Constant-temperature, chemical reactions

The most important themiodynamic property of a substance is the standard Gibbs energy of fomiation as a fimetion of temperature as this infomiation allows equilibrium constants for chemical reactions to be calculated. The standard Gibbs energy of fomiation A G° at 298.15 K can be derived from the enthalpy of fomiation AfT° at 298.15 K and the standard entropy AS° at 298.15 K from... 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

The procedure of Beutier and Renon as well as the later on described method of Edwards, Maurer, Newman and Prausnitz ( 3) is an extension of an earlier work by Edwards, Newman and Prausnitz ( ). Beutier and Renon restrict their procedure to ternary systems NH3-CO2-H2O, NH3-H2S-H2O and NH3-S02 H20 but it may be expected that it is also useful for the complete multisolute system built up with these substances. The concentration range should be limited to mole fractions of water xw 0.7 a temperature range from 0 to 100 °C is recommended. Equilibrium constants for chemical reactions 1 to 9 are taken from literature (cf. Appendix II). Henry s constants are assumed to be independent of pressure numerical values were determined from solubility data of pure gaseous electrolytes in water (cf. Appendix II). The vapor phase is considered to behave like an ideal gas. The fugacity of pure water is replaced by the vapor pressure. For any molecular or ionic species i, except for water, the activity is expressed on the scale of molality m ... 

Electron movement across the electrode solution interface. The rate of electron transfer across the electrode solution interface is sometimes called k. This parameter can be thought of as a rate constant, although here it represents the rate of a heterogeneous reaction. Like a rate constant, its value is constant until variables are altered. The rate constants of chemical reactions, for example, increase exponentially with an increasing temperature T according to the Arrhenius equation. While the rate constant of electron transfer, ka, is also temperature-dependent, we usually perform the electrode reactions with the cell immersed in a thermostatted water bath. It is more important to appreciate that kei depends on the potential of the electrode, as follows ... 

A change in temperature, however, does force a change in the equilibrium constant. Most chemical reactions exchange heat with the surroundings. A reaction that gives offbeat is classified as exothermic, whereas a reaction that requires the input of heat is said to be endothermic. (See Table 13-2.) A simple example of an endothermic reaction is the vaporization of water ... 

Duration of a cycle of HHP operation is defined as time required for reaction hydrogenation/dehydrogenation in pair hydride system. This time determines heat capacity of HHP. Duration of a cycle depends on kinetics of hydrogenation reactions, a heat transfer between the heated up and cooling environment, heat conductivities of hydride beds. Rates of reactions are proportional to a difference of dynamic pressure of hydrogen in sorbers of HHP and to constants of chemical reaction of hydrogenation. The relation of dynamic pressure is adjusted by characteristics of a heat emission in beds of metal hydride particles (the heat emission of a hydride bed depends on its effective specific heat conductivity) and connected to total factor of a heat transfer of system a sorber-heat exchanger. The modified constant of speed, as function of temperature in isobaric process [1], can characterize kinetics of sorption reactions. In HHP it is not sense to use hydrides with a low kinetics of reactions. The basic condition of an acceptability of hydride for HHP is a condition of forward rate of chemical reactions in relation to rate of a heat transmission. 

Passing over to the computation of the rate constants of specific reactions, we again emphasize that the J(R) expansion from (37) in a power series of R is not necessary. It only enables one to obtain analyzable relations through application of different models of a solid. In the general case the problem of the calculation of low-temperature chemical reaction rate constants requires consecutive solution of two problems search of convenient PESs and averaging of the imaginary part of the action along the optimal path from relation (49). 

Finally, this work demonstrates the capability of the transition-state theory to provide accurate rate constants of chemical reactions, at least at temperatures at which tunneling plays a relatively negligible role. 

The experimental evidence presented in Fig. 1 shows that, at constant temperature, the reaction rate is not affected by the size of catalyst when the latter is varied from 3 to 3 2-in. This indicates that the rate constants, derived from the experimental data, represent those for the chemical process during the reaction and that mass diffusion in or out the pores of the catalyst does not affect appreciably the rate of the over-all process. This conclusion can be checked by computing the value of the rate constant per unit volume of reactor for the case of a reaction completely limited by diffusion. This rate constant,, is given by (2) = 10 - /VifMa, where... 

