Thermodynamic properties of the n-hexane and benzene system at elevated temperatures

The total vapour pressure and the composition of the liquid of the n-hexane and benzene mixtures have been measured under equilibrium conditions at 90, 110, 130, 150, 170 and 190°C. The corresponding vapour phase compositions were estimated using an expression of the liquid phase activity coefficient as a function of composition of the liquid phase. Several expressions were compared and the three-constant Redlich and Kister equation was found to give the best fit to the experimental vapour pressure data. The virial equation of state as well as a modified Redlich and Kwong equation were used to express the deviation of the vapour phase from the ideal. Results were compared and the discrepancy was found to be within the experimental tolerance. The low values of the liquid phase activity coefficients indicated that the behaviour of this particular system was not far from ideal. Also, it was found that the degree of deviation from the ideal decreased with the increase in temperature. The excess Gibbs free energy of mixing was calculated and it was found to be non-symmetrical with liquid composition. On increasing the temperature of the system, the liquid composition corresponding to the maximum G^E tended to shift to a lower n-hexane concentration, while at fixed liquid composition, G^E initially decreased and then remained stationary or increased again. This was thought to be due to differences in the molar volumes of the two components.     

Thermodynamic properties of methanol–benzene mixtures at elevated temperatures

The total pressure and the compositions of the vapour and liquid phases of the methanol–benzene system have been determined under equilibrium conditions at 100°, 120°, 140°, 160°, 180°, 200° and 220° for ten levels of concentration. The corresponding activity coefficients of methanol and benzene are reported; their values indicate that the equilibrium data are thermodynamically consistent. An azeotrope is found at all temperatures, its methanol content increasing as the temperature is increased. The relationship log P_az = 6·5098—(1,766/T) expresses the interdependence of the azeotrope vapour pressure P_az(lb/in² abs.) and temperature T(°K). Estimates of integral heat of mixing (H^E) and entropy change due to mixing (S^E) as functions of liquid composition (x_meth) have been made from the excess free energy of mixing G^E,(T) x_meth functions. Both H^E and S^E at a given x are positive increasing functions of temperature. These phenomena are discussed in terms of the dissociation of methanol ‘polymer’ and the formation of benzene–methanol ‘complexes’.     

Excess Gibbs free energy of butyl acetate with cyclohexane and aromatic hydrocarbons at 308.15K

Molar excess Gibbs free energies of mixing (C ^E ) for butyl acetate+cyclohexane or benzene or toluene or o- or m- or p-xylene were calculated by using Barker’s method from the measured vapor pressure data by static method at 308.15±0.01 K over the entire composition range. The G ^E values for the binary mixtures containing cyclohexane or benzene are positive; while these are negative for toluene, o-, m- and p-xylene system over the whole composition range. The G ^E values of an equimolar mixture for these systems vary in the order: cyclohexane>benzene>o-xylene>m-xylene>p-xylene>toluene. The G ^E values for these systems were also calculated by Sanchez and Lacome theory using the previously published excess enthalpy and excess volume data. It is found that while values of G ^E from Sanchez and Lacombe theory are in reasonably good agreement with those calculated by Barker method for m-xylene and p-xylene mixtures, agreement is very poor for other systems although they predict the sign of G ^E data except in the case of mixtures containing benzene.     

Polymer cosolvent systems

Summary In this paper we have studied the behaviour of PMMA in the binary mixture CCl₄/n-butyl chloride by viscometry, light scattering and dyalisis. We have found that the CCl₄/n-butyl chloride mixture behaves as cosolvent in the range 10 < u₂ < 90% n-butyl chloride. The n-butyl chloride is preferentially adsorbed in the whole composition range. The obtained results are discussed attending to G^E and the liquid order.     

