A predictive model for the enthalpies of hydration of zeolites

American Mineralogist, Volume 94, pages 565–577, 2009

0003-004X/09/0004–565$05.00/DOI: 10.2138/am.2009.3028 565

A predictive model for the enthalpies of hydration of zeolites

PhiliPPe Vieillard1,* and romain mathieu2

1CNRS/INSU FRE 3114 Hydrasa, 40 Ave du Recteur Pineau, 86022, Poitiers cedex, France2Centre de Recherches Pétrographiques et Géochimiques, INSU/CNRS-UPR 2300, Nancy Université, BP 20, 54501

Vandoeuvre les Nancy, France

abstract

A compilation of the average hydration enthalpies per mole of water of 145 diversely originat-ing zeolites measured using different technical methods [76 data from transposed-temperature drop calorimetry (TTDC), 57 data from immersion calorimetry (IC), 6 data from phase equilibria (PE), 5 data from gas-adsorption calorimetry (GAC), and 3 data from hydrofluoric acid solution calorimetry (HF)] was generated. Statistical regressions between three parameters involving the average hydration enthalpy per mole of water {∆Hhyd-W, ∆Hhyd-W/(Al/Si), ln[–∆Hhyd-W/(Al/Si)]}and six parameters namely: (1) the charge defined by the Al/Si ratio; (2) the ratio of the framework charge to the number of H2O molecules (Al/H2O); (3) the framework density (FD) calculated from the molecular volume of the anhydrous zeolite, FDanh, and hydrated zeolite, FDhyd; (4) the average cation electronegativity in the exchange site characterized by parameter ∆HO=(site A)aq; and (5) the intracrystalline water porosity (WP) determined from the volume of liquid water that can be recovered upon thorough outgassing of the hydrated zeolite. The regressions were performed by taking into account either the nature of the measurement technique, or the nature of the zeolite family. Within the zeolites from the TTDC and IC populations (133 data), the best results were obtained with ln[–∆Hhyd-W/(Al/Si)] and Al/(Al + Si). Whatever the measurement technique, considering the nature of the zeolite family having a constant framework density of the anhydrous form (129 data), the Al/(Al + Si) ratio remains the best parameter and the enthalpy of hydration can be expressed as follows:

∆Hhyd-w = –(Al/Si)*e{5.491 – 4.674*[Al/(Al + Si)]}

This general relationship can be improved by considering the following parameters: FDanh, ∆HO=(site A)aq, WP and a new parameter that is the product of three parameters Al/Si, ∆HO=(site A)aq, and WP weighing the variation of the water porosity related to the nature of the cation and to the total charge of the exchange site. Therefore, an understanding of the chemical formulae and unit-cell volumes of anhydrous and hydrated zeolites is required to evaluate the enthalpy of hydration with an accuracy of ±3.25 kJ/mol H2O.

Keywords: Hydration enthalpy, integral hydration enthalpy, zeolites, framework density, anhydrous zeolites, hydrated zeolites, thermal stability, water porosity, zeolite X, zeolite Y

introduction

Zeolites are microporous minerals with large extra-framework sites that incorporate both exchangeable cations and water mol-ecules. Equilibrium in the zeolite–H2O system affects the stability and efficiency of zeolites as adsorbing agents, cation exchangers, catalysts, or molecular sieves. The response of zeolites to changes in temperature and/or water vapor pressure is of great interest in a large variety of natural and technological environments. Studies of the hydration-dehydration behavior of zeolites can be used to determine hydration energetics and to predict hydration states as a function of temperature and PH2O.

By measuring the enthalpy of dehydration of cordierite, Carey and Navrotsky (1992) showed for the first time a relationship between the enthalpy of hydration and Al/H2O (ratio of the frame-

work charge to the number of H2O molecules, at saturation). The data tested in this relationship were essentially sodium zeolites that were mostly derived from experimental measurements by Barrer and Cram (1971). When measuring the enthalpies of hydration of Na+-, K+-, and Ca2+-saturated clinoptilolites, Wilkin and Barnes (1999) demonstrated a relationship between the thermodynamic properties of the hydration water, the nature of the cation, and the framework charge. They showed that for isoionic zeolites with maximum water saturation, the enthalpy of hydration is a function of the framework charge [Al/(Al + Si)]. Bish and Carey (2001) provided an interesting compilation of hydration enthalpies of various zeolites saturated with different cations and showed a correlation between the enthalpy of hydra-tion and the Al/H2O ratio (ratio of the framework charge to the number of H2O molecules at maximal saturation) for zeolites with a same cation. This analysis was extended to K+-, Ca2+-, * E-mail: [email protected]

VIEIllARD AND MATHIEU: PREDICTION OF ENTHAlPIES OF HYDRATION OF ZEOlITES566

and Mg2+-saturated zeolites. These authors concluded that, for a constant Al/H2O ratio, the enthalpy of hydration decreases ac-cording to Mg2+ ≅ Ca2+ > Na+ > K+. Since the year 2000, many measurement techniques have been developed and some possible reasons for different results obtained from different methods have been discussed, especially focusing on the differences between “fully hydrated state” and “fully dehydrated state” on the one hand, and on the reversibility of hydration-dehydration processes on the other. The question as to whether the enthalpy of hydration per one water molecule is really dependent on the cation type has not yet been resolved. Yang and Navrotsky (2000) employed high-temperature calorimetry on ion-exchanged zeolite Y, but observed no correlation between enthalpy of hydration and cation charge density (z/r) in contrast to results by other methods like immersion calorimetry (Barrer and Cram 1971; Coughlan and Carroll 1976). Recently, Sun et al. (2006) and Sun and Nav-rotsky (2008) have obtained two sets of experimental hydration enthalpies for various cation-exchanged beta zeolites in different saturation states. The enthalpies of hydration of li- and Na-beta zeolites have been measured by Sun et al. (2007) and provide values for different saturation states. However, a general method for predicting the average enthalpy of hydration for any zeolite having a wide range of chemical compositions and throughout different zeolite families has not been formulated to date.

The purpose of this paper is to bring together the ther-mochemical data relating to the hydration of anhydrous zeolites to form a systematic and predictive model for the enthalpies of formation of hydrated aluminosilicate zeolites. We considered the dependence of the energetics of hydration on the nature of the measurement methods as well as on the framework type, aluminum content, charge-balancing cation, type of cations located in the exchangeable site, and on the number of water molecules. We defined a set of linear equations that describe the average enthalpies of hydration for all zeolites.

exPerimental methodsThe enthalpy for the full hydration of an anhydrous zeolite can be written:

M nii

i n

n n N

c

=

=

∑

( ) + (1

Al Si O H OAl Si 2H O 2. )) →

( )=

=

∑l ii

i n

n n NM nc

1

Al Si O HAl Si 2H O. 22O( )

(1)

The enthalpy of this reaction, the integral hydration enthalpy, ∆Hhyd-Z can be obtained via (Z refers to the bulk zeolite):

∆

∆

H

H Mf ii

i n

n

c

hyd-Z

AlA

=

°

=

=

∑,2981

ll Si 2Si H OH O 2n N

f i

O n

H M

( ) ( )

−

°

. .

