Statistical Associating Fluid Theory Research Articles

Surface tension of droplets and Tolman lengths of real substances and mixtures from density functional theory

The curvature dependence of interfacial properties has been discussed extensively over the last decades. After Tolman published his work on the effect of droplet size on surface tension, where he introduced the interfacial property now known as Tolman length, several studies were performed with varying results. In recent years, however, some consensus has been reached about the sign and magnitude of the Tolman length of simple model fluids. In this work, we re-examine Tolman's equation and how it relates the Tolman length to the surface tension and we apply non-local classical density functional theory (DFT) based on the perturbed chain statistical associating fluid theory (PC-SAFT) to characterize the curvature dependence of the surface tension of real fluids as well as mixtures. In order to obtain a simple expression for the surface tension, we use a first-order expansion of the Tolman length as a function of droplet radius Rs, as δ(Rs) = δ0 + δ1/Rs, and subsequently expand Tolman's integral equation for the surface tension, whereby a second-order expansion is found to give excellent agreement with the DFT result. The radius-dependence of the surface tension of increasingly non-spherical substances is studied for n-alkanes, up to icosane. The infinite diameter Tolman length is approximately δ0 = -0.38 Å at low temperatures. For more strongly non-spherical substances and for temperatures approaching the critical point, however, the infinite diameter Tolman lengths δ0 turn positive. For mixtures, even if they contain similar molecules, the extrapolated Tolman length behaves strongly non-ideal, implying a qualitative change of the curvature behavior of the surface tension of the mixture.

Carbon dioxide solubilities in tricyanomethanide-based ionic liquids: Measurements and PC-SAFT modeling

This work reports the measurements of the solubility of carbon dioxide (CO2) in three tricyanomethanide based ionic liquids (ILs) constituted by different cations: 1-butyl-3-methylimidazolium, 1-butyl-4-methylpyridinium, 1-butyl-1-methylpyrrolidinium in order to investigate the effect of the cation on the solubility. The solubility of CO2 have been determined using high-pressure variable volume cell in a range of temperature from T = (292.13–367.85) K and pressure up to 121.6 bars. A high solubility of CO2 in the 1-butyl-4-methylpyridinium tricyanomethanide was observed in comparison with the other cation. It was found that the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) may be used to represent with good accuracy the experimental data of CO2 solubility in tricyanomethanide based ionic liquid.

Mutual Influence of Furfural and Furancarboxylic Acids on Their Solubility in Aqueous Solutions: Experiments and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) Predictions

Furan compounds are of mounting global interest due to their biorenewable nature and their potential to replace petroleum-based compounds as feedstocks in manufacturing. In this work the solubilities of furfural and the furancarboxylic acids 2-furoic acid (FA), 5-formyl-2-furancarboxylic acid (FFA), and 2,5-furandicarboxylic acid (FDCA) in aqueous solutions and organic solvents were investigated experimentally and by modeling with perturbed-chain statistical associating fluid theory (PC-SAFT). The PC-SAFT pure-component parameters of the solutes FA, FFA, and FDCA and one binary parameter between each solute and each solvent were adjusted to fit experimentally determined solubilities of each solute in each organic solvent or in water. Pure-component parameters of furfural were fitted to experimental density data and vapor-pressure data, and a binary interaction parameter was fitted to capture the solubility behavior of furfural in water. Modeling of pH effects enhanced predictions of the mutual influences ...

Extensive Study of the Capabilities and Limitations of the CPA and sPC-SAFT Equations of State in Modeling a Wide Range of Acetic Acid Properties

The accurate description of many thermodynamic properties of acetic acid and its mixtures can be a challenge to model with standard thermodynamic models such as local-composition activity coefficient models and cubic equations of state. A possible solution is offered by association equations of state, e.g., those belonging to the statistical associating fluid theory (SAFT) family. While several researchers have studied the use of SAFT variants to model acetic acid properties (pure compound and mixtures), with few exceptions, those studies focused exclusively on phase equilibria including vapor pressure and density. Other important properties, such as the speed of sound, second virial coefficient, compressibility factor, enthalpy of vaporization, and isobaric heat capacity have not been considered yet. Few studies investigate which is the appropriate association scheme to be used for acetic acid. In this work, we compare the capabilities of two association models, cubic plus association (CPA) and simplifie...

