Enthalpy–entropy compensation for isosteric state adsorption at near ambient temperatures

Abstract

List of symbols AbstractThe adsorption process at near ambient temperatures indicated that the EEC (enthalpy-entropy compensation) is affected by three basic thermodynamic values: ∆H, ∆S and T. The consequence is that it is possible to determine an isosteric straight (symbol H − S) without experimental studies based on the slope coefficient T iso , which is the constant arising from the expected temperature range (about 0-60 °C). Therefore, EEC curves can be obtained by appropriate modification of the temperature range. In the case of entropy of adsorption, the decisive influence is the entropy of gas. For visualization and characterization of this impact, we proposed resolute pointer µ (Eq. 25), through which it is observed that for small values of the equilibrium vapor pressure, as P → 0, there are significant deviations from the isosteric straight H − S. The case where P → P 0 followed a gradual grouping of experimental data in accordance with the relationship with H − S. We used the three-parameter equation for exothermic processes. For the extrapolated conditions, the so-called point of zero adsorption represented the enthalpy and entropy of adsorption, whose values are analogous to previous results in the literature, which can be considered an appropriate analytical method to determine these two thermodynamic values.

Moisture sorption behavior and thermodynamic properties of dry‐crystallizedPalada payasam(rice flakes milk pudding) mix determined using the dynamic vapor sorption method

“…The net isosteric heat (q st ) and differential molar entropy (∆S) exhibited a linear relation (Figure 4) with coefficient of determination of R 2 of 0.9994, implying that the compensation existed between the two quantities. This linear relationship between q st and ∆S for water sorption has been previously reported for various food products (Fasina, 2006;McMinn, Al-Muhtaseb, & Magee, 2005;Mianowski & Urbańczyk, 2017;Pushpadass et al, 2014;Sharma et al, 2009;Thanuja & Ravindra, 2014).…”

“…The isokinetic temperature ( T B ) and free energy constant (∆ G ) estimated using Equation (9) by linear regression for all sets of data were obtained as 491.53 K and 1.129, respectively, whereas the value of harmonic mean temperature ( T hm ) derived from Equation (10) as 269 K. The statistical test proposed by Krug, Hunter, & Grieger, (1976), wherein if the condition of T B ≠ T hm with linear correlation between q st and ∆ S was satisfied, it was implied as a further validation of the compensation theory for the sorption process (Goula et al, 2008; Lamharrar et al., 2007; Mianowski & Urbańczyk, 2017). Furthermore, Leffler (1955) reported that, if T B > T hm , the process was enthalpy‐driven, while the sign of the value of ∆ G provided a means for prediction of spontaneity of water sorption; a negative sign was reflective of a spontaneous process and vice versa (Apostolopoulos & Gilbert, 1990).…”

“…The compensation theory proposes a linear relationship between net isosteric heat of sorption ( q st ) and change in differential molar entropy (∆ S ) as given in Equation (9) (Goula, Karapantsios, Achilias, & Adamopoulos, 2008; Lamharrar et al., 2007; Mianowski & Urbańczyk, 2017). …”

“…The isokinetic temperature (T B ) and free energy constant (∆G) estimated using Equation (9) by linear regression for all sets of data were obtained as 491.53 K and 1.129, respectively, whereas the value of harmonic mean temperature (T hm ) derived from Equation (10) as 269 K. The statistical test proposed by Krug, Hunter, & Grieger, (1976), wherein if the condition of T B ≠ T hm with linear correlation between q st and ∆S was satisfied, it was implied as a further validation of the compensation theory for the sorption process (Goula et al, 2008;Lamharrar et al, 2007;Mianowski & Urbańczyk, 2017).…”

Kinetics and Thermodynamics Studies of Copper(II) Adsorption onto Activated Carbon Prepared from Salacca zalacca Peel

“…The value of ∆H° gives information whether the adsorption is exothermic or endothermic. The adsorption process is exothermic if the value of ∆H° is negative and the adsorption process is endothermic if the value of ∆H° is positive (Denayer, and Baron, 2005;Miawnowski, and Urbanczyk, 2017). The value of ∆S° related to the degree of freedom of the adsorbed species.…”