,∆ 298ii

i n

n n N

c

=

=

∑

( )

1

Al Si OAl Si

− ∗ ( )°n H fH O 2 liq2

H O∆ ,298

(2)

Here, liquid water was used as a reference in all calculations: its enthalpy of formation is ∆H°f H2Oliq = –285.83 kJ/mol (Cox et al. 1989). The average hydration enthalpy per mole of water, ∆Hhyd-W, can be derived from the integral hydration en-thalpy ∆Hhyd-Z using the following relationship (W refers to the water molecule):

∆Hhyd-W = ∆Hhyd-Z/nH2O (3)

As the integral hydration enthalpy ∆Hhyd-Z is the integral function of the partial molar enthalpy hydration from nH2O = 0 (corresponding to an anhydrous zeolite) to a maximal value of nH2Omax (corresponding to the fully hydrated zeolite), the partial

molar enthalpy of hydration relative to the liquid water, dh, which is the derivative function of ∆Hhyd-Z, becomes

∆Hn

dh dnn

n n

hyd-ZH O2

H2O=

=

=

∫1

0* . (4)

Quantitative enthalpies of hydration are difficult to obtain. Different meth-odologies for obtaining hydration energetics can lead to different values for the same compound.

Immersion calorimetry (IC) provides measurements of integral enthalpies of hydration as a function of the degree of hydration. Barrer and Cram (1971) and Coughlan and Carroll (1976) performed several measurements on different zeolites with various cations. The advantages of the method are as follows: (1) direct measurement of the enthalpy of hydration and necessary knowledge of the amount of H2O in the sample while immersed in water; (2) accurate measurement of the initial state of dehydration; and (3) potential for irreversible changes in the zeolite structure during dehydration.

Enthalpy of hydration can be determined from phase equilibrium (PE) measure-ments by the isoteric method in which data are plotted as lnP (or lnK) vs. 1/T at constant hydration state. The slope of these lines gives the enthalpy of hydration. Carey and Bish (1996), Wilkin and Barnes (1999), and Fialips et al. (2005) used this technique to determine the hydration enthalpy of K-, Na-, Ca-clinoptilolites, and Ca-chabazite, respectively. One of the difficulties associated with this method includes the indirect nature of the measurement that requires fitting the data to extract the enthalpy of hydration.

With the transposed-temperature drop calorimetry (TTDC), enthalpy of hydra-tion data are obtained by measurements of the heat evolved from a sample dropped at room temperature into a calorimeter maintained at 700–800 °C, (Shim et al. 1999; Yang et al. 2001; Kiseleva et al. 1996a, 1996b, 2001a; Sun et al. 2006, 2007; Sun and Navrotsky 2008). One of the difficulties associated with this measurement method includes enthalpy effects due to irreversible structural changes at 700–800 °C (the effect depends on whether the collapse is exothermic or endothermic). Data from Petrovic and Navrotsky (1997) suggest moderate exothermic effects of 1–3 kJ/TO2 basis, which would lead to calculated enthalpies of hydration that are not as negative as assumed.

With gas-adsorption calorimetry (GAC), enthalpies of hydration data are measured by exposing a bed of zeolite to differing H2O-vapor pressures. Petrova et al. (2001) obtained some values for the clinoptilolite. Some of the difficulties associated with this method include kinetic limitations on attainment of equilibrium (slow kinetics requires a very sensitive and stable calorimeter).

With hydrofluoric acid solution calorimetry (HF), enthalpies of hydration data are obtained by measuring the difference in the enthalpy of a solution in HF acid at about 70 °C of a hydrated and an anhydrous zeolite (Johnson et al. 1982, 1991, 1992a). One difficulty associated with this technique is the potential for irreversible changes in the dehydrated samples.

The 145 average enthalpies of hydration of different zeolites with their chemical formula were compiled from the literature (Table 11). This figure is greater than the one given by Bish and Carey (2001) because new data from measurements of hydration enthalpies performed between 2000 and 2007 have been included. These new data relate to various zeolites, in particular β zeolites (Sun et al. 2006, 2007; Sun and Navrotsky 2008), chabazite (Fialips et al. 2005), brewsterite (Ogorodova et al. 2005), erionite (Ogorodova et al. 2001), gmelinite (Ogorodova et al. 2002b), epistilbite (Ogorodova et al. 2002b), stellerite (Kiseleva et al. 2001b), gonnardite, thomsonite, natrolite, mesolite, and scolecite (Kiseleva et al. 1997). Among these selected data, two criteria have been checked systematically: (1) the integral hydra-

1Deposit item AM-09-014, Table 1 (145 average enthalpies of hydration of different zeolites with their chemical formula), Table 3 (unit-cell volumes of the hydrated zeolites), and Table 11 (comparison of the experimental enthalpies of hydration vs. the predicted enthalpy of hydration from column 11 of Table 10). Deposit items are available two ways: For a paper copy contact the Business Office of the Mineralogical Society of America (see inside front cover of recent issue) for price information. For an electronic copy visit the MSA web site at http://www.minsocam.org, go to the American Mineralogist Contents, find the table of contents for the specific volume/issue wanted, and then click on the deposit link there.

VIEIllARD AND MATHIEU: PREDICTION OF ENTHAlPIES OF HYDRATION OF ZEOlITES 567

tion enthalpy includes the phase transition enthalpy, and (2) the chemical formulae of zeolites are perfectly balanced.

With regard to the first criterion, most zeolites selected by Bish and Carey (2001) are zeolites with a collapse temperature above 700 °C. However, some compounds with a collapse temperature below 700 °C were added by these authors, i.e., stilbite and heulandite, the measurements of which have been performed by Kiseleva et al. (2001a). The latter indicated that the values of the integral hydration enthalpies include the phase transition enthalpies observed during dehydration of these minerals. The same attention was given to the new minerals added in this work.

The second criterion was applied to all minerals, and five minerals showed a false or incomplete structural formula, among which H- and la-bearing Y zeolites (Yang and Navrotsky 2000).

The average enthalpy of hydration exhibits a wide range of values from Rb-BEA (–5.29 kJ/mol H2O) to li-BEA zeolites (–79.02 kJ/mol H2O). Data from immersion calorimetry (IC) and transposed temperature drop calorimetry (TTDC) are more numerous than those from the other methods and encompass a large range of different zeolites.

definitions of Parameters characterizing zeolites

Six parameters characterizing the chemical properties of zeolites: Al/Si, Al/H2O, ∆HO=(site A), FDanh, FDhyd, and WP are proposed in this section. The choice of these parameters is justi-fied and details of the calculations are given below.

Al/Si and Al/H2O ratiosAl/Si ratio and Al/H2O ratio (ratio of the Al content to the

saturated water content of H2O molecules, a parameter already used by Bish and Carey 2001) were considered in this study and were calculated for each zeolite (Table 11). The Al/Si ratio = [(nAl + nFe)/nSi] is one of the major discriminating factors between many different zeolites, with some zeolites tending toward the siliceous end and others typically being more aluminous. The Al/Si ratio is related to the expression Al/(Al + Si) by the fol-lowing equation:

AlAl Si

Al Si+( )

=+

1

1 1

. (5)

∆HO=(site A)Vieillard and Jenkins (1986a, 1986b, 1986c) used parameter

∆HO= Mz+(aq) in the model of prediction of enthalpy of hydra-tion in different hydrates. This parameter characterizes a given cation Mz+ and is defined as the difference between the enthalpy of formation of the corresponding oxides ∆H°f (MiOxi)(c) and the enthalpy of formation of the corresponding aqueous cation ∆H°f (Mi

zi+)(aq):

∆ ∆ ∆H aqz

ii x (c) i

z +

aO M x M O Mi

i

i= + ° °= ( ) − ( )1 H Hf f ( qq)

(6)

where z is the charge of the cation Mz+, and x is the number of O atoms combined with one atom of M in the oxide (x = z/2), so that the difference in Equation 6 refers to one O atom. A set of internally consistent values of ∆HO=Maq

zi+ is proposed here (Table 2). These values are mostly from Robie and Hemingway (1995) for oxides and from Johnson et al. (1992b) for aqueous cations. Vieillard (2000) and Vieillard and Tardy (1988, 1989) showed a close relationship between parameter ∆HO=Mz+(aq) and the

difference in electronegativity between cation and oxygen, thus pointing out the affinity of a cation to oxygen.

