Antoine Equation Research Articles

Derivation of full range vapor pressure equation from an arbitrary point

An equation was proposed to obtain the full range of vapor pressures (VPs) for a substance at an arbitrary point of VP data. The basic model is a vapor pressure equation in the form of a reduced Antoine equation derived from the van der Waals equation. Here, Antoine constant C is defined as c by dividing it into gas constant and critical temperature, and is expressed as a polynomial function of reduced temperature. Previously, the exponents were integers, but have been improved to real numbers. Edmister’s formula is a special case in which the Antoine constant C divided by the critical temperature in Chen’s equation is 0. Since this is equivalent to polynomial of c being zero, the intercept can be set to zero. The results, estimated using the derived equation, were compared with VP data for 76 substances. The error rate of the equation using the acentric factor as a variable was 0.49%. This was lower than the 0.50% error rate of the Lee-Kesler method. Meanwhile, by using the correlation between the coefficients, the VP equation can be derived at any one point of VP data other than the acentric factor. For 76 substances, the equation derived from the corresponding VPs at reduced temperatures of 0.25 ∼ 0.95 in increments of 0.05 showed a mean error rate of 0.68%. This can be considered an accuracy equivalent to the Lee-Kesler method, which has the limitation of deriving a VP equation only at the reduced temperature of 0.7.

Investigation on Saturation Vapor Pressure of NH3–H2O–LiBr in Absorption Energy Storage System

Energy storage technology applied between building energy and renewable energy exhibits inherent characteristics of continuity, stability, and high efficiency of energy density. To improve the energy storage density and efficiency of solution absorption energy storage system, an innovative method is proposed by adding ammonia to regulate the saturated vapor pressure of Lithium Bromide solution, which is used as the energy storage working fluid for the absorption energy storage system. Based on the static method principle of vapor–liquid equilibrium of multiple working fluids, a testing platform for the vapor pressure of multiple working fluids was built. The pressure of the Lithium Bromide solution and the Lithium Bromide solution added Ammonia with a concentration of 58% were measured. The results show that the pressure of the Lithium Bromide solution added Ammonia is 2–5 times higher than that of the Lithium Bromide solution. The maximum relative deviations between the calculated value of the models fitted by Antoine equation and Peng Robinson state equation and the experimental value are 4.65% and 10.88%, respectively. That indicates that the model fitted by Antoine equation is more precise for the calculation of the equilibrium pressure of the ternary working fluid. The equilibrium pressure of the Lithium Bromide solution added Ammonia is predicted by the model fitted by the Antoine equation.

Equilibrium vapor pressure of aqueous sodium acetate and potassium acetate solutions used as working fluids in frost-free air–source heat pumps at 263–328 K

Aqueous solutions of sodium acetate (CH3COONa) and potassium acetate (CH3COOK) are considered effective alternative heat exchange media for frost-free air–source heat pumps (FFASHPs) owing to the low corrosiveness, low viscosity, and low cost. Equilibrium vapor pressure is the most crucial property that characterizes freezing point and latent heat transfer. However, studies on this property, especially in subzero temperature ranges are scarce. This study was conducted to experimentally investigate the equilibrium vapor pressure of CH3COONa and CH3COOK solutions. The developed apparatus and procedures were based on the static method, and validated by evaluating the vapor pressure of distilled water, n-heptane, and calcium chloride (CaCl2) aqueous solution. Their average absolute deviations were within 1.94%. As the temperature increased from 263 to 328 K and solute concentration increased from 9.27 to 33.81 wt%, 124 data points of the vapor pressure of the CH3COONa and CH3COOK solutions were obtained, ranging from 0.2759 to 13.2608 kPa. Modified Antoine equation and ion interaction (Pitzer) model were established for correlation of the experimental data. The average absolute deviations of the CH3COONa and CH3COOK solutions produced by Antoine equation were 2.08 and 2.48%, respectively. Those produced by Pitzer model further decreased to 1.36 and 1.45% due to the import of osmotic coefficient and the accuracy improvement. Furthermore, according to the experimental and calculation results, the vapor pressure of the CH3COONa solution was lower than that of the CH3COOK solution. Therefore, under the same antifreezing conditions, the CH3COONa solution facilitates latent heat absorption from ambient air, while the CH3COOK solution is conducive to achieve regeneration. The results of this study provide foundational data for the vapor pressure of the two solutions and can promote their application in FFASHPs.

