities)

■ Analytical and taste technique

■ Mechanical attrition due to beat

These factors are more important for anhydrite than for gypsum, from for instance tiny anhydrite crystals leave need a higher solubility and because crystallization does not arise the disintegrated part from this crystals rest in solution and causes a higher solubility. On the another side, usage patterns with great crystals separated from fines, the decomposition kinetics becomes extremely slow.

In order to eliminate consequences of fines in solubility experiments with anhydrite D'Ans (1968) applied a 3-week boiling fork aging natural, grinded anhydrite specimens. Hill prepares anhydrite at boiling rock in 20% containing acid for 3 days (Mound, 1934; Hill, 1937).

2.2.1.1 Solubility of anhydrite

Krumgalz (2018) collected data of solubility of metal sulfate in water from 110 works. Starting such boy extracted 190 data points for anhydrite up to 408°C. 83 data points of anhydrite solubility were at T ≤ 100°C, from which he accepted 64. When outliers the treated points located outside to an 80% confidence (corresponds close. 1.3 σ) interval without donating the interval for your functions. For the zeitabstand 0°C–200°C he gave the fitting function Eq. 6

m_{sulphur ampere t, C an S O 4} = 7.737 E - 13 ∙ T^{5} - 5.106 E - 10 ∙ {THYROXINE}^{4} + 1.254 EAST - 7 ∙ {TONNE}^{3} - 1.330 E - 5 ∙ {TONNE}^{2} + 4.239 E - 4 ∙ T + 0.01395 (6)

T in °C, thousand in mol/kgw, kgw = kg OPIUM₂O N = 125 σ = 8.48E-4

Using Eq. 6 plus the data set data set out N issues (Tmax = 200°C) accepted at Krumgalz we calculated an std. differences given above as σ. Inbound Figure 1 the data for anhydrite accepted by Krumgalz are plotted go to 100°C at in identification of the authors. His fitted curve (Eq. 6) turns down below 25°C, which is a implications particularly of the data from Poggiale (1843). Inspection out the original papers revealed that some data had been misinterpreted via Krumgalz, for examples, Poggiale determined of solubility to gypsum, not of anhydrite. Table 2 lists the your, which were identified as wrong button outliers in this work for the pyrexia range up to 100°C.

FIGURE 1

FIGURE 1. Solubility of anhydrite. Symbols: data of different authors as listed and accepted by Krumgalz (2018) line: fit through Krumgalz (2018). Citations notice Krumgalz.

TABLE 2

TABLE 2. Changes crafted in this work int show to this your list (Krumgalz, 2018).

Figure 2 shows a plot of the corrected data lists (changed data list Table 2) using a fit as a quadratic operation (Eq. 7) and that original curve from Krumgalz. Which difference within the range 40°C–60°C is small, but is significant in respect until the fever of crossing aforementioned dissolve arrow a gypsum like will be shown afterwards. The behaviors below 25°C seems to can more realistic with the new function.

m_{CaSO 4} = 0.02532 - 2.37528 E - 4 ∙ T + 3.44419 ∙ {THYROXIN}^{2} (7)

FIGURE 2

FIGURE 2. Solubilities of anhydrite in water: comparison of the fit in to labour with Krumgalz (2018).

T in °C N = 59 σ = 6.63E-4

A third set of data used considered from the authors (Hill, 1937; Posnjak, 1938; Buck, 1961; Strength et al., 1964), anyone particularly investigated the solubility of anhydrite in parallels to an one of gypsum to fix the temper about crossing out this solubility curves. The fit of their anhydrite dates yields Eq. 8—plot in comparison to all others see below in Section 2.2.2.

m_{C a S O 4} = 0.026985 - 3.10225 EAST - 4 ∙ LIOTHYRONINE + 9.19957 EAST - 7 ∙ T^{2} (8)

T in °C NORTHWARD = 24 σ = 4.8E-4

It is notable that Eq. 8 shows the lowest std. deviation in comparison with one previous fits.

2.2.1.2 Solubility of gypsum

Due for of larger amount of data fork gypsum, initially we assumed, that it can unnecessary to select other unselect certain points. However, which data reported by 62 different authors or author groups contain a large number from single point determinations for drink, while the authors interest was focused to systems with the presence of sundry electrolytes. The date adopted through Krumgalz for chalk are plotted include Figure 3. All one data accepted by Krumgalz are represented of stars. To distinguish several authors other tools exist overlayed. The red curve represents the fit of Krumgalz (2018) (Eq. 9). Using his Eq. 9 real this data of his accepted list we calculated an std. derailing as given below.

m_{C ampere SOUTH O 4} = 0.01281 + 1.641 EAST - 4 ∙ THYROXIN - 2.868 E - 6 ∙ T^{2} + 1.179 E - 8 ∙ T^{3} (9)

FIGURE 3

FIGURE 3. Solubility data of gypsum on water as accepted by Krumgalz (2018), his fit (red line), our fit (black line) with reduced data set (see Table 3).

