Thermodynamic Equilibrium Constants Research Articles

Temperature‐Dependent Left‐ and Right‐Twisted Conformational Changes in 1:1 Host‐Guest Systems: Theoretical Modeling and Chiroptical Simulations

An efficient strategy for high‐performance chiral materials is to design and synthesize host molecules with left‐ and right‐ (M‐ and P‐) twisted conformations and to control their twisted conformations. For this, a quantitative analysis is required to describe the chiroptical inversion, chiral transfer, and chiral recognition in the host‐guest systems, which is generally performed using circular dichroism (CD) and/or proton nuclear magnetic resonance (1H‐NMR) spectroscopies. However, the mass‐balance model that considers the M‐ and P‐twisted conformations has not yet been established. In this study, we derived the novel equations based on the mass‐balance model for the 1:1 host‐guest systems. Then, we further applied them to analyze the 1:1 host‐guest systems for the achiral calixarene‐based capsule molecule, achiral dimeric zinc porphyrin tweezer molecule, and chiral pillar[5]arene with the chiral and/or achiral guest molecules by using the data obtained from the CD titration, variable temperature CD (VT‐CD), and 1H‐NMR experiments. The thermodynamic parameters (ΔH and ΔS), equilibrium constants (K), and molar CD (Δε) in the 1:1 host‐guest systems could be successfully determined by the theoretical analyses using the derived equations.

Temperature-Dependent Left- and Right-Twisted Conformational Changes in 1:1 Host-Guest Systems: Theoretical Modeling and Chiroptical Simulations.

An efficient strategy for high-performance chiral materials is to design and synthesize host molecules with left- and right- (M- and P-) twisted conformations and to control their twisted conformations. For this, a quantitative analysis is required to describe the chiroptical inversion, chiral transfer, and chiral recognition in the host-guest systems, which is generally performed using circular dichroism (CD) and/or proton nuclear magnetic resonance (1H-NMR) spectroscopies. However, the mass-balance model that considers the M- and P-twisted conformations has not yet been established. In this study, we derived the novel equations based on the mass-balance model for the 1:1 host-guest systems. Then, we further applied them to analyze the 1:1 host-guest systems for the achiral calixarene-based capsule molecule, achiral dimeric zinc porphyrin tweezer molecule, and chiral pillar[5]arene with the chiral and/or achiral guest molecules by using the data obtained from the CD titration, variable temperature CD (VT-CD), and 1H-NMR experiments. The thermodynamic parameters (ΔH and ΔS), equilibrium constants (K), and molar CD (Δε) in the 1:1 host-guest systems could be successfully determined by the theoretical analyses using the derived equations.

Advanced thermodynamic approach to adsorption of charged adsorbates from aqueous electrolyte solutions