The electronegativity of site A, ∆HO=(site A), represents the weighted average of ∆HO=Mz+(aq) of nc different cations in the exchanged site A:

∆∆

H

i i H aqz

i 1

i n

A

O (site A)n x O M i

c

=

= +

=

=

=( )∑ * *

x. (7)

The number of O atoms balancing site A (in extra-framework sites) is then:

xA i ii 1

i n

n xc

==

=

∑ * . (8)

From the chemical composition of the zeolite given in Table 11, the ∆HO=(site A) can be calculated from the values of ∆HO=Maq

zi+ (Table 2) and are given in Table 31.

Framework density of the anhydrous zeolite, FDanh, and the hydrated zeolite, FDhyd

To show the porous nature in a given zeolite, we chose the framework density (FD), as defined by Meier and Olson (1971) and Meier et al. (1996), and obtained as [(Al + Fe + Si)/unit-cell vol]·1000 (i.e., number of tetrahedral atoms per 1000 Å3). The lower the FD, the larger the proportion of the structure occupied by voids and channels. In our study, two parameters are to be considered and correspond to two different hydration states.

The unit-cell volumes of the hydrated zeolites can be mea-sured at 298.15 K and are given for all natural zeolitic minerals (Table 31). The unit-cell volume determinations performed on a zeolite that has been heated and then returned to room tempera-ture (without being sealed) are strongly affected by the fast zeolite rehydration. Therefore, only unit-cell determinations performed “ex situ” (i.e., under anhydrous conditions) are considered as reli-able and are much less numerous than those for hydrated zeolites

Table 2. Enthalpies of formation of oxides and ions at 298.15 K and calculated parameter ∆HO=Mz+ (aq) of selected cations

Oxides ∆H°f. 298.15K Ions ∆H°f. 298.15K ∆HO=Mz+(aq) (kJ/mol) (kJ/mol) (kJ/mol)Li2O –597.90* Li+(aq) –278.5‡ –40.90Na2O –414.80* Na+(aq) –240.3‡ 65.80K2O –363.20* K+(aq) –252.1‡ 141.00Rb2O –339.00* Rb+(aq) –251.12‡ 163.24Cs2O –346.00* Cs+(aq) –258.0* 170.0BaO –548.10* Ba+2(aq) –532.5* –15.6SrO –591.30* Sr+2(aq) –550.9* –40.4CaO –635.10* Ca+2(aq) –543.0‡ –92.1MgO –601.60* Mg+2(aq) –467.0‡ –134.6FeO –272.00* Fe+2(aq) –90.416§,|| –181.58MnO –385.20* Mn+2(aq) –220.8* –164.4ZnO –350.46* Zn+2(aq) –153.39‡ –197.07La2O3 –1793.68† La+3(aq) –709|| –124.8H2O liq –285.83* H+(aq) 0.0* –285.83* Robie and Hemingway (1995).† Robie et al. (1978).‡ Johnson et al. (1992b).§ Parker and Khodakovskii (1995).|| Shock and Helgeson (1988).


(Table 31). When the unit-cell volumes of the anhydrous forms are not available at 298 K, the unit-cell volumes of anhydrous zeolites measured at high temperature are selected instead. As-suming that the mean value of the thermal expansion coefficient of the unit-cell volumes of anhydrous zeolites is about α = 40 × 10–6 K–1 (Fei 1995), the difference in unit-cell volume between the phase measured at the temperature corresponding to total dehydration and at that at 298 K yields a maximum increase in volume of the order of 2%.

When some unit-cell volume values of zeolites (anhydrous or hydrated) are not available, as for X-, A-, and Y-zeolites, the bibliographical compilation shows that in some zeolite fami-lies, particularly in the X-zeolites and the A-zeolites, unit-cell volume data are more numerous in the anhydrous forms than in the hydrated forms, contrary to what is observed in the Y-zeolite family. To give a consistent set of unit-cell volume data for the anhydrous and hydrated zeolites, a few zeolites characteristic of the different families for which the unit-cell volumes are available for both forms were selected. These selected values in both hydration states will allow for determination of the miss-ing unit-cell volumes of the other zeolites saturated by different cations from the volumetric data available in one of the two states (anhydrous or hydrated). The assessed values of these volumetric entities are detailed in Table 31 and display an uncertainty of ±2%. Framework densities of anhydrous (FDanh) and hydrated zeolites (FDhyd) are calculated and provided in Table 31.

Water porosity (WP) All naturally occurring zeolites contain molecular water

in the form of intracrystalline molecules that can be removed by heat and evacuation and that can normally be re-sorbed by exposing the crystals to water vapor. Water is a small polar molecule able to penetrate into the intracrystalline channels and cavity systems in zeolites and varies in content as a continuous function of temperature and pressure. Barrer and Cram (1971) expressed the enthalpy of hydration as a function of the degree of saturation, θ, which is the ratio of initial water content to the number of water moles to saturate the intracrystalline free volume. At the lowest saturation values (θ and nH2O close to 0), the enthalpy of hydration per molecule of water is very large but diminishes as θ increases. In fully hydrated zeolites (θ = 1), the number of water molecules nH2O reaches the maximal value nH2Omax. The number of water molecules in the chemical formula of zeolites compiled in Table 11 is different and does not indicate a “fully saturated state” or a “partially saturated state” at room temperature. Barrer (1982) proposed an evaluation of the total intracrystalline pore volume by determining the volume of liquid water that can be recovered upon thorough outgassing of the fully hydrated zeolite. Assuming that the unit-cell volume of zeolitic water is the same as that of liquid water (Vu.c.H2O = 29.89 Å3), during hydration-dehydration processes, the water porosity (WP) can be calculated as the volume of liquid water in 1 Å3 of crystal and is expressed as follows:

WP H O

u.c. hyd

2=( )

29 89. * n

V (9)

where Vu.c.hyd represents the unit-cell volume of a hydrated zeolite

containing nH2O water molecules. Assuming that the number of water molecules nH2O varies from 0 to nH2Omax, the unit-cell vol-ume of a zeolite can be directly related to the number of water molecules. For example, Bish (1984) showed significant changes in the unit-cell volume of clinoptilolites during the hydration-dehydration process. In zeolites, the variations in unit-cell volumes as a function of the number of water molecules may be simple or complex to model because they depend on the behavior of the zeolites and on the stability of the zeolite structure as a function of temperature, as well as on the reversibility issues in the hydration-dehydration mechanisms. These functions of partial hydration volume may be obtained specifically for each zeolite from XRD measurements coupled to thermo-gravimetric analyses. Although such variations in the unit-cell volume do occur, let us assume a linear variation in the unit-cell volume as a function of the number of water molecules:

