Dehydration equilibria calculation

If the equilibrium constant of the chemical reaction (such as complex stability constant, hydration-dehydration equilibrium constant, or the piCa of the investigated acid-base reaction) is known, limiting currents can be used to calculate the rate constant of the chemical reaction, generating the electroactive species. Such rate constants are of the order from 104 to 1010 Lmols-1. The use of kinetic currents for the determination of rate constants of fast chemical reactions preceded even the use of relaxation methods. In numerous instances a good agreement was found for data obtained by these two independent techniques. 

A recent paper by Singh et al. summarized the mechanism of the pyrazole formation via the Knorr reaction between diketones and monosubstituted hydrazines. The diketone is in equilibrium with its enolate forms 28a and 28b and NMR studies have shown the carbonyl group to react faster than its enolate forms.Computational studies were done to show that the product distribution ratio depended on the rates of dehydration of the 3,5-dihydroxy pyrazolidine intermediates of the two isomeric pathways for an unsymmetrical diketone 28. The affect of the hydrazine substituent R on the dehydration of the dihydroxy intermediates 19 and 22 was studied using semi-empirical calculations. ... 

The UV absorption spectra of sodium nitrite in aqueous solutions of sulfuric and perchloric acids were recorded by Seel and Winkler (1960) and by Bayliss et al. (1963). The absorption band at 250 nm is due either to the nitrosoacidium ion or to the nitrosyl ion. From the absorbancy of this band the equilibrium concentrations of HNO2 and NO or H20 —NO were calculated over the acid concentration ranges 0-100% H2S04 (by weight) and 0-72% HC104 (by weight). For both solvent systems the concentrations determined for the two (or three) equilibrium species correlate with the acidity function HR. This acidity function is defined for protonation-dehydration processes, and it is usually measured using triarylcarbinol indicators in the equilibrium shown in Scheme 3-15 (see Deno et al., 1955 Cox and Yates, 1983). 

When the activity of each species in a reaction is known, we can determine the temperature (or temperatures) at which the reaction is in equilibrium. As an example, we calculate the temperature at which gypsum (CaS04 2 H2O) dehydrates to form anhydrite (CaS04). The RXN commands... 

In principle the velocity of dehydration could be measured if a physical rather than a chemical method were available for removing the unhydrated carbonyl compound at a rate comparable to its hydration. It was claimed by Bieber and Triimpler (1947a) that this could be achieved by the removal of formaldehyde in a rapid gas stream, the rate of which appeared to be dependent on the pH of the solution. However, attempts to repeat their experiments have proved unsuccessful moreover, although they give no experimental details, calculation in terms of known kinetic and equilibrium constants shows that for a 1-ml liquid sample a gas flow of at least 30 litres/min would be required to produce an appreciable perturbation of equilibrium conditions (Bell and Evans, 1966). It is thus clear that this method has no practical application, at least to formaldehyde solutions. 

Salwin and Slawson (1959) found that stability in dehydrated foods was impaired if several products were packaged together. A transfer of water could take place from items of higher moisture-vapor pressure to those of lower moisture-vapor pressure. These authors determined packaging compatibility by examining the respective sorption isotherms. They suggested a formula for calculation of the final equilibrium moisture content of each component from the iso-... 

The pyranose 35 and the furanose 164 are stable in neutral solution at room temperature, and are separable by column chromatography without equilibration. On heating, or by acid catalysis (0.1 M hydrochloric acid, room temperature, 35 hours), an equilibrium between forms 35 and 164 is established. From the optical rotation, the ratio of the six-membered to the five-membered ring is calculated to be about 2 1. Alkaline catalysis causes very rapid attainment of equilibrium, but, simultaneously, decomposition occurs. The 5-acetamidopyranose 35 is, after attainment of its equilibrium, stable toward acids, and shows no dehydration reaction to form 3-pyridinol. However, under conditions in which the N-acetyl group is hydrolytically removed (heating with 2 M hydrochloric acid), 35 is transformed into 3-pyridinol through the intermediate formation of free 5-amino-5-deoxy-D-xylopyranose. ... 