This study present estimation of the thermodynamic parameters and the influence of ionic activity coefficient on the thermodynamic equilibrium constant of adsorption of phosphates on fly ash. The adsorption was conducted over a wide range of initial phosphate concentrations at different pH values pH = (3; 7; 10). The adsorption results were treated using the Langmuir, Freundlich and Sips adsorption isotherms, which provide information about the maximum adsorption capacity. The Langmuir and Sips isotherms were a satisfactory fit to the adsorption data, especially at pH = 3, with an acceptable regression coefficient over the entire concentration range, Langmuir (r2 = 0.9737) and Sips (r2 = 0.9969). The estimated maximum phosphate sorption capacity of fly ash was 6.21 ± 0.68 (mmol·g−1) according to Langmuir and 4.19 ± 0.16 (mmol·g−1) according to the Sips model, at pH = 3.0. However, there is no data in the published literature for estimating the thermodynamic parameters of the phosphate adsorption process using thermodynamic models for activity coefficients. Novel approach of this paper was determination of the thermodynamic equilibrium constant and Gibbs free energy, using the Pitzer ion-interaction model to predict the nature of adsorption. The Pitzer-ion interaction model was used for the mixed ionic systems, taking into consideration the effect of other present ions besides phosphates in the equilibrium solution resulting from fly ash desorption. The procedure for comprehensive estimation of the ion activity coefficient at maximum adsorption capacity and the dimensionless thermodynamic equilibrium constant using Langmuir's and Sips’s constants was presented. The calculated value of the phosphate activity coefficient in the equilibrium solution was γH2PO4,e = 0.7003 ± 0.0027 and the converted molar activity coefficient was γH2PO4,e = 0.6903 ± 0.0027. The estimated values of Gibbs free energy were: ΔGL = −6.788 ± 0.521 kJ·mol−1 based on Langmuir equilibrium constant and ΔGa = −7.707 ± 0.527 kJ·mol−1 based on activity and thermodynamic equilibrium constant. According to Sips model, the adsorption process is even more spontaneous, with the Gibbs free energy calculated using the phosphate activity coefficient and the thermodynamic equilibrium constant, ΔGa = −9.707 ± 0.617 kJ·mol−1. Consideration of the ionic activity coefficient is particularly important for large, charged adsorbates at higher concentrations, as the absolute difference in free energy for adsorption is app. 12 %. The scientific contribution is reflected in obtaining the necessary and more accurate information for the improvement of adsorption processes and possibly for the upgrading of fly ash in overall wastewater treatment technology.

Evaluation of Thermodynamic Model of Pd(II) Complex Formation with Isosaccharinic Acid

Palladium-107 is one of the selected radionuclides in the safety assessment of geological disposal of radioactive waste. Although isosaccharinic acid (ISA) forms strong complexes with many elements and enhances element solubility, the thermodynamic evaluation of the complex of Pd with ISA has not been conducted. In this study, the solubility of Pd(OH)2 at pH 8.5–12.5 in the presence of ISA was investigated under inert gas (N2) atmosphere. Furthermore, the coordination state of aqueous Pd and ISA was investigated by X-ray absorption and Fourier transform infrared spectroscopy, respectively. According to experimental results, the number of OH ligands in the mixed complex depends on pH. The thermodynamic model and conditional equilibrium constants of the Pd-ISA complex were estimated by slope analyses of solubility experiments at different pH levels and ionic strengths based on the specific ion interaction theory. Hence, the impact of complexation with ISA on Pd(II) solubility under disposal conditions could be quantified using the proposed thermodynamic models in this study.

An Investigation into the Stability Source of Collagen Fiber Modified Using Cr(III): An Adsorption Isotherm Study.

The enhanced hydrothermal stability of leather, imparted by little Cr(III), has traditionally been ascribed to strong coordinate bonds. However, this explanation falls short when considering that the heat-induced shrinking of collagen fiber is predominantly driven by rupturing weak H-bonds. This study explored the stability source via adsorption thermodynamics using collagen fiber as an adsorbent. Eleven isotherm models were fitted with the equilibrium dataset. Nine of these models aptly described Cr(III) adsorption based on the physical interpretations of model parameters and error functions. The adsorption equilibrium constants from six models could be transformed into dimensionless thermodynamic equilibrium constants. Based on the higher R2 of the van't Hoff equation, thermodynamic parameters (∆G°, ∆H°, ∆S°) from the Fritz-Shluender isotherm model revealed that the adsorption process typifies endothermic and spontaneous chemisorption, emphasizing entropy increase as the primary driver of Cr(III) bonding with collagen. Thus, the release of bound H2O from collagen is identified as the stability source of collagen fiber modified by Cr(III). This research not only clarifies the selection and applicability of the isotherm model in a specific aqueous system but also identifies entropy, rather than enthalpy, as the principal stability source of Cr-leather. These insights facilitate the development of novel methods to obtain stable collagen-based material.

