The most widely applied method represents the determination of the solubility 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 cross each other the constants K I I ∅   a n d   K I I I ∅ are equal and thus this temperature represents the conversion or transition temperature between gypsum and anhydrite. Note that right-hand side of Eq. 4 becomes zero in pure water (a_w = 1) or dilute solutions, for which a_w = 1 might be assumed.

In electrolyte solutions the transition temperature will decrease, since a_w < 1. This is easily shown by combining Eqs 1, 4 and solving for T (Eq. 4a). The standard data ∆ R H ∅ and ∆ R S ∅ ∆ R H ∅ ∆ R S ∅ − 2 R l n a w = T (4a) are independent on electrolyte composition and ln(a_w) becomes negative. Thus, a positive value is added in the denominator, which requires a reduced T to maintain equality in Eq. 4a. The crossing-point of the solubility curves of gypsum and anhydrite as a function of electrolyte concentration at T < T (transition, water) yields the electrolyte concentration, where at the chosen temperature both solids are in equilibrium. If the water activity is known at the given electrolyte concentration and solution temperature then through Eq. 4a a relation between water activity and transition temperature can be established. The relation is independent on the type of electrolyte.

At the transition temperature in pure water or dilute solutions the water a_w can be set to 1.0, which according to Eq. 4 gives ∆ R G I ∅ = 0 = ∆ R H I ∅ − T t r a n s   ∆ R S I ∅ (5)

The right-hand side contains only quantities, which can be determined calorimetrically and thus are independent on kinetics of crystallization. When the reaction enthalpy and entropy of reaction (I) are determined as function of T, then through Eq. 5 the T_trans can be calculated.

A diversity of thermodynamic and equilibrium data can be combined using an activity model within a framework of Eqs 1–4. The success depends on an appropriate data assessment and a compromise between number of adjustable parameters and accuracy of data description.

In Table 1 references are listed in which the transition temperature was predicted using the different methods.

The most direct way to determine the transition temperature is to determine experimentally the solubility of gypsum and anhydrite in dependence on temperature. Due to the slow kinetics of anhydrite crystallization gypsum can exist metastable for long time in aqueous suspension considerable above the transition temperature. Vice versa anhydrite can exist metastable below the transition temperature due to low 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, the determination of the crossing point is experimentally feasible. The more difficult part in such an investigation represents the solubility curve of anhydrite. In water below 80°C it is practically not possible to achieve saturation by crystallizing anhydrite from a supersaturated solution. Saturating water by dissolving anhydrite is also a slow process. Thus, the experimenter is not sure whether saturation was reached or not after a certain time. Other factors are also important for the observed solubility values of anhydrite, these are:

■ Purity of natural anhydrite

These factors are more important for anhydrite than for gypsum, since for instance tiny anhydrite crystals will have a higher solubility and because crystallization does not occur the dissolved part from these crystals remains in solution and causes a higher solubility. On the other side, using samples with large crystals separated from fines, the dissolution kinetics becomes extremely slow.

In order to eliminate effects of fines in solubility experiments with anhydrite D'Ans (1968) applied a 3-week boiling for aging natural, grinded anhydrite samples. Hill prepared anhydrite by boiling gypsum in 20% sulfuric acid for 3 days (Hill, 1934; Hill, 1937).

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

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

As one can see from Figure 4, the transition temperature shifts to lower values, when correcting the data set of Krumgalz and even lower (Figure 5), if one selects and combines the data of the authors (Hill, 1937; Posnjak, 1938; Bock, 1961; Power et al., 1964), who had 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 in Figure 6. Locating the crossing points in enlarged plots yields

(Hill, 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 from a non-aged anhydrite)

The variation is very much smaller than from the statistical fits of the individual solubility curves of gypsum and anhydrite from different authors, who have investigated the solubility of either gypsum or anhydrite. The two values from Posnjak originate from two qualities of anhydrite he had used. The higher temperature results from the solubility of an anhydrite prepared by heating gypsum for a few hours at 500°C without aging, the lower is from a natural sample, which Posnjak himself assigns as the more reliable datum. The conclusion from all these considerations is that pure statistical treatment of assumed reliable data yield a transition temperature between 42°C and 45°C with a broad confidence interval of ±8°C. The particular designed experiments to determine the transition temperature by solubility determinations of both solid phases by the respective authors gave 42°C with a scatter of only ±1°C. Separate fitting of their results for gypsum and anhydrite gave the same transition temperature, but a wider scatter (±3°C). These facts hint on methodic differences (errors), which are compensated, when investigating both phases with the same (analytical, sampling) technique. From our personal experience we know, that beside other factors, sampling techniques have a large effect on the results of solubility determinations. They are quite individual and a detailed description would be too lengthy for a publication in scientific journal. In conclusion, 42°C ± 1°C should be considered as the correct transition temperature in water.