This chapter discusses the intenelation between mechanical properties, molecular mobility and chemical reactivity of curing epoxy-amine thermosets, illustrated by examples of how the charge recombination luminescence (CRL), heat-capacity and rate constants of chemical reactions are influenced by gelation and vitrification during isothermal cure. A comparison of dynamic mechanical, CRL and modulated temperature DSC data shows that vitrification is accompanied by an increase in CRL and a decrease in heat-capacity, and that the heat-capacity and CRL continue to change after the viscoelastic properties have levelled out. It is also shown how the rate constant of an intermolecular secondary amine reaction, measured by near infirared spectroscopy, is sensitive to gelation, whereas the intramolecular rate constant instead is sensitive to vitrification. 

The rate constant gives us valuable information about the kinetics of a chemical reaction. Perhaps most importantly, the magnitude of the rate constant tells us whether or not a reaction proceeds quickly. If the rate constant is small, the reaction is likely to proceed slowly. By contrast, a large rate constant indicates a rapid reaction. Rate constants for chemical reactions range over many orders of magnitude. We should also point out that the value of the rate constant depends on the temperature of the reaction. (We will consider temperature dependence further in Section 11.5, but it may take some time to get used to the idea of a constant that is a function of a variable.) The temperature dependence of the rate of a reaction is described in terms of the rate constant, as we ll see in Section 11.5. 

Moreover, the van t Hoff equation for the temperature dependence of the equilibrium constant of chemical reactions dlniiC(T) ... 

The half-life of the uranium isotope is about 1 X 10 times larger than the half-life of the polonium isotope. Unlike the rate constants for chemical reactions, moreover, the rate constants for nuclear decay are unaffected by changes in environmental conditions, such as temperature and pressure (see Table 17.1). 

R. L. Jaffe, Rate Constants for Chemical Reactions in High-Temperature Nonequilibrium Air , AIAA Progress in Astronautics and Aeronautics Thermo-physical Aspects of Re-entry Flows, Vol. 103, edited by J. N. Moss and C. D. Scott, New York, 1986, p. 123 R. L. Jaffe, The Calculation of High-Temperature Equilibrium and Nonequilibrium Specific Heat Data for 7 2, O2 and ATO , AIAA Paper 87-1633, AIAA 22nd Thermophysics Conference, Honolulu, HI, June 1987. 

Clary DC, Stoecklin TS, Wickham AG. (1993) Rate constants for chemical-reactions of radicals at low-temperatures. J. Chem. Soc. Faraday Trans. 89 2185-2191. 

Temperature range of delivered heat. All of the endothermic high-temperature chemical reactions are dissociation reactions that operate at nearly a constant temperature. Heat should be delivered over a small temperature range. 

The reaction rate depends on a temperature term (with Boltzmann and Planck constants), the pseudo-equilibrium constant for formation of the transition state, a pressure term and finally fugacities f of reactants and activation state. The last term also represents SCF properties, but determination or calculation is difficult. However, with further modifications, the rate constants of chemical reactions relate to the activation volume of the transition state. The logarithmic nature of the equation implies that large pressure changes are necessary to affect the reaction rate significantly ... 

IVTANTHERMO consists of several databases and a set of algorithms and programs. The databases contain auxiliary data, for example, fundamental physical constants, atomic masses of elements etc. -, constants necessary for the calculations of thermodynamic functions primary experimental data on equilibrium constants of chemical reactions and on saturated vapor pressure of substances thermochemical constants tabulated values of thermodynamic properties for wide temperature intervals. 

If we are dealing with the problem of industrial optimization or fault analysis of an existing plant, the flowsheet and equipment of this industrial process have been specified, the physico-chemical parameters such as the equilibrium constants of chemical reactions or the heat capacity of materials have been all specified, the process can be described by another series of dimensionless numbers such as the relative pressure (P/Po), relative temperature (T/To), relative volume (VA o), and so on. Based on the above-mentioned concept, we can see that the theoretical basis of the data processing methods for industrial optimization and fault diagnosis is relevant to dimensional analysis in this respect. 

The endothermic high-temperature chemical reactions of dissociation require constant temperatures therefore, waste must be delivered over small temperature ranges. 

The rate constants of chemical reactions increase strongly with temperature (thermal reactions) on the contrary, those of nuclear reactions are independent of temperature and do not change with time. 

Henry s law The mass of gas which is dissolved by a given volume of a liquid at constant temperature is directly proportional to the pressure of the gas. The law is only obeyed provided there is no chemical reaction between the gas and the liquid. 

As seen in previous sections, the standard entropy AS of a chemical reaction can be detemiined from the equilibrium constant K and its temperature derivative, or equivalently from the temperature derivative of the standard emf of a reversible electrochemical cell. As in the previous case, calorimetric measurements on the separate reactants and products, plus the usual extrapolation, will... 

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