Comments on the calculation of thermodynamic adsorption equilibrium constant using the distribution coefficient in Journal of Molecular Liquids 380 (2023) 121725

This comment discussed the calculation of the standard equilibrium constant thermodynamic parameters about the paper published in Journal of Molecular Liquids 380 (2023) 121725. Recently, Khankhasaeva et al. (2023) published a high academic paper to reveal the adsorption kinetic and thermodynamic regularities of diclofenac (DCF) on Fe2O3-pillared montmorillonites (Fe-PMts). Although the author tries to convert the distribution coefficient (Kd) to the standard equilibrium constant (Ko), the calculation formula is incorrect due to the confusion of adsorbate and adsorbent. This creates dimension for Ko obtained from Eq. (2). In this comment, the origin and background of this kind of error is analyzed and the method for correcting the error is presented. We hope this comment clarifies the essence of calculating the standard equilibrium constant by using the distribution coefficient, so others avoid the propagation of this kind of error.

A new surface structural approach for modeling the charging behavior of kaolinite

The concentration of ions in equilibrium with soils and sediments is a function of various interconnected chemical reactions. The charging behavior of minerals provides a set of fundamental information required to model these interactions. Accordingly, in this study, the charging behavior of kaolinite was measured at three concentrations (0.004, 0.04 and 0.40 M) of three electrolytes (LiNO3, NaNO3 and KNO3) using potentiometric titration. The experimental data were described using the CD-MUSIC-G&T model in which ≡AlOH0.5−, ≡SiO− and ≡X− were defined as reactive functional groups on aluminol edge, silanol edge and basal planes, respectively. The charging behavior was a function of the type and concentration of the background electrolytes, but changes in the concentration more than changes in the type of electrolytes affected the surface charge. The thermodynamic equilibrium constants (logK) of the reactions of H+, Li+, Na+, K+ and NO3− with aluminol group were obtained as 9.50, 1.62, 1.37, 1.29 and 10.28 and with silanol group as 4.94, 1.58, 1.79, 2.03 and < −10, respectively. The logK of 4.94 shows that the interaction of H+ ion with the kaolinite ≡SiO− is much stronger than its interaction with the same group on the quartz. The capacitance of both inner and outer Stern layers was measured to be 1.94 F/m2, showing the strong interaction of electrolyte ions with the edge surface. In addition, the equilibrium constants of the reactions of Li+, Na+ and K+ with ≡X− group were obtained as −0.40, −0.02 and 0.32, respectively, which have the same order as reacted with the silanol group. At pH below pHPZC (i.e., <6.3 ± 0.2), increasing ionic strength reduced the surface charge of kaolinite; because increasing electrolyte concentration increased the negative charge on the silanol edge more than increasing the positive charge on the aluminol edge. In addition, it seems that the negative potential due to the isomorphic substitution in the polyhedrons near the edge of kaolinite poses an inward attractive force on the central cations of the edge polyhedrons, which in turn reduces the bonding capacity of ≡Al−OH0.5− and/or ≡Si−O−. Thereby, the adsorption energy of proton and cations on the edge surface may increase due to isomorphic substitution in adjacent polyhedrons.

A Review of the Essence of Stability Constants in the Thermodynamic Assessments of Chemical Compounds

Background: This treatise discusses the following topics: • Chemical compounds • Factors affecting stability of chemical compounds • Stability constants • The significance of stability constants vis-a-vis equilibrium constant, Keq The different forms of stability constant are reviewed and the thermodynamic assessment of stability constant is explained. Method: The approach involved the review from reputable authors and writers, of the topics that are associated with stability constant and the generalization is remarked following the thermodynamic assessment of the stability constant of chemical compounds. Findings: The thermodynamic analysis of stability constant of chemical compounds and of reactions shows that reactions proceed in the direction of decreasing Gibb’s free energy, G, where the standard reaction Gibb’s free energy, ∆rG0 = ∆fG0 (B) - ∆fG0 (A), defines the formation of the pure substance B, from the pure substance A, at its standard state. Conclusion: RTlnK = -∆r G0 is the link between thermodynamic data and the equilibrium constant (stability constant), K. When ∆r G0 &gt; 0, K &lt; 1 and at equilibrium the partial pressure of A exceeds that of B. This means that the reactant A is favored in the equilibrium. When ∆r G0 &lt; 0, K &gt; 1 and at the equilibrium the partial pressure of B exceeds that of A. The product B is favored in the equilibrium. The equation is an exact thermodynamic relation. The equilibrium constant, K, when expressed in terms of activities, is called a thermodynamic equilibrium constant