Vapor Pressure and Enthalpy of Vaporization of Guanidinium Methanesulfonate as a Phase Change Material for Thermal Energy Storage.

This paper reports the vapor pressure and enthalpy of vaporization for a promising phase change material (PCM) guanidinium methanesulfonate ([Gdm][OMs]), which is a typical guanidinium organomonosulfonate that displays a lamellar crystalline architecture. [Gdm][OMs] was purified by recrystallization. The elemental analysis and infrared spectrum of [Gdm][OMs] confirmed the purity and composition. Differential scanning calorimetry (DSC) also confirmed its high purity and showed a sharp and symmetrical endothermic melting peak with a melting point (Tm) of 207.6 °C and a specific latent heat of fusion of 183.0 J g-1. Thermogravimetric analysis (TGA) reveals its thermal stability over a wide temperature range, and yet three thermal events at higher temperatures of 351 °C, 447 °C, and 649 °C were associated with vaporization or decomposition. The vapor pressure was measured using the isothermogravimetric method from 220 °C to 300 °C. The Antoine equation was used to describe the temperature dependence of its vapor pressure, and the substance-dependent Antoine constants were obtained by non-linear regression. The enthalpy of vaporization (ΔvapH) was derived from the linear regression of the slopes associated with the linear temperature dependence of the rate of weight loss per unit area of vaporization. Hence, the temperature dependence of vapor pressures ln Pvap (Pa) = 10.99 - 344.58/(T (K) - 493.64) over the temperature range from 493.15 K to 573.15 K and the enthalpy of vaporization ΔvapH = 157.10 ± 20.10 kJ mol-1 at the arithmetic mean temperature of 240 °C were obtained from isothermogravimetric measurements using the Antoine equation and the Clausius-Clapeyron equation, respectively. The flammability test indicates that [Gdm][OMs] is non-flammable. Hence, [Gdm][OMs] enjoys very low volatility, high enthalpy of vaporization, and non-flammability in addition to its known advantages. This work thus offers data support, methodologies, and insights for the application of [Gdm][OMs] and other organic salts as PCMs in thermal energy storage and beyond.

Comparing Antoine parameter sources for accurate vapor pressure prediction across a range of temperatures.

Determining the vapor pressure of a substance at the relevant process temperature is a key component in conducting an exposure assessment to ascertain worker exposure. However, vapor pressure data at various temperatures relevant to the work environment is not readily available for many chemicals. The Antoine equation is a mathematical expression that relates temperature and vapor pressure. The objective of this analysis was to compare Antoine parameter data from 3 independent data sources; Hansen, Yaws, and Custom data and identify the source that generates the most accurate vapor pressure values with the least bias, relative to the referent data set from the CRC Handbook of Chemistry and Physics. Temperatures predicted from 3 different Antoine sources across a range of vapor pressures for 59 chemicals are compared to the reference source. The results show that temperatures predicted using Antoine parameters from the 3 sources are not statistically significantly different, indicating that all 3 sources could be useful. However, the Yaws dataset will be used in the SDM 2.0 because the data is readily available and robust.

