Thermodynamic parameters , estimated

Thermodynamic Parameter Estimation by Nonlinear Regression. Although commercial DSC software contains routines for extracting thermodynamic parameters from data, we have found these too restrictive. In general, users must... 

Table 16.1 Kinetic and thermodynamic parameters estimated by the RE, the first-order, and the power law kinetics and their interrelation.

Hugoniot data have been fitted by the equation = Cq + su + qu, where Uj is the shock velocity and the associated particle velocity. Griineisen parameters have been obtained from best estimates of zero pressure thermodynamic parameters, which are sometimes of dubious value. The pressures and velocities describing the valid range of the fits do not necessarily indicate the onset or completion of a transition. 

At2) the authors estimated values of 11.6 kcal.mole and —7 cal.deg mole , using thermodynamic parameters foundbySutcliffeand Weber for the equilibrium. Comparisons have been made of the activation parameters obtained for this exchange system with those obtained for similar systems . 

Estimation of parameters. Model parameters in the selected model are then estimated. If available, some model parameters (e.g. thermodynamic properties, heat- and mass-transfer coefficient, etc.) are taken from literature. This is usually not possible for kinetic parameters. These should be estimated based on data obtained from laboratory expieriments, if possible carried out isothermal ly and not falsified by heat- and mass-transport phenomena. The methods for parameter estimation, also the kinetic parameters in complex organic systems, and for discrimination between models are discussed in more detail in Section 5.4.4. More information on parameter estimation the reader will find in review papers by Kittrell (1970), or Froment and Hosten (1981) or in the book by Froment and Bischoff (1990). 

Parameter estimates should not differ by orders of magnitude from those evaluated using well established methods of thermodynamics or known from the literature several rules concerning adsorption phenomena have been worked out by Boudart et al. (1967) the optimal parameter estimates should not differ very much from the initial guesses if the latter were determined in well designed separate dedicated experiments. 

The implicit LS, ML and Constrained LS (CLS) estimation methods are now used to synthesize a systematic approach for the parameter estimation problem when no prior knowledge regarding the adequacy of the thermodynamic model is available. Given the availability of methods to estimate the interaction parameters in equations of state there is a need to follow a systematic and computationally efficient approach to deal with all possible cases that could be encountered during the regression of binary VLE data. The following step by step systematic approach is proposed (Englezos et al. 1993)... 

Parameter Estimation in Activity Coefficients Thermodynamic Models... 

The activity coefficients are evaluated from the above phase equilibrium data by procedures widely available in the thermodynamics literature (Tassios, 1993 Prausnitz et al. 1986). Since the objective in this book is parameter estimation we will provide evaluated values of the activity coefficients based on... 

A value of kjkp = 17 000 has been determined for partitioning of the acetophenone oxocarbenium ion [12+] in water.15,16 It is not possible to estimate an equilibrium constant for the addition of water to [12+], because of the instability of the hemiketal product of this reaction. However, kinetic and thermodynamic parameters have been determined for the reaction of [12+] with methanol to form protonated acetophenone dimethyl ketal [12]-OMeH+ and for loss of a proton to form a-methoxystyrene [13] in water (Scheme 10).15,16 Substitution of these rate and equilibrium constants into equation (3) gives values of AMeoH = 6.5 kcal mol-1 and Ap = 13.8 kcal mol-1 for the intrinsic... 

The hydrogens within the octahedral olefin-dihydride intermediate are transferred consecutively with overall cis addition, and the rate-determining step (k9) is olefin insertion to give the alkyl- hydride. Kinetic and thermodynamic parameters for nearly all the steps of Fig. 1 have been estimated for the cyclohexene system. Because the insertion reaction is generally believed to require a cis disposition of the hydride and olefin... 

The addition of dioxygen to the cyclohexadienyl radical is also reversible [86]. The following thermodynamic parameters were estimated for such equilibrium A//=21kJmol 1 and AA= 84 J mol-1 K-1. 

Martinez, M. R., "Estimation of Gas-Phase Thermodynamic Parameters," Quantum Chemistry Program Exchange, Program 244 (1974). 

This chapter contains examples of optimization techniques applied to the design and operation of two of the most common staged and continuous processes, namely, distillation and extraction. We also illustrate the use of parameter estimation for fitting a function to thermodynamic data. 

It has been suggested that an increase in the coordination number of vanadium from 4 to 5 already takes place in the second protonation step, i.e. when [H2V04] is formed (21). For reactions (1) and (2), however, the protonation constants and thermodynamic parameters are comparable with those reported for P04 and As04 , providing firm evidence that reaction (2) is not accompanied by incorporation of water in the vanadate ion (15, 17). Further, the estimated thermodynamic quantities for reaction (6), AH° = -39 kJ/mol and AS0 = —51 J/(mol K), obtained by extrapolation from the experimental values for reactions (1) and (2) and those for the three protonation steps of P04 and As04 , are not typical of a simple protonation reaction (17). For such a reaction the entropy change is normally a positive quantity often amounting to 100 50 J/(mol K) and the enthalpy... 

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