The influence of activity coefficient and equilibrium constant models on the speciation of aqueous solutions of H&lt;sub&gt;2&lt;/sub&gt;SO&lt;sub&gt;4&lt;/sub&gt;–MgSO&lt;sub&gt;4&lt;/sub&gt;–Al&lt;sub&gt;2&lt;/sub&gt;(SO&lt;sub&gt;4&lt;/sub&gt;)&lt;sub&gt;3&lt;/sub&gt; at 235 and 250°C

Supersaturation occurs in many industrial applications promoting reactive crystallisation between the reactants to form solutes. These solutes accumulate during precipitation, leading to the formation of scales on the inner walls of the reactor and particularly around the stirrer, causing modifications in the hydrodynamics. This encrustation is responsible for process shutdowns in continuous crystallisation processes. Supersaturation control is essential for industrial processes aimed at controlling or inhibiting the formation of these solids. Knowledge of mineral solubility and chemical speciation is required to account for the composition of the complexes in the system in their various solid or aqueous forms. This speciation is obtained by considering the thermodynamic equilibrium constants of the dissociation/complexation reactions involved in the system, the pressure, and the activity coefficients of the chemical species in their molecular or electrolyte form. From these thermodynamic quantities and the state of the system, we can predict the direction of the reaction. This study highlights the risk of the lack of experimental information on equilibrium constants at high temperatures and moderate pressures. Our goal is to evaluate the accuracy of existing models classically used to predict the equilibrium constant in such very hard conditions encountered in hydrometallurgical processes. Furthermore, we demonstrate the influences of equilibrium constants estimation and activity coefficient models on the speciation of H&lt;sub&gt;2&lt;/sub&gt;SO&lt;sub&gt;4&lt;/sub&gt;–Al&lt;sub&gt;2&lt;/sub&gt;(SO&lt;sub&gt;4&lt;/sub&gt;)&lt;sub&gt;3&lt;/sub&gt;–MgSO&lt;sub&gt;4&lt;/sub&gt; systems, forming hydronium alunite and kieserite in the laterite liquor of hydrometallurgical processes

Revisiting Isothermal Effectiveness Factor Equations for Reversible Reactions

Ion exchange resins have many industrial applications, namely as sorbents and catalysts. In solid-catalyzed reactions, intraparticle reaction-diffusion competition is generally described by effectiveness factors calculated numerically or analytically in the case of isothermal particles and simple rate laws. Although robust, numerical calculations can be time-consuming, and convergence is not always guaranteed and lacks the flexibility of user-friendly equations. In this work, analytical equations for effectiveness factors of reversible reactions derived from the general scheme A+B⇌C+D are developed and numerically validated. These effectiveness factors are analytically expressed in terms of an irreversible nth order Thiele modulus (specifically written for the nth order forward reaction), the thermodynamic equilibrium constant, the ratios of effective diffusivities, and the ratios of surface concentrations. The application of such analytical equations is illustrated for two liquid phase reactions catalyzed by Amberlyst-15, specifically the synthesis of ethyl acetate and acetaldehyde dimethyl acetal. For both reactions, the prediction of the concentration profiles in isothermal batch reactors achieved errors between 1.13% and 3.38% for six distinct experimental conditions. Finally, the impact of non-ideal behavior upon the multicomponent effective diffusivities, subsequently conveyed to the effectiveness factors, is enlightened.

Mechanically Robust and Room Temperature Self-Healing Ionogel Based on Ionic Liquid Inhibited Reversible Reaction of Disulfide Bonds.