By the way, a thorough discussion, why the high value of the transition temperature of van’t Hoff (1912) is wrong can be found by Posnjak (1938). In brief, the conclusions of van’t Hoff are based on misinterpretations of tedious dilatometric and tensiometric measurements of hydration/dehydration reactions of gypsum into hemi-hydrate and anhydrite in water and electrolyte solutions.

Several authors supposed that equilibration times to reach the solubility equilibrium with anhydrite are shorter in electrolyte solutions than in pure water, particularly in solutions of sulfuric acid. To the knowledge of the present authors no quantitative examination of this effect was published until now. However, about 20 years ago, occasionally we made an observation, which underlines this kinetic effect. A company producing electrolytic copper from baths of CuSO₄ in solutions of sulfuric acid at about 40°C asked us to identify the type of scale on the electrodes forming regularly after about one to 2 weeks. This scale was pure anhydrite (determined by means of XRD patterns) deposited from impurities in the electrolytic baths. In pure water gypsum would form at these temperatures. Unfortunately, that time we did not further examine the phenomenon. The preferred preparation method of Hill (1937) to obtain well-crystallized anhydrite was boiling in 20% sulfuric acid. He reported crystal sizes of 20–30 μm (Hill, 1934). Doubtless, this points also to an improved crystallization kinetics of anhydrite in electrolyte solutions.

Bearing in mind these observations one could expect more precise determinations of the crossing-points of the anhydrite and gypsum solubility curves in electrolyte solutions. On the other side, accurate analytical determination of low concentrations of calcium and sulfate is more difficult in presence of a large excess electrolytes. Whereas the gypsum solubility was investigated in a large number of electrolyte solutions, this is not true for anhydrite. Zdanovskii, A. B. and Vlasov, G. A. (1968) determined the solubility of both phases in solutions of H₂SO₄ at T = 10°C, 25°C, 35°C, 42°C, and 50°C. Wang et al. (2013) reported such investigations for T = 25°C, 50°C, 75°C, and 90°C. The results for 25°C are shown in Figure 7. The black curves represent the data of Zdanovskii, A. B. and Vlasov, G. A. (1968). They cross each between 2.4–2.6 mol/kgw H₂SO₄. The data for anhydrite of Wang et al. (2013) are considerably higher, whereas both authors data agree for gypsum at m_H2SO4 ≤ 1.5 mol/kgw. At higher concentration of H₂SO₄ the data of Wang et al. fall below the curve of Zdanovskii and Vlasov. Unfortunately, Wang et al. did not continue the investigation of gypsum up to the crossing point with anhydrite. Extrapolating their gypsum curve crosses that of anhydrite at approx. 4 mol/kgw H₂SO₄. The data of Zdanovskii and Vlasov at 35°C are plotted in Figure 8. The solubility of anhydrite and gypsum equals at m_(H2SO4) = 1.4 mol/kgw. Figure 9 shows the analogous plot for 42°C. Here the crossing point is located at about 0.35 mol/kgw. Figure 10 shows the results for T = 10°C, the only data available below 25°C. In this case the crossing-point is at 5.5 mol/kgw with an uncertainty of about ±0.5 mol/kgw. As expected, the data show that the crossing point shifts to lower H₂SO₄ concentrations with increasing temperature. All the data at temperatures higher than 42°C showed lower solubility for anhydrite than for gypsum in line with the results on the gypsum-anhydrite equilibrium in pure water.

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

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

In sodium chloride solutions corresponding solubilities for gypsum and anhydrite were reported at different temperatures. Figure 13 shows plots for 25°C. In order to fix the crossing-point, data near this point were linearly fitted (see insert in Figure 13). Another plot is shown in Figure 14 for T = 40°C. The data for anhydrite are from Bock (1961), whereas for gypsum also other data have been added (Sborgi, 1926; Marshall, W. L. et al., 1964; Marshall and Slusher, 1966; Block and Waters, O. B., 1968). Up to 2 mol/kgw NaCl the results for gypsum agree, at higher concentrations the data diverge. The crossing-point with the anhydrite curve of Bock can be located between 1.1 and 1.8 mol/kgw NaCl. Data at 50°C gave higher solubilities for gypsum in the entire concentration range (Bock, 1961; Zen, 1965).

In Table 5 the data for the crossing-points in the electrolyte solutions mentioned above are summarized and complemented with the corresponding water activities. According to Eq. 4 and Eq. 4a all data should be located on a common curve T = f(lna_w). In Figure 15 the data from Table 5 are plotted together with the theoretical curve (see Section 2.3). The latter is obtained when applying the caloric equation Eq. 21 from Robie et al. (1989). As can be seen from Figure 15, the transition temperatures determined from solubilities in different electrolyte solutions scatter around the theoretical curve. For every experimental datum the two symbols connected by a line reflect the uncertainty for that datum as can be read-off as m_min and m_max from Table 5. Thus, the transition temperatures determined from solubility curves in electrolyte solutions are in accordance with the calorimetric result (Section 2.3), but do not reduce the uncertainty. Although one could hope for improved crystallization and dissolution kinetics of anhydrite other factors like analytics at high electrolyte concentration obviously effect the precision of results.