Baudilio Coto

Vapour-liquid equilibrium of the ethanol–propanal system

A Gibbs–Van Ness type apparatus for total vapour-pressure measurements of binary mixtures has been developed. Vapour–liquid equilibrium data for the ethanol–cyclohexane system at 298.15 K have been obtained and compared with previous literature data. Data reduction has been carried out by a modified Barkers method using a Pade approximant to describe to excess Gibbs energy. The vapour–liquid equilibrium data for the ethanol–propanal systems have been measured over the whole concentration range at 298.15, 308.15 and 318.15 K. These mixtures show negative deviations from ideality. The calculated values for the excess functions are large and negative, and the calculated values for the concentration–concentration correlation function are lower than ideal values. This experimental behaviour is analysed in terms of the UNIQUAC model and several versions of the UNIFAC model.

Bulk and surface properties of the highly non-ideal associated mixtures formed by methanol and propanal

Bulk (vapour–liquid equilibrium and excess enthalpy data) and surface (surface tension) properties of the highly non-ideal associated mixtures formed by methanol and propanal have been measured. The vapour–liquid equilibrium data have been obtained at 288.15, 298.15, 308.15 and 318.15 K using a Gibbs–Van Ness type apparatus. These mixtures show negative deviations from ideality, including a negative azeotrope in the methanol-rich region. The calculated values for the excess Gibbs energy are very large and negative, and their absolute value decreases sharply with increasing temperature. The calculated values for the concentration–concentration correlation function are lower than those corresponding to an ideal mixture and exhibit a minimum in the middle of the concentration range. The excess enthalpy data have been obtained at 4.00 MPa and 298.15 and 318.15 K by means of a high-pressure flow calorimeter. Values for the excess enthalpies are very exothermic and in agreement with those calculated from the excess Gibbs energies. The surface tension has been measured at 298.15 K. Values for the relative surface adsorption calculated from the surface tension and the chemical potentials indicate that the surface is significantly enriched in propanal for mixtures rich in methanol. A complex composition dependence of the concentration profiles can be inferred. The lattice-fluid and the lattice-fluid associated solution models have been used to describe the bulk properties of the methanol–propanal mixtures.

Bulk and surface properties for the methanol–1,1-dimethylpropyl methyl ether and methanol–1,1-dimethylethyl methyl ether systems

Bulk (vapour–liquid equilibrium data) and surface (surface tension) properties of the mixtures formed by methanol and the branched ethers 1,1-dimethylpropyl methyl ether (tert-amyl methyl ether or TAME) and 1,1-dimethylethyl methyl ether (tert-butyl methyl ether or MTBE) have been studied. A Gibbs–Van Ness type apparatus for total vapour pressure measurements was used to obtain vapour–liquid equilibria (VLE) data for methanol–TAME at 298.15 and 318.15 K. The system shows positive deviations from Raoults law with an azeotrope. The surface tension, γ, for methanol–TAME and methanol–MTBE mixtures was measured at 298.15 and 308.15 K. Values for the relative surface adsorption calculated from the surface tension and the chemical potentials indicate that the surface is enriched in ether. The lattice-fluid, the lattice-fluid associated solution, and the extended real association solution models have been used to describe the bulk properties of the methanol–TAME mixtures. The model proposed by Rice and Teja has been used to describe the surface tension of the methanol–MTBE and methanol–TAME mixtures.

Simultaneous description of excess enthalpy and vapour–liquid equilibrium data of associated mixtures by means of a lattice–fluid model

Excess enthalpies (HE) and vapour-liquid equilibrium (VLE) data for several associated mixtures have been analysed by means of the lattice–fluid model (LF) and the lattice–fluid associated solution model (LFAS). The systems considered were selected in order to include a variety of associated solutions, and exhibit self- and cross-association interactions. The inclusion of the chemical contribution in the LFAS model makes it necessary to fit any parameter within the physical contribution. In general, the LFAS model represents an improvement in the overall description of the excess functions of associated mixtures, while in some cases the use of the LF model leads to unrealistic values of the physical interaction parameters.