Although highly desired, it is difficult to develop mechanically robust and room temperature self-healing ionic liquid-based gels (ionogels), which are very promising for next-generation stretchable electronic devices. Herein, it is discovered that the ionic liquid significantly reduces the reversible reaction rate of disulfide bonds without altering its thermodynamic equilibrium constant via small molecule model reaction and activation energy evolution of the dissociation of the dynamic network. This inhibitory effect would reduce the dissociated units in the dynamic polymeric network, beneficial for the strength of the ionogel. Furthermore, aromatic disulfide bonds with high reversibility are embedded in the polyurethane to endow the ionogel with superior room temperature self-healing performance. Isocyanates with an asymmetric alicyclic structure are chosen to provide optimal exchange efficiencies for the embedded disulfide bonds relative to aromatic and linear aliphatic. Carbonyl-rich poly(ethylene-glycol-adipate) diols are selected as soft segments to provide sufficient interaction sites for ionic liquids to endow the ionogel with high transparency, stretchability, and elasticity. Finally, a self-healing ionogel with a tensile strength of 1.65±0.08MPa is successfully developed, which is significantly higher than all the reported transparent room temperature self-healing ionogel and its application in a 3D printed stretchable numeric keyboard is exemplified.

Characterization of the Fe(III)-Tiron System in Solution through an Integrated Approach Combining NMR Relaxometric, Thermodynamic, Kinetic, and Computational Data.

The Fe(III)-Tiron system (Tiron = 4,5-dihydroxy-1,3-benzenedisulfonate) was investigated using a combination of 1H and 17O NMR relaxometric studies at variable field and temperature and theoretical calculations at the DFT and NEVPT2 levels. These studies require a detailed knowledge of the speciation in aqueous solution at different pH values. This was achieved using potentiometric and spectrophotometric titrations, which afforded the thermodynamic equilibrium constants characterizing the Fe(III)-Tiron system. A careful control of the pH of the solution and the metal-to-ligand stoichiometric ratio allowed the relaxometric characterization of [Fe(Tiron)3]9-, [Fe(Tiron)2(H2O)2]5-, and [Fe(Tiron)(H2O)4]- complexes. The 1H nuclear magnetic relaxation dispersion (NMRD) profiles of [Fe(Tiron)3]9- and [Fe(Tiron)2(H2O)2]5- complexes evidence a significant second-sphere contribution to relaxivity. A complementary 17O NMR study provided access to the exchange rates of the coordinated water molecules in [Fe(Tiron)2(H2O)2]5- and [Fe(Tiron)(H2O)4]- complexes. Analyses of the NMRD profiles and NEVPT2 calculations indicate that electronic relaxation is significantly affected by the geometry of the Fe3+ coordination environment. Dissociation kinetic studies indicated that the [Fe(Tiron)3]9- complex is relatively inert due to the slow release of one of the Tiron ligands, while the [Fe(Tiron)2(H2O)2]5- complex is considerably more labile.

Influence of the model used for the calculation of equilibrium constants at moderate temperature for electrolytes

The formation of a solid mineral deposit can cause major problems in the conduct of industrial processes such as high pressure acid leaching. Knowledge of the chemical speciation and solubility product of the mineral can help control or inhibit its formation. This speciation is based on knowledge of the thermodynamic equilibrium constants of the dissociation/complexation reactions involved in the system and their temperature dependence. It also depends on the concentration of the different species in the system, the pressure and the activity coefficients of the chemical species present in their molecular or electrolytic form. From these thermodynamic quantities and the state of the system, it is possible to predict the direction of evolution of the reaction, i.e. whether the reactants or the products of the chemical reactions are favoured. This work presents and compares different models for the calculation of activity coefficients for ionic strengths between 0.001 – 6 molal and the calculation of thermodynamic equilibrium constants at temperatures up to 300°C (at zero ionic strength). It confirms the need for reliable thermodynamic data for modeling aqueous systems.