Prediction of isobaric and isothermal vapour–liquid equilibria from limited experimental data

Malesinski's method for prediction of isobaric vapour–liquid equilibrium data using a single experimental datum on a T–x isobar has been modified and extended to a more general case where the molar entropies of vaporisation of the components are not necessarily equal and the non-ideality in the vapour phase is considered. However, it is assumed that the solution behaves like a strictly regular one over the temperature range in question, that is, the constant A in the expression for excess free energy: g^E=Ax₁x₂ is independent of temperature. The method has been illustrated for several systems and is found to be highly satisfactory for non-polar–non-polar as well as polar–non-polar systems in which the boiling points of the pure components are not much different. Incorporating temperature dependence of the constants in the Redlich–Kister equation for excess free energy, a method has been developed for predicting isothermal vapour–liquid equilibrium data at several temperature levels from equilibrium values at a single pressure. For testing the validity of this method, predicted results have been compared with the available experimental data for zeotropic as well as azeotropic systems comprising non-polar–non-polar, polar–non-polar and polar–polar mixtures, and the method has been found to be satisfactory for all systems.     

Studies concerning charged nickel hydroxide electrodes. II. Thermodynamic considerations of the reversible potentials

In this paper the thermodynamics of mixing are applied to account for the independence of the discharge potential of the nickel hydroxide electrode as a function of nickel oxidation state. The constant potential region is considered to arise from the formation of a pair of co-existing solid solutions having a composition predetermined by the magnitude of the interactions between the oxidized and reduced species. From considerations of the excess-energy terms, it can be shown for a symmetrical potential/ composition profile, that the constant potential region is identical with the standard potentialE ₀. The influence of asymmetry on the changes inE ₀ are discussed. Consideration has also been made of the influence of dissociation of oxidized and/or reduced species on the potential determining equations. The removal of n-type defects from the nickel(II)-rich phase on discharge is considered to be responsible for the observed secondary discharge plateau at potentials 300 mV more cathodic than normal. This non-equilibrium behaviour can be explained in terms of a mixed pn-semiconducting material.List of symbols E electrode potential at constant pH(V) - E ₀ standard electrode potential (V) - R the gas constant (J K^–1 mole^–1) - F the Faraday constant (C g-equiv^–1) - T the absolute temperature (K) - ^aH⁺ proton activity in the electrolyte - a _z activity of oxidized species z - a _y activity of reduced species y - _H+ chemical potential of the proton - _e chemical potential of the electron - _z ^o standard chemical potential of species z - _z chemical potential of species z - _y ^o standard chemical potential of species y - _y chemical potential of species y - _H,e chemical potential of the proton/electron pair - x _y orx mole fraction of reduced species y - x _z mole fraction of oxidized species z - G _M total free energy of mixing (J mole^–1) - G _R free energy of reaction (J mole^–1) - G _I free energy of mixing under ideality (J mole^–1) - G _E excess free energy (J mole^–1) - A,A _i andB _i interaction energy parameters (J mole^–1) - x _u mole fraction of y in co-existing phase u - x _v mole fraction of y in co-existing phase v - _y activity coefficient of undissociated reduced species y - _z activity coefficient of undissociated oxidized species z - _y ^± mean ionic activity coefficient of y - _z ^± mean ionic activity coefficient of z - _y activity coefficient of y in phase u - _z ^u activity coefficient of z in phase u - _y ^v activity coefficient of y in phase v - _z ^v activity coefficient of z in phase v - I current (A) - S cross-sectional area (cm²) - L conductor length (cm)     