Vu.c.hyd = Vu.c.anh + k*nH2O (10)

where Vu.c.anh represents the unit-cell volume of the anhydrous zeolite. Parameter k weights the variation in the unit-cell volume between an anhydrous zeolite and a fully hydrated zeolite per one water molecule. This parameter can be calculated from the avail-able unit-cell volumes of anhydrous and fully hydrated zeolites given in Table 31. With the exception of natrolite, tetranatrolite, and gonnardite, the k values are generally lower than the unit-cell volume of liquid water. It is interesting to observe that the order of magnitude of the k values is close to that of maximal contraction of unit-cell volumes with respect to the volumes of the hydrated zeolites, ∆V, calculated by Cruciani (2006). The knowledge of the number of water molecules and the unit-cell volume of anhydrous and hydrated zeolites are required for the calculation of the water porosity:

WP H O

u.c.anh H O

2

2

=+ ( )

29 89. *

*

n

V k n (11)

given in Table 31.Correlations are used between the six parameters previously

defined within different groups of zeolites distributed according to the nature of experimental data (Table 4). Two populations of zeolites such as “all data” and “data from ‘TTDC’ and ‘IC’ mea-surements” have been created in this study to test the variability and the generalization of the regression coefficients. Due to their low sampling numbers, the regression coefficients from the “HF,” “GAC,” and “PE” measurement groups are not displayed.

Within the four different groups “all data,” “TTDC + IC,” “TTDC,” and “IC,” Table 4 shows us parameters Al/Si, ∆HO=(site A) and WP are independent each other. Parameters FDanh and FDhyd are interrelated, showing a close relation with the nature of the zeolitic framework. The Al/H2O shows a negative correlation with the degree of hydration expressed by WP. It should be kept in mind that parameter Al/H2O is in fact a combination of Al/Si, FDhyd, and WP by the following equation:

Al

H OFDWP S2

hyd=

+

29 891000

11

. **

*ii Al

. (12)


results

Correlations are used between the enthalpy of hydration per molecule of H2O and six parameters: Al/(Al + Si), Al/H2O, ∆HO=(site A), FDanh, FDhyd, and WP within different groups of zeolites distributed according to the nature of experimental data (Table 5). Contrary to what was observed by Carey and Nav-rotsky (1992) and Bish and Carey (2001), parameter Al/H2O (at saturation) is not a significant parameter explaining the enthalpy of hydration because of poor correlation coefficients (–0.193, –0.244, and –0.229 for zeolites from the “TTDC,” “IC,” and “TTDC + IC” groups, respectively).

As suggested by Wilkin and Barnes (1999), parameter Al/(Al + Si) appears as the one explaining the enthalpy of hydration within the majority of the experimental data derived from the

“TTDC” and “IC” measurement groups, separately. By plotting the enthalpy of hydration vs. Al/(Al + Si), it is observed noted that when Al/(Al + Si) increases, the enthalpy of hydration di-minishes more slowly within the IC data group than within the “TTDC” data group (Fig. 1). This difference in slope between the two most significant zeolite populations derived from the TTDC and IC calorimetric measurements suggests that for the same Al/(Al + Si) ratio, the measurements performed by TTDC calorimetry are more negative that those performed by immersion calorimetry. The two regression equations for “TTDC” and “IC” groups, displayed in Figure 1, indicate clearly that enthalpy of hydration is not equal to 0 for zeolites having no exchange cations in extra-framework sites [Al/Si and Al/(Al + Si) = 0]. These il-logicalities show that other ways exist to search for relationships between the enthalpy of hydration and parameters Al/Si or Al/

Table 4. Different regressions between following parameters: ∆HO=(site A), WD, Al/Si, FDanh, FDhyd, and Al/H2O All data (145 data) TTDC + IC groups (133 data) Al/H2O ∆HO=(site A) FDanh FDhyd Al/Si WP Al/H2O ∆HO=(site A) FDanh FDhyd Al/Si WPAl/H2O 1 –0.006 0.124 0.145 –0.121 –0.719 1 –0.007 0.156 0.178 –0.145 –0.730∆HO=(site A) –0.006 1 –0.038 –0.052 –0.057 –0.178 –0.007 1 –0.081 –0.098 –0.044 –0.158FDanh 0.124 –0.038 1 0.956 –0.409 –0.462 0.156 –0.081 1 0.952 –0.386 –0.461FDhyd 0.145 –0.052 0.956 1 –0.539 –0.530 0.178 –0.098 0.952 1 –0.529 –0.535Al/Si –0.121 –0.057 –0.409 –0.539 1 0.540 –0.145 –0.044 –0.386 –0.529 1 0.544WP –0.719 –0.178 –0.462 –0.530 0.540 1 –0.730 –0.158 –0.461 –0.535 0.544 1

TTDC group (76 data) IC group (57 data) Al/H2O ∆HO=(site A) FDanh FDhyd Al/Si WP Al/H2O ∆HO=(site A) FDanh FDhyd Al/Si WPAl/H2O 1 0.018 0.039 0.070 –0.032 –0.797 1 0.436 –0.012 –0.038 0.484 –0.448∆HO=(site A) 0.018 1 –0.109 –0.172 –0.210 –0.158 0.436 1 0.110 0.107 –0.126 –0.546FDanh 0.039 –0.109 1 0.914 0.421 –0.069 –0.012 0.110 1 0.991 –0.721 –0.749FDhyd 0.070 –0.172 0.914 1 0.308 –0.143 –0.038 0.107 0.991 1 –0.760 –0.744Al/Si –0.032 –0.210 0.421 0.308 1 0.310 0.484 –0.126 –0.721 –0.760 1 0.501WP –0.797 –0.158 –0.069 –0.143 0.310 1 –0.448 –0.546 –0.749 –0.744 0.501 1

Table 5. Different regressions concerning the enthalpy of hydration: ∆Hhyd-W, ∆Hhyd-W/(Al/Si), ln[–∆Hhyd-W/(Al/Si)] vs. ∆HO=(site A), EWD, Al/(Al + Si), FDanh, FDhyd, and Al/H2O

All data (145 data) TTDC + IC groups (133 data) ∆Hhyd-W ∆Hhyd-W/(Al/Si) ln[–∆Hhyd-W/(Al/Si)] ∆Hhyd-W ∆Hhyd-W/(Al/Si) ln[–∆Hhyd-W/(Al/Si)]Al/(Al + Si) –0.352 0.725 –0.833 –0.374 0.723 –0.834Al/H2O –0.224 –0.348 0.313 –0.229 –0.386 0.367FDanh –0.381 –0.388 0.586 –0.424 –0.354 0.548FDhyd –0.291 –0.464 0.670 –0.332 –0.448 0.654∆HO=(site A) 0.319 0.191 –0.158 0.360 0.203 –0.171WP 0.168 0.720 –0.732 0.172 0.739 –0.757

TTDC group (76 data) IC group (57 data) ∆Hhyd-W ∆Hhyd-W /(Al/Si) ln[–∆Hhyd-W /(Al/Si)] ∆Hhyd-W ∆Hhyd-W/(Al/Si) ln[–∆Hhyd-W /(Al/Si)]Al/(Al + Si) –0.678 0.595 –0.622 –0.497 0.862 –0.934Al/H2O –0.193 –0.297 0.303 –0.244 0.190 –0.270FDanh –0.520 0.040 0.089 0.046 –0.843 0.826FDhyd –0.462 –0.040 0.191 0.101 –0.844 0.843∆HO=(site A) 0.410 0.207 –0.206 0.293 –0.082 0.136WP 0.131 0.650 –0.652 –0.103 0.576 –0.568

figure 1. Relationships between the average enthalpy of hydration, (a) ∆Hhyd-W

and Al/(Al + Si) and between (b) ∆Hhyd-W/(Al/Si) and Al/(Al + Si).