PREDICTING THE FLARE TEMPERATURE OF BINARY FUEL

A method for calculating the flash point from the results of simulating liquid–solid equilibrium at constant pressure using the Gibbs equation is discussed. A model is used to predict the flash point of the mixture based on the modified Le Chatelier equation, the Antoine equation and a model for estimating the activity coefficient. The flammability hazard of liquids is primarily characterized by their flash point. The flash point is defined as the temperature at which a liquid evaporates and forms a flammable mixture with air. To measure the flash point, closed and open type devices are used. In closed-type devices, the state of equilibrium between the liquid and vapor components of the mixture is studied. Open type devices take into account the interaction of a mixture of flammable liquids with the atmosphere. The flash point of a mixture is a critical property, but experimental data for many mixtures are lacking and obtaining such data is expensive and time-consuming. Therefore, the development of mathematical models for analyzing the state of the environment under conditions of increasing risk of emergency situations is an important scientific and practical task. This paper examines the possibility of predicting the flash point in closed-type devices, i.e. the influence of atmospheric conditions is not taken into account in this approximation. Several models for predicting the flash point for mixtures of various types have been proposed previously. Keywords: binary mixtures, flash point, boiling point, activity coefficients, solvation coefficient, association coefficient.

PUFFIN: A path-unifying feed-forward interfaced network for vapor pressure prediction

Accurate vapor pressure prediction is crucial for various applications, but obtaining precise measurements for certain compounds is resource- and labor-intensive. This challenge is amplified when a temperature-dependent relationship is required. To address this, we introduce PUFFIN (Path-Unifying Feed-Forward Interfaced Network), a machine learning approach that combines transfer learning with a specialized inductive bias node (inspired by the Antoine equation) to enhance vapor pressure prediction. PUFFIN outperforms alternative strategies that lack inductive bias or use generic compound descriptors by leveraging inductive bias and transfer learning using graph embeddings. The framework's incorporation of domain-specific knowledge overcomes data limitations and shows promise for broader chemical compound analysis applications, including the prediction of other physicochemical properties. An important aspect of our proposed approach is its partial interpretability, as the inductive Antoine node yields network-derived Antoine equation coefficients.

Density, vapor pressure, enthalpy of vaporization and heat capacity of (E)-isobutyl cinnamate

The density of (E)-isobutyl cinnamate at 297.95–535.20 K was measured using a capillary pycnometer and linearly related to temperature. The vapor pressure of (E)-isobutyl cinnamate at 420.15–570.05 K was measured by the ebulliometric method, and correlated by Antoine equation with an average relative deviation of 1.11 %. The vaporization enthalpy ΔvapH (Tb) of (E)-isobutyl cinnamate at normal boiling point was obtained based on the Clausius-Clapeyron equation. The standard vaporization enthalpy ΔvapH (298.15 K) was calculated to be 73.67±0.5 kJ·mol−1 by Othmer's method and verified by the Corresponding State Group Contribution (CSGC) method. The heat capacities at saturation vapor pressure (CSL) of (E)-isobutyl cinnamate were measured at 298.15–533.15 K by an automatic calorimeter and correlated by a quadratic polynomial.

Vapor-liquid equilibria in the 1-methylpyrrolidine + 1-butylimidazole binary system: Experimental measurements and theoretical modelling

In this study, a comprehensive investigation of the 1-methylpyrrolidine + 1-butylimidazole binary system was conducted to establish a valuable foundation for process design. Isobaric binary vapor − liquid equilibrium (VLE) data was measured (80 data points) at 50.0, 20.0, 10.0, and 7.5 kPa using dynamic equilibrium cell (VLE 602) and found that no azeotrope existed throughout the entire operating pressure range. Thermodynamic consistency was validated using the Redlich − Kister area test (9.56801%). The vapor pressure of 1-butylimidazole was determined through direct measurement (12 data points) of the equilibrium temperature at different pressures and the Antoine equation parameters were regressed based on the acquired data. The VLE data were regressed using maximum likelihood (ML) method, and binary interaction parameters (BIP) were estimated for NRTL–HOC, UNIQUAC, Van Laar, and Wilson models. The model validation demonstrated consistency between calculated and experimental values for temperature and mole fraction of the vapor phase. In addition, dipole moment (μ) values were evaluated by quantum chemical calculations using the Hartree–Fock (HF) method through GAMESS package. The density (12 data points), the sound velocity (12 data points), the refractive index (3 data points), and the normal boiling points (3 data points) were also measured for binary mixtures and pure components.

