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In this study, experiments were conducted to investigate the liquid drop spreading behavior on the grooved surface. The critical volume and the critical angle at which the water drop started to spread on the grooved surfaces were determined by the shadow method. It was found that the drop spreading on the grooved surface is a catastrophe process and the critical values vary with the groove structures. A thermodynamic method was proposed for predicting the critical drop volume spreading on the grooved surfaces with different structures. The consistency between the theoretical and experimental results is concluded to be satisfactory.

Experimentally determined critical temperatures (Tc) and critical pressures (Pc) are reported for 64 compounds. In addition, the critical volume (Vc) has been experimentally determined for 14 of these compounds. The compounds in this study are of industrial interest in process design, simulation, and safety. These data also extend our understanding of and ability to predict these properties from group contribution methods.

In this work, a trainable feed-forward back-propagation network was developed by employing the Levenberg-Marquardt training algorithm to predict the surface tension of binary refrigerant mixtures. 1260 experimental data were collected from reliable literature to train and test the network. Temperature, critical pressure, critical temperature, critical volume and acentric factor of the binary mixtures were selected as input variables of the proposed network. The optimum number of hidden layers was determined to be 1, with 19 neurons in the hidden layer. Tan−sigmoid and purelin functions was chosen as the transfer functions in the hidden and output layers, respectively. The results revealed that the ANN has the capability to correlate and estimate the surface tension accurately with an overall %AARD and correlation coefficient values of 0.7582 and 0.9997, respectively. In addition, the results were compared to different well-known correlations and models which indicated a better performance of the developed ANN.

Simultaneous description of critical point, vapor pressure and liquid density with an equation of state has been a hot research topic. In this work, the possibilities and limitations of the Cubic Plus Association equation of state for describing these properties of associating fluids have been studied. First a procedure is developed to determine the energy and co-volume parameters by converting the system of three equations at the critical point to a single variable root-finding problem. The procedure is then used in parameter estimation to simultaneously match the critical temperature and pressure as well as fit the vapor pressure and liquid molar volume of typical associating fluids. The performance of the estimated parameters is subsequently compared with the parameters fitted only to vapor pressure and liquid molar volume. The possibility of introducing an extra adjustable parameter to improve the performance is further explored. The results show that, for the studied associating fluids, the Cubic Plus Association equation of state with the obtained parameters can match the critical temperature and pressure exactly, fit the vapor pressure within 2% and the liquid molar volume within 3–4% in the range of temperature up to 0.95 critical temperature, while the model overpredicts the critical volume up to 18%.

In this work, different methods capable of estimating some properties of fatty acid methyl esters (FAMES) and fatty acid ethyl esters (FAEES) have been evaluated. The results for Tb indicated that the methods of Constantinou and Gani and Marrero and Gani should be applied for FAMES and FAEES, respectively. The evaluation of the methods for critical properties and acentric factor was performed by comparisons between the experimental values and output values by the Racket–Soave equation. The results indicated that different packages should be applied for FAMES, FAEES, and hydroxy-esters. For critical volume estimations, the method of Marrero and Pardillo should be used for any alkyl ester present in biodiesel. Three versions of the group contribution (GCVOL) method as well as the Rackett–Soave equation were employed to estimate pure alkyl esters and biodiesel density. All these methods showed good results in moderate temperatures, but only Rackett–Soave is indicated for high temperatures. A final validation...

The permeability of light gases in a series of different glassy polymers is analyzed through a thermodynamic-based approach for solubility and diffusivity. The nonequilibrium thermodynamic model for glassy polymers describes the solubility of the different penetrants; diffusivity is given as the product of a mobility factor and a thermodynamic factor. The latter is predicted by the nonequilibrium lattice fluid thermodynamic model, while the mobility coefficient is determined using the experimental permeability data. For rather soluble penetrants (e.g., CO2), a plasticization factor is also accounted for, considering the mobility to depend exponentially on penetrant concentration, as often observed experimentally. The model is able to describe accurately the experimental behavior in a simple and effective way, considering only two adjustable parameters. The mobility coefficient is found to depend on the penetrant size (critical volume) and on the fractional free volume of the polymer matrix, following rather general and reasonable correlations. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2776–2788, 2015