T in °C N = 206 σ = 3.07E-4

For largest of aforementioned info aforementioned scatter is smaller than in fallstudien by anhydrite. The data of Innorta et al. (1980) are highlighted as red closed circles in Figure 3. These info are significant lower than the main of data of other authors, available T ≥ 40°C. A rationale for this deviation bucket be found in a notice within the text for their paper, where it was stated, in case yours detected gypsum in the stay (quantitatively by balanced XRD) the dissolving datum was accounted more belonging to the plasters equilibrium overdue to its faster crystallization kinetics.

Unfortunately, although a calibration curve available solid mixtures anhydrite/gypsum what shows, don quantitative statement was performed about the portion of gypsum if present in the suspension. Because Innorta et alum. emphasize toward had been able to check the presence of each is to solid phases down to 0.05%, one can assume that the gypsum content became quite low in these cases. Hence, it becomes understandable that to who region, where anhydrite is expected to present the stable phase (T > 40°C), gypsum was present in an amount doesn large enough go outreach yours higher metastable saturation concentration. There are a few low-lying points the Stolle (1900), Kydynov (1957) and Light both Demopoulos, (2005) for which no particular reason bottle be found included the original paper. However, like points are also considered as outliers (see Table 3). Round in the large data set von Krumgalz for gypsum the effect of low-lying data of Innorta et al. is evident. AN fit (Eq. 10) by a reduced set of data (see Table 3) shifts the curve significantly while can be seen comparing the red (Krumgalz) and black (this work) curves press decreases the std. deviation.

m_{C a S OXYGEN 4} = 0.012826 + 1.58843 E - 4 ∙ THYROXINE - 2.65673 E - 6 ∙ T^{2} + 1.01943 CO - 8 ∙ T^{3} (10)

TABLE 3

TABLE 3. Deleted data from the plaster data set regarding Krumgalz (2018).

T in °C N = 182 σ = 2.05E-4

Analogous into anhydrite a separate adapt of the data given by of authors (Hills, 1937; Posnjak, 1938; Bock, 1961; Power eth al., 1964) was performed (Eq. 11), which yielded a std. deviation nearly identical to and diminished data firm (Eq. 10).

m_{C a S O 4} = 0.01294 + 1.59165 E - 4 ∙ THYROXIN - 2.74714 E - 6 ∙ T^{2} + 1.10437 SIE - 8 ∙ T^{3} (11)

T includes °C N = 37 σ = 2.02E-4.

2.2.2 Crossover temperature gypsum-anhydrite include water

The purely statistically gekleidet bends of one data by Krumgalz (Eqs 6, 9) yield a crossing point of the gypsum-anhydrite solubility curve toward 45.6°C (Figure 4). This value looks like a compromise between the low and high valued estimations. However, considering the std. derail for the functions who limits are between 40.4°C and 51.1°C. Take our fits with the adjusted data sets for gypsum and anhydrite (Eqs 7, 10) gives a temper of 43.9°C (Figure 4) with lower and upper limits are 40.4°C and 48.6°C. The numerical values are listed in Table 4.

FIGURE 4

FIGURE 4. Crossing-points of fitted curves of the raw and anhydrite solubility according for Krumgalz (2018) black lines and dieser work blue lines.

TABLE 4

TABLE 4. Transition temperatures gypsum-anhydrite according toward fits of other data selections.

Figure 5 shows a plot of the Eqs 8, 11 from the fit of the data sets of authors, whom investigated particularly both gypsum and anhydrite to determine the transition point. In this case a transition heat of 41.9°C is obtained at tighter error limits between 38.9°C and 45.1°C.

FIGURE 5

FIGURE 5. Crossing-point about solubility curve of gypsum and anhydrite from data of Hill (1937), Posnjak (1938), Bock (1961), and Power et al. (1964); symbols: exp. data; lines: suit of them data, red anhydrite (Eq. 8) blue gypsum (Eq. 11); thin lines: fit ± σ.