Elasticity,tear strength,and strength of adhesion of soft PVC gels

An experimental study is described of the tensile modulus E of elasticity, tear strength G_c, and strength G_a of adhesion to a Mylar substrate, for PVC gels prepared with a wide range of PVC concentrations and with four different plasticizers. The modulus E, measured under quasiequilibrium conditions, was found to be approximately proportional to c³, where c is the volume concentration of PVC. The tensile behavior suggests that the molecular strands comprising the undiluted elastic network are relatively short, only about 26 C atoms long. G_c under threshold conditions was found to vary with c^2.25 and to be considerably larger than (about 10 X) the value expected for a molecular network of short PVC chains. This difference is attributed to yielding of crystallites before molecular rupture can take place. Adhesion of PVC gels to Mylar was relatively weak. Both the tear strength and strength of adhesion were strongly dependent upon rate of fracture propagation and temperature, in good accord with the WLF rate-temperature equivalence for simple glass-forming substances. Thus, the strength of PVC gels appears to be determined largely by the glass temperature of the composition, and not by the amount or type of plasticizer except insofar as they affect the glass temperature.     

Experimental and analytical study of countercurrent flow limitation in vertical gas/liquid flows

An experimental and analytical study of adiabatic countercurrent flow limitation (flooding) in single vertical ducts is reported. The experiments were carried out in a rectangular channel using saturated liquid and vapour of Refrigerant 12 (CCl₂F₂). The steady-state liquid delivery (flooding) curves as well as local pressure drop and void fraction distributions in the countercurrent flow were measured in a range of system pressures from p/p_crit = 0.16 to p/p_crit = 0.31, and for various total liquid injection rates and locations. The measured flooding curves j₁ = f(j_g) as well as pressure drop and void fraction during partial liquid delivery (j₁ < j₁ⁱⁿ) were not affected either by the axial liquid feed location or by the excess liquid rate carried upwards by the vapour. Moreover, for given flow conditions during flooding pressure drop and void fraction were essentially the same at different axial positions. Radial void fraction distributions evaluated from optical fibre probe data indicate an annular-type flow pattern. Based on this experimental evidence, a mechanistic core/film flow model was developed for the calculation of flooding. The analytical results are compared with the present high pressure and with comparable atmospheric pressure experimental data, showing reasonable overall predictions not only of the flooding curves, but also of the pressure drop in countercurrent flow.     

The use of a specific function to estimate maximum methane production in a batch‐fed anaerobic reactor

A readily biodegradable substrate was used to assess the value of using a mathematical function of y = y_maxexp^m/x as a simplified method of determining the maximum methane production (G_max) in a batch anaerobic reactor. Experimental results to test the method used three different initial substrate loadings in pre‐acclimatised completely mixed anaerobic reactors. Gas production was found to follow a typical trend that has previously been described by first order reaction kinetics; for the purpose of fitting the linearisation, it requires a value for maximum cumulative methane production. Use of the modified specific function to yield the equation G = G_maxexp^m/t showed that the experimental gas production curve could be estimated with a high degree of similarity. This was confirmed by a statistical analysis using the method of residuals which gave a correlation coefficient (R²) greater than 0.97 between experimental and estimated values. Using a graphical linearisation of the specific function produced a simplified method of predicting G_max. The value obtained was then used in a first order kinetic model to derive the specific coefficient rate (K_o), which was in agreement with other methods used for its determination. Copyright © 2004 Society of Chemical Industry     

On Determination of Azeotrope Coordinates from gE for Binary Isothermal and Isobaric Systems

A relatively simple procedure is described to calculate the coordinates, temperature (T_az), pressure (P_az), and composition (x_1az), of an azeotrope (for either an isothermal or isobaric binary system at low pressure and with a single or double homogeneous azeotrope) from an expression for the liquid‐phase excess molar Gibbs function (g^E). General results are based on (?g^E/?x₁)_az = RT_az ln[p₂*(T_az)/p₁*(T_az)], and P_az = (γ₁p₁*)_az = (γ₂p₂*)_az, where R is the gas constant, p* is saturation vapour pressure, and γ is liquid‐phase activity coefficient. Specific results are given for the Redlich‐Kister, van Laar, Wilson, and NRTL equations. Numerical examples are provided for both an isothermal and an isobaric system. The procedure provides a means to obtain azeotrope coordinates that are consistent with a g^E expression obtained either from experimental data or from a model. It is applicable to polyazeotropy, whereas the criteria given previously are generally not applicable to polyazeotropy.     