This work investigates the hidden details that are responsible for the practical success of cubic equations of state (EOS) in phase equilibrium calculations. A detailed consideration of the van der Waals method for evaluating the pure compound EOS parameters sheds new light on the reasons why the elimination of the actual critical volume as parameter was also adopted in the Redlich–Kwong and the Peng–Robinson (PR) frameworks. It is shown that an interesting relationship for the critical compressibility factor arising from the Martin–Hou method opens a new door for future exploration of different frameworks. A consideration of the key steps of Soave's reasoning for determining the temperature dependence of the attractive parameter explains the larger success of the Stryjek–Vera modification of PR EOS over the PR EOSs. A reference to the extension of cubic EOS to calculate liquid densities and enthalpies and a ready to use algorithm for the evaluation of the roots of a cubic equation are included for instructional purposes. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2824–2831, 2015

Based on the developed physicomathematical model of detonation attenuation and suppression in a methane-oxygen mixture by means of addition of a cloud of inert particles, the influence of the volume fraction of particles and their diameter on the detonation wave velocity is analyzed. Detonation limits in terms of the volume fraction of particles in methane-oxygen and methane-hydrogen-oxygen mixtures are found. A comparison with our previous data on suppression of detonation in a hydrogen-oxygen mixture shows that the critical volume fractions of particles resulting in detonation wave suppression in the methane-hydrogen-oxygen mixture are greater than those in the hydrogen-oxygen mixture.

This paper presents the calculation method allowing one to obtain the matched magnitudes of critical parameters of hydrocarbon gases with an accuracy comparable to the errors of the experimental methods. The ratios obtained allow an assessment of the values of the critical temperature, critical pressure, critical volume, acentric factor, and compressibility in the homologous series of alkanes up to C100. The critical parameters for alkanes 4 < nC < 40 calculated using formulas presented in the article demonstrated good consistency with the experimental data. The proposed values of critical constants for normal alkanes can be used to calculate the physiochemical properties of the compounds, while the calculation methods can be used to determine the critical constants of hydrocarbon components of other homologous series.

The gene expression programming (GEP) strategy is applied for presenting two corresponding states models to represent/predict the surface tension of about 1,700 compounds (mostly organic) from 75 chemical families at various temperatures collected from the DIPPR 801 database. The models parameters include critical temperature or temperature/critical volume/acentric factor/critical pressure/reduced temperature/reduced normal boiling point temperature/molecular weight of the compounds. Around 1,300 surface tension data of 118 random compounds are used for developing the first model (a four-parameter model) and about 20,000 data related to around 1,600 compounds are applied for checking its prediction capability. For the second one (a five-parameter model), about 10,000 random data are applied for its development, and 11,000 data are used for testing its prediction ability. The statistical parameters including average absolute relative deviations of the results form dataset values (25 and 18% for the first and second models, respectively) demonstrate the accuracy of the presented models. © 2012 American Institute of Chemical Engineers AIChE J, 59: 613–621, 2013

Ignition behavior of bituminous coal dust deposited between two hot surfaces forming wedges of 60�, and 90� is experimentally studied. Three thermocouples placed along the symmetry plane of the wedge cross-section at various heights from the apex (lowermost, middle and top) are used to record the transient temperature data. Results show that ignition always occurs around the region surrounding the top thermocouple in the case of 60� wedge and both the top and the middle regions in the case of 90� wedge. The trends are explained by investigating three parameters affecting the ignition behavior, namely, the heat transfer from the hot plate to the coal dust, the subsequent chemical heat release, and the heat transfer between different regions within the coal dust. Furthermore, an experimental setup, similar to the standard ASTM E 2021 test, is used to determine the minimum ignition temperatures of coal layers of various thicknesses and to assess the ignition scenario in the wedge configuration using an effective length scale. Measured quantities such as minimum hot plate temperature that causes ignition and the ignition time, as well as the transient heat release rate and heat conducted between various zones, calculated based on the temperature data are used to quantify the three parameters and their effects on ignition behavior. � 2011 The Combustion Institute.