(Al + Si) as these two parameters are related.When, for example, the enthalpy of hydration is divided by the

Al/Si ratio, i.e., (∆Hhyd-W)/(Al/Si), is plotted as a function of the Al/(Al + Si) parameter (Fig. 1b), the correlation lines calculated for each one of the four groups (except for GAC) show a con-vergence, i.e., a same slope. The correlation coefficients (Table 5) between (∆Hhyd-W)/(Al/Si) and the six parameters show that in all compounds (without distinction of the nature of the ther-modynamic measurements), in the majority of the compounds from the “TTDC” and “IC” groups and in the compounds from the “IC” group, the Al/(Al + Si) parameter appears as the best parameter explaining the (∆Hhyd-W)/(Al/Si) parameter. In the set of data derived from the high-temperature calorimetric data set (TTDC), the poorest correlation (R = 0.595) between (∆Hhyd-W)/(Al/Si) and Al/(Al + Si) is explained by the significant dispersion of the enthalpies of hydration of the partially hydrated β zeolites (Sun et al. 2006, 2007; Sun and Navrotsky 2008).

By assuming enthalpy of hydration is never endothermic and considering the Napierian logarithm of (∆Hhyd-W)/(Al/Si) as a function of Al/(Al + Si), a marked improvement is observed (Fig. 2) with respect to the previous figure. The correlation coefficients between ln[(–∆Hhyd-W)/(Al/Si)] and Al/(Al + Si) (Table 5) seem to improve in almost all populations (“TTDC + IC”, “all data,” and “IC”). The general equation for all zeolites is written as follows:

ln[(–∆Hhyd-W)/(Al/Si)] = A + B*[Al/(Al + Si)]. (13)

Developing and isolating ∆Hhyd-W gives:

∆Hhyd-W = –(Al/Si)*e{A + B*[Al/(Al + Si)]}. (14)

Parameters A and B, respectively, represent the intercept point and the slope of the regression line between ln[(–∆Hhyd-W)/(Al/Si)] and Al/(Al + Si). Consequently, the general relation-ships tested for the different zeolite groups give the following relationships:

● For all zeolites (without distinction of the nature of the calorimetric measurements, i.e., 145 data):

∆Hhyd-w = –(Al/Si)*e{5.443 – 4.283*[Al/(Al + Si)]}; R2 = 0.694. (15)

● For those zeolites derived from the two largest groups (TTDC + IC) (133 data):


● For those zeolites derived from the TTDC group (77 data):


● For those zeolites derived from the IC group (76 data):


Within the two largest population groups (“TTDC” and “IC”) derived from different measurement techniques, the relation-ship between ln[(–∆Hhyd-W)/(Al/Si)] and parameter Al/(Al + Si) displays roughly the same slope. This does not mean that for an equally charged compound (constant Al/Si), the thermody-namic measurements of the enthalpy of hydration by calorimetry (TTDC) will yield values that are more negative that those given by immersion calorimetry (IC). The reason for this is that the nature of the zeolites within each one of the “TTDC” and “IC” groups is highly diversified (Figs. 3a and 3b). A great difference between these two groups is readily observed. The “IC “group contains a few families of equally charged compounds (constant Al/Si) having the same structure but displaying a great diversity of cations located in the exchange sites A and a great variation in the number of water molecules bonded to the cations located in the exchange sites. By contrast, the “TTDC” group, to the exclusion of the β zeolite, Y zeolite, and clinoptilolite families, contains a multitude of isolated points (a single cation, a single structure, and a constant number of water molecules). To clear up this ambiguity, parameter ln[(–∆Hhyd-W)/(Al/Si)] was tested within a set of compounds characterized by different family groups having a similar structure and regardless of the nature of the measurements of the enthalpy of hydration.

Nine families of compounds were selected and are given in Table 6. The data obtained from a single type of measurement are derived from those compounds belonging to the β-, l-, X-, and A-zeolite and ferrierite families. In these series, each family has the same structure in which are located the different cations occupying the exchange sites A and a variable number of water molecules bound to the cations in the exchangeable sites. By contrast, those compounds belonging to the four zeolite families (Y-zeolite, clinoptilolite, chabazite, and mordenite) have enthalp-ies of hydration measured by at least two different techniques. Homogeneity is observed within the four families, each being characterized by a suitable crystal structure and a constant Al/Si ratio. The plots of ln[(–∆Hhyd-W)/(Al/Si)] vs. Al/(Al + Si) given in Figure 4 are directed to nine different groups of zeolite families (139 data). A relationship exists between ln[(–∆Hhyd-W)/(Al/Si)] and Al/(Al + Si) and is given by the following equation

figure 2. Relationships between ln[–∆Hhyd-W /(Al/Si)] and Al/(Al + Si).

0.0 0.2 0.4Al(Al + Si)


(R2 = 0.754):

ln[(–∆Hhyd-W)/(Al/Si)] = 5.491 – 4.674*[Al/(Al + Si)]. (19)

With (∆Hhyd-W)/(Al/Si), the correlation is not as good (R2 = 0.543) and gives the following equation:

(∆Hhyd-W)/(Al/Si) = –191.0 + 379.48*[Al/(Al + Si)]. (20)

The rearrangement of the Equation 19 leads to a direct rela-tionship between the enthalpy of hydration, ∆Hhyd-W and Al/Si:

∆Hhyd-w = –(Al/Si)*e{5.491 – 4.674*[Al/(Al + Si)]}. (21)

Improvement of the prediction of enthalpy of hydrationThe standard error of the enthalpy of hydration obtained with

Equation 21 is ±7.00 kJ/mol H2O. This large error is essentially related to the great dispersions of points observed within the different families having an identical Al/Si ratio, i.e., to the di-versity of the cations occupying the exchange site A, the nature of the zeolite structure and the number of water molecules of zeolites present in the different exchange sites at the time of the calorimetric measurements. Consequently, this model needs to be improved by using physico-chemical parameters obtained from quantifiable parameters for each zeolite.

For each zeolite, four parameters—framework density of anhydrous zeolite (FDanh), and of hydrated zeolite (FDhyd), mean ∆HO=cation in the exchangeable site A, and intracrystalline water porosity (WP)—were considered in this study and are calculated from the chemical formula and the unit-cell volume for each zeolite (Table 3).

By plotting ln[(–∆Hhyd-W)/(Al/Si)] as a function of the four

figure 3. Relationships between ln[–∆Hhyd-W/(Al/Si)] and Al/(Al + Si): (a) zeolites belonging to the TTDC group; (b) zeolites belonging to the IC group.

figure 4. Relationships between ln[–∆Hhyd-W/(Al/Si)] and Al/(Al + Si) within the nine different families of zeolites.