Combined Experimental, Theoretical, and Molecular Simulation Approach for the Description of the Fluid-Phase Behavior of Hydrocarbon Mixtures within Shale Rocks

An experimental, theoretical, and molecular simulation consolidated framework for the efficient characterization of the adsorption and fluid-phase behavior of multi-component hydrocarbon mixtures within tight shale rocks is presented. Fluid molecules are described by means of a top-down coarse-grained model where simple Mie intermolecular potentials are parametrized by means of the statistical associating fluid theory. A four-component (methane, pentane, decane, naphthalene) mixture is used as a surrogate model with a composition representative of commonly encountered shale oils. Shales are modeled as a hierarchical network of nanoporous slits in contact with a mesoporous region. The rock model is informed by the characterization of four distinct and representative shale core samples through nitrogen adsorption, thermogravimetric analysis, and contact angle measurements. Experimental results suggest the consideration of two types of pore surfaces: a carbonaceous wall representing the kerogen regions of a ...

Prediction of the temperature dependence of densities and vapor pressures of nonpolar hydrocarbons based on their molecular structure and refractive index data at 20 °C

In a previous publication, a one-parameter equation based on the perturbed chain version of the statistical associating fluid theory, assisted by a group contribution method (1P-PC-SAFT) was proposed for cases where limited experimental data are available (Evangelista and Vargas, Ind. Eng. Chem. Res., 2017). The method was proven to be robust when a single vapor pressure data point was used for the PC-SAFT parameter tuning. Motivated by this fact, a methodology for estimating a saturation data point from refractive index and molecular weight was developed in this work. The proposed correlations also represent an alternative method for calculating critical properties and acentric factor for non-polar hydrocarbons as a function of their molecular weight and refractive index. These alternative correlations to find critical properties can be readily applied to cubic equations of state or methods based on the principle of the corresponding states. The predictive capability of the proposed methodology was assessed over a wide range of temperatures and pressures. Average absolute deviations of 8.24% in vapor pressure and 2.04% in saturated liquid density were obtained for ten representative compounds consisted of aliphatic, aromatics, and cyclic nonpolar hydrocarbons. The results obtained in this work confirm that with the proposed methodology it is possible to relate molecular structure and refractive index of liquid nonpolar hydrocarbons at 20 °C to their density and vapor pressure at high temperatures.

Thermodynamics of carbon dioxide-hydrocarbon systems

Understanding the thermophysical properties for mixtures of CO2 and hydrocarbons at reservoir conditions is very important for the correct design and optimization of CO2-enhanced oil recovery and carbon storage in depleted oil or gas fields. In this paper, we present a comprehensive thermodynamic study of the prototype system (CO2 + n-heptane) comprising highly-accurate measurements of the saturated-phase densities, compressed-fluid densities, and bubble and dew points at temperatures from 283 K to 473 K and pressures up to 68 MPa over the full range of composition. We use these results to examine the predictive capability of two leading thermodynamic models: the Predictive Peng-Robinson (PPR-78) equation of state and a version of the Statistical Associating Fluid Theory for potentials of the Mie form, known as SAFT-γ Mie. Both of these models use group contribution approaches to estimate interaction parameters and can be applied to complex multi-component systems. The comparison shows that both approaches are reliable for the phase behavior. Neither model is entirely satisfactory for density, with each exhibiting absolute average relative deviations (AARD) from the experimental data of about 4% for the saturated-phase densities and 2% for the compressed-fluid densities; however, SAFT-γ Mie is found to be much more accurate than PPR-78 for the compressibility, with an overall AARD of 6% compared with 18% for PPR-78.

Thermodynamic Modeling of Multicomponent Liquid–Liquid Equilibria in Ionic Liquid Systems with PC-SAFT Equation of State

This work is a continuation and extension of previously published study showing that the perturbed-chain statistical associating fluid theory (PC-SAFT) is an efficient and robust approach for calculating thermodynamic properties of the mixtures containing ionic liquids (ILs) [J. Phys. Chem. B 2012, 116, 5002–5018]. The modeling strategy presented in the original paper was based on application of infinite dilution activity coefficients of molecular solutes in ILs (γ∞) to calculate binary corrections for the PC-SAFT combining rules. In this work, the idea is further investigated, in particular extended to a broader spectrum of pure fluids (the model parametrization is provided for almost 100 ILs), and evaluated based on a large compilation of liquid–liquid equilibrium (LLE) data, including more than 400 distinct and diverse ternary systems and a number of higher systems. Three PC-SAFT modeling strategies are proposed and systematically reviewed in order to elucidate an effect of γ∞ data on the quality of LL...