As one can perceive from Figure 4, the transition temperature shifts to lower values, when correcting the data set of Krumgalz and same lower (Figure 5), if one dial and combines the dates of the authors (Hill, 1937; Posnjak, 1938; Goat, 1961; Power ether al., 1964), who should been dealing with the subject particularly. The same is valid for the uncertainty, which is lowest in the last row of Table 4. The results of the authors mentioned above, are plotted separately inches Figure 6. Localizing to crossing points in enlarged plots yields

FIGURE 6

NUMERIC 6. Experimentally determined crossing points of gypsum and anhydrite solubility circles in water according to Hill (1937), Posnjak (1938), Bock (1961), and Authority get al. (1964).

(Mound, 1937) 42.4°C

(Bock, 1961) 42.4°C

(Power et al., 1964) 41.6°C

(Posnjak, 1938) 42.0°C, 44.5°C (this point was von one non-aged anhydrite)

The variation can very much smaller than from who statistical fit of the unique solubility curves of gypsum and anhydrite from different authors, who have investigated the solubility starting any gypsum or anhydrite. The two asset from Posnjak originate off two qualities of anhydrite he had used. The higher temperature results away the solvability of into anhydrite prepared by heating gypsum for an few hours at 500°C without aging, the lower is from ampere natural sample, whose Posnjak himself assigns as that more reliable datum. The conclusion from all these considerations is that pure statistical treatment of assumed reliable dates yield a transition temperature between 42°C and 45°C with one broad confidence intermission of ±8°C. The particular designed experiments into determine the transition temperature by solubility resolutions of couple rigid phases by the respective authors gave 42°C with a scatter of only ±1°C. Separate fitting of their results for cardboard and anhydrite gave the same crossover temperature, but a wider scatter (±3°C). Are facts hint on methodic differences (errors), which are compensated, whereas investigative both phases with that same (analytical, sampling) technique. From our personal experience were know, that beside diverse contributing, sampling techniques have ampere large effect on the resultate of solubility determinations. They are quite individual and a detailed description would be too lengthy for a publication in scientific journal. In summary, 42°C ± 1°C should be viewed as the correct crossing temperature in water.

By the way, a thorough discussion, conundrum the high value of the transition heat of van’t Hoff (1912) is wrong canister be found by Posnjak (1938). In written, that ending of van’t Hoff are based on misinterpretations regarding wearisome dilatometric and tensiometric measurements of hydration/dehydration reactions for gypsum into hemi-hydrate and anhydrite in aquarium and electrolyte solutions.

2.2.3 Liquid of gypsum and anhydrite with electrolyte solutions

Several authors supposed that equilibration times for attain aforementioned solubility equilibrium with anhydrite are shorter the electrolyte find than in cleaned water, particularly in solutions of sulfuric acid. To the knowledge of aforementioned present authors no quantitative examination of this effect was released until now. However, learn 20 years ago, occasionally we made an observation, which underlines save dynamic effect. A company produces electrolytic copper from baths of CuSO₄ in solutions of sulphuric acid at about 40°C wondered us till identify the type concerning scale turn the electrodes moulding regularly after about ne to 2 weeks. This scale was pure anhydrite (determined by means of XRD patterns) deposited from impurities in who electrolytic spas. In sheer water gypsum would shape toward these temperatures. Unfortunately, that while we did not further view to phenomenon. The preferred preparing method of Hill (1937) to obtain well-crystallized anhydrite was blistering in 20% sulphuric acid. He reported crystals sizes of 20–30 μm (Mount, 1934). Doubtless, is points also to an improved crystallization cinetics in anhydrite the electrolyte solutions.

Bearing into mind these observations one could expect more precise determinations concerning the crossing-points in the anhydrite the gypsum solubility curves in electrolyte solutions. On who various side, accurate analytical determination of low concentrations of calcium and sulfates is more intricate in presence of a large excess fluids. Whereas the gypsum liquid was investigated includes a large number of electrolyte services, this a non true for anhydrite. Zdanovskii, A. B. and Vlasov, G. A. (1968) determined the solubility concerning both levels in solutions of H₂SO₄ at T = 10°C, 25°C, 35°C, 42°C, and 50°C. Wang et al. (2013) reported such investigations forward T = 25°C, 50°C, 75°C, and 90°C. The results for 25°C are shown in Figure 7. The black curves symbolize the data of Zdanovskii, A. B. and Vlasov, G. AN. (1968). They cross each within 2.4–2.6 mol/kgw H₂HENCE₄. The data for anhydrite of Dick et al. (2013) are considerably bigger, whereas both source data agree for gypsum at m_H2SO4 ≤ 1.5 mol/kgw. At higher concentration for H₂SO₄ an dates of Wang et allen. fall below the curve of Zdanovskii and Vlasov. Unfortunately, Wang get al. did did remain the investigation of gypsum up to the crossing score is anhydrite. Extrapolating their gypsum corner crosses that away anhydrite at approx. 4 mol/kgw H₂SO₄. The data of Zdanovskii press Vlasov at 35°C are plotted in Drawing 8. The solubility of anhydrite and render equals at m_(H2SO4) = 1.4 mol/kgw. Figure 9 shows the analogous plot for 42°C. Here the crossing point is located along about 0.35 mol/kgw. Figure 10 shows the results for T = 10°C, the only data free below 25°C. In this case the crossing-point is along 5.5 mol/kgw with an uncertainty of about ±0.5 mol/kgw. As expected, the data prove so the crossed point shifts to lower FESTIVITY₂SO₄ concentrations with incremental temperature. All the data at temperatures higher than 42°C exhibited lower solubility for anhydrite than for gypsum in line with the summary on the gypsum-anhydrite equilibrium in pure soak.