An apparatus for determining high-pressure liquid-vapour equilibrium data. I. The methanol—ethanol system

An apparatus for determining high-pressure liquid–vapour equilibrium data has been developed and proved to operate satisfactorily. The apparatus operates isothermally. Results have been obtained for the ethanol–methanol system at the following temperatures: 100°, 120°, 140° and 160°. The results are shown to be thermodynamically consistent within the limits of the accuracy of their determination. The ‘ideal activity coefficients’ (i.e. calculated assuming that the gas phase behaviour is ideal) are correlated with the mole fraction of the component in the liquid phase by Margules-type equations (1) and (2). The accuracy of these equations is greater than predictions based on fugacities. From equations (5), (6) and (1) or (2) in the paper it is possible to estimate any pair of liquid-vapour equilibrium compositions for any specified pressure P and temperature T. Alternatively, for a specified P and liquid composition, the corresponding T and vapour composition may be calculated.     

Gas dispersion in air‐lift reactors: Contribution of the turbulent part of the added mass force

Gas dispersion in an airlift reactor focusing on the closure law on turbulent contribution of added mass is presented. A data bank for bubbly flow in an airlift reactor is presented. The liquid velocity is measured by hot film anemometry and gas fraction and velocity are measured with an optical probe. The sensitivity of numerical simulations of gas dispersion to the modeling of turbulent contribution of added mass is shown. Without the turbulent contribution, the bubbles move toward the region where the turbulence is high and the pressure is low. When the turbulent contribution is introduced, the bubble migration towards the low pressure region is counter‐balanced and the void fraction profile is significantly modified. The modeling of the turbulent contribution of added mass is expressed in terms of the turbulent correlations in the gas phase, u_Gi^′u_Gj^′ , that can be related to the Reynolds stress in the liquid phase, u_i^′u_j^′ . © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Vapour—liquid equilibria of the systems acetone—benzene,benzene—cyclohexane and acetone—cyclohexane at 25°C

Vapour—liquid equilibrium data for the binary systems acetone—benzene, benzene—cyclohexane and acetone—cyclohexane have been determined experimentally at 25°C. The reduction producers based on P - x - y as well as on P - x isothermal data sets, which incorporate usual thermodynamically consistent models expressing the dependence of activity coefficients of liquid composition, have been examined for representing the reported results. Nonideal behaviour of the both phases has been taken into account. Thermodynamic consistency of the data has been shown by comparing of the experimentally obtained vapour compositions with those calculated from P - x data using the best of the examined models for activity coefficients.     

Phase equilibria of the propylene glycol/CO2 and propylene glycol/ethanol/CO2 systems

The high-pressure vapour–liquid phase equilibria (P–T–x–y) of the binary mixture propylene glycol/CO₂ have been experimentally investigated at temperatures of (398.2, 423.2 and 453.2) K over the pressure range from (2.5 to 55.0) MPa using a static-analytic method. Furthermore, the high-pressure vapour–liquid phase equilibria (P–T–x–y) of the ternary mixture propylene glycol/CO₂/ethanol at constant temperatures of (398.2, 423.2 and 453.2) K and at constant pressure of 15.0 MPa have been determined using a static-analytic method. Initial concentrations of components in propylene glycol (PG)/ethanol (EtOH) mixture vary from 10 up to 90 wt.%. In general, for binary system it was observed that the solubility of CO₂ in the heavy propylene glycol reach phase increases with increasing pressure at constant temperature. On the contrary, the composition of gaseous phase is not influenced by the pressure or the temperature. On average the solubility of PG in light phase of CO₂ amounts to 30 wt.%. The system behaviour at temperature of 398.2 K was investigated up to 70.0 MPa and a single-phase region was not observed. Above the pressure 60.0 MPa a single-phase region of the system was observed for the temperature of 423.2 K. For the temperature of 453.2 K the single-phase was observed above the pressure of 48.0 MPa. For ternary system it was observed that the composition of heavy phase is slightly influenced by the temperature when the mass fraction of EtOH in initial mixture is higher than 50 wt.%. If the mass fraction of PG in initial mixture is higher than 50 wt.%, the composition of heavy phase is not influenced by the temperature anymore. The composition of the PG, EtOH and CO₂ in light phase remains more or less unchanged and it is not influenced by the conditions.     