Oil desulfurization using deep eutectic solvents as sustainable and economical extractants via liquid-liquid extraction: Experimental and PC-SAFT predictions

The reduction of the sulfur content in crude oil is of utmost importance in order to meet the stringent environmental regulations. Thiophene and its derivatives are considered key substances to be separated from the crude oil. In previous works, six deep eutectic solvents (DESs) based on tetraethylammonium chloride, tetrahexylammonium bromide and methyltriphenylphosphonium bromide as hydrogen bond acceptors (HBAs) and polyols (ethylene glycol and glycerol) as hydrogen bond donors (HBDs) were successfully applied for the extraction of thiophene from {n-alkane + thiophene} mixtures via liquid-liquid extraction. One of the objectives of this work was to study the effect of the aliphatic hydrocarbon type/length (e.g. n-hexane vs n-octane) on the extraction performance of the same DESs. Extraction performance was evaluated by the selectivity and the thiophene distribution coefficient. Based on new experimental data, higher selectivities and lower thiophene distribution coefficients were obtained when thiophene was extracted from n-octane instead of n-hexane. Another objective was to predict the phase behavior of the ternary systems {n-alkane + thiophene + DES} using Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). The PC-SAFT “pseudo-pure component” approach was applied, in which a DES was considered as a pseudo-pure compound (not a mixture). The pure-component parameters of the DESs were obtained by fitting to liquid density data, which were measured at temperatures between 298.2 K and 323.2 K. Binary interaction parameters were fitted to experimental binary LLE data for the systems {n-alkane + DES} and {thiophene + DES} at 298.2 K and atmospheric pressure, while the LLE data of the ternary systems {n-alkane + thiophene + DES} were fully predicted. It was found that the distribution coefficients and selectivity of the ternary systems containing DESs could be qualitatively well predicted using this model.

Phase Equilibrium Study of the Ternary System CO2 + H2O + Ethanol At Elevated Pressure: Thermodynamic Model Selection. Application to Supercritical Extraction of Polar Compounds

The purpose of this study is to select an appropriate thermodynamic model among the ones available in commercial process simulators for representing the phase behavior of the carbon dioxide + ethanol + water system. The following versions of the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) cubic equations of state (EoS) were considered: Panagiotopoulos-Reid, modified Panagiotopoulos-Reid, Huron-Vidal-NRTL, Modified Huron-Vidal (MHV2-UNIFAC), Predictive Soave-Redlich-Kwong (PSRK) and Volume-Translated Peng–Robinson (VTPR). The Polar Perturbed-Chain SAFT EoS deriving from the Statistical Associating Fluid Theory (PPC-SAFT) was also selected for the present investigation. This study highlighted that the optimal thermodynamic models for the application of interest have to be chosen among the VTPR, PSRK and MHV2-UNIFAC EoS. Once identified a suitable thermodynamic model for the CO2 + ethanol + water ternary system, it has been possible then to simulate the extraction process of polar compounds from natural products and to discuss how water influences the process efficiency.

Viscosity Prediction for Petroleum Fluids Using Free Volume Theory and PC-SAFT

In this study, free volume theory (FVT) in combination with perturbed-chain statistical associating fluid theory is implemented for viscosity prediction of petroleum reservoir fluids containing ill-defined components such as cuts and plus fractions. FVT has three adjustable parameters for each component to calculate viscosity. These three parameters for petroleum cuts (especially plus fractions) are not available. In this work, these parameters are determined for different petroleum fractions. A model as a function of molecular weight and specific gravity is developed using 22 real reservoir fluid samples with API grades in the range of 22 to 45. Afterward, the proposed model accuracy in comparison with the accuracy of De la Porte et al. with reference to experimental data is presented. The presented model is used for six real samples in an evaluation step, and the results are compared with available experimental data and the method of De la Porte et al. Finally, the method of Lohrenz et al. and the method of Pedersen et al. as two common industrial methods for viscosity calculation are compared with the proposed approach. The absolute average deviation was 9.7 % for free volume theory method, 15.4 % for Lohrenz et al., and 22.16 for Pedersen et al.

