Total Mole Fraction Research Articles

Thermodynamic properties of borazole at temperatures from 0 to 310 K

The temperature dependence of the molar heat capacity C°p,m for borazole (c-B3N3H6) has been studied at temperatures from 13 K to 310 K in a vacuum adiabatic calorimetric cryostat within 0.002·Cp,m. The temperature and enthalpy of melting of borazole as well as the total mole fraction of impurities have been determined. From the values obtained the thermodynamic functions ΔT0H°m, ΔT0S°m and Φ°m have been calculated in the temperature range 0 to 310 K, and the thermochemical quantities of formation: ΔfH°m, ΔfS°m, and ΔfG°m for borazole have been estimated also at T = 298.15 K and p = 101.325 kPa. The properties of borazole have been compared with those of benzene.

Optimum Cut of Separating Element as Function of Total Separation Factor and Mole Fraction of Component to be Separated

For a simplified model of separating elements where a total separation factor αβ is independent of values of cut ϑ (0≤ϑ≤1), an optimum cut ϑopt in the sense that the cut makes a separative power δU maximum, was derived in terms of αβ, and a mole fraction xF (0≤x F≤1) of the component to be separated. When values of xF is nearly equal to zero, the optimum cut ϑxF opt≃0 decreases and approaches to near 0, as the total separation factor becomes larger. On the contrary, when xF is nearly equal to 1, the optimum cut ϑxF opt≃1 was found from calculation to be 1-ϑxF opt≃0, and increases and approaches to near 1, as the total separation factor becomes larger. Moreover, in the case of xF =0.5, the optimum cut is 0.5 regardless of αβ. Generally, the optimum cut ϑopt(xF ) was solved to be in the form of a linear interpolation of the boundary values, ϑxF opt≃0 and ϑxF opt≃1.

Optimum Cut of Separating Element as Function of Total Separation Factor and Mole Fraction of Component to be Separated.

For a simplified model of separating elements where a total separation factor αβ is independent of values of cut ϑ (0≤ϑ≤1), an optimum cut ϑopt in the sense that the cut makes a separative power δU maximum, was derived in terms of αβ, and a mole fraction xF (0≤x F≤1) of the component to be separated. When values of xF is nearly equal to zero, the optimum cut ϑxF opt≃0 decreases and approaches to near 0, as the total separation factor becomes larger. On the contrary, when xF is nearly equal to 1, the optimum cut ϑxF opt≃1 was found from calculation to be 1-ϑxF opt≃0, and increases and approaches to near 1, as the total separation factor becomes larger. Moreover, in the case of xF =0.5, the optimum cut is 0.5 regardless of αβ. Generally, the optimum cut ϑopt(xF ) was solved to be in the form of a linear interpolation of the boundary values, ϑxF opt≃0 and ϑxF opt≃1.

Rate constant and products of the reaction Cl + CS 2 in air

A steady-state system involving the photolysis of Cl 2 as a source of Cl has been used to investigate the reaction of Cl with CS 2 at 293 ± 3 K in a 420 l reaction chamber coupled to FTIR and mass spectrometers. Using a relative rate technique, the measured effective rate constant was found to be dependent on the total pressure and mole fraction of O 2 present in the system. In 760 Torr synthetic air, the overall rate constant for the Cl + CS 2 reaction is(0.83 ± 0.17) × 10 −13 cm 3 molecule −1s −1. SO 2, COS and COCl 2 are the main reaction products.

Dielectric Constant Measurements on the p-Dioxane: Acetonitrile Cosolvent System

Static dielectric constant values were re-evaluated for the binary solvents, p-dioxane: acetonitrile and p-dioxane: methanol, over the complete mole fraction range. Earlier investigations on these systems were too incomplete to permit useful comparisons to be made among trends in excess dielectric constant vs. mole fraction functions for the cosolvents. Acetonitrile is one of the common dipolar aprotic solvents used for the study of medium effects upon the electrolytic conductance of ionic solutes, polarographic and cyclic voltammetric behavior of solute species, and nonaqueous acid-base titrations. Similarly, p-dioxane has long been employed as a nonpolar but fundamental solvent for electrochemical investigations; in most instances p-dioxane has been used as a cosolvent paired with a strong hydrogen bond donor, such as water or one of the simpler alkanols. For the latter, mixtures can be selected to represent a very broad dielectric constant range. Ionic association and ion-solvent interactions have been examined by D'Aprano and Triolo (1967) in the specific binary system, p-dioxane: acetonitrile, but their work was limited to only four solvent mixtures for this interesting solvent pair. Because of the very incomplete data base available for the fundamental properties of these solvent mixtures, a new investigation of the dielectric constants for the acetonitrile: p-dioxane system was extended over the total mole fraction range from pure p-dioxane to pure acetonitrile. Comparisons were also made to other binary solvents having one of these components in common.