Antoine Equation Coefficients for Novichok Agents (A230, A232, and A234) via Molecular Dynamics Simulations

The flexible models of Novichok agents (A230, A232, and A234) from previous molecular dynamics simulations (MDSs) have been employed to create a parameter set for the Antoine equation of each of the three liquids. Furthermore, for the needs of this paper, new models of Novichok agents were created and studied via MDS due to the fact that the exact molecular structure of these compounds has been a matter of discussion in the last few years; however, recently, the literature favors a particular set of structures. Therefore, to cover our study holistically, both of the proposed molecular formulas were employed in the simulations and discussion. A range of ambient conditions was selected, and the data from the molecular dynamics simulations were employed to give the best possible fit in the selected vapor pressure range. When looking at the results for the two structures of A230, A232, and A234, we can see that, despite their differences, the A and B coefficients have the same magnitude in both cases (structures proposed by Ellison and Hoenig and structures proposed by Mirzayanov). Moving from the Ellison and Hoenig to Mirzayanov structures for substances A230 and A234 revealed a decrease (slight to major) in factors A and B of the Antoine equation. However, in the case of A232, where the Mirzayanov structure produces higher coefficients, this does not hold true. Overall, the Antoine equation of the studied agents will be an essential tool for understanding the behavior of these substances under different conditions.

Phase Equilibrium Properties of Binary Systems (Furfural + Ethanol or Butan-2-ol) at Several Temperatures

The vapor pressures of the binary mixtures (furfural + ethanol) and (furfural + butan-2-ol) along with the pure component ethanol were measured using the static apparatus for VLE measurements (static device) between temperatures of 283 and 363 K. The generated results from this work were correlated using semi-empirical correlations as described by the Antoine equation. The excess Gibbs function was computed at assorted constant temperatures and applied to fit a fourth-order Redlich–Kister equation utilizing the Barker’s technique, as these two systems in study exhibited positive deviations in GE at all temperatures studied over the whole composition range. The Modified UNIFAC (Do) model, UNIQUAC model, and the NRTL model together with the Peng-Robinson-Sheng-Lu equation of state (PRSL EoS) were also employed, and excellent results were observed in the modeling of the total pressure. The Redlich–Kister equation was applied successfully for modeling the thermodynamic excess properties.

Perfluoro(7-methylbicyclo[4.3.0]nonane) and Perfluoro(butylcyclohexane): Physicochemical, Thermophysical, and Spectral Data

New physicochemical data for perfluoro(7-methylbicyclo[4.3.0]nonane) and perfluoro(butylcyclohexane) with a purity ≥ 0.991 mass fraction are presented: the temperature and heat of the solid–liquid phase transition, the dependence of saturated vapor pressure, viscosity, density (liquid molar volume), and refractive index on temperature; the coefficients of the Antoine equation; 19F and 13C NMR and FTIR spectra; and gas chromatography–mass spectrometry data. For the perfluoro(7-methylbicyclo[4.3.0]nonane)–perfluoro(butylcyclohexane) binary system, the dependences are given: refractive index (at 15 °C) and density (at 20 °C) on the composition and boiling point on the composition in the pressure range from 20 kPa to atmospheric pressure. The average integral value of the relative volatility coefficient for various concentration ranges at atmospheric pressure is determined.

Optimal Designs for Antoine’s Equation: Compound Criteria and Multi-Objective Designs via Genetic Algorithms

Antoine’s Equation is commonly used to explain the relationship between vapour pressure and temperature for substances of industrial interest. This paper sets out a combined strategy to obtain optimal designs for the Antoine Equation for D- and I-optimisation criteria and different variance structures for the response. Optimal designs strongly depend not only on the criterion but also on the response’s variance, and their efficiency can be strongly affected by a lack of foresight in this selection. Our approach determines compound and multi-objective designs for both criteria and variance structures using a genetic algorithm. This strategy provides a backup for the experimenter providing high efficiencies under both assumptions and for both criteria. One of the conclusions of this work is that the differences produced by using the compound design strategy versus the multi-objective one are very small.