Chemical speciation models based upon the Pitzer activity coefficient equations, including the propagation of uncertainties. III. Seawater from the freezing point to 45 °C, including acid-base equilibria

A quantitative understanding of pH, acid-base equilibria, and chemical speciation in natural waters including seawater is needed in applications ranging from global change to environmental and water quality management. In a previous study (Humphreys et al., 2022) we implemented a model of solutions containing the ions of artificial seawater, based upon the use of the Pitzer equations for the calculation of activity coefficients and including, for the first time, the propagation of uncertainties. This was extended (Clegg et al., 2022) to include the Tris buffer solutions that are used to calibrate the seawater total pH scale. Here we apply the same methods to develop a model of solutions containing the ions of standard reference seawater, based upon studies by Millero and co-workers. We compare the predictions of the model to literature data for: the dissociation of dissolved CO2 and bicarbonate ion; boric acid dissociation; saturation with respect to calcite, the ion product of water, and osmotic coefficients of seawater. Estimates of the uncertainty contributions of all thermodynamic equilibrium constants and Pitzer parameters to the variance of the calculated quantity are used to determine which elements of the model need improvement, with the aim of agreeing with properties noted above to within their experimental uncertainty. Further studies are recommended. Comparisons made with several datasets for carbonate system dissociation in seawater suggest which are the most reliable, and identify low salinity waters (S < 10) as a region for which dissociation constants of bicarbonate are not yet accurately known. At present, the model is likely to be most useful for the direct calculation of equilibria in natural waters of arbitrary composition, or for adjusting dissociation constants known for seawater media to values for natural waters in which the relative compositions of the major ions are different.

Revisiting the calculation of thermodynamic parameters of adsorption processes from the modified equilibrium constant of the Redlich–Peterson model

AbstractBACKGROUNDThe adsorption equilibrium constant of the Langmuir model (KL; L mol−1) has been applied as the standard thermodynamic equilibrium constant, , for calculating the thermodynamic parameters (∆G°, ∆S°, and ∆H°) of an adsorption processes by using the van't Hoff equation. Some authors have (directly and indirectly) applied the constant KRP (L kg−1) of the Redlich–Peterson model for such calculations. However, this is an incorrect application because the unit of KRP is not suitable (it is not an equilibrium constant). Its new adsorption equilibrium constant, Ke(RP) (L mol−1), was revisited based on aRP (L mol−1)g. In the literature, there is still uncertainty regarding the application of aRP as for calculating the thermodynamic parameters. Therefore, the present study aimed to evaluate the feasibility of applying Ke(RP) to calculate thermodynamic parameters using available literature data. The thermodynamic parameters obtained from Ke(RP) were compared to those from KL. A case study using a biosorbent for adsorbing methylene blue dye at different temperatures was carried out to re‐verify the feasibility.RESULTSThe Redlich–Peterson model is only valid when its exponent is in a strict range (0 ≤ g ≤ 1). The Redlich–Peterson model (68%; 227 observations collected from 52 published papers) describes adsorption equilibrium datasets better than the Langmuir model. The negative ΔG° values obtained based on Ke(RP) (11.7–47.6 kJ mol−1) were significantly different (p = 2.98 × 10−12) from those on KL (12.2–40.8 kJ mol−1). The magnitudes of ΔH° obtained based on Ke(RP) were significantly different (P &lt; 0.05) to those on KL; however, such differences did not affect conclusions drawn on dominant mechanism adsorption (physical or chemical). The magnitude of ΔH° for chemisorption (involved in covalent bonds) is higher than 200 kJ mol−1. For the case study, the ∆H° (kJ mol−1) and ∆S° [J mol−1 × K−1] values calculated based on Ke(RP) (11.65 and 111.5) were like those on KL (11.34 and 110.4, respectively).CONCLUSIONA new equilibrium constant, Ke(RP) (L mol−1), of the Redlich–Peterson model can be applied as for calculating the thermodynamic parameters (∆G°, ∆S°, and ∆H°) of an adsorption processes under specific cases (i.e., F, H, and L‐shaped adsorption isotherms). Most of the adsorption processes (98%) involve physical adsorption. © 2022 Society of Chemical Industry (SCI).