Thermodynamic modeling of vapor-liquid equilibria and excess properties of the binary systems containing diethers and n-alkanes by cubic equation of state

A comparison of the performances of two different approaches of cubic equations of state models, based on a classical van der Waals and mixing rules incorporating theG ^E equation, was carried out for correlation of Vapor-Liquid Equilibria (VLE), H^E and C _P ^E data alone, and simultaneous correlation of VLE+H^E, VLE+C _P ^E , H^E +C _P ^E and VLE+H^E +C _P ^E data for the diethers (1,4-dioxane or 1,3-dioxolane) with n-alkane systems. For all calculations the Peng-Robinson-Stryjek-Vera cubic equation of state (PRSV CEOS) was used. A family of mixing rules for the PRSV CEOS based on the Modified van der Waals one-fluid mixing rule (MvdW1) and two well-known CEOS/G^E mixing rules (MHV1 and MHV2), was considered. The NRTL equation, as the G^E model with linear or reciprocal temperature dependent parameters, was incorporated in the CEOS/G^E models. The results obtained by the CEOS/G^E models exhibit significant improvement in comparison to the MvdW1 models.     

Electro-oxidation of benzene in a fixed bed reactor

A fixed bed electrochemical reactor was used in the laboratory to oxidize benzene to quinone. The reactor consisted of a 3 mm thick bed of 1 mm lead shot, 0.5 m long by 0.05 m wide, sandwiched between a lead feeder plate and an asbestos diaphragm which was compressed against a stainless steel cathode plate. A dispersion of benzene in aqueous sulphuric acid was passed through the reactor and the rates of production of quinone, hydroquinone, carbon dioxide, oxygen and hydrogen, together with the cell voltage and pressure drop, were obtained for a range of operating conditions.Concentrations of quinone in the benzene product varied from 0.04 to 0.31 M and current efficiencies for quinone were in the range 22 to 55%. In a single pass of 1 M acid and benzene through the reactor at 25° C the quinone efficiency fell from 53% to 39% as the average superficial current density increased from 0.4 to 2.0 kA m^–2. At an average superficial current density of 2.0 kA m^–2 the quinone efficiency decreased with an increase in process temperature (25 to 50° C), but increased with increases in acid concentration (1 to 4 M), acid flow (0.5 to 1.0 cm³ s^–1), benzene flow (0.05 to 10 cm³ s^–1) and co-current nitrogen gas flow (0 to 32 cm³ s^–1 at STP). Recycling the 4 M sulphuric acid at 25° C raised the concentration of quinone in the product benzene but decreased the net current efficiency for quinone. Corresponding changes were observed in the cell voltage and in the current efficiencies for hydroquinone, carbon dioxide and oxygen. The results are discussed in terms of the process stoichiometry, electrode kinetics and mass transfer for three-phase flow in a fixed bed reactor.Nomenclature A Acid flow - a ₁ Liquid/liquid specific interfacial area - a _s Liquid/solid specific interfacial area - B Benzene flow - d ₃₂ Sauter mean drop diameter - d _P Particle diameter - E Current efficiency - F Faraday number - I Total current - i _l Superficial transfer-limited current density - K Liquid/liquid distribution coefficient - k _c Liquid/liquid mass transfer coefficient in continuous phase - k _s Liquid/solid mass transfer coefficient - L _c Superficial liquid load — continuous phase - L _d Superficial liquid load — disperse phase - Q _A Quinone concentration in aqueous phase - V ⁰ Standard electrode potential - z Number of electrons per equivalent     