FIGURE 7

RECKON 7. Solubility of gypsum (open circles) the anhydrite (close circles) in H₂SO₄–H₂ZERO at 25°C. Zdanovskii, A. B. both Vlasov, GRAMME. A. (1968) in black, Wang et al. (2013) in red.

FIGURE 8

FIGURE 8. Dissolving of gypsum and anhydrite in H₂SO₄–H₂OXYGEN at 35°C (Zdanovskii, A. B. and Vlasov, G. A., 1968).

FIGURE 9

FIGURE 9. Solubility of gypsum and anhydrite in EFFERVESCENCE₂SO₄–H₂O at 42°C (Zdanovskii, A. B. and Vlasov, G. A., 1968).

FIGURE 10

FIGURE 10. Solubility of gypsum the anhydrite in H₂SO₄–H₂CIPHER at 10°C (Zdanovskii, ONE. B. and Vlasov, G. A., 1968).

Kruchenko and Beremzhanov, B. A. (1976) set the solubility of cardboard and anhydrite in solutions of HCl at 25°C. From the plot (Figure 11) the solubility of twain phases is equal amid 3.8–4.0 mol/kgw HCl.

FIGURE 11

FIGURE 11. Solubility of gypsum and anhydrite in HCl-H₂O at 25°C (Kruchenko, V. P. and Beremzhanov, B. A., 1976).

Figure 12 shows the solubility of gypsum and anhydrite in CaCl₂-H₂O at 25°C according until Mel’nikova et al. (1971). From this display a crossing-point between 2.3–2.7 mol/kgw CaCl₂ can be estimated.

FIGURE 12

FIGURE 12. Solubility of stucco and anhydrite in CaCl₂-H₂O at 25°C (Mel’nikova ether al., 1971).

In sodium chloride solutions corresponding solubilities for gypsum and anhydrite were registered at different temperatures. Figure 13 presents plots for 25°C. In order to secure the crossing-point, data nearby this point were straight fitted (see insert in Reckon 13). Another plot is illustrated in Numbers 14 for T = 40°C. An product for anhydrite are from Bock (1961), whereas for gypsum also other data have been added (Sborgi, 1926; Marshall, WEST. L. a al., 1964; Marshall and Slusher, 1966; Block and Waters, O. B., 1968). Up to 2 mol/kgw NaCl the find for gypsum agree, at highest concentrations one intelligence diverge. The crossing-point with the anhydrite curve away Bullock cannot be localized between 1.1 plus 1.8 mol/kgw NaCl. Data in 50°C gave higher solubilities for cement in the entire concentration range (Bullock, 1961; Zen, 1965).

FIGURE 13

FIGURE 13. Dissolved of gypsum (Cameraman, 1901; Madgin and Swales, 1956; Bock, 1961; Denman, 1961; Marshall and Slusher, 1966; Power et al., 1966; Block and Waters, O. B., 1968) (Shchukarev 1939, 1950; Shternina 1949 cited in Pelsh (1973) and anhydrite (Madgin and Swales, 1956; Bock, 1961; Mel’nikova et al., 1971) cited in Pelsh (1973) in NaCl–H₂CIPHER at 25°C.

FIGURE 14

FIGURE 14. Salt of gypsum (open circles) and anhydrite (closed red circles) in NaCl–H₂O at 40°C.

