On Conditions of Solvability of the Goursat Problem for Generalized Aller Equation

© 2018, Allerton Press, Inc. In terms of coefficients of an equation under consideration, we derive 16 variants of collections of conditions of resolvability of this equation in quadratures. Every collection consists of three identities that interconnect five coefficients appearing in left-hand side of an equation

Internal and external factors promoting the Diels-Alder reaction

The basic chemical and physical factors determining the rate and equilibrium of the Diels-Alder reaction under standard and high hydrostatic pressures were considered. The search for favorable conditions for this process makes it possible to extend the range of potential reactants and to perform reactions that earlier considered to be forbidden. © 2013 Springer Science+Business Media New York

Dynamics of alcohol consumption by the population in the period before and during the Covid-19 pandemic in the Russian Federation

The purpose of the study is to analyze the dynamics of alcohol consumption by the population in the period before and during the COVID-19 pandemic in the Russian Federation.Цель исследования – анализ динамики потребления алкоголя населением в период до и во время пандемии COVID-19 в РФ

Solvent effect on the enthalpy of solution and partial molar volume of the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate

Enthalpies of solution and partial molar volumes of the ionic liquid 1-butyl-3- methylimidazolium tetrafluoroborate were determined in 15 solvents of different polarity. Very large differences of the enthalpies of solution (Δ ΔsolHIL = 38.9 kJ·mol -1) and partial molar volumes (ΔVIL = 43 cm 3·mol -1) are nearly the same as observed for lithium perchlorate solutions. These results clearly indicate that the low values of the macroscopic polarity parameters of [bmim]BF 4 do not correspond with the large differences of the intermolecular interactions in IL solutions. The values of the partial molar volume of the cation, V [bmim]+, were estimated for the first time. The changes of the partial molar volumes, V IL, reflect mainly the changes of anion volume, V BF4. The rate of the Diels-Alder reaction of 9,10- dimethylanthracene with maleic anhydride in the [bmim]BF 4 medium was nearly the same as in common molecular solvents. © Springer Science+Business Media, LLC 2012

Energy and volume activation parameters of the retro-Diels-Alder reaction in different solvents

The temperature and pressure effects on the decay rate of an adduct obtained from 9-chloroanthracene and tetracyanoethene by a Diels-Alder reaction were studied. The rate constants (298.2 K) and the enthalpies, entropies, and volumes of activation were determined for the retro-Diels-Alder reaction in different solvents. The data obtained confirm a possible decrease in the molar volume of the solvated adduct upon partial bond cleavage on the way to the transition state. The reversal of the sign in front of the activation volume cannot be indicative of a changed reaction mechanism. © 2009 Springer Science+Business Media, Inc

Compressibility of liquids. Rule of noncrossing V-P curvatures

Weight analysis of the liquid introduced into the stainless steel bomb under pressures up to 1 kbar in the temperature range of 20-50°C at the interval of 10°C was performed for 1,4-dioxane, acetonitrile, toluene, ethyl acetate, chlorobenzene, and n-hexane. The coefficients of the Tait equation were determined for all of the solvents at each temperature. There was a clear linear relation between the tangent bulk modulus (1/βT) at atmospheric pressure (1 bar) and the secant bulk modulus at 1 kbar; 1/βT = 0.9865 × (1000 V0/ΔV 1kbar) - 4559 was found at a wide range of temperatures for different liquids, including glycerol and even mercury. This represents the rule of noncrossing P-V curvatures for the liquids. Using the correlation, it is possible to predict the coefficients (C, B) of the Tait equation from the experimental data of βT at 1 bar or, on the other hand, to calculate the value of βT from experimental compression at high pressures. © 2008 American Chemical Society

Homo-Diels-Alder reaction of a very inactive diene, bicyclo[2,2,1]hepta-2, 5-diene, with the most active dienophile, 4-phenyl-1,2,4-triazolin-3,5-dione. Solvent, temperature, and high pressure influence on the reaction rate