Hydrophobic surface properties of fluoropolyetherimide blends for pervaporation membranes

The well‐known polyetherimide (ULTEM 1000) is obtained by step‐reaction of bisphenol. A diphthalic anhydride (BAPA) with m‐phenylene diamine and newly related fluorinated poly etherimides synthesized from BAPA and 2,3‐bis(2,2,3,3,4,4,5,5,5‐nonafluoropentyl)butan‐1,4 diamine (NFD) led to compatible blends over the entire range of composition. Miscible one‐phase blends have been suggested by a good correlation of T_g versus NFD monomer unit weight fraction (w) (Fox and Couchman equations) and a regular morphology by scanning electron microscopy. Surface energy of blend films fell from 45.3 to 27.4 mJ m^?2 for w ≥ 0.1 corresponding to a NFD molar fraction y ≥ 0.06. Cast‐evaporated films from fluorinated copolyetherimides and blends with y < 0.15 were ductile and gave conveniently hydrophobic non‐porous membranes that withstood the experimental conditions of pervaporation tests. Copyright © 2003 Society of Chemical Industry     

Study of the Homologous Retention Increment in Flat-Bed Chromatography

Abstract

Relations between the chromatographic retention of various classes of homologous compounds in flat-bed chromatography systems and the thermodynamic properties of the latter were investigated. Provided the retention of solute (i) is due to liquid-liquid partition, the R_Mi is related to the partial molar excess Gibbs free energies of the solute in the mobile and stationary phases, G^E _im and G^E _is , by R_Mi = [(G^E _im - G^E _is )/ 2.3RT] - log A, where R and T are the universal gas constant and the absolute temperature of the system, respectively, and A = d_mM_sφ_m/d_sM_mφ_s, d, M, and φ denoting the densities, molar masses, and cross-sectional areas of the mobile and the stationary phases, m and s, respectively. The difference in the partial molar excess Gibbs free energies per solute methylene group in the mobile and in the stationary phase, related with the R_M increment per methylene group of solute by G^E _m (CH₂) - G^E _s (CH₂) = 2.3RTR_M (CH₂), can be used to characterize the difference in the polarities of the phases.     

Synthesis and characterization of side-chain liquid crystalline polysiloxanes

The synthesis and characterization are described for a series of side-chain liquid crystal polysiloxanes using polyhydrosilylation reaction between a poly(hydrogen methyl-co-dimethylsiloxanes),-(OSiHMe)_x,-(OSiMe2)_y-, where x/y was 13/87, 30/70, 55/45, 73/27 and 98/2, and [4-(allyloxy)benzoyll biphenyl mesogenic group. The side-chain liquid crystal polysiloxanes were characterized by¹H NMR,¹³C NMR, IR, gel permeation chromatography (GPC), differential scanning calorimetry (DSC) and optical polarizing microscopy. The dimethylsiloxane segment factors governing thermal transition temperatures and activation energy (E_a) of the nematic-to-isotropic phase transition are discussed.     

Thermodynamic Properties of Associated Solutions II. Mixtures of the Type A + B + ABj

The theory of ideal associated solutions of the type A + B + AB_j is investigated. Equations describing the chemical equilibrium, number average molecular weight, activity coefficients and excess thermodynamic functions are given. For the type of association considered, G^E is always negative, H^E has the same sign as the standard enthalpy of the association reaction, ΔH°, and S^E can have positive or negative values. The excess entropy of mixing as a function of composition has a fairly complicated shape, especially in the region where the enthalpy and the free energy term compensate for each other. The extremum properties of the thermodynamic functions are at the stoichiometric mole fraction × = 1/(1 + j), and the functions have an asymmetric parabola-like form.