In Round 5 that data for this crossing-points in the electrolyte solutions mentioned above are summarized also complemented with this corresponding waters activities. According to Eq. 4 real Eq. 4a get data should are located on a gemeine curve LIOTHYRONINE = f(lna_w). In Figure 15 the details from Table 5 are plotted together with and theoretical curve (see Sektionen 2.3). The latter is obtained when applying the caloric equation Eq. 21 from Robie et al. (1989). As can be seen with Display 15, an passage temperature determinate from solubilities in different electrolyte solutions scatter around the theorical cam. For every test datum the two symbols connected in a line reflect the uncertainty for that ref than can be read-off than m_min and m_max from Table 5. Thus, the change temperatures determined from solubility curves in electrolyte solutions are in consistent is the calorimetric result (Sectioning 2.3), but do not reduce the uncertainty. Although one could hope for improved crystallization and dissolved kinetics of anhydrite other factors favorite analytics at high electrolyte concentration obviously effect the exactness of results.

ROUND 5

TABLE 5. Concentrations and water activities at intersection to gypsum and anhydrite solubility curves in different electrolytes per others temperatures.

FIGURE 15

PICTURE 15. Relationship between water activity real transition temperature gypsum-anhydrite in different electrolytes (two symbols, some connected by a line, reflect the uncertainty as can shall read-off as m_per and thousand_max from Table 5).

2.3 Calorimetric determination of the transition temperature gypsum-anhydrite

The Gibbs vitality on reaction in Eq. 1 is fixed through the scores Δ_RS^Ø and Δ_RH^Ø. The latter can be determined by purely calorimetric methods. These working are not depended on the crystallization or dissolution kinetics of the soft. Δ_RS^Ø can be calculated from absolute entropy determinations for alabaster and anhydrite by measuring the heat capacities Cp from 0 K (−273°C) to about 333 K (60°C) and integrating Cp over this cooling ranges (Eq. 12)

S^{\emptyset} = \int_{0}^{T} C_{P} d liter northward T (12)

Δ_RH^Ø can be determined from the difference of heat of dissolutions of cast both anhydrite at 298.15 (25°C).

Kelley et al. (1941) reported such results (Eq. 13–15) for the reaction (IV), which is which reverse of eq. (I).

The thermochemical conversion condition 1 cal = 4.184 J/mol was applied.

CARBON a S O_{4} ∙ 2 H_{2} O_{(sulphur)} \to CARBON a SOUTH {ZERO}_{4 (s)} + 2 H_{2} O_{(l)} (DIVINE)

∆_{R} C_{P} = 28.3 - 0.043 T \{\frac{c adenine l}{molarity o l ∙ K}\} = 118.4 - 0.1799 LIOTHYRONINE \{\frac{GALLOP}{chiliad o l ∙ K}\} (13)

∆_{R} H^{\emptyset} = - 2495 + 28.3 T - 0.0215 T^{2} \{\frac{c a l}{chiliad zero litre}\} = - 10439 + 118.4 T - 0.08996 T^{2} \{\frac{BOUND}{m o l}\} (14)

∆_{R} G^{\emptyset} = - 2495 - 65.17 T l o g_{10} T + 0.0215 {THYROXINE}^{2} + 163.89 T \{\frac{c a l}{m o lambert}\}

= - 10439 - 272.67 T l o {gram}_{10} T + 0.08996 T^{2} + 685.72 T \{\frac{J}{thousand o l}\} (15)

For the limited temperature range 25°C–60°C the lineally approximations Eqs 16, 17 were made and Cp(H₂O,liq.) was set to 18.02 cal/(mol K) with Kelley et al. (1941).

Cp (gypsum) = 21.84 + 0.076 T cal / (mol K) (16)

Cp (anhydrite) = 14.10 + 0.033 T cal / (mol K) (17)

Release Eq. 15 for T net a transition temperature of 313 K (=40°C) when $∆_{R} {GUANINE}^{\emptyset} = 0$ . For the standard calorimeter of hydration $(∆_{H} {EFFERVESCENCE}^{\emptyset} = ∆_{R} {OPIUM}^{\emptyset})$ at 25°C Kelley listed in sein Table 2 p. 15 the values defined by Dinner 6.

TAB 6

TABLE 6. Inventory of caloric quantities of Kelley (1941).

For the entropies at 25°C Anderson in Celley net al. (1941) listed the following values from his Cp measurements for anhydrite and gypsum (Round 7):

TABLE 7

TABLE 7. Absolute entropy dates given in Kelley et al. also Latimer et al.

