Article pubs.acs.org/jced
Thermodynamics of Inorganic Hydration and of Humidity Control, with an Extensive Database of Salt Hydrate Pairs Leslie Glasser* Nanochemistry Research Institute, Department of Chemistry Curtin University, GPO Box U1987, Perth, Western Australia 6845, Australia S Supporting Information *
ABSTRACT: Water is ubiquitous, and its presence in the ambient humid air means that it may constitute an uncontrolled variable in chemical processes. Methods for humidity control may involve complete removal of water and its vapor by procedures such as evaporation under vacuum, use of drying agents such as silica gel, adjustment to a desired humidity by use of saturated aqueous solutions, or adjustment to a desired humidity by use of a pair of related salt hydrates (such as CuSO4·3H2O + CuSO4·5H2O). By the phase rule, the presence of three phases at a fixed temperature (in the latter two cases) ensures a constant equilibrium humidity. The thermodynamics of these chemical means of humidity control is presented, together with a database of almost 300 salt hydrate pairs which may be considered for humidity control by mixing into the reaction medium. However, the possibility of interaction of the hydrates with the reaction medium should not be neglected.
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given temperature, such a pair of hydrates develops a fixed equilibrium aqueous vapor pressure. In this paper, we discuss the simple thermodynamics of hydration and also its application to humidity control by means of salt hydrate pairs. We provide a database of almost 300 salt hydrate pairs which may be suitable for humidity control. Some of this material has been considered in a previous publication,10 with respect to the thermodynamic relations among hydrates with the same anhydrous parent.
INTRODUCTION
Water is ubiquitous, and its presence in the ambient humid air means that it may constitute an uncontrolled variable in chemical processes: water content affects the physical properties of ionic liquids and of electrolyte solutions in general;1 in biocatalysis, in both organic media2,3 and ionic liquids,4 reaction rates may be reduced by low water content, while high water content may accelerate undesirable hydrolysis reactions. Given such issues, it is important to acknowledge or control the presence of water in the experimental environment, whether by reducing the system to dryness by such means as evaporation under vacuum5 or by the use of chemical drying agents such as silica gel and phosphoric or sulfuric acids, or by controlling the ambient humidity. One method of ambient humidity control is isolation of the system in a container also containing solutions of drying agents at suitable aqueous concentration6 or of saturated aqueous solutions.7,8 Additionally, water which cannot be conveniently removed may need to be accounted for, perhaps by the “standard addition method”, SAM,9 where the properties of the medium having a sequence of known concentrations of water are extrapolated back to zero water content. Resorting to separate solutions may be inconvenient; moreover, the vapor pressure will alter should the concentration of the control solution alter via absorption or loss of water to the local environment. An alternative remedy is to mix a pair of related salt hydrates into the reaction medium; at a © 2014 American Chemical Society
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THERMODYNAMICS OF HYDRATION AND OF HUMIDITY CONTROL Hydration. Water enters into association with inorganic salts in a variety of ways: most intimately as an hydroxide, but often as a semi-independent molecular entity bound by Coulombic and other interactions, leading to the formation of hydrates. However, thermodynamics is independent of the assumed form of the hydrated material. In the present context, we consider the thermodynamics of inorganic materials represented as simple hydrates only. A number of studies11−18 have shown that the thermodynamic properties of simple hydrates are generally additive; that is, each water added to an inorganic chemical formula adds a characteristic amount to the thermodynamic properties of the material. These properties include molar volume, formation Received: December 12, 2013 Accepted: January 23, 2014 Published: February 4, 2014 526
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where Δn = n − m, and m may be zero, then representing the parent salt. We may regard this reaction as sublimation of water from the higher hydrate, following eq 2. In this situation, eq 4 applies