Density, viscosity, saturated vapor pressure, and isobaric vapor–liquid equilibrium for 4‑fluoronitrobenzene and 2-fluoronitrobenzene

Density and viscosity data of pure liquid 4‑fluoronitrobenzene and 2‑fluoronitrobenzene were determined in the temperature range from 303.15 to 353.15 K at the local atmospheric pressure of 100.8 kPa. Saturated vapor pressures of the two isomers and isobaric vapor–liquid equilibrium (VLE) data for the binary system of the two isomers at 10.0 kPa were measured experimentally by a modified Rose still. The relationship of density to temperature is accurately correlated by the DIPPR equation. The viscosity data were well described by the Litovitz, Ghatee, VFT, and Andrade equations. Among them, Andrade equation shows the best accuracy. Both Antoine and Riedel equations can successfully correlate the relationship between saturated vapor pressure and temperature, while Riedel equation is more accurate due to the small average relative deviation. The binary VLE data were correlated with NRTL and Wilson models, and the binary interaction parameters were obtained. The VLE data predicted by the obtained parameters are in good agreement with the experimental data, and the binary system did not exhibit azeotropic behavior. The thermodynamic properties of the pure components described above and the vapor–liquid equilibrium data provided are critical for the design and operation of the distillation of the isomeric mixture of 4‑fluoronitrobenzene + 2-fluoronitrobenzene.

Analysis and Experimental Study on Water Vapor Partial Pressure in the Membrane Distillation Process.

In membrane distillation, the vapor pressure difference is the driving force of mass transfer. The vapor pressure is generally assumed by the saturation pressure and calculated by the Antoine equation. However, in the actual operation process, the feed solutions usually flow in a non-equilibrium state, which does not meet the theoretical and measurement conditions of the vapor-liquid equilibrium (VLE) state. This study tested the actual water vapor pressure of the pure water, lithium bromide (LiBr) solution, lithium chloride (LiCl) solution, and calcium chloride (CaCl2) solution under different flow conditions. The results showed that the actual water vapor pressure was lower than the saturation pressure overall, and the difference increased with temperature but decreased with the mass concentration. Therefore, in vacuum membrane distillation (VMD), air gap membrane distillation (AGMD), and sweeping gas membrane distillation (SGMD), the membrane flux calculated by water vapor saturation pressure was higher than the actual membrane flux, and the relative difference decreased and was less than 10% after 60 °C. In direct contact membrane distillation (DCMD), the water vapor pressure difference on both membrane sides was almost the same by using the saturation vapor pressure or the tested data since the pressure errors were partially offset in parallel flow or counter-flow modes.

Thermophysical characterization of terpenoid based hydrophobic deep eutectic solvent and its Vapour-Liquid equilibrium studies with furfural

The sustainable transition to cleaner production techniques over the last decade has projected deep eutectic solvents as alternative solvents to replace toxic volatile organic solvents especially in green extraction technologies. However, processes based on such newly developed solvents pose hindrances in industrial applicability due to lack of sufficient data for process design and scale up. Prospectively, a new hydrophobic deep eutectic solvent (HDES) that has been utilized for the selective extraction of biomass derived furfural from its aqueous solutions composed of thymol and 1-tetradecanol in 2:1 M ratio has been subjected to exhaustive thermo-physical characterization and phase equilibrium measurements in the present study. The various physico-chemical properties of the HDES such as density, viscosity, ionic conductivity as well as refractive index and acidity were measured as a function of temperature from 293.15 K to 333.15 K and suitably correlated. The thermal limit of operation for the HDES was analyzed through thermo-gravimetric analysis while its structural characterization was conducted by Fourier transform infrared spectroscopy. A modified Othmer type ebulliometer was used for the vapour pressure measurements of the HDES from 2.4 to 10.4 kPa and the experimental data was fit to the Antoine and Clark-Glew equations. Further, the isobaric vapour liquid equilibrium data at different sub-atmospheric pressures for the HDES and furfural system was generated and data regression using the non-random two liquid (NRTL) model was used to derive the optimized binary interaction parameters.