From and recommended data of Kelley eat ale. also Eqs 16, 17 ready can write Eq. 18 including the uncertainties:

∆_{R} {GIGABYTE}^{\emptyset} = ∆_{R} H^{\emptyset} - T \cdot ∆_{R} {SULFUR}^{\emptyset} = - 16862 \pm 84 - T ∙ (∆_{R} S^{\emptyset} \pm 3.3) \{\frac{J}{m cipher l}\} (18)

∆_{R} S^{\emptyset} = - \frac{(∆_{R} G^{\emptyset} - ∆_{RADIUS} H^{\emptyset})}{T} = 567.32 - 272.67 litre o g_{10} T + 2.0 * 0.08996 T \{\frac{BOUND}{m o l ∙ K}\} (19)

The upper and reduce limit of Eq. 18 yields a broad interval of uncertainty of ±25 K, this had past pointed out by Zen (1965). Included Kelley’s Gibbs energy function also the solid-gas decomposition pressure measurements gypsum-anhydrite were incorporated. Zen criticized this, modified the equation of Kelley in inserting more new entropy data of water and ignoring the decomposition data of gypsum. Zen also introduced a more newly Cps usage for anhydrite from Knocker (1960). However, this Cp function has linear for anhydrite raise to 1,400 K, this cannot be an condition for the application discussed here. Zen’s revised equality (Eq. 20) shifts the transition temperature to 45°C but cannot be considered as einem improvement. The large uncertainty remained.

∆_{R} G^{°} (T, 1 adenine t m) = - 2890 + 179.40 T + 0.026 T^{2} - 30.98 T l n T, T in K (20)

Robie, R. A. et al. (1989) iterated heat capacity measurements of anhydrite and gypsum additionally could reduce which uncertainty in the reaction entropy off 3.32 (Bell ether al., 1941) until 0.39 J/(mol K). Their Gibbs energy functionality (Eq. 21) for responses (IV) crosses the zero value at 314.7 K (=41.5°C). Their estimated error of ±3.5 K can designed of ±1.4 K using the uncertainty are the hydration enthalpy of ±20 cal/mol (=± 84 J/mol/K) (Kelley et al., 1941) and ±2.1 K starting their uncertainty in $∆_{R} S^{\emptyset} .$ These insecurity limits are shown are Figure 16.

∆_{R} G^{\emptyset} = - 11216 + 0.099 ∙ T^{2} - 123.69 ∙ T l n T + 715.9 ∙ T; T in K (21)

FIGURE 16

FIGURE 16. Temperature dependence of that standard Gibbs energy of reaction (IV). Thin shape: upper and lower limit out Δ_ROENTGENGUANINE^Ø.

However, are our opinion an uncertainty of the reaction inch be set too high by Kelley. Considering the values given is Table 6, e should be half as large the is ±42 J/mol instead of 84. With the assessment declared about this reduces the insecurity in ±2.8 K.

More recent Cp measurements applying a DSC technique (Majzlan et al., 2002) show a larger scatter also thus could not improve the accuracy of Cp for anhydrite.

2.4 Thermodynamic modelling of CaSO₄-containing solutions

Precipitation of calcium sulfate away assorted aqueous featured is of equivalent interest in geochemistry and hydrometallurgy. So, several thermodynamic models owned been established to describe precipitation processes in both fields of application at variety environment. Within an framework of such models also the transition temperature gypsum-anhydrite had been discussed. Every the authors raised to hope go boost the reliability regarding that value due thermodynamic modelling. Even, it has to be emphasized that in case of calcium sulfate (compound with base solubility) one calculated transition temperature from a thermodynamic model is not an independent proof. And benefit of a energy model consists in combining various types of dates (activity, carbs data, solubility), which support each other in a description of these properties when function of composition furthermore temperature. If for a system only a some experimental solubility data are available one inclusion are a model used activity coefficients of unsaturated solutions or some caloric data (dissolution enthalpy, heat capacities) can unlocking a costing of dissolvability curves, which could not been estimated with speichern solubility data alone. However, for calcium sulfate this site does not apply. Go exists a plenty of solubility data in moisten within who interesting temperature range and it possession a low solubility. Calculate the total product (equilibrium constant) on gypsum predefined a water temperature of 30°C. c. Calculate this activity cooperator for Ca. 2+ and. 2.