Recently, our laboratory proposed a new universal method for the prediction of properties of organic compounds, such as the critical temperature, critical pressure, critical volume, critical compressibility factor, normal boiling point, and melting point. Here, the positional distributive contribution method is extended for the prediction of the enthalpy of vaporization of organic compounds at their normal boiling point (ΔvapHb). In this method, the position factor was used to take into account longer distance interactions, which could distinguish the overall isomer including the cis- and trans- or Z- and E- structure of organic compounds for their thermodynamics properties. The results indicate that our model provides very satisfactory results. The overall average absolute difference for ΔvapHb prediction of the 311 organic compounds is 1.00 kJ·mol−1, and 2.7 % is the relative deviation. Compared to those currently used prediction methods (including Riedel, Chen, Vetere, Liu, and Joback and Reid), the ne...

Comparison of properties of diatomite and kaoline in paints were studied in dependence on their volume concentration (PVC). Model paints were prepared containing increasing filler contents, PVC = 5% up to the critical volume concentration of the pigment (CPVC). The properties of the prepared coatings were tested by laboratory corrosion tests in both the neutral salt mist and the condensation moisture environments. The effect of diatomite and kaoline PVC on mechanical and anticorrosion protective properties of coats based on epoxide and epoxy–ester binders was studied. It was established that diatomite can be used as a filler in anticorrosion protective coatings.

It is a widely unknown or unrecognized fact that the vapor−liquid critical points of pure compounds and also of mixtures form a sail-like surface in the three-dimensional space of temperature, pressure, and molar volume or density. The available experimental critical points of all pure compounds lie on or near that critical surface with some exceptions caused mainly by extraordinary intermolecular interactions (e.g., strong acids or polar compounds like water). For this surface and therefore the relation among the three critical properties, simple relation equations, transformable and explicit in each property, were evaluated and optimized. With these equations the critical volume, pressure, or temperature can be calculated from the two remaining properties with an average absolute deviation of less than 5 % over a set of recommended critical points for 421 organic compounds. This relation is also applicable for the critical properties of binary and multicomponent mixtures. Therefore, a unique tool is ava...

A simple and accurate model to predict the density of ionic liquids is presented. The proposed model is based on a generalized correlation that has been conveniently modified and experimental literature data have been used to fit the five model parameters, to finally propose an equation that allows predicting densities of any ionic liquid. The model uses the critical temperature, the critical volume, the normal boiling temperature and the molecular mass to estimate the density at temperatures commonly used in ionic liquid applications (270–360 K). A set of 602 density data for 146 ionic liquids has been used in the study. The results were compared with predictions of ten generalized corresponding states principle correlations available in the literature. These generalized correlations have not been applied to ionic liquids before so the appropriateness and accuracy of these models to ionic liquid density estimation are unknown until now. Results show that the new simple correlation gives low deviations and can be used with confidence in thermodynamic and engineering calculations.

A groupcontribution method was developed to predict critical tempertaures, pressures and volumes of hydrocarbon compounds. The method was tested with satisfactory accuracy. The absolute average deviations obtained between experimental and calculated values are 0.36%, 4.6% and 1.7% respectively for critical temperature, critical pressure and critical volume.

The liquid-vapor critical temperatures of individual 1,3-dimethyl-and 1,3,5-trimethyladamantanes and their binary mixtures with cyclohexane were determined over the entire range of composition by means of the ampule method. It was found that an excess of the critical temperatures over calculated values reached 20 K for both mixtures studied. The predictive capabilities of several calculation methods are discussed.

