Temperature effects on equilibrium constants

A distinct temperature effect on equilibrium constants is to be noted in Table VII. Velocity constants, likewise, are influenced very considerably by temperature. Ingram and Vas (1950b) calculated ki at 20° C. (4.85 X 10 ) and /c2 at 37° C. (1.55 X 10 ), thus showing an approximately 3-fold increase in the value of the addition rate constant in going from 20° to 37° C. 

Giauque, whose name has already been mentioned in connection with the discovery of the oxygen isotopes, calculated Third Law entropies with the use of the low temperature heat capacities that he measured he also applied statistical mechanics to calculate entropies for comparison with Third Law entropies. Very soon after the discovery of deuterium Urey made statistical mechanical calculations of isotope effects on equilibrium constants, in principle quite similar to the calculations described in Chapter IV. J. Kirkwood s development showing that quantum mechanical statistical mechanics goes over into classical statistical mechanics in the limit of high temperature dates to the 1930s. Kirkwood also developed the quantum corrections to the classical mechanical approximation. 

As the reaction temperature increases, the equilibrium constant diminishes, since complex formation is accompanied by heat liberation. Sterically hindered phenols form loose complexes because of the impeding effect of voluminous alkyl substituents in the ortho-position. Hydrogen bonding reduces the activity of phenols, which was first observed in the studies of the effects of cyclohexanol and butanol on the inhibitory activity of a-naphthol in cyclohexane [9]. This phenomenon was investigated in detail with reference to the oxidation of methylethylketone [10]. The k7 values for some inhibitors of the oxidation of ethylbenzene and methylethylketone are given below (333 K) [10,46] ... 

The Hood s equation was based on the experimental results. Some theoretical significance to this equation was given by Vant Hoff (1884) on the basis of the effect of temperature on equilibrium constants. This idea was extended by Arrhenius in his attempt to obtain the relation between rate constant and temperature. The relation obtained was successfully applied by him to the effect of temperature data for a number of reactions and the equation is usually called the Arrhenius equation. 

Also, AH values are required to calculate the temperature dependence of equilibrium constants. For aU these reasons, it is desirable to have tables of AH values available, so that the enthalpies of various transformations can be calculated readily. In many of these calculations, we make use of Hess s law, which is now firmly established on the basis of the first law of thermodynamics. We can then calculate AH for reactions for which the heat effect is difficult to measure but that can be expressed as sums of reactions with known values of AH. 

Changing the column temperature can produce a variety of additional effects. Temperature changes the balance between enthalpy and entropy effects on retention mechanisms. Changing the temperature changes the equilibrium constants of both solvent and solutes, and it changes the... 

Chemical reactions at supercritical conditions are good examples of solvation effects on rate constants. While the most compelling reason to carry out reactions at (near) supercritical conditions is the abihty to tune the solvation conditions of the medium (chemical potentials) and attenuate transport limitations by adjustment of the system pressure and/or temperature, there has been considerable speculation on explanations for the unusual behavior (occasionally referred to as anomalies) in reaction kinetics at near and supercritical conditions. True near-critical anomalies in reaction equilibrium, if any, will only appear within an extremely small neighborhood of the system s critical point, which is unattainable for all practical purposes. This is because the near-critical anomaly in the equilibrium extent of the reaction has the same near-critical behavior as the internal energy. However, it is not as clear that the kinetics of reactions should be free of anomalies in the near-critical region. Therefore, a more accurate description of solvent effect on the kinetic rate constant of reactions conducted in or near supercritical media is desirable (Chialvo et al., 1998). 

Water, however, has the opposite effect. Actual equilibrium constants at various temperatures are given in Table 7. A detailed study of the effect of pressure on urea conversion is given in Ref. 17. 

In this chapter we will find that when isomers are in chemical equilibrium, it is convenient to treat isomer groups like species in order to reduce the number of terms in the fundamental equation. We will also discuss the effect of ionic strength and temperature on equilibrium constants and thermodynamic properties of species. More introductory material on the thermodynamics of chemical reactions is provided in Silbey and Alberty (2001). 

When considering the effect of temperature on equilibrium constant, the sign and magnitude of AH° are the determining factors. However, the spontaneity of a reaction is determined by the sign and magnitude of AS°, which determines the effect of temperature. 

Know the effect of temperature on equilibrium constants, free energy, and entropy and enthalpy changes. 

I continue to feel that the study of the volume changes in protein reactions is sorely neglected. They may be determined by dilatometry and by the effects of pressure on protein equilibrium constants. The results complement the results of the determination of enthalpy changes as measured by calorimetry and the effects of temperature on equilibrium constants. Much useful insight at the molecular level can be obtained from a knowledge of volume changes... 

Temperature effects on coating response behavior are varied. For reversible equilibrium-based sensors, increased temperature results in decreased sensitivity. An example of this tonperature-dependent response behavicM- is provided in Figure S.4 for a PIB-coated SAW device exposed to dichloroediane (DCE) vapor. From Figure 5.4(a) it can be seen that the response (in Hz) increases steadily as the concoitration of DCE increases, but that the sltqte of the response curve decreases with increasing temperature. This decreased sensitivity is due to the Arrhenius-type decrease in the equilibrium constant, K (see Sections 5.4.1 and... 

Equivalently, we can describe the shifts in terms of the effect of temperature on equilibrium constants. The equilibrium constant for an endothermic reaction increases with increasing temperature, while that for an exothermic reaction decreases with increasing temperature. 

The WGS reaction (Eq. 6.1) is slightly exothermic (AH = -41.16kJ/mol, gas phase) and is a typical example of reaction controlled by equilibrium, especially at higher temperatures. The equilibrium constant is a function of temperature. The reaction proceeds without change in the number of moles and in consequence pressure does not have any significant effect on equilibrium. For pressures between 10 and 50 bar, the following expressions are recommended for the equilibrium constant as a function of temperature 5... 

The similarity coefficient, a, can be temperature dependent although reference dissociation constants are determined at 25 °C under standard conditions which usually involve water solvent and zero ionic strength. It is therefore the aim to carry out all measurements of equilibrium constants and rate constants under these conditions or to extrapolate from other temperatures. The temperature effect on the similarity coefficient, a, is only meaningful if the standard dissociation equilibria are for the standard temperature. Measuring a values for different temperatures against standard equilibria at these same temperatures introduces the uncertainty due to the temperature variation of the standard a. 

It has been already discussed (e.g. Eq, (3.18)) that the PZC can be considered as a linear function of log A of a surface reaction responsible for proton adsorption and dissociation. Once this reaction is defined, the standard thermodynamic approach (Section 2.II) can be applied, and the temperature effect on the equilibrium constant can be calculated by combining Eqs, (2.20) and (2,24). 

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