Peng-Robinson-based association equation of state for hydrofluorocarbon refrigerants

The objective of this work was to develop an association equation of state for hydrofluorocarbons. The functional form of the proposed equation was the dimensionless Helmholtz energy given by the sum of two terms: one from a modified Peng-Robinson equation and the other from the Statistical Associating Fluid Theory equation. The equation included seven adjustable coefficients fitted, for each component, to pρT, vapour pressures, isochoric heat capacities and speeds of sound. The fluids studied were difluoromethane (HFC-32), pentafluroethane (HFC-125), 1,1,1,2-tetrafluoroethane (HFC-134a), 1,1,1-trifluoroethane (HFC-143a), and 1,1-difluoroethane (HFC-152a). The calculated percentage overall average absolute deviations were 2.084 in pρT, 5.278 in vapour pressures, 2.282 in saturated-liquid densities, 3.459 in isochoric heat capacities, 3.613 in isobaric heat capacities, and 4.637 in speeds of sound. Those results were significantly better than the accuracy of the standard Peng-Robinson equation for the fluids of interest. This work included an ancillary equation in the same formalism of the proposed equation of state but having only to the cubic term, thus constituting a refitted modified Peng-Robinson-like equation. Finally, this work also included a preliminary application to the system (HFC-32 + HFC-125) with AADs in pρT and in vapour pressures of 2.703 and 3.661%, respectively.

Experimental and predictive PC-SAFT modeling results for density and isothermal compressibility for two crude oil samples at elevated temperatures and pressures

Rapid growth in world oil demand is driving the oil and gas industry to search for petroleum in deep wells where elevated temperatures and pressures prevail. Accurate knowledge of thermodynamic properties such as density and isothermal compressibility at in-situ conditions is necessary to estimate the recoverable oil from these deep reservoirs. Yet, crude oil density data in the open literature for pressures exceeding 155 MPa are scarce or nonexistent.In this study, we present density data for two Gulf of Mexico crude oils at pressures from 3 to 276 MPa and temperatures up to 523 K. Measurements on the liquid fraction of the crude oil were made along three isotherms at temperatures T = (323, 423, and 523) K and at pressures from near-ambient platform to ultra-deep reservoir conditions. The liquid fraction of the crude oils or “dead” oils contained numerous components including alkanes, branched-alkanes, cyclo-alkanes, aromatics, resins, and asphaltenes. For simplicity, the composition of each dead oil was represented as three pseudocomponents - saturates, aromatics and resins, and asphaltenes. Methane gas at two concentrations (5 and 10 wt%) was added to the dead oils to obtain synthetic live crude oils. Experimental density data for the two live oil samples are also reported at four isotherms and similar pressure conditions. The uncertainty in the reported densty data is less than ±1%. A Tait relationship was used to correlate the measured density data; from this relationship, a reference value for isothermal compressibility was obtained. The present density and isothermal compressibility data have been compared with predictions from the Perturbed Chain version of the Statistical Associating Fluid Theory (PC-SAFT) without the use of any fitting parameters. A special set of new PC-SAFT parameters accurate for one-phase calculations at high-pressure, high-temperature conditions was used; these parameters were predicted with a knowledge of the measured aromaticity of the oil under investigation. Oil density values were predicted to within 1–4% of experimental values on average, and isothermal compressibility values were within 1–10% on average.

Light-scattering data of protein and polymer solutions: A new approach for model validation and parameter estimation

The development of separation processes for polymers or proteins from aqueous solutions requires a high amount of experimental effort, including phase-equilibrium data such as solid-liquid, liquid-liquid or vapor-liquid equilibria. This effort can be reduced by means of thermodynamic models. This work presents a new method for parameter estimation and validation of thermodynamic models by means of static-light-scattering (SLS) measurements. In this work the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) was used to predict directly the SLS data (Rayleigh ratio) of macromolecular solutions. In a first step, SLS data were measured for binary water/polyethylene glycol (PEG molecular weight ranging from 2000 to 12000 g/mol) mixtures and for binary water/lysozyme mixtures. Applying pure-component PC-SAFT parameters from literature, the SLS data of these binary mixtures were successfully predicted with PC-SAFT. In a second step, one binary interaction parameter between lysozyme and PEG was adjusted to new experimental SLS data of buffered PEG/lysozyme/water solutions with PEG6000 concentration of 20 g/L. Finally, SLS data for buffered ternary PEG/lysozyme/water solutions with PEG of different molecular weights (2000–12000 g/mol) and different concentrations (1–50 g/L) were accurately predicted with PC-SAFT. Thus, (1) the proposed approach allows predicting SLS data, and (2) the method provides an access to the estimation of model parameters by means of experimental SLS data, which are accessible with much less effort than experimental phase-equilibrium data.

