sorption, adsorption, isobars, Zhurnal Fizicheskoi Khimii, Pleiades Publishing, Inc., experimental data, approximation results, adjustable parameters, hydrates, Russia, lithium bromide, Moscow State University, Water Vapor, Russian Journal of Physical Chemistry, Boreskov Institute of Catalysis, Siberian Branch, Russian Academy of Sciences, silica gel, Boreskov Institute of Catalysis, Siberian Division, Yu
Russian Journal of Physical Chemistry
, Vol. 79, No. 9, 2005, pp. 14901493. Translated from Zhurnal Fizicheskoi Khimii, Vol. 79, No. 9, 2005, pp. 16801683. Original Russian text
Copyright © 2005 by Tokarev, Okunev, Safonov, Kheifets, Aristov. English translation
Copyright © 2005 by Pleiades Publishing, Inc. PHYSICAL CHEMISTRY OF SURFACE PHENOMENA
Approximation Equations for Describing the Sorption Equilibrium between Water vapor
and a CaCl2-in-silica gel
Composite Sorbent M. M. Tokarev*, B. N. Okunev**, M. S. Safonov**, L. I. Kheifets**, and Yu. I. Aristov* * Boreskov Institute of Catalysis, Siberian Division, Russian Academy of Science
s, pr. Akademika Lavrent'eva 5, Novosibirsk, 630090 Russia ** Faculty of Chemistry, Moscow State University
, Vorob'evy gory, Moscow, 119899 Russia Received October 5, 2005 Abstract--The Polanyi potential F = RTln(p/ps) was demonstrated to adequately describe the sorption equilibrium between water vapor and a CaCl2-in-silica gel composite sorbent. Approximation formulas for calculating the dependence of the value of adsorption of water on F and the dependence of heat of sorption on the adsorption value were derived. A comparison of experimental and theoretical data for a temperature-independent curve and sorption isobars was performed.
Recently, a number of composite water sorbents of salt-in-porous matrix type have been synthesized. Halogenides , sulfates , and nitrates  of alkaline and alkaline-earth metals in silica gels, aluminum oxide, porous carbons, and other  matrices were used. Isobars and/or isotherms of sorption of vapor on these sorbents were measured over a wide range of temperatures. In , the possibility of using the Henry, Freundlich, DubininAstakhov, and BrunauerEmmett Teller equations for describing the activity of water in aqueous bulk solutions of H2SO4, CaCl2, LiBr, LiCl, LiI, MgCl2, and NaOH and in solutions of CaCl2 and LiBr in pores of silica gel, aluminum oxide, and porous carbon was explored. It was found that solutions in pores can be adequately described using the Polanyi adsorption potential in the form
F = RTln(p/ps),
where T is the temperature, K; p is the pressure in the gas phase; ps is the saturation pressure of water vapor at T; and R is the universal gas constant. This potential was introduced by Dubinin  based on the Polanyi potential theory of adsorption . At the same time, the best description of the experimental dependence of the sorption value A was obtained not within the framework of the DubininAstakhov equation  but by using the polynomial
lnA = a + bF + cF2,
where a, b, and c are empirical coefficients. For exam- ple, for SSV-1M sorbent (CaCl2 in KSM silica gel), the relative Standard deviations
between the calculated data from the experimental were found to be 1.5 and 0.5% for the first and second equations, respectively .