Influence of solvent and salt on kinetics and equilibrium of esterification reactions

The influence of the solvent N-methyl-2-pyrrolidone (NMP) and the salt LiCl on the esterification of acetic acid (HAc) or propionic acid (HProp) with ethanol (EtOH) was investigated. Reaction kinetics were measured at T = 323 K and p = 1.01325 bar using in situ FTIR spectroscopy. Further, a thermodynamic activity-based kinetic approach was applied to predict the influences of NMP and LiCl on kinetics and equilibrium using ePC-SAFT advanced. The mole-fraction-based ‘intrinsic’ reaction-rate constants and the thermodynamic equilibrium constants were determined using the activity-based kinetic approach. These reaction constants allowed predicting the influences of the reactant ratio, NMP, and LiCl on homogeneity, reaction kinetics, and equilibrium in good agreement with the experimental data. The activity coefficients of the acid allowed understanding the experimental findings: they decreased upon NMP addition, which explains the slower reaction kinetics with NMP and they increased upon LiCl addition, which explains the faster kinetics with LiCl.

Determination of association equilibrium constant from single molecule fluorescence localization microscopy.

Single molecule fluorescence localization microscopy provides molecular localization with a precision in the tens of nanometer range in the plane perpendicular to the light propagation. This opens the possibility to count molecules and correlate their locations, starting from a map of the actual positions in a single molecule super resolution image. Considering molecular pair correlation as an indication of interaction, and a way to discern them from free molecules, we describe a method to calculate thermodynamic equilibrium constants. In this work, we use as a test system two complementary homo-oligonucleotides, one strand marked with Cyanine 3.5 and the other with Alexa Fluor 647. Hybridization is controlled by the amount of each strand, temperature, and the ionic force, and measured in steady state emission. The same samples are examined in Stochastic Optical Reconstruction Microscopy (STORM) experiments with split-field simultaneous two-colour detection. The effect of multiblinking, labelling-detection efficiency, and determination of the critical distance for association are discussed. We consistently determine values in STORM coincident with those of the bulk experiment.

Investigation of Thermodynamic, Kinetic, and Isothermal Parameters for the Selective Adsorption of Bisphenol A.

Herein, a novel imprinted solid-phase extraction cartridge was fabricated to investigate the kinetic, thermodynamic, and isothermal parameters for the selective adsorption of Bisphenol A (BPA). The imprinted polymeric cartridges (BMC) for the BPA adsorption were fabricated in the presence of a template and functional monomer using the in situ polymerization technique. To prove the efficiency and selectivity of BMC, the nonimprinted polymeric cartridges (BNC) and the empty polymeric cartridges (EC) were also fabricated with and without functional monomer using the same manner for the preparation of BMC. The characterization of cartridges was performed by elemental analysis, Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy (SEM), Brunauer–Emmett–Teller (BET) surface area measurements, and swelling tests. BPA removal studies were performed by analyzing some parameters such as temperature, BPA concentration, flow rate, salt type, and concentration. The highest capacity was determined as 103.2 mg BPA/g polymer for a 0.75 mL/min flow rate of 0.75 M (NH4)2SO4 containing 200 mg/L BPA solution at 50 °C. NaOH (1.0 M) was used as a desorption agent. The reusability performance was examined by performing 10 consecutive cycles. The solid-phase extraction (SPE) performance was also checked to determine the enrichment and extraction recovery factors for tap water and synthetic wastewater samples. Temkin, Langmuir, Freundlich, and Dubinin–Radushkevich isotherm models were applied to BPA adsorption data examining the adsorption mechanism, surface properties, and adsorption degree. The most suitable isotherm model for BPA adsorption was determined as the Langmuir isotherm model. The thermodynamic parameters (ΔG°, ΔH°, and ΔS°) were investigated to reveal the thermodynamics of adsorption. Adsorption thermodynamic parameters (ΔH°, ΔS°, and ΔG°) were calculated using the thermodynamic equilibrium constant (thermodynamic equilibrium constant, K°) values that change with temperature. It was determined that BPA adsorption was spontaneous (ΔG° < 0) and endothermic (ΔH° > 0) and entropy increased (ΔS° > 0) at the temperatures studied in the BPA adsorption process. The rate control step in the adsorption process was examined by applying pseudo-first-order and pseudo-second-order kinetic models to the adsorption data for the investigations of BPA adsorption kinetics, and the pseudo-second-order kinetic model was found to be more suitable for describing BPA adsorption kinetics. In examining the selectivity of cartridges, structural analogues of hydroquinone, phenol, β-estradiol, and 8-hydroxyquinoline were tested.