Measurement and Modeling of Isobaric Vapor–Liquid Equilibrium of Water + Glycols

We present new experimental data on the isobaric vapor–liquid equilibria (VLE) of four binary mixtures of water with ethylene glycol, diethylene glycol, triethylene glycol, or tetraethylene glycol, measured at three different system pressures (0.05, 0.07, and 0.1 MPa). Water activity coefficients were estimated from the mixtures boiling temperatures and used to rationalize the effect of the increasing glycols chain length on the molecular interactions with water. The soft statistical associating fluid theory (SAFT) equation of state was used to describe the experimental VLE data of these highly nonideal systems, providing insights into the molecular interactions leading the macroscopic behavior of the mixtures. Glycols and water were both modeled as associating molecules, with models and parameters from previous works, in a transferable manner. Soft-SAFT accurately reproduces the experimental data using one single, state independent, binary interaction parameter to correct the mixtures dispersive energy. It is further shown that the parametrization obtained from the pure glycols can be used to provide accurate predictions of the water activities in aqueous solutions of PEGs of higher molecular weight (600–6000 g/mol) highlighting the soft-SAFT robustness and the soundness of the parametrization used.

Pure Substance and Mixture Viscosities Based on Entropy Scaling and an Analytic Equation of State

This study proposes a simple model for viscosities, based on entropy scaling, for real substances and mixtures. The residual entropy is calculated with the perturbed chain polar statistical associating fluid theory (PCP-SAFT). The model requires two or three pure component parameters, noting, however, that an entirely predictive group contribution approach as proposed in our previous work [Loetgering-Lin O.; Gross J. Ind. Eng. Chem. Res. 2015, 54, 7942–7952] gives also very good results. Overall, 140 real substances are considered with relative mean deviations from experimental data of about 5% (without excluding “outliers”). We performed molecular simulations for mixtures of simple model fluid in order to determine a suitable mixture model. A completely predictive approach for viscosities of real mixtures is thereby obtained. The model is evaluated for 566 mixtures with about 34,500 experimental data points of various complexity (i.e., nearly ideal systems as well as highly asymmetric mixtures). Mixtures...

In-situ determination of crystallization kinetics in ASDs via water sorption experiments

Amorphous solid dispersions (ASD) are intended to improve the bioavailability of poorly water-soluble active pharmaceutical ingredients. However, the development of long-term stable ASDs is often limited by the unwanted crystallization of the incorporated active pharmaceutical ingredient. Robust detection and quantification of crystal formation - especially at temperatures and humidites relevant for long-term storage tests - are essential for understanding crystallization phenomena. In this work, the crystallization kinetics in spray-dried nifedipine/poly (vinyl acetate) ASDs was investigated by measuring the time-dependent water sorption behavior at constant storage conditions. By coupling these experiments with thermodynamic predictions of the water sorption in amorphous and crystallized ASDs using the Perturbed-Chain Statistical Associating Fluid Theory, the amount of crystallized nifedipine as function of time could be determined in-situ just by weighing the ASD samples and without any calibration. The experimental findings were validated by X-ray diffraction measurements. Metastable ASDs with nifedipine contents between 70 wt% and 90 wt% were investigated at relative humidities between 60% RH and 90% RH and in a temperature range between 30 °C and 40 °C. Storage at high temperature and at high RH, and high nifedipine contents dramatically increased the crystallization rates.