Vapor pressure curves and isobaric vapor–liquid equilibrium for binary systems with compounds obtained from glycerol to be used as components of a bio-diesel mixture

The search of new renewable fuels and the interest of finding new uses for the abundant subproducts of many industrial processes have prompt Eni S.p.A to develop a technology for producing biofuels from glycerol. One of the compounds involved in this process is 2-ethyl-4-ethoxymethyl-1,3‑dioxolane (PrEDO). In this paper their temperature - vapor pressure curve has been determined experimentally as well as binary vapor–liquid equilibrium data at different pressures of systems where this compound is involved.The experimental vapor pressure data of PrEDO have been fitted with the Antoine equation. The vapor liquid equilibrium data have been correlated and calculated with UNIFAC, UNIQUAC, NRTL and Wilson to analyze their use when designing distillation processes.

A prediction method of vapor pressures for pure substances

From the viewpoint of engineering, a new prediction method of vapor pressures was proposed by directly determining the coefficients of the vapor pressure equation from a boiling point, or a single point vapor pressure data (Ohe, 2019). The proposed method was applied for various kinds of organic substances with satisfactory accuracy. It has the potential to be applied for inorganic substances, since it has no limitation for predicting vapor pressures. In this paper, the method is applied to thirty-seven inorganic substances: rare-earth elements, general inorganic substances, isotopes, and the whole average error is 5.04% with satisfactory accuracy. When predicting, the temperature range of the predicted vapor pressure and the reference vapor pressure must be in agreement with each other. The reason is that even for the same substance, the coefficients of the vapor pressure equation differ when the temperature range is different, resulting in greater error. The Clausius-Clapeyron and the Antoine equations were selected as the vapor pressure ones. Various vapor pressure equations have been proposed, but since the method uses a slope in the straight line of the logarithmic value of the vapor pressure against the reciprocal of the absolute temperature, other equations cannot be used. Furthermore, the Wagner equation requires a critical constant and cannot be used to estimate substances that have only boiling point data. However, if the temperature range is not wide, the Antoine equation can be calculated with the same accuracy as the Wagner equation.

Thermal Stability Calculation and Experimental Investigation of Common Binary Chloride Molten Salts Applied in Concentrating Solar Power Plants

A computational study on thermal stability was conducted the first time, combining the modified quasi-chemical model, the Antoine equation, and the adiabatic flash evaporation calculation principle to design a method to calculate the system pressure-temperature (P-T) phase diagram of binary chloride molten salts. The evaporation temperature of the molten salt obtained by analyzing the P-T phase diagram of the eutectic molten salt clearly defined the upper limit of the optimal operating temperature of the mixed molten salt. The results indicated that the upper-temperature limits of NaCl-KCl, NaCl-CaCl2, KCl-CaCl2, NaCl-MgCl2, and KCl-MgCl2 are determined to be 1141 K, 1151 K, 1176 K, 1086 K, and 1068 K. The maximum working temperature was measured experimentally using a thermogravimetric analysis (TGA), and the relative error between the calculation and experiment was calculated. The maximum error between the calculated and experimental values of the maximum operating temperature was 6.02%, while the minimum was 1.29%, demonstrating the method’s high accuracy. Combined with the lowest eutectic temperature and the upper-temperature limits of binary chloride molten salts, the stable operating temperature ranges of NaCl-KCl, NaCl-CaCl2, KCl-CaCl2, NaCl-MgCl2, and KCl-MgCl2 are 891~1141 K, 750~1151 K, 874~1176 K, 732~1086 K, and 696~1086 K.

The Antoine Equation of RP-3 Aviation Kerosene Based on a Five-Component Model Blending Fuel

The Antoine Equation of RP-3 Aviation Kerosene Based on a Five-Component Model Blending Fuel