Improper Estimation of Thermodynamic Parameters in Adsorption Studies with Distribution Coefficient KD (qe/Ce) or Freundlich Constant (KF): Considerations from the Derivation of Dimensionless Thermodynamic Equilibrium Constant and Suggestions

Adsorption processes often include three important components: kinetics, isotherm, and thermodynamics. In the study of solid–liquid adsorption, “standard” thermodynamic equilibrium constant [Formula: see text]; dimensionless) plays an essential role in accurately calculating three thermodynamic parameters: the standard Gibbs energy change (∆ G°; kJ/mol), the standard change in enthalpy (∆ H°; kJ/mol), and the standard change in entropy [∆ S°; J/(mol × K)] of an adsorption process. Misconception of the derivation of the [Formula: see text] constant that can cause calculative errors in values (magnitude and sign) of the thermodynamic parameters has been intensively reflected through certain kinds of papers (i.e., letters to editor, discussions, short communications, and correspondence like comment/rebuttal). The distribution coefficient ( K D) and Freundlich constant ( K F) have been intensively applied for calculating the thermodynamic parameters. However, a critical question is whether K D or K F is equal to [Formula: see text]. This paper gives (1) thorough discussion on the derivation of thermodynamic equilibrium constant of solid–liquid adsorption process, (2) reasonable explanation on the inconsistency of (direct and indirect) application of K D or K F for calculating the thermodynamic parameters based on the derivation of [Formula: see text], and (3) helpful suggestions for improving the quality of papers published in this field.

Exploring uncertainty in thermodynamic modeling of the lead carbonate aqueous system

Abstract Thermodynamic models of the lead carbonate aqueous system have been used in prior studies to evaluate the effect of water chemistry on lead solubility and corrosion scale composition in water distribution systems. A common challenge in these studies is uncertainty arising from the thermodynamic equilibrium constants (logK values) used to parameterize the models. The objective of this study is to evaluate the way in which uncertainty in logK values propagates through thermodynamic models of the lead carbonate system and provide guidance for future modeling efforts. This was done by conducting a full factorial statistical analysis implemented using a custom Python (v3) code coupled with a PHREEQC (v1.4.2) geochemical model, along with batch lead solubility experiments. Two lead carbonate solid phases (cerussite and hydrocerussite) and nine aqueous lead complexes are considered in the geochemical model with conditions simulated ranging from pH 4 to 11 and dissolved inorganic carbon (DIC) ranging from 0 to 250 mg C/L. Main effect analysis indicates that model uncertainty is predominately associated with logK values for five species (in order of decreasing effect): hydrocerussite, , cerussite, PbOH+, and PbCO3o, with model uncertainty varying depending on the specific pH and DIC conditions simulated. Interaction effects show that logK values cannot be selected independently, as their influence on lead solubility is connected. Finally, by considering uncertainty in logK values it was possible for the thermodynamic model to match batch hydrocerussite solubility experimental data over a range of pH and DIC conditions. Six combinations of logK values that provided a good match between the simulated and experimental data were determined with the average difference between the simulated and experimental lead concentrations calculated to be 0.031 mg/L when the recommended logK value combination was used.