A set of conventional feedforward multilayer neural networks have been proposed to predict basic properties (e.g., critical temperature (Tc), critical pressure (Pc), critical volume (Vc), acentric factor (ω) and molecular weight (MW)) of pure compounds and petroleum fractions based on their normal boiling point (Tb) and liquid density at 293 K. The accuracy of the method is evaluated by its application for basic property estimation of various components not used in the development of the method. Furthermore, the performance of the method is compared against the performance of the other alternatives reported as the most accurate and general methods for basic property prediction. Results of this comparison show that the proposed method outperforms the other alternatives using the same parameters, both in accuracy and generality. Furthermore, the accuracy of the proposed method is almost similar to the accuracy of the only general method despite the fact that the number of parameters required for the proposed method is less than the other alternative.

The available data of thermal conductivity at different temperatures are used to develop a method to predict the thermal conductivity of hydrocarbons. The proposed correlation based on heat capacity at 25°C, molecular weight, acentric factor, critical compressibility factor, critical volume, and temperature. The proposed new correlation shows significantly better correlation with average absolute error 4.8%.

For the four aliphatic C4H8 isomers (1-butene, isobutene, cis-2-butene, and trans-2-butene), densities, vapor pressures, and critical constants were measured, thus filling several gaps in the thermodynamic data for these compounds. Densities of the four isomers were measured with a computer-controlled high temperature, high-pressure vibrating-tube densimeter system (DMA-HDT) in the subcritical and supercritical states. The densities were measured at temperatures from 273 to 523 K and pressures up to 40 MPa (1725 overall data points), for which densities between 83 and 677 kg/m3 were covered. The uncertainty in density measurement was estimated to be better than 0.1% in the liquid and compressed supercritical states. Near the critical temperature and pressure, the uncertainty increases to a maximum of 1%. Using a variable volume apparatus with a sapphire tube, vapor pressures and critical data were determined. Vapor pressures were measured from about 280 K up to near the critical point with an uncertainty of ±(0.1 kPa + 0.001P kPa and 0.07 K). The critical points were determined visually with an uncertainty of 1% for the critical volume, 0.1 K for the critical temperature, and 5 kPa for the critical pressure. The new vapor pressures and compressed liquid densities were correlated with the TRIDEN model. The new data along with other literature measurements were used to develop fundamental Helmholtz equations of state and are reported by Lemmon and Ihmels [E.W. Lemmon, E.C. Ihmels, Fluid Phase Equilib. 228–229 (2005) 173–187] in part II of this project.

A new equation to predict critical volume for hydrocarbon compounds has been developed. The proposed new equation is based on molecular weight and boiling temperature, and it shows a significantly better correlation with the average absolute deviation (AAD) of 0.3% and 4.8% for two groups of hydrocarbon.

A new technique for predicting saturated liquid densities of alkanes at 25°C as a function of reduced temperature, acentric factor, critical volume, and molecular weight has been suggested. This new model shows good results in data fitness with an average absolute error (AAE) of 2.6% for 27 data point.

A generalized liquid molar volume at the normal boiling point correlation has been developed. The correlation is based on experimental molar volume data. The characterization properties for estimation are critical volume, boiling point, critical temperature, and acentric factor. Detailed analysis shows that the proposed correlation fits the data from 28 experimental measurements of liquid molar volume, with an overall absolute error of 2.1%.

We have developed a continuous theory for grinding of solids in batch and continuous mills which includes only a few parameters, the values of which can be obtained directly from data on a laboratory scale batch mill. This allows an easy scale-up from a laboratory-scale batch mill to an industrial continuous mill. Furthermore, the analysis presented indicates that a characteristic material parameter, the “ critical volume ”, plays an important role on the grinding process in general, and it is the only parameter which is affected by the additives. The performance of industrial mills is due to the influence that additives may have on the value of the critical volume.

A predictive equation, based on the Stokes–Einstein equation, was developed for the determination of infinite-dilution molecular diffusion coefficients in supercritical and high-temperature liquid solvents ( T r ≥0.7). An extensive database on diffusion was collected through the literature in order to evaluate the proposed equation and to determine the accuracy of the predictions with no additional parameter adjustment. The predictions were good, with an average absolute deviation 8.2% for 113 binary systems and 1332 data points. The input data required for the correlations are the solute molecular weight, temperature and density, and the solvent basic properties (molecular weight, critical temperature and critical volume).

