Equilibrium constants thermodynamic data

From the temperature variation of the equilibrium constant, thermodynamic parameters for the reaction were also obtained. The extent of formation of [Mo(CO)5l]" was found to be cation-dependent, and while equilibrium constants of 39 and 21 atm L moF were obtained for Bu4P and pyH+, none of the anionic iodide complex was observed for Na. Despite this variation, there seemed to be no correlation between the concentration of [Mo(CO)5l]" and the rate of the catalytic carbonylation reaction. It was proposed that [Mo(CO)5] and [Mo(CO)5l] are spectator species, with the catalysis being initiated by [Mo(CO)5]. Based on the in situ spectroscopic results and kinetic data, a catalytic mechanism was suggested, involving radicals formed by inner sphere electron transfer between EtI and [Mo(CO)5]. 

Equimolal proportions of the reactants are used. Thermodynamic data at 298 K are tabulated. The specific heats are averages. Find (1) the enthalpy change of reaction at 298 and 573 K (2) equilibrium constant at 298 and 573 K (3) fractional conversion at 573 K. 

The basic thermodynamic data for the design of such reactions can be used to assess the dissociation energies for various degrees of dissociation, and to calculate, approximately, tire relevant equilibrium constants. One important source of dissociation is by heating molecules to elevated temperamres. The data below show the general trend in the thermal dissociation energies of a number of important gaseous molecules. 

Cycloheptatrienes are in many cases in rapid equilibrium with an isomeric bicy-clo[4.1.0]heptadiene. The thermodynamics of the valence isomerism has been studied in a number of instances, and some of the data are given below. Calculate the equilibrium constant for each case at 25°C. Calculate the temperature at which K= for each system. Are the signs of the enthalpy and entropy as you would expect them to be Can you discern any pattern of substituent effects from the data ... 

Steps 1 and 2 require thermodynamic data. Eigure 2-1 shows the equilibrium constants of some reactions as a function of temperature. The Appendix at the end of this chapter gives a tabulation of the standard change of free energy AG° at 298 K. 

Lunazzi et al. [84JCS(P2)1025] reported the first reliable data on the behavior of 1,2,3-triazole 20 in solution (Scheme 21). Using NMR at 300 MHz and lowering the temperature