Nonlinear regression model for the representation of dielectric constants for binary aprotic solvents

For many cosolvent systems which are important in analytical chemistry, including nonpolar:polar aprotic pairs, the static dielectric constant (epsilon) is a continuous but nonlinear function of the solvent composition. Rational functions were applied to such systems in place of the more conventional polynomial regressions for epsilon = f(X). Advantages which the rational functions have for the economical storage of dielectric constant data include a reduction in the number of empirical coefficients required because of only a first power dependence on mole fraction (X) and a computational simplicity in reproducing reliable epsilon values over the total mole fraction range. The equations were tested on eight nonlinear data sets for nonpolar:polar solvent pairs. Also, current values for dielectric constants and indexes of refraction were used in a critical review of the Bekarek equations for the estimation of ..pi../sup */ dipolarity numbers of aromatic hydrocarbons as nonselected solvents. 23 references, 2 figures, 4 tables.

Critical point measurements on nearly polydisperse fluids

AbstractThe critical temperatures, pressures and volumes of several mixtures containing CO2, C2H6, C3H8, and C4H10 have been measured using a heavy walled, variable volume, cylindrical glass vessel. In each mixturre the relative proportions of the three hydrocarbon solutes to one another were changed; total solute mole fraction never exceeded 0.1. A detailed study of the mixture CO2 + C3H8 shows that the critical temperature exhibits a minimum at a C3H8 mole fraction of 0.0265. Our mixture data are analyzed using a polydisperse model of dilute solutions.

The influence of oxygen and total pressure on the surface oxidation rate of bituminous coal

The intrinsic reaction rates of several bituminous coals and a carbon black have been studied over a range of particle temperatures (1700–2200 K), total gas pressures (5.5–10 atm) and oxygen mole fractions (0.1–0.5) in a conventional shock tube. The surface reaction rates (based on external surface area) of the coals were observed to vary inversely with total pressure while no such dependence was noted for the carbon black. In conjunction with observations of reducing diameter burnout mode and large surface reaction rate Arrhenius activation energies, these results suggest the existence of a roughsphere kinetics regime. The true reaction order with respect to oxygen partial pressure measured at constant gas temperature is observed to be nearly 1/2; however, correction for the accompanying increase in particle temperature reduces the overall order to about 1/5. The true activation energies for both coals are about 34 kcal/mole over the temperature range studied. When corrected for pore penetration, the intrinsic reaction rates of the coals are observed to be greater than those measured for the carbon black and those predicted by a recent correlation in the temperature range of 1500 to 2100 K.

Studies in char gasification—III: The combustion zone

The fluidized bed steam-oxygen-char gasifier is modelled by treating the bed as one in which the solids are well mixed and the gases are in plug flow. This model permits a detailed analysis of the combustion zone. The entire reactor is assumed to be at a uniform temperature. From the results of the model calculations, it was concluded that the assumption of negligible combustion zone thickness made in the earlier two papers is acceptable This model predicts higher total carbon conversion and methane mole fraction in the product gas than the lumped model analysed in an earlier paper.

A stepwise dilution technique for measuring the static dielectric properties of liquid mixtures Dielectric behaviour of ethanol in cyclohexane, n-hexane, carbon tetrachloride, benzene, p-xylene, and carbon disulphide

Dielectric constants at audio-frequency have been measured for solutions of ethanol in various non-polar solvents in the range x(C 2H 5OH) ≈ 6 × 10 −4 to 0.2 using a stepwise dilution technique. The mixtures studied are: ethanol + cyclohexane at 283.15, 298.15, and 318.15 K; ethanol + n-hexane, +benzene, +carbon tetrachloride, + p-xylene, and +carbon disulphide at 298.15 K. The results are analysed in terms of a number of theories to obtain the apparent dipole moment as a function of mole fraction. This quantity varies considerably with both the solvent and the mole fraction. It is concluded that the aromatic solvents and carbon tetrachloride interact with the free OH groups on the monomeric alcohol and terminal OH groups of linear hydrogen-bonded chains. This has the effects that (a) the absolute amounts of the hydrogen-bonded species are lower in these solvents than at the same total mole fraction of alcohol in n-hexane, cyclohexane, or carbon disulphide, and (b) the ratio of cyclic to linear associated forms is lower in the aromatic solvents and carbon tetrachloride than in the other solvents. These effects account qualitatively for the great difference in the apparent dipole moment observed in various solvents.

Equilibria among point defects in GdF3–doped CaF2

EPR and dielectric relaxation measurements, reported earlier, have been combined to produce estimates of the mole fraction (n′) of pairs formed of substitutional Gd3+ ions and F− interstitials as a function of total GdF3 mole fraction (M) and temperature at which the crystals are annealed prior to rapid cooling. Over the range of M from 1×10−4 to 27×10−4, n′ rises to a saturation value when M increases to about 10−3. At constant M, n′ goes through a maximum at anneal temperatures from about 1073 to 1273 K. The rate of the annealing reaction increases with M and with decreasing sample size, and the density increases with increasing M faster than the interstitial model predicts. A qualitative model of the annealing process is suggested, in which F− interstitials react with an atmospheric constituent (probably HF) to form an immobile complex that provides remote charge compensation for the cubic Gd3+ ions. The remaining free F− interstitials are trapped by Gd3+ ions during quenching to form the pairs.