Table 6. Different families of zeolites selected in regression calcula-tions independently of the nature of measurements

Nat. Nb Al/Si Data sources meas. data mean std. dev. Zeolite BEA TTDC 28 0.07 0.00 Sun et al. (2006); Sun and Navrotsky (2008)Zeolite BEA-Li TTDC 8 0.33 0.00 Sun et al. (2007)Zeolite BEA-Na TTDC 11 0.27 0.00 Sun et al. (2007)Zeolite Y TTDC 6 0.40 0.01 Yang and Navrotsky (2000)Zeolite Y IC 9 0.43 0.01 Barrer and Cram (1971)Zeolite Y IC 4 0.42 0.01 Coughlan and Carroll (1976)Chabazite TTDC 1 0.46 – Shim et al. (1999)Chabazite TTDC 1 0.45 – Ogorodova et al. (2002a)Chabazite IC 6 0.41 0.00 Barrer and Cram (1971)Chabazite PE 1 0.46 – Fialips et al. (2005)Clinoptilolite HF 1 0.24 – Johnson et al. (1991)Clinoptilolite TTDC 5 0.22 0.00 Yang et al. (2001)Clinoptilolite IC 4 0.22 0.02 Carey and Bish (1997)Clinoptilolite GAC 3 0.19 0.01 Petrova et al. (2001)Clinoptilolite PE 5 0.23 0.00 Carey and Bish (1996)Zeolite L IC 4 0.33 0.00 Coughlan and Carroll (1976)Zeolite X IC 4 0.81 0.00 Coughlan and Carroll (1976)Zeolite X IC 10 0.83 0.00 Barrer and Cram (1971)Zeolite A IC 3 1.00 0.08 Coughlan and Carroll (1976)Zeolite A IC 8 1.00 0.06 Barrer and Cram (1971)Ferrierite IC 4 0.19 0.00 Barrer and Cram (1971)Mordenite IC 1 0.20 – Barrer and Cram (1971)Mordenite HF 1 0.19 Johnson et al. (1992a)Mordenite TTDC 1 0.33 Ogorodova et al. (2000)Note: Nb of data = 129.


parameters FDanh, FDhyd, ∆HO=(site A), and WP, for the nine zeolite families (129 data), several interesting observations can be made (Fig. 5).

The correlations between ln[(–∆Hhyd-W)/(Al/Si)] and param-eters FDanh (R2 = 0.499, Fig. 5a) and FDhyd (R2 = 0.555, Fig. 5b) are not as good as those observed with Al/(Al + Si) (Eq. 12). The small discrepancy between the correlation coefficients tested for FDanh and FDhyd shows that these parameters have the same effects on ln[(–∆Hhyd-W)/(Al/Si)] in the nine zeolite families. It appears clearly that the enthalpy of hydration will be a function of both parameters Al/(Al + Si) and FDanh (or FDhyd). For the same zeolite (constant framework density), the enthalpy of hydration is function of the ratio Al/(Al + Si).

Figure 5c displays the relationships between ln[(–∆Hhyd-W)/(Al/Si)] and ∆HO =(site A) within the nine families of zeolites [due to the weak dispersion of ∆HO=(site A) in the mordenite group, data from this group are not represented]. It appears that the correlation between ln[(–∆Hhyd-W)/(Al/Si)] and param-eter ∆HO=(site A) not only works for different families having constant framework density values and Al/Si ratios but also for constant saturation states. Correlation coefficients and regres-sion equations have been calculated for each family (Table 7) by considering the following linear expression:

ln[(–∆Hhyd-W)/(Al/Si)] = a*[∆HO=(site A)] + b. (22)

For each of the eight families (i.e., constant FD), ln[(–∆Hhyd-W)/(Al/Si)] decreases when parameter ∆HO=(site A) becomes more positive, i.e., from Zn2+[∆HO=(site A) = –168.59] to Cs+ [∆HO=(site

A) = +138.86]. This means that at constant Al/Si ratio, the enthalpy of hydration increases in the order Cs+ ≈ Rb+ < K+ < Na+ < Ba2+ ≈ Sr2+ ≈ Li+ < Ca2+ < Mg2+ ≈ Mn2+ ≈ Zn2+. The poor regression coefficient observed within the clinoptilolite family illustrates the problem of different results obtained from different measurement methods (HF, TTDC, IC, GAC, and PE) because different sets of water molecules are often involved as pointed by Bish and Carey (2001). In the β-zeolite series saturated by alkali and alkaline earth cations (Sun et al. 2006; Sun and Navrotsky

figure 5. Relationships between ln(–∆Hhyd-W/(Al/Si)] and parameters within the nine different families of zeolites: (a) anhydrous framework density FDanh; (b) hydrated framework density FDhyd; (c) average electronegativity of cations in site A, ∆HO=(site A); (d) water porosity.

Table 7. Different regressions concerning the enthalpy of hydration in different families of zeolites with constant FD and Al/Si (Eq. 22)

a b R2

Zeolite β* –0.003 4.80 0.83Zeolite β† –0.003 5.42 0.84Zeolite Y –0.001 3.78 0.40Chabazite –0.002 4.20 0.61Clinoptilolite –0.0004 4.85 0.02Zeolite L –0.005 4.62 0.86Zeolite X 0.0001 3.39 0.00Zeolite A –0.0001 3.21 0.04Ferrierite –0.0004 4.66 0.15* Fully hydrated.† Partially hydrated.


2008), there are, in reality, two sets of data: (1) corresponding to a high hydration state (empty triangles) and (2) correspond-ing to a partial hydration state (filled triangles). The number of water molecules is required to improve the relationships between enthalpy of hydration and parameter ∆HO=(site A).

For eight families, ln[(–∆Hhyd-W)/(Al/Si)] is plotted vs. WP (Fig. 5d) and gives a correlation of R2 = 0.527. However, in each one of the nine families (with the exception of clinoptilolite), a close correlation is observed between WP and ln[(–∆Hhyd-W)/(Al/Si)]. This means that in each family (constant FD), for a constant Al/Si ratio, a dependence is observed between water porosity WP close to maximum saturation and the nature of the cation located in the exchange site A defined by ∆HO=(site A). The Zn-, Mg-, Ca-, and li-bearing zeolites having a high content of water molecules are located toward high WP values, while the K-, Rb-, and Cs-bearing zeolites having a low water content are located toward low WP values. In the same way, at a given WP and constant Al/Si ratio, the average hydration enthalpy decreases from calcium-bearing zeolites to cesium-bearing zeolites. This suggests that the low water level in K-, Rb-, and Cs-bearing zeolites can be largely but not entirely attributed to the diminished available space due to large cations, along with the fact that the calculations of water porosity (WP) are based on a constant molecular volume of the water in zeolite channels as an assumption.

To show the influence of the nature of the cation and the charge on water porosity, we used the hydration enthalpy data measured under two or more hydration states. The thermody-namic data of beta-zeolites measured by Sun et al. (2006, 2007) and Sun and Navrotsky (2008) as a function of water porosity (WP) are represented in details in Figure 6a. Thirteen families of BEA zeolites were distributed into three data sets as follows: (1) enthalpies of hydration of low-charge beta-zeolites (Al/Si = 0.07) saturated by alkaline cations (points 1 to 5) and alkaline-earth cations (points 6 to 9); (2) enthalpies of hydration of high-charge Na- and li-beta-zeolites (Al/Si = 0.272 and 0.334) (lines a to d); and (3) enthalpies of hydration of high-charge beta-zeolites (Al

= 0.245) saturated by Ca and Mg (points e and f). All these data show that at constant Al/Si and ∆HO=(site A), ln[(–∆Hhyd-W)/(Al/Si)] decreases when the number of water molecules increases, i.e., WP increases. This fundamental property observed in this case corroborates the works of Bish and Carey (2001) and should be considered exclusively as a fundamental key in the develop-ment of a relationship between the enthalpy of hydration and the number of water molecules.