To characterise the functionally Important motions in hydrated myoglobin, simulations on its hydrated CO complex have been performed by Steinbach and Brooks [35], In this study the temperature and hydration dependence of equilibrium dynamics was investigated. The authors performed two sets of MD simulations, torsionally restrained and unrestrained calculations on dehydrated carbonmonoxy myoglobin at different temperatures between 100 K and 400 K were compared to that on the hydrated protein. They found that the dehydrated protein exhibits almost exclusively harmonic fluctuations at all temperatures, while remarkable anharmonic motions have been detected in the hydrated protein at about 200 K independently whether the torsions were constrained. The... 

Reversible reactions. Many solid-gas reactions are reversible, e.g., dehydration of crystal hydrates, so that rate equations for such processes should include terms for the rate of the reverse reaction. If the rates of contributing forward and reverse reactions are comparable, the general set of kinetic models (Table 3.3.) will not be applicable. The decomposition step in a reversible reaction thus needs to be studied [94] under conditions as far removed from equilibrium as possible (e.g. low pressures or high flow rates of carrier gas) and sensitive tests are required for determining whether the kinetics vary with the prevailing conditions. Sinev [95] has calculated that, for the decomposition of calcium carbonate, the rate of the reverse reaction is comparable with that of the forward reaction even when small sample masses (10 mg) and high flow rates (200 cm s ) of inert gas are used. Interpretation of observations becomes more difficult and the reliabihty of conclusions decreases if local inhomogeneities of kinetic behaviour develop within the reactant mass. 

The equilibrium values for the dehydration of ethanol to ethylene have been calculated by Francis 08 and show that ethanol has a considerable tendency to decompose into ethylene. 

These latter calculations give a value of K = 0.00376 for the hydration of ethylene or K = 266 for the dehydration of ethanol at 450° C. If this value represents more nearly the correct equilibrium, then the conversion of ethylene to ethanol under the above conditions would be decreased still further to a value of approximately 40 per cent. At atmospheric pressure and this temperature the decomposition of ethanol is practically complete at equilibrium. 

The differences in the C=0 vibrational frequencies of the citric acid and its decarboxylation byproducts (CE, I, ME) has been used to extract reaction kinetic information (Figure 8). Figure 7 (a) shows a plot of the relative variation of the ratios of the 1653 cm" and 1740 cm peaks with the progression of the reaction. These calculations indicate that the reaction rapidly approaches equilibrium at these hydrothermal conditions. This observation is consistent with those of Cody et al. for this system at similar conditions [25]. Additional information regarding the progression of the dehydration reactions can be inferred from the changes in the ratios of the CH (2930 cm ) and the OH (3430 cm ) peaks as shown in Figure... 

Figure 37 Formation of 3(S)- and 3(fl)-hydroxybutyryl-CoA by ECH. Experimentally, the equilibrium constant is 7.5. Since the two enantiomers have the same energy, K2 must also be 7.5. Ab initio studies predict that frans-2-crotonyl-CoA is 12 kJ mol more stable than the c/s isomer, giving an equilibrium constant between the two enantiomers of 0.0079 (K4). K3, the equilibrium constant for the dehydration of 3(fl)-hydroxybutyryl-CoA to c/s-2-crotonyl-CoA, can then be calculated from the relationship K3 = K4/K2 = 0.001. Reproduced with permission from W. J. Wu Y. Feng X. Fie FI. S. Flofstein D. P. Raleigh P. J. Tonge, J. Am. Chem. Soc. 2000, 122, 3987.

Normally of course the expression for the variation of K with P is simpler than this, perhaps because all three states of matter may not be present, but also because it is quite unusual to use a variable pressure standard state for constituents whose fugacities are known or sought, (because this adds complexities rather than simplifying matters), and the In Qig) term is therefore essentially never required. To take a real example, let s consider the brucite-periclase reaction again. We have discussed the variation of the equilibrium constant for the brucite-periclase-water reaction with temperature at one bar, and showed that the equilibrium temperature for the reaction at one bar is about 265°C. Calculation of the equilibrium temperature of dehydration reactions such as this one at higher pressures was discussed briefly in 13.2.2. Here we will discuss the reaction in different terms to demonstrate the relationships between activities, standard states and equilibrium constants. 

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