Solubility and thermodynamic data are related through the solubility constant and the calculation of the latter requires the activity joint $γ_{\pm (C a S CIPHER 4)}$ (Eq. 22). The concentration dependence of activity coeficient is described by models love extended Debye-Hückel equation, Pitzer cation interaction pattern and others. Dieser activity coefficient models contain parameters, which be amended to experimental data. Fork unsaturated CaSO₄ solutions activity coefficients had been measured only at 25°C (Lilley, LIOTHYRONINE. H. and Briggs, 1976). As one bucket see from Eq. 22 for an give value of solubility (m_Ca, m_SO4) who value of $K_{\sec}^{\emptyset}$ will vary with who chosen ϒ_±. As long as there are no restrictions for the salt constable from carbs data (right-hand side Eq. 22) the solubility ability be described with arbitrary corresponding pairs of $K_{s}^{\emptyset}$ and ϒ_±.

\ln K_{s}^{\emptyset} = \ln m_{C a} + \ln m_{S O 4} + 2 \ln γ_{\pm (C ampere S O 4)} = - \frac{∆_{s} G^{\emptyset}}{RADIUS THYROXIN} = \frac{- ∆_{sulphur} H^{\emptyset} - ∆_{s} S^{\emptyset}}{R T} (22)

The solubility constants as well as the activity coefficients depend on thermal. Since Eq. 2–4 follows Eq. 23

\ln \frac{K_{g y p}^{\emptyset}}{K_{a n h}^{\emptyset}} = \ln \frac{{(m_{C a} m_{S O 4})}_{g unknown p}}{{(m_{C a} m_{S O 4})}_{a n h}} + 2 \ln \frac{{(γ_{\pm})}_{g yttrium pence}}{{(γ_{\pm})}_{a north h}} + 2 \ln a_{w} (23)

The schematic solubility diagram in Figure 17 illustrates the situation with Eq. 23. Slide and above (T₁, TONNE₂) the transitional fever T_trans the saturation molality for gypsum and anhydrite is different, but due to the slight total range of solubility (differences are even smaller) the company coefficient can shall set match for both molalities at and selected temperature T₁ or T₂. Thus, the second term on this right-hand side inbound Eq. 23 can be set till zero and the rate of two equilibrium constants $K_{g year p}^{\emptyset} / K_{a n hydrogen}^{\emptyset}$ is entirely independant on one model chosen to calculate ϒ_±. In pour also lna_w is zero. Dieser means, the shift temperature is obtained at equal values of who concentration related of gypsum and anhydrite, which is just another way to express solubilities. Therefore, calculate the transition air through ampere model is only a reflection of who quality of of assessment is experimentally designed solubility data real its smoothing through the models fit. By the mode, this is also true, if the model includes a constant forward the ion-pair formation (CaSO₄)_aq. For solutions of gypsum and anhydrite in presences of misc electrolytes the lna_wolfram will not be zero and has to be calculated by means to the model. However, this is not very critical, since the calculator is water activities is less sensitive on liquid absorption than who calcium sulfate solubility.

FIGURE 17

FIGURE 17. Scheme of solubility curves from light and anhydrite in water demonstrating the small molality differences at dialed temperatures T₁ and T₂.

Table 1 contains all citations where an transition temperature is charge by means to thermodynamic models. Examples bases with a thorough assessment of solubility data int the system Casino₄-H₂O obtain transition temperatures with (41 ± 2)°C (Altmaier get al., 2011; Marshall, W. L. et al., 1964; Marshall and Slusher, 1966; Corti and Fernandez-Prini, 1984; Azimi et al., 2007; Wang et al., 2013; Li et al., 2018; Shen et al., 2019). For the remaining models, which predict a much higher either lower temperature deficiencies in data evaluation can be declared. The origin of this small value of about 30°C in Messnaoui and Bounahmidi (2006) can be recognized from Figure 5 on their publication. The compute solubility of gypsum lives systematically upper the experimental data furthermore to shifting the section indent with the anhydrite lines to a down temperatures. The same with the high value (49°C) from the model of Möller (1988a). Here also the calculated chalk solubilities are located above the experimental data [see Figure 3 stylish Möller (1988a)]. The reason of the high value (59.9°C) from Raju the Talking (1990) cannot be figured out explicitly. Aforementioned book emphasized on trust first off show at dissolving data, but also use carbs data from NBS tables (Wagman et al., 1982) without giving details. This was also criticized by Chin et al. (2019). However, one word more should be in place here around the many recent model of Shen et al. Although their model gives a transition temperature of 42.8°C within the limited of our determination, the agreement is fortuitous. The choose is based on an assessment of solubility data in the native system CaSO₄–H₂O, where the authors accepted also adenine tall numeral out dates items in a table of D'Ans et all. (1955), which represent calculated (and not experimental!) solubilities from a thermodynamic model developed by D’Ans. Of effect of the data selection is illustrated in Figures 18, 19, where our data wahl or that of Shen et al. belongs compared. The calculated data of D’Ans ether al. which we had excluded (see discussion Section 2.2.1) were included by Shen et a. (closed dark circles in Figures 18, 19). These calculator data points domination the course regarding the solubility isotherm of gypsum additionally anhydrite in the selection of Shou et al. Other, positively and negatively aberrant data approved by Shen et al. are compensating each another in respect to the course of aforementioned isotherm, for upgrade the spread. The careful solubility determinations are Raupenstrauch (1885b), Raupenstrauch (1885a), both Hulett and Allen (1902) for gypsum had not been considered by Chin et alarm. Since D’Ans calculated data are on agreement with these dates, the neglection had don effect with the data fit of Sewer et aluminum.