enthalpy, entropy, and thus Gibbs energy. This implies that the properties of hydrates may readily be approximated from the properties of their parent or hydrated neighbors (e. g., knowing a thermodynamic property of, say, CuSO4, the same property for CuSO4·nH2O may be estimated by using a known additive value). More detailed examination10 does show a small but generally consistent additional variation in Gibbs energy as one proceeds from a lower to higher hydrate in a sequence. An important observation is that there are many hydrates in a sequence which are either unknown or unobserved even though the thermodynamic systematics suggest that they could exist. It is a matter of some conjecture as to the reasons for the absence of these hydrates; there may possibly be some kinetic or metastability issues which interfere with their formation.10 Saturated Aqueous Solution.19 The vapor pressure, p, above a saturated aqueous salt solution is related to the water activity by aw = p/p°, where p° is the vapor pressure of pure water at the same temperature.2 Strictly, the vapor pressure should be substituted by the fugacity, f, which is a measure of the pressure corrected for nonideal gas behavior. However, no such correction is required in most circumstances for water since calculations demonstrate that “it is justified to treat water as ideal gas under saturation pressure in most equilibrium situations”.20 The solution is saturated when sufficient solute is present, and three phases are then present: namely, excess solute, saturated aqueous solution, and aqueous vapor. Applying the thermodynamic phase rule (F = C − P + 2) in these circumstances (C = 2, P = 3, with fixed temperature reducing the term “2” to “1”) yields an invariant condition (F = 0). Thus, the saturated solution exerts a constant vapor pressure which may be utilized for humidity control. The saturated solution of an inorganic salt will have an equilibrium aqueous vapor pressure which is a function of the ambient temperature and (to a small extent) the ambient pressure. The effect of temperature on the vapor pressure will be described by the Clapeyron equation, which is fundamental to equilibria between two phases
dp ΔS = dT ΔV
ΔG◦ = −RT ln KP KP =
Figure 1. Vapor pressures of aqueous copper sulfate systems at 25 °C, with vapor pressure data for the hydrate pairs from Castellan19no primary source of data is provided there, but that may be found elsewhere.21 See text for an explanation of diagram. p(CuSO4 + CuSO4·H2O) = 0.02 Torr; p(CuSO4·H2O + CuSO4·3H2O) = 4.3 Torr; p(CuSO4·3H2O + CuSO4·5H2O) = 7.9 Torr; p(saturated solution + CuSO4)8 = 22.5 Torr; saturation concentration: n(H2O)/ mol CuSO4 = 40.4. The final curve for the unsaturated solution extends in the limit to the vapor pressure of pure water (23.8 Torr at 25 °C8). Note: 1 Torr ≅ 1 mmHg ≅ 133.3 Pa.
Since a gaseous phase at rather low pressures is involved, the equation may be extended to the Clausius−Clapeyron and van’t Hoff equations, by applying the ideal gas law to substitute for the ΔV term and utilizing the equilibrium sublimation property ΔsublS = ΔsublH/T
vertical line in the figure until the hydrate alters in overall composition. In the presence of a pair of hydrates, the vapor pressure is constant until one or other hydrate disappears. (An interesting aside is that a container of hydrate from a supplier must almost inevitably be a mixture unless the hydrate has a very low vapor pressure.) The saturated solution also provides a constant vapor pressure. This behavior allows a system of a pair of salt hydrates or of a saturated solution to provide constant humidity environments. This stair-step sequence of vapor pressures with an increasing extent of hydration while perhaps familiar is not, in fact, quite typical. It is not necessary that the formation properties of a set of hydrates vary in the systematic fashion shown for the cupric sulfates. Figure 2 shows the behavior for the calcium chloride hydrates. In an earlier publication10 we demonstrated that the cumulative effect of increasing extent of hydration is to systematically alter the formation Gibbs energy of the hydrate toward zero, so that there is a limit to the possible extent of hydration in a family of hydrates. Figure 2 (and similar
(2)
2
Salt Hydrate Pairs. When the equilibrium of a salt hydrate pair (such as CuSO4·3H2O + CuSO4·5H2O) at a given temperature is involved, then we again recognize the presence of three phases (two solids plus water vapor in this case). Applying the thermodynamic phase rule yields an equivalent invariant condition. A general chemical reaction equation for a salt hydrate pair may be formulated as: CA·nH 2O/Δn → CA·mH 2O/Δn + H 2O