Similar results were obtained for lithium bromide aqueous solution
s in pores of alumina and carbon . For all of the three sorbents, the sorption of water was not accompanied by the formation of crystal hydrates of fixed composition and, therefore, the composition of the system varied continuously. As a result, the sorption isobars were smooth functions of the temperature and could be readily described analytically. The isobars for SSV-1K sorbent (CaCl2 in KSK silica gel) exhibited sharp transitions associated with the formation of crystal hydrates of constant composition (CaCl2 · (H2O)N, where N = 1/3, 2, and 4 ). In the region of these transitions, the lithium bromidewater system
is monovariant. At N > 4, an aqueous solution of calcium chloride
is formed in the pores and the system becomes divariant. Previously, equilibrium sorption was analytically described by the equation lnp(H2O) = a(T) + b(T)/T, where a(T) = a0 + a1T + a2T2 + a3T3 + a4T4, b(T) = b0 + b1T + b2T2 + b3T3 + b4T4. The equation contains ten adjustable parameters . These parameters were determined by fitting this equation to isosteres of sorption of water on SSV-1K sorbent. The isosteres were not measured directly--they were calculated from the experimental isobars obtained in , a procedure that may incur uncontrollable errors. Consequently, the initial isobars could be satisfactorily described by the above polynomial only within a narrow range of sorption values (2 < N < 4). In this work, the isobars of sorption of water by SSV-1K composite were described by a polynomial with the F potential used as the variable over a wide range of sorption vari-
APPROXIMATION EQUATIONS FOR DESCRIBING THE SORPTION EQUILIBRIUM N, mol/mol 15
Fig. 1. Temperature-independent curve of sorption of water vapor by SSV-1K composite. The lines and points show the experimental data
and approximation by Eq. (2), respectively.
ation of 2 < N < 10, so that the regions of formation of crystal hydrates and solutions were covered.
APPROXIMATION OF DEPENDENCE OF ADSORPTION OF WATER ON THE POLANYI POTENTIAL
To approximate the generalized dependence of the sorption of water vapor N (mol/mol) on SSV-1K sorbent on the F (J/mol) potential, we used the polynomial
lnN = a + bF + cF2,
where a, b, and c are adjustable coefficients. The exper- imental dependence N = f(F) (Fig. 1) exhibited several segments with sharp transitions between them:
Since it was impossible to approximate the stepwise transitions by a single polynomial, each segment (except for the last one) was approximated separately with the corresponding set of the adjustable coefficients. In addition, within the second segment, the
experimental points exhibited a significant scatter; therefore, the points located markedly above the main body of points  were excluded from consideration. The approximation results are listed in Table 1. Figure 1 shows the calculated temperature-independent curves of sorption for both segments (solid line
s). The curves satisfactorily describe the experimental data  over the entire range of variation of F. Figure 2 shows the experimentally measured isobars of sorption and those calculated by Eq. (2) using the coefficients listed in Table 1. It is obvious that the initial isobars are satisfactorily described by the suggested approximation over the entire range of sorption values (2 < N < 10). Note, however, that the proposed approximation failed to describe the experimental data at N < 2 because of the sorption value being sharply dependant on the Polanyi potential in this region, a behavior reflecting the specifics of the physicochemical processes in the system . In addition, as can be seen from Fig. 2, the approximation curves deviated from the experimental data in the regions of existence of hydrates (within N = ±0.06); small as it is, this deviation may appear critical for certain analytical calculations. The simplest way to
Table 1. Values of the adjustable coefficients a, b, and c in Eq. (2) that provided the best approximation of the two segments of the temperature-independent curve of sorption of water by SSV-1K composite
c Ч 109
3.0133 Ч 104
RUSSIAN Journal of Physical Chemistry
Vol. 79 No. 9 2005
1492 N, mol/mol
8 1 4
TOKAREV et al. solve the problem is to divide the entire range of sorption into a large number of segments and describe each segment by a separate approximation equation. For example, by dividing the sorption range into six segments, it is possible to describe the equilibrium curves of the sorption more accurately. Results of such an analysis are shown in Table 2 and Figs. 3 and 4; as can be seen, the measured and calculated data agree closely for both the temperature-independent curve and the sorption isobars.
Fig. 2. Isobars of sorption of water vapor on SSV-1K composite. The points and lines are the experimental data (at water vapor pressure
s of (1) 8.7, (2) 12.4, (3) 23.4, (4) 31.6, (5) 70.6, and (6) 133 mbar) and approximation by Eq. (2), respectively.
2 4 6 8 10 12
Fig. 3. Temperature-independent curve of sorption of water vapor on SSV-1K composite. The experimental data and approximation by the equations from Table 2 are designated by points and lines, respectively.