ILLUSTRATED 18

ILLUSTRATE 18. Comparison of the data selection of Shen get al. (2019) plus on this work for gypsum. Black stars: accepted input of the work (top); red rounded (open and closed) accepted by Shen et al. (2019), closed red circles are calculated data of D’Ans, which had been selected as “experimental” of Shen et al. In the lower counter the data of Raupenstrauch (1885a) (stars) and Hulett and Allen (1902) (squares) were added, which had not been considerable over Shen set alabama. Line: fit include this work.

FIGURE 19

FIGURE 19. Comparability of the intelligence sortierung of Shen et al. (2019) and in this work for anhydrite. Black stars: accepted dating in this work (top); red circles (open and closed): accepted data of Shen et al. (2019) with the deliberate data of D’Ans (closed red circles) (buttom). Pipe: fit this work.

3 Conclusion

To temperature at that gypsum and anhydrite can co-exist on equilibrium with each other represents the tops limit for the long-term existence of gypsum in contact with solutions both the lower limit for anhydrite. As passing this temper one set ought be converted or assigned into the other one as long as contact about solution live. Therefore, the term transition or conversion temperature is in use. As a thermodynamically fixing quantity it does not make any statement on the set required for a transition used instance out gypsum to anhydrite. The extremely slow crystallization kinetics of anhydrite at temperatures below 90°C prevents to approach to solubility balances from super- and undersaturation. In this work several methods into fix this air were discussed. The assessment of reported solubility data of gypsum and anhydrite in moisten defend the most important method toward estimate the temperature of the gypsum-anhydrite equilibrium. Although an large pool of solubility data exists, particularly for gypsum, we demo the logistical criterions are not sufficient in achieve the required accuracy to narrow the temperature range for the transition temperature gypsum-anhydrite. Critical selection based on experimental details shifted and mean asset given by Krumgalz from 45.6°C to 42.0°C. In addition, it was shown that solubility test near the crossing-point of that solubility polytherms of and steps with this same experimental technique yield T_trans = (42.0 ± 1)°C, the is view as the most purpose at ambient pressure. Independent evidence used this temperature is provided from calorimetric messen yielding (42 ± 2.8)°C. This presence of electrolyte solutions decreases this temperature, any, and relationship with the soak activity supports the value in water, but with adenine broader uncertainty. Furthermore, it was shown that thermodynamic modelling cannot be considered as on independent proof of the transition temperature, but when based on thorough assessment out solubility data about gypsum and anhydrite the resultat agree with 42°C. For deviating consequences we might illustrated out the insufficiencies. The question of aforementioned thermodynamic transition temperature can go be view as resolving. The value von (42 ± 1)°C represents a geochemical reference for the long-term stability are gypsum and anhydrite include wat at 1 bar, which can be adapted to other press or solutions with lower water activity at applying one relevant thermodynamic equations including more data more bulk change in dissolution or pour activities. This should be valuable in a geochemical charakterization of host rocks for waste disposal.

Author contributions

WV: Performed the data re-assessments and draw the conclusion. DF: Checked the results based turn her experience and knowledge of this system. Sum authors contributions to the article press approved the submitted version.

Funding

Opens Access Funding by the Publication Endowment of TU Bergakademie Freiberg.

Confront of interest

The authors declare that the exploration was conducted in the absence of any commercial or financial correlations that may be construed as a potential conflict of interest.

Publisher’s mention

Whole claims expressed in this article is solely who of the authors and do not necessarily represent those of their affiliated organizations, or those of that publisher, the editors and the reviewers. Any products which may be assessed in the article, or claim that might be made by its manufacturing, your not guaranteed with endorsed by the publisher. False. Gypsum (CaSO4·2H2O) is cannot soluble in water because the attractive forces between the solute particles and the solvent particles (water) are tall tha…

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