(4)
Since each of the two solid hydrates are in their standard reference states (p = p°) of unit activity, Kp = (p/p°)vap = aw. Figure 1 illustrates this behavior. In the presence of only one hydrate, the vapor pressure is indeterminate, changing along a
(1)
Δ H° d ln p or = subl 2 dT RT ⎛ p⎞ Δ H° ⎛ 1 1⎞ ln⎜ ⎟ = − subl ⎜ − ⎟ = A − B/T ⎝ R T° T⎠ ⎝ p° ⎠
where
Δn (p /p°)1/ m ‐ hydrate (p / p°)vap Δn (p /p°)1/ n ‐ hydrate
(3) 527
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results: that is, vapor pressures at 25 °C, values of the standard enthalpy of sublimation of the water, ΔsublH° (which yield the temperature coefficients, B (eq 2)), together with values of the standard entropy of sublimation, ΔsublS°. The HSC Chemistry database collates data from numerous sources, generally the standard thermodynamic databases,27−36 to which reference may be made for detailed information on the materials. Our data are listed as tables in the Supporting Information, where Table S1 lists the data in alphabetical order of the chemical formulas, while Table S2 lists the same data in order of the equilibrium pressures. It should be appreciated that the thermodynamic calculations involve the differences between numerically large quantities, so that any errors are amplified, further compounded by exponentiation in the calculation of the corresponding vapor pressures and metastability in some of the hydrates. As a consequence, the calculated vapor pressures should ideally be supported by experimental verification. Halling2 has provided a list of 48 salt hydrate pairs, together with temperature coefficients, suitable for humidity control in biocatalytic experiments, based on experimental data from the older literature, now further supported by experimental measurements on 13 salt hydrate pairs.3 Data for 20 of these whose vapor pressures correspond well with the current thermodynamic database values are included in our listing. There is agreement between the calculated vapor pressures in our database and experimental values2,3 to about 10% for vapor pressures above 10 Torr, but the values are (not unexpectedly) much more discordant for very low vapor pressures. Recent experience37 notes that acid−base effects need to be taken into consideration in regard to the use of salt hydrate pairs in biocatalytic experiments, and other factors relevant to the medium into which the salt hydrate pairs are to be placed (such as solubility) should also be taken into account.
Figure 2. Vapor pressures of aqueous calcium chloride systems at 25 °C. Vapor pressure data in Table S1: p(CaCl2 + CaCl2·H2O) = 0.0 Torr; p(CaCl2·H2O + CaCl2·2H2O) = 30.0 Torr; p(CaCl2·2H2O + CaCl2·4H2O) = 1.7 Torr; p(CaCl2·4H2O + CaCl2·6H2O) = 6.6 Torr p(saturated solution + CaCl2)8 = 4.3 Torr; saturation concentration: n(H2O)/mol CaCl2 = 7.6. The final curve for the unsaturated solution extends in the limit to the vapor pressure of pure water (23.8 Torr at 25 °C8).
diagrams for other hydrate families) shows that individual hydration steps each have their own thermodynamics, depending on the detailed structural effects which determine the thermodynamics. In terms of Gibbs energies for the calcium chloride hydrates, the parent/monohydrate pair is rather stable, while the mono/dihydrate pair is relatively unstable. The di/ tetrahydrate pair is quite stable, but the tetra/hexahydrate pair is less so. Finally, calcium chloride in saturated solution provides some stabilization, with a reduction in the aqueous vapor pressure. This reduction is due to the large aqueous solubility of calcium chloride; by contrast, copper sulfate is much less soluble, and the saturated vapor pressure increases over that of the tri/pentahydrate pair. A further pertinent case is the family of magnesium sulfate hydrates: it has recently been confirmed22,23 that the tetrahydrate (starkeyite) is metastable, thus affecting the thermodynamic systematics of the group. (The Gibbs energies for this family are listed in Table 2 of our earlier analysis,10 where the value of −1147.5 kJ·mol−1 for the parent in the first column was incorrectly transcribed as −1174.5 kJ·mol−1this causes small errors in the subsequent columns but does not affect any conclusions.) An interesting case is the salt hydrate pair Na2SO4·10H2O + Na2SO4, which has an equilibrium water vapor pressure at 25 °C of 19.9 Torr as calculated from Gibbs energies (19.0 Torr measured3), although there is an intervening heptahydrate, Na2SO4·7H2O. The heptahydrate is metastable and cannot form in the presence of the decahydrate,24 so that it does not affect the decahydrate + anhydrate equilibrium.