A new method is proposed in this paper to predict the critical pressures of hydrocarbon mixtures by reversely using the Riedel equation which is used for calculating vaporization heat. The parameters used in the calculation are boiling temperature, critical temperature, critical volume and vaporization heat of the pure substances. The reliability of the method is discussed on the basis of the results obtained by predicting the critical pressures of many binary hydrocarbon–hydrocarbon and hydrocarbon–non-hydrocarbon mixtures. The proposed method is rather simple and can be used for rapid estimation of the critical pressures of hydrocarbon mixtures.

Based on the free-volume-type diffusion model, new correlations are developed to estimate the tracer diffusion coefficients of liquid and solid solutes in supercritical solvents. The correlations are tested to predict various solute–solvent systems with good results. The input data required for the correlations are the solute molecular weight, temperature, density and the solvent basic properties (molecular weight, critical temperature, critical volume and critical pressure).

New correlations, based on the rough hard-sphere theory and an extensive literature database, were developed for the determination of the binary diffusion coefficients of liquid and solid solutes in supercritical solvents. The correlations were tested to predict 107 solute-solvent systems with good results. The input data required for the correlations are the solute molecular weight, temperature, density and the solvent basic properties (molecular weight, critical volume, and critical pressure).

Based on the hard-sphere theory and an extensive literature database, new correlations are developed to estimate the binary diffusion coefficients of liquid and solid solutes in supercritical solvents. The correlations can predict the behavior of the binary diffusion coefficients in a range of the reduced solvent density larger than 0.21, with an average absolute error of 7.8% for 107 systems and 1167 data points. The input data required for the correlations are the solute molecular weight, temperature, and density and the solvent basic properties (molecular weight, critical volume, and critical pressure).

A new method based on atomic and structural contributions is proposed for estimating the critical volumes of organic liquids. The proposed method gives more accurate values compared with the methods of Lydersen, Joback and Somayajulu, the average absolute deviations being 2.3%, 3.2%, 3.1.% and 2.7% respectively for these four methods when tested against the experimental data for 279 organic liquids. The methods of Ambrose and Fedors recommended by the API technical data book for hydrocarbons and the AIChE data prediction manual for non-hydrocarbons gave overall average deviations of the same order as those for the Lydersen et al. method. The proposed constants can also be used to calculate the volume of liquids at the normal boiling point, with accuracies better than or comparable to those of the existing methods.

Geometric volume has been used for correlating ten molecular and thermodynamic properties of a particular category of halomethane refrigerants. The properties have been selected such that their conformity to certain specified norms qualify a compound as a good refrigerant. Based on the developed correlations, these properties have been predicted for the entire range of halomethanes belonging to the same category. A number of new halomethanes have emerged as potentially capable refrigerants. Existing refrigerants are mostly low geometric volume compounds. However, for some of the properties, namely, critical volume, critical density, density of saturated vapour pressure at boiling point and thermal conductivity, higher geometric volume compounds are as efficient as the lower volume members.

International audience; In this article, artificial neural network group contribution (ANN-GC) method is applied to calculate and estimate critical properties including the critical pressure, temperature, and volume and acentric factors of pure compounds. About 1700 chemical compounds from various chemical families have been investigated to propose a comprehensive and predictive model. Using this dedicated model, we obtain satisfactory results quantified by the following absolute average deviations of the calculated and estimated properties from existing experimental values: 1.1 % for critical pressure, 0.9 % for critical temperature, 1.4 % for critical volume, and 3.7 % for acentric factor.