Solvent, temperature, and high pressure influence on the rate constant of homo-Diels-Alder cycloaddition reactions of the very active hetero-dienophile, 4-phenyl-1,2,4-triazolin-3,5-dione (1), with the very inactive unconjugated diene, bicyclo[2,2,1]hepta-2,5-diene (2), and of 1 with some substituted anthracenes have been studied. The rate constants change amounts to about seven orders of magnitude: from 3.95.10-3 for reaction (1+2) to 12200 L mol-1 s-1 for reaction of 1 with 9,10-dimethylanthracene (4e) in toluene solution at 298 K. A comparison of the reactivity (ln k2) and the heat of reactions (r-nH) of maleic anhydride, tetracyanoethylene and of 1 with several dienes has been performed. The heat of reaction (1+2) is -218 ± 2 kJ mol-1, of 1 with 9,10-dimethylanthracene -117.8 ± 0.7 kJ mol-1, and of 1 with 9,10-dimethoxyanthracene -91.6 ±0.2 kJ mol-1. From these data, it follows that the exothermicity of reaction (1+2) is higher than that with 1,3-butadiene. However, the heat of reaction of 9,10- dimethylanthracene with 1 (-117.8 kJ mol-1) is nearly the same as that found for the reaction with the structural C=C counterpart, N-phenylmaleimide (-117.0 kJ mol-1). Since the energy of the N=N bond is considerably lower (418 kJ/bond) than that of the C=C bond (611 kJ/bond), it was proposed that this difference in the bond energy can generate a lower barrier of activation in the Diels-Alder cycloaddition reaction with 1. Linear correlation (R = 0.94) of the solvent effect on the rate constants of reaction (1+2) and on the heat of solution of 1 has been observed. The ratio of the volume of activation (V≠) and the volume of reaction (V r-n) of the homo-Diels-Alder reaction (1+2) is considered as "normal": V≠/Vr-n = -25.1/-30.95 = 0.81. Copyright © 2012 John Wiley & Sons, Ltd

Enthalpies of solution and partial molar volumes of magnesium perchlorate in alcohols and salt effect of acceleration of the Diels-Alder reaction

Densities and enthalpies of solution at 25°C were measured for dilute solutions of magnesium perchlorate (MP) in some alcohols using the Anton Paar DSA 5000M vibrating tube densimeter and differential calorimetric measurements. In all studied solvents the solution of MP was highly exothermic and large solvent volume contraction was observed. Maximum effect was obtained in methanol and ethanol solutions. Acceleration effect of the Diels-Alder reaction of 9,10-dimethylanthracene with acrylonitrile (in medium of acrylonitrile) in the presence of salts LiClO4, Mg(ClO4)2 and GaCl3 was as 18:160:59,000. © 2011 Elsevier B.V

Studying the effect of high pressure on the cycloaddition reactions of maleic anhydride and substituted anthracenes

The kinetics (rate, activation, and volume) of the high-pressure (up to 2500 bar) Diels-Alder reactions of maleic anhydride with 9-phenylanthracene and 9,10-dimethylanthracene in toluene is investigated. © 2013 Pleiades Publishing, Ltd

Anomalies in the change of volumetric parameters of the Diels-Alder reaction in solution

In this article negative values of the activation volume in retro-Diels-Alder reactions are interpreted in terms of the different possibilities of penetration of the solvent molecules into the sterically branched structures of the adduct and activated complex. Empty spaces, inaccessible to penetration of solvent molecules, lead to increases of the molar volume of the screened adducts in solution and, consequently, to a less negative value of the Diels-Alder reaction volume. The values of partial molar volumes of anthracene, maleic anhydride and the adducts cyclopentadiene-maleic anhydride, anthracene-maleic anhydride and anthracene-tetracyanoethylene, in several solvents, were calculated from the solution density data. © Springer Science+Business Media, LLC 2012