Evaluation of Thermodynamic Models for Predicting Phase Equilibria of $$\hbox {CO}_{2}$$ CO 2 + Impurity Binary Mixture

For the design and operation of $$\hbox {CO}_{2}$$ capture and storage (CCS) processes, equation of state (EoS) models are used for phase equilibrium calculations. Reliability of an EoS model plays a crucial role, and many variations of EoS models have been reported and continue to be published. The prediction of phase equilibria for $$\hbox {CO}_{2}$$ mixtures containing $$\hbox {SO}_{2}$$ , $$\hbox {N}_{2}$$ , NO, $$\hbox {H}_{2}$$ , $$\hbox {O}_{2}$$ , $$\hbox {CH}_{4}$$ , $$\hbox {H}_{2}\mathrm{S}$$ , Ar, and $$\hbox {H}_{2}\mathrm{O}$$ is important for $$\hbox {CO}_{2}$$ transportation because the captured gas normally contains small amounts of impurities even though it is purified in advance. For the design of pipelines in deep sea or arctic conditions, flow assurance and safety are considered priority issues, and highly reliable calculations are required. In this work, predictive Soave–Redlich–Kwong, cubic plus association, Groupe Europeen de Recherches Gazieres (GERG-2008), perturbed-chain statistical associating fluid theory, and non-random lattice fluids hydrogen bond EoS models were compared regarding performance in calculating phase equilibria of $$\hbox {CO}_{2}$$ -impurity binary mixtures and with the collected literature data. No single EoS could cover the entire range of systems considered in this study. Weaknesses and strong points of each EoS model were analyzed, and recommendations are given as guidelines for safe design and operation of CCS processes.

New electrolyte SAFT-VR Morse EOS for prediction of solid-liquid equilibrium in aqueous electrolyte solutions

This work presents a new SAFT-VR Electrolyte equation of state (SAFT-VRE Morse EOS) that can predict solid-liquid equilibrium and second order derivative properties of electrolyte solutions. In this study, variable range statistical associating fluid theory (SAFT-VR Morse) EOS was extended to electrolyte solutions. In this model short-range interactions were mimicked by SAFT-VR Morse EOS, and long-range and solvation interactions were modeled by Debye-Hückle and Born terms respectively. Global ion parameters were adjusted using single electrolyte mean ionic activity coefficient (MIAC) and solution densities data at 25 °C and 1 atm. Using obtained ion-specific parameters, thermodynamic properties of aqueous electrolyte solutions such as MIAC, osmotic coefficient, vapor pressure, Gibbs free energy of hydration and excess enthalpy of solution were predicted without any adjustable parameter. Then, the model capability was evaluated in phase behavior calculations over a wide range of salt concentrations. In this respect, solid-liquid equilibrium (SLE) phase diagrams for mixed-electrolyte were predicted up to high temperatures. The results show that the model can predict the MIAC, osmotic coefficient, vapor pressure, and SLE of mixed electrolyte solutions up to 100 °C. Obtained results prove that SAFT-VRE Morse can efficiently be utilized for electrolyte solutions. We attribute this capability to utilizing the SAFT-VR Morse EOS as dispersion term.

Standard Gibbs Energy of Metabolic Reactions: III The 3-Phosphoglycerate Kinase Reaction.

The glycolytic pathway is one of the most studied metabolic pathways to date. This work focuses on determining the standard Gibbs energy of reaction (ΔRg0) of the first adenosine triphosphate-yielding reaction step of glycolysis, namely, the 3-phosphoglycerate kinase (PGK) reaction. Trustworthy values of ΔRg0 are required for thermodynamic approaches to determine single reaction conversions or even fluxes of metabolic reactions. In literature, the observed ΔRg0,obs values are usually determined directly from the experimental equilibrium composition data without accounting for the nonideality of the reaction mixture. That is the reason why the observed ΔRg0,obs values do not present consistent standard data as they are a function of the concentration, pH, and pMg. In this work, a combination of experimentally determined equilibrium composition data and activity coefficients of the reacting agents was used to determine ΔRg0 values for the temperatures 303, 313, and 323 K at pH 7. The activity coefficients were predicted with the thermodynamic model electrolyte perturbed-chain statistical associating fluid theory (ePC-SAFT). The ePC-SAFT parameters were taken from literature or fitted to new experimental osmotic coefficients. At 313.15 K, a value for ΔRg0 of −16.2 ± 0.2 kJ/mol was obtained. This value is about 4 kJ/mol less negative than what is usually considered as an accepted standard value. The reason behind this discrepancy was found to be the activity coefficients of the reacting agents, which dramatically influence the equilibrium position of the PGK reaction. On the basis of the temperature-dependent ΔRg0 values, the standard enthalpy of reaction was determined and found to be ΔRh0 = −49 ± 9 kJ/mol.