Sheng W. and Lu H.-C, 1991. Studies on vapor-liquid equilibrium near the critical line for fluid mixtures: description of coexistence densities of binary mixtures. Fluid Phase Equilibria, 66: 143-159. Two expressions for describing the coexistence densities of vapor-liquid equilibrium binary mixtures are formulated by employing renormalization group theory predictions for the thermodynamic properties of fluids near the critical point. A least square fit of coexistence density data is made by using general and relatively simple equations and yields calculated values that are in excellent agreement with the experimental data over a wide range of systems, pressures and temperatures. The method presented here is also able to predict the critical volume and critical pressure of binary mixtures.

bstract - This work presents a new predictive method for the estimation of properties of pure organic substances. Each compound is assigned a molecular graph or an adjacency matrix representing its chemical structure, from which properties are then obtained as a summation of all contributions associated with functional groups and chemically bonded pairs of groups. The proposed technique is applied to the estimation of critical temperature, critical pressure, critical volume and normal boiling point of 325 organic compounds from different chemical species. Accurate predictions based solely on chemical structure are obtained

We propose the following method for predicting the critical volume from the van der Waals volumes: V c = A x V vdw = 5.36 x V vdw , where A is a universal constant,which can be used to predict the critical volume for a wide variety of substances: alkanes, alkenes, cycloalkanes, alcohols, carboxylic acids, amines, aromats and other. We use van der Waals volumes given in the DIPPR data compilation (Daubert and Danner, 1989). The new predictive method has been compared with two other methods: the Lydersen method (1955), and the Fedors method (1979)

Mean polarizabilities α0(λ0, T) and second virial coefficients B(T) of the gases Ar, CH4, C2H8, C3H8 and C(CH3)4 are determined from refractive indices measured with an interferometer in the ranges 260 K ≤ T ≤ 366 K, 0 ≤ p ≤ 3 bar of temperature T and pressure p (λ0 = 546.266 nm). The following results are discussed: 1 α0 depends linearly on T. 2 For each gas B(T)/Vc respectively B(T)/AR can be fitted best versus (Tc/T)2 by two straight lines, which are different for the ranges Tc T (Tc = critical temperature, Vc = molar critical volume, AR = 4 πNA α0/3). 3 In the range T > Tc the straight line is common to all gases, whereas in the range T < Tc the straight lines are different for all gases. 4 For all gases a linear correlation between α0 respectively AR and Vc exists.

Critical loci are shown for a recently proposed four constant noncubic equation of state based on the significant structure model. The new equation features superior liquid density representation, more meaningful molecular parameters, and fits the critical point exactly. A number of systems have been studied including those typically used in hydrocarbon processing and supercritical extraction. Comparisons are made with the cubic equation of state of Soave and its variations proposed by Peneloux. It is shown that the new equation gives comparable phase diagrams but with improved density representation. Based on the results of 58 systems, the new equation is capable of representing critical temperature to within 3.6%, critical pressure to within 3.3% and critical volume to within 7.3%, including systems containing methane.

An extensive critical evaluation of available correlations for predicting critical properties of binary defined hydrocarbon as well as some multicomponent hydrocarbon and hydrocarbon-nonhydrocarbon mixtures is presented using all available literature data. The Li method is recommended for critical temperature prediction based upon its accuracy and simplicity, although the Chueh-Prausnitz method is equivalent in accuracy. The Kreglewski method is most accurate for critical pressure prediction. All methods evaluated yielded high errors for the critical properties of methane-containing mixtures. Current correlations on critical volume are discussed, and correlational work on prediction using an excess volume approach is described.

Volumetric data of nonpolar gaseous mixtures are analyzed in terms of the theory of corresponding states. Special attention is given to an analysis of the second virial coefficient and to the calculation of pseudocritical constants. Second virial coefficients are calculated from experimental data for ten binary systems. These coefficients, with those previously published, are correlated by means of a generalized equation involving three parameters for each component: the critical volume, the reduced temperature, and the acentric factor. Equations are derived for the pseudocritical temperature and pressure of mixtures. These equations are considerably more accurate than those given by Kay's rule. Because of the complexity of the proposed equations for the pseudocritical parameters, a simplified pseudocritical method is presented which is sufficiently accurate for most chemical engineering purposes, especially at reduced temperatures exceeding 1.3.