Vapour-liquid equilibria for the binary system cyclohexane-1,1-dimethylethyl methyl ether (MTBE) at 298.15, 308.15 and 318.15 K

Vapour–liquid equilibrium data are reported for the binary mixtures formed by cyclohexane and the branched ether 1,1-dimethylethyl methyl ether (tert-butyl methyl ether or MTBE). A Gibbs–Van Ness type apparatus was used to obtain total vapour pressure measurements for cyclohexane–MTBE mixtures at 298.15, 308.15 and 318.15 K. The system exhibits very small deviations from Raoults law with a nearly ideal behaviour. No temperature effect on vapour compositions is observed. Results are analysed in terms of the Peng–Robinson equation of state and the Wong–Sandler mixing rule, the lattice-fluid model, the UNIQUAC model, and the UNIFAC and modified UNIFAC models.

Monte Carlo method to explain the probabilistic interpretation of atomic quantum mechanics

Quantum mechanics description of physical and chemical systems is included in books of Physics, General Chemistry or Physical Chemistry including mathematical, graphical, and conceptual descriptions. Mathematical calculations are complex and are covered only in advanced courses. Main problem in the first degree courses is the understanding of the probabilistic interpretation of quantum mechanics. The Monte Carlo method is based on probabilistic concepts and its application to quantum calculations can be carried out quite straightforward. In this work, a simple Monte Carlo method was used to obtain a sequence of random electron coordinates according to the probability given by the wave function. Electron is seen as a shot whose appearance is only accepted and plotted when probability is high enough. Hydrogen atom was studied as it is a familiar system for most students and its description can be easily related to previous knowledge of atomic orbitals. The objective of the present work is to supply all the crucial points that students need to create their own program to plot atomic orbitals according to the above ideas. All the numerical details are indicated in order to get the proposed programming project as a simple task. Student should be able to generate random electron coordinates, to compute wave functions and probabilities, and to obtain plots according to the right probabilistic interpretation of quantum mechanics. In order to show the quantitative obtained plots some results were shown. Typical s, p, and d orbitals were obtained and compared to the usual angular and radial representation.

Broadening of polymer chromatographic signals: Analysis, quantification and correction through effective diffusion coefficients

Average molecular weights and polydispersity indexes are some of the most important parameters considered in the polymer characterization. Usually, gel permeation chromatography (GPC) and multi angle light scattering (MALS) are used for this determination, but GPC values are overestimated due to the dispersion introduced by the column separation. Several procedures were proposed to correct such effect usually involving more complex calibration processes. In this work, a new method of calculation has been considered including diffusion effects. An equation for the concentration profile due to diffusion effects along the GPC column was considered to be a Fickian function and polystyrene narrow standards were used to determine effective diffusion coefficients. The molecular weight distribution function of mono and poly disperse polymers was interpreted as a sum of several Fickian functions representing a sample formed by only few kind of polymer chains with specific molecular weight and diffusion coefficient. Proposed model accurately fit the concentration profile along the whole elution time range as checked by the computed standard deviation. Molecular weights obtained by this new method are similar to those obtained by MALS or traditional GPC while polydispersity index values are intermediate between those obtained by the traditional GPC combined to Universal Calibration method and the MALS method. Values for Pearson and Lin coefficients shows improvement in the correlation of polydispersity index values determined by GPC and MALS methods when diffusion coefficients and new methods are used.

Euler algorithm to solve reaction kinetic equations: Mathematical formulation, programing, and applications

Integration of rate laws to obtain the several concentrations in terms of time is well described in books of General Chemistry, Physical Chemistry, or Chemical Engineering including mathematical and graphical descriptions. When several reactions have to be considered simultaneously, the mathematical solution of involved differential equations became difficult for students and is a good task from the mathematical point of view. Qualitative interpretation has interest from the chemical and engineering point of view and it is usually related with the change of concentrations along reactions which in turns modifies the rate of the several processes involved. In this work, no differential equations are solved analytically and no functions are obtained in order to reduce the mathematical complexity for students but a numerical solution is obtained by using the differential method and the computation of changes in concentration. A general formulation of the involved equations is presented including the effect of reactant concentration in the rate laws and an arbitrary number of simultaneous reactions. Details for numerical solution of involved equations are indicated and the task for students is to create their own program to solve the rate laws. Student should be able to input a set of compounds and reactions, to compute the evolution of concentrations of the several species with time and to plot such concentrations. Some applications with increasing complexity were computed and analyzed. In order to show the quantitative obtained results, comparison with analytical functions was carried out for simple systems.