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DISCUSSION Thermodynamics establishes the following relation for a reaction 3 with materials each in their standard reference states (a pressure of 1 bar) and a fixed temperature Δ r G° = Δ r H ° − T Δ r S °
(5)
Calculation from the database yields the standard reaction Gibbs energy, ΔrG°/Δn, corresponding to the formation of 1 mol of H2O(g) under the specific condition of the pure solids in their standard states at the given temperature and the water vapor in the ideal gas state at 1 bar pressure. Equation 4 then provides a value for the equilibrium constant, Kp, from which the vapor pressure may be calculated. Positive values of ΔrG°/ Δn will yield vapor pressures which increase from zero as ΔrG°/Δn decreases from large values. A zero value of ΔrG°/Δn will yield a pressure of 1 bar, while negative values will yield pressures greater than 1 barthese two conditions imply unstable hydrates. From the supporting tables, we note that the standard reaction entropy for these dehydration reactions is roughly constant, at 146 ± 11 J·K−1·mol−1, as seen in Figure 3 (this mean value may be compared with the value of 140.5 J·K−1· mol−1 for the sublimation of ice10). This is not unexpected since the reaction produces a gas having a nearly constant entropy from a pair of solids with small entropy differences. This then leads to the observation in Figure 4 that there is an approximately linear relation between the standard Gibbs energy and standard reaction enthalpy: the larger the standard
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HUMIDITY CONTROL DATABASES Saturated Solutions. A database giving the aqueous vapor pressures (that is, the relative humidity generated) of 27 saturated solutions is available in the Handbook of Chemistry and Physics8 and as ASTM Standard Practice E-104-02.25 Salt Hydrate Pairs. We have collected data for almost 300 salt hydrate pairs, using the HSC Chemistry database26 and its Excel “Add-In” to generate the appropriate thermodynamic 528
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deviation, since all of these rare-earth data values are derived from the same source.34
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ASSOCIATED CONTENT
S Supporting Information *
A thermodynamic database at 25 °C for almost 300 salt hydrate pairs is provided. Table S1 lists the data in alphabetical order of chemical formulas (including unreliable results in red italics, selected on the basis of unusual values for the enthalpy or entropy of reaction); Table S2 has the same data (without the unreliable results), sorted into numeric sequence of the aqueous vapor pressures. This material is available free of charge via the Internet at http://pubs.acs.org.
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Figure 3. Frequency distribution of the standard sublimation entropy, ΔsublS°, per mole of water from salt hydrates into the gas phase, at 1 bar pressure. The mean value is 146 ± 11 J·K−1·mol−1; see data in Table S1.
AUTHOR INFORMATION
Corresponding Author
*Telephone: + 61 8 9266-3126. Fax: + 61 8 9266-4699. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
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Figure 4. Plot of standard Gibbs energy of salt pair reaction per mole of H2O(g) against the corresponding standard enthalpy of reaction. The least-squares fit to the data in blue diamonds has the equation: (ΔrG°/Δn) = 0.993 (ΔrH°/Δn) − 42.3, with correlation coefficient, R2 = 0.96. The following prominent outlier reactions, represented by red squares, have been omitted from the linear fit: NH4(UO2)2 F5 ·3H 2O = NH4(UO2 )2 F5 + 3H 2O(g)
PuO2 (OH)2 · H 2O = PuO2 (OH)2 + H 2O(g)
CuHPO4 · H 2O = CuHPO4 + H 2O(g) Cu3(PO4 )2 ·3H 2O = Cu3(PO4 )2 + 3H 2O(g) Eu(IO3)3 · 2H 2O = Eu(IO3)3 + 2H 2O(g)
Gibbs dehydration energy, ΔrG°, the larger the temperature coefficient of the dehydration, ΔrH° (cf. eq 2). Thus, salt hydrate pairs with small positive values of ΔrG° will generate moderate vapor pressures which will vary little with temperature. This contrasts with the situation for saturated salt solutions where temperature variation of the aqueous vapor pressure may be a significant complication. A group of hydrates worthy of attention is the rare-earth metal phosphate hydrates. An examination of the sorted Table S2 shows that these materials generally have the largest Gibbs energies and enthalpies in the table although other metal phosphates are more widely dispersed. It is not clear whether this is a real pattern of behavior or whether it is a systematic 529
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