In einem sehr kleinen Kugelfallviskosimeter wurden die Viskositaten vom Polyathylenphthalat-Polyester und seiner Losungen in Anisol und Nitrobenzol im Grundmolverhaltnis 1/10, 1/8, 1/4, 1/3, 1/2, 1/1, 1/0,5 und 1/0,2 uber den gesamten Temperaturbereich gemessen. Die Beschreibung der Meswerte nach der sog. Vogel-Gleichung ergab die Moglichkeit zur Definition zweier flussiger Zustande: des behindert- und freiflussigen Zustandes Fur den letzteren gilt T0 = 0 und freies Volumen vf(T0) = 0, fur den ersteren T0 · 0 und vf(T0) · 0. Beim reinen Losungsmittel Anisol konnten zwei behindertflussige Zustande, bei den Losungen infolge der Mesbereichsbeschrankung nur einer festgestellt werden. Die Ubergangstemperaturen lassen sich aus der Annahme einer Additivitat der freien Volumina berechnen. Die Werte des effektiven kritischen Platzwechselvolumens sind im Bereich der freien Flussigkeit groser als in dem der behinderten. The viscosities of polyethylenephthalate and its solutions in anisole and nitrobenzene in a molar ratio of 1/10, 1/8, 1/4, 1/3, 1/2, 1/1, 1/0.5, and 1/0.2 have been measured over the entire temperature range. The Vogel equation was used for the description of the experimental values. It permitted the definition of two fluid phases: the free and hindered liquid. The free liquid is characterized by the condition T0 = 0 and the free volume vf (T0) = 0, the hindered fluid follows the condition T0 · 0 and vf (T0) · 0. Pure anisole showed two hindered fluid phases, the polyestersolutions only one due to the temperature limitation of the measurements. The position of the transitiontemperature can be explained under the assumption of an additivity of the free volumes. The effective critical volume for the viscous flow is larger in the free than in the hindered liquid state.

Lennard-Jones force constants calculared from viscosity values at normal pressures for nearly forty nonpolar organic and inorganic substances have been used to develop relationships for the estimation of these constants from the critical temperature and volume of the substance. The product of the critical temperature and volume TcVc was found to correlate linearly with the force constant modulus . When the collision diameter ρ was plotted against the cube root of the critical volume on log-log coordinates, a straight line of slope 5/4 resulted. The corresponding relationship was found to predict ρ values with an average deviation of 3.1% when compared with values calculated from viscosity measurements. The temperature force constant ϵ/κ was found to vary as the 5/6 power of the critical temperature, and the resulting relationship produced an average deviation of 10%.

The van der Waals' constanta a andb evaluated from structural considerations of the unsaturated aliphatic hydrocarbons are used to calculate the critical constants for these types of compounds. For these unsaturated hydrocarbons, both van der Waals' constants are calculated through the additive contribution of unsaturated bonds to the van der Waals' constants of the corresponding saturated aliphatic hydrocarbons calculated according to a method previously proposed (6). With both van der Waals' constants available, the critical temperatures, pressures, and volumes for these types of compounds can be obtained. By use of this approach, the critical temperatures, pressures, and volumes of several olefins, diolefins, and acetylenes have been calculated. These calculated values have been compared whenever possible with values reported in the literature to produce an average percentage deviation of 1.3 for the critical temperature, 3.0 for the critical pressure, and 1.5 for the critical volume. In this comparison questionable literature values have been included, and consequently the reported deviations present the worst possible expectation.

An estimation method for critical properties that is easily available for both organic and inorganic compounds with considerable accuracy is proposed. In this method critical temperature, critical pressure and critical volume can be estimated solely from data of the normal boiling point and the liquid density of pure substance by means of succesive approximations that are repeated until calculated critical pressure (Pc) converges. The average errors of Tc, Pc and Vc for about 24O substances studied were 1.39, 2.61 and 2.OA percent, respectively, but the errors for nitrogen compounds, bromide compounds, metallic elements, and compounds associated in the vapor phase were sometimes larger.