N, mol/mol 12 2 3 5 6 4 8 1 4
0 20 40 60 80 100 120 140 t, °C Fig. 4. Isobars of sorption of water vapor on SSV-1K composite. The points and lines represent, respectively, the experimental data and approximations by the equations from Table 2.
APPROXIMATION OF THE DEPENDENCE OF THE HEAT OF SORPTION ON THE ADSORPTION OF WATER
For many numerical calculations, e.g., simulations of dynamic adsorption processes, it is necessary to use approximation formulas for the isosteric heat of sorption, the derivation of which was another task of this work. The isosteric heat of adsorption was calculated as follows. Expressing ps in terms of the ClapeyronClausius equation for saturated water vapor,
ln(ps) [mbar] = C L/(RT),
(where L = 43450 J/mol is the heat of evaporation of water and C = 20.96), and substituting it into the Polanyi Eq. (1), we obtained
lnp = C (L + F)/RT.
Interpreting this formula in terms of the Clapeyron Clausius equation yielded the following results. By definition, at N = const, the isosteric heat of adsorption H (H < 0) is given by d(ln pH2O )/d(1/RT). Consequently, by virtue of the hypothesis that N and F are uniquely related, at F = const, we have
H = L + F.
This expression agrees with the results obtained in [14, 15] if the latter are modified on the assumption that the adsorbate density is temperature-independent. The physical meaning of Eq. (3) is that the adsorption of one mole of water is accompanied by the liberation of heat
H, kJ/mol 70 2 50 1 0 2 4 6 8 10 12 14 N, mol/mol Fig. 5. Dependence of the heat of sorption H on the sorption value: (1) calculated and (2) calorimetrically measured .
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 9 2005
APPROXIMATION EQUATIONS FOR DESCRIBING THE SORPTION EQUILIBRIUM
Table 2. Approximation formulas for calculating the dependence of N on F obtained by dividing the temperature-independent curve into six segments
No. F, kJ/mol
>5.322 4.869ln(F) +12.231 0.31
2 5.3225.7839 2.2137F + 15.932
3 5.783910.5 0.058917(F10.5)2
4 10.510.84 2.6387F + 29.521
5 10.8411.15 1.2533F + 14.512
55.731exp(0.4155F) 6.5 Ч 103
in the quantity required for a reversible isothermic transfer of one mole of adsorbate from the liquid to the gas phase plus for a change in the enthalpy of one mole of gas associated with the decrease of the pressure from ps (saturation vapor pressure) to the initial pressure p. Using the above approximation formulas for the dependence of the adsorption value on the Polanyi potential and Eq. (3), one can easily calculate the dependence of the isosteric heat of adsorption on the sorption value N (Fig. 5). A comparison of these data with the results of the calorimetric measurements performed in  shows that the analytic equations derived adequately describe the qualitative behavior of the dependence of the heat of sorption on the sorption value (Fig. 5). At N > 2, the heat is approximately equal to the heat of evaporation of an aqueous solution of calcium chloride (H 45 kJ/mol) and is virtually constant. In the region of formation of CaCl2 dihydrate, a sharp increase in H is observed, an effect associated with the stronger bonding of water molecules
in the hydrate. The differences in the absolute value of heat of sorption at high sorption values (in the region of formation of solutions) and in the region of existence of hydrates were found to be 24 kJ/mol (close to RT 2.5 kJ/mol) and 1520 kJ/mol, respectively. The difference between the values of heat of sorption in the region of formation of hydrates exceeds significantly RT. This phenomenon requires further analysis.
ACKNOWLEDGMENTS This work was supported by the INTAS, grant no. 03-51-6260. REFERENCES 1. Yu. I. Aristov, M. M. Tokarev, G. DiMarko, et al., Zh. Fiz. Khim. 71, 253 (1997) [Russ. J. Phys
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RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 9 2005
MM Tokarev, BN Okunev, MS Safonov