For the 13 families of BEA zeolites derived from the three groups, ln[(–∆Hhyd-W)/(Al/Si)] is expressed as a function of WP by the following equation:

ln[(–∆Hhyd-W)/(Al/Si)] = a*WP + b (23)

in which a and b values are determined by regression equations (Table 8). Considering the 9 points of low-charge BEA-zeolites (points 1 to 9), a correlation is observed between the slope a of Equation 23 and the nature of the cation [∆HO=(site A)]. This shows that for a similar variation in WP, the more electro-positive (i.e., the bigger) the cation, the greater the variation of ln[(–∆Hhyd-W)/(Al/Si)]. Considering the high-charge beta-zeolites (points a to f), observations are complicated by the presence of abnormal hydration enthalpy data from BEA zeolites saturated by li and Na in domains of very small WP values (lines a and c, Fig. 6a). These abnormalities are probably related to the difficulties in measuring the enthalpies of formation of totally anhydrous li- and Na-BEA zeolites. Excluding these two points and assuming a linear relationship between ln[(–∆Hhyd-W)/(Al/Si)] and WP for the four series of points from high-charge beta-zeolites (lines b and d, Fig. 6a), a relationship is also observed between the slope a of Equation 23 and the nature of the cation and presents a different value from that observed within the low-charge BEA-zeolites. These observations reveal that coefficient a in Equation 23 is not strictly constant but is thought to be related to the nature of the cation and also to the Al/Si charge. The theoretical WP is no longer independent on the nature of the cation and the charge, and may become a new parameter called effective water porosity

figure 6. (a) Relationships between ln[–∆Hhyd-W/(Al/Si)] and water porosity WP within the 13 different families of zeolites BEA. (b) Relationships between slope of Equation 23 (parameter a) and ∆HO=(site A) within the 13 different families of zeolites BEA (see Table 8 for labels 1 to 9 and a to f).


by the following equation:

EWP = WP*[∆HO=(site A)]*(Al/Si). (24)

General relationships of hydration enthalpy To improve the evaluation of the hydration enthalpy, (Eq.

19) in the nine zeolite families (129 points) and the six param-eters Al/(Al + Si), FDanh, FDhyd, ∆HO=(site A), WP, and EWP as defined previously may be considered in this work, which yields the following correlation equation:

ln[(–∆Hhyd-W)/(Al/Si)] = A + B*[Al/(Al + Si)] + C*FDanh + D*FDhyd + E*[∆HO=(site A)] + F*WP + G*EWP. (25)

Table 9 gives the correlation coefficients and the values of coefficients A to G of Equation 25 tested with different possible combinations of parameters. The enthalpy of hydration seems to be well explained by at least four parameters, i.e., the Al/Si charge, the density of the zeolite structure under anhydrous state FDanh, the nature of the cations located in the exchange sites ∆HO=(site A), and the effective water porosity of the WP zeolite (column 1 of Table 9). The density of the zeolite structure under hydrated state (FDhyd, columns 2 and 4) or the effective water porosity (EWP, columns 3 and 4) do not contribute to the improvement of the evaluation of hydration enthalpy. However, an improvement of Equation 25 is observed if water porosities

(independent of the nature of the cations and the charge) on the one hand and the contribution of the nature of the cations and the charge in the effective water porosity on the other hand are involved together (column 5 of Table 9). This shows that the water molecules taking part in the hydration mechanism in the channels are neither totally independent of nor totally dependent on the nature of the cations and the charge, but intimately inter-woven. This might explain that the volume of a water molecule is not strictly constant volume but might display a slight varia-tion related to the nature of the cation and to the total charge of the exchange site.

Testing again Equation 25 on all zeolites from the two major measurement groups (TTDC + IC, i.e., 133 data) yielded coef-ficients A to G of Equation 25 and correlation coefficients (Table 10). The results lead to the same conclusions as drawn from the previous case and, surprisingly, the correlation coefficients seem better than those given in Table 9.

The examination of the coefficients related to the five pa-rameters of column 11 of Table 10 shows that the variation in hydration enthalpy is very sensitive to the small variations in each one of the four physico-chemical entities. For example, when the Al/Si charge increases by 10%, the enthalpy of hydra-tion increases by 1.4 kJ/mol. The density of the zeolite structure under anhydrous state FDanh is a very sensitive parameter in the evaluation of the hydration enthalpy because a 2% increase in the unit-cell volume brings about an increase by 4–5 kJ/mol H2O for the enthalpy of hydration. When parameter ∆HO=(site A) increases by 50 kJ/mol (transition from Ca2+ to Mg2+, for example), the enthalpy of hydration decreases by 2–3 kJ/mol H2O. Concerning parameter WP, the value of which may theo-retically vary from 0 to a value corresponding to the maximum water porosity, the enthalpy of hydration decreases but the order of magnitude is essentially related to the nature of the cations. These values are given for information only and depend on the nature of the other parameters.

The standard errors are obtained through different populations of measurements: std. err. = ±4.29 kJ/mol for all data (145 data); std. err. = ±4.00 kJ/mol for TTDC and IC data (133 data), std. err. = ±5.02 kJ/mol for the “TTDC” data (76 data); and std. err. = ±2.68 kJ/mol for the “IC” data (57 data).

Table 8. Different regressions concerning the enthalpy of hydration in different families of zeolites with constant FD and Al/Si: ln[–∆Hhyd-W/(Al/Si)] = a*WP + b

Zeolite BEA Number ∆HO=(site A) Al/Si a b R2

of line (Fig. 6a) (kJ/mol) Li-BEA* 1 –75.34 0.069 –1.862 5.80 1Na-BEA* 2 –53.31 0.069 –1.871 5.81 1K-BEA* 3 32.41 0.074 –1.996 5.18 1Rb-BEA* 4 131.04 0.070 –2.047 5.00 1Cs-BEA* 5 88.22 0.073 –2.097 5.37 1Mg-BEA† 6 –159.79 0.076 –1.630 5.84 1Ca-BEA† 7 –114.11 0.080 –1.682 5.83 1Sr-BEA† 8 –64.31 0.079 –1.841 5.68 1Ba-BEA† 9 –58.83 0.080 –1.863 5.64 1Li-BEA‡ a –72.50 0.334 –1.644 5.40 0.710Li-BEA‡ b –72.50 0.334 –2.156 5.58 0.942Na-BEA‡ c 12.41 0.272 –1.364 4.65 0.522Na-BEA‡ d 12.41 0.272 –1.983 4.83 0.922Ca-BEA† e –101.26 0.247 –1.538 5.10 1Mg-BEA† f –147.10 0.245 –1.349 4.97 1* Sun et al. (2006).† Sun and Navrotsky (2008).‡ Sun et al. (2007).

Table 9. Different regressions concerning the enthalpy of hydration in nine families of zeolites (129 data) with six parameters: Al/(Al + Si); FDanh, FDhyd, ∆HO=(site A), WP, and EWP (Eq. 25)

Coeff. 1 2 3 4 5 6Constant A 4.450 4.376 3.774 3.569 4.347 4.276Al/(Al + Si) B –2.774 –2.761 –3.643 –3.565 –2.791 –2.777FDanh C 0.073 0.099 0.078 FDhyd D 0.079 0.113 0.084∆HO=(site A) E –0.002 –0.002 –0.003 –0.003 –0.003 –0.003WP F –1.554 –1.550 –1.441 –1.442EWP G 0.007 0.007 0.005 0.004R2 0.892 0.887 0.845 0.839 0.900 0.894Stand error (kJ/mol) ±4.62 ±4.70 ±5.08 ±5.21 ±4.37 ±4.47

Table 10. Different regressions concerning the enthalpy of hydration in the TTDC+IC populations (133 data) with six parameters: Al/(Al + Si), FDanh, FDhyd, ∆HO=(site A), WP, and EWP (Eq. 25)

Coeff. 7 8 9 10 11 12Constant A 4.780 4.620 3.907 3.459 4.698 4.516Al/(Al + Si) B –2.745 –2.628 –3.593 –3.357 –2.752 –2.625FDanh C 0.052 0.088 0.056 FDhyd D 0.062 0.116 0.067∆HO=(site A) E –0.002 –0.002 –0.003 –0.003 –0.003 –0.003WP F –1.682 –1.708 –1.565 –1.592EWP G 0.008 0.008 0.006 0.006R2 0.902 0.896 0.841 0.834 0.914 0.908

Stand err. All data (145 data)(kJ/mol) ±4.50 ±4.76 ±5.18 ±5.22 ±4.29 ±4.52TTDC+IC (133 data) (kJ/mol) ±4.26 ±4.52 ±5.10 ±5.23 ±4.00 ±4.26TTDC (76 data) (kJ/mol) ±5.16 ±5.55 ±6.62 ±6.77 ±5.02 ±5.41IC (57 data)(kJ/mol) ±3.11 ±3.35 ±3.14 ±3.46 ±2.68 ±2.93


Hydration enthalpies predicted from column 11 of Table 10 vs. measured hydration enthalpies are displayed in Figure 7 de-pending on the nature of the zeolite family. For each data outside the interval area (±4 kJ/mol H2O), a horizontal interval bar whose length is equal to the error of measurement was affected.

discussion

In Figure 7, it can be seen that the enthalpy of hydration of Na- and K-clinoptilolites from Wilkin and Barnes (1999) and chabazite from Fialips et al. (2005) obtained by phase equilibria are outside the interval area (points in dotted circle). The pos-sible sources of errors are probably related to the difficulty to obtain the indirect measurements required for extracting the enthalpy of hydration and also to the nature of the various bonds in zeolitic water.

When Al/Si and Al/(Al + Si) = 0, the hypothetical integral enthalpy of water in zeolites obtained by extrapolation of col-umn 11 of Table 10, is 0, which corresponds to the enthalpy of hydration of water in cordierite (2.2 ± 1.6 kJ/mol from Carey and Navrotsky 1992). Unlike zeolites, water in cordierite is not coordinated by cations, so the molecular environment of H2O in cordierite is similar to that of H2O in water. This shows that Equation 25 may serve as a predictive tool to model the enthalpy of hydration of water in zeolites.

As previously mentioned, hydration enthalpy data from BEA zeolites saturated by li and Na in domains of very small WP values might be in error, despite the large standard errors. All enthalpy of hydration values of lithium-saturated β-zeolites dis-play underestimated values with respect to experimental values. From NMR studies on zeolites BEA, Sun et al. (2007) showed that, in li-BEA, the Al atoms are mainly (87.5%) in the zeolitic

tetrahedral framework, while a small fraction (about 12.5%) is outside the framework, but the coordination is not well justified. One may wonder whether the presence of extra-framework Al atoms is involved in the overestimation of the enthalpy of hydration. By contrast, this abnormality is not observed on Na-BEA zeolites because the aluminum is all tetrahedral. From this observation, column 11 of Table 10 is recalculated without li-BEA (9 data) and rearranged:

∆Hhyd-W

Al/ A

AlSi

e

=−

−

*

. . *4 664 2 787 ll+Si FD O site Aanh H( )

+ − (=0 056 0 003. * . * ∆ ))

− +{ }1 520 0 0047. * . *WP EWP

(26)

The regression coefficient becomes better (R2 = 0.937) and the standard errors are obtained through different populations of measurements: std. err. = ±3.46 kJ/mol for all data (136 data); std. err. = ±3.07 kJ/mol for “TTDC” and “IC” data (124 data), std. err. = ±3.41 kJ/mol for the “TTDC” data (67 data) and std. err. = ±2.66 kJ/mol for the “IC” data (57 data). Table 111 gives the comparison of the experimental enthalpies of hydration vs. the predicted enthalpy of hydration from Equation 26.

It should be noted that the standard error within data derived from measurements by immersion calorimetry (±2.66 kJ/mol) is lower that that within data derived from high-temperature calorimetric measurements (±3.41 kJ/mol). This difference may have several causes. The mean values of k between both groups of population (“TTDC” and “IC”) remain the best explanatory parameter: among the zeolites derived from the high-temperature calorimetric measurement group, some display a very signifi-cant volume contraction during dehydration, which may have

figure 7. Relationships between the predicted enthalpy of hydration from column 11 of Table 10 and the measured enthalpy of hydration of all zeolites.


an effect on the architecture density as well as on the effective water porosity in some zeolites. All synthetic zeolites forming the bulk of the immersion calorimetric data yield very good results, which suggest that the effective water porosity could be considered as a simple function with the water content. These zeolites show indeed very small volume differences between the anhydrous state and the hydrated state, but the lack of data of partial hydration enthalpies in the different zeolites does not permit expression of the effective water porosity as a function of the number of water molecules.

The assumption of a linear relationship between the unit-cell volume and the number of water molecules (WP) on the one hand, and the contribution of both parameters WP and EWP in Equation 26 on the other hand are necessary to explain the dif-ferences in the enthalpies of hydration of β zeolites measured under two hydration states (Sun et al. 2006, 2007; Sun and Navrotsky 2008). On the one hand, this shows that different water types do not exist because water molecules form a sort of energy continuum (Bish and Carey 2001). The function relating the number of water molecules to the water porosity of a zeolite may depend on its hydration-dehydration behavior as a function of temperature. On the other hand, the volume of molecular water used in parameter WP is not constant but is believed to be slightly influenced by the nature of the cation and the charge. Therefore, in zeolites with a similar charge, the partial molar enthalpies of hydration-dehydration are believed to display a gradient related to the nature of the cation.

Please refer to the excellent work by Barrer and Cram (1971) who showed that within the four zeolites (NaX, NaY, NaA, and NaCa-bearing chabazite), the partial molar enthalpy as a function of the hydration degree may display different functions.

This is the reason why the fundamental relationship verifying the enthalpy of hydration by means of the chemical composi-tion and the accurate knowledge of the unit-cell parameters of anhydrous and hydrated zeolites needs to be improved by using new data of hydration enthalpy of the partially hydrated zeolites on the one hand, and a better fit of the effective water porosity as a function of the hydration degree on the other hand. Then, the thermodynamic description of the hydration-dehydration process can be modeled as a function of pressure and temperature with the contribution of predicted enthalpies of hydration and predicted entropies of hydration.

acknowledgmentsFinancial support for this report was partly provided by Centre National de la

Recherche Scientifique (CNRS, France) and Agence Nationale pour la gestion des Déchets Radio-Actifs (ANDRA, France). Two anonymous reviewers are thanked for their careful reviewing and their pertinent remarks. Nathalie Fradin is thanked for providing the linguistic reviewing. This is contribution CRPG no. 1948.

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Manuscript received May 26, 2008 Manuscript accepted noveMber 17, 2008Manuscript handled by david cole

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A predictive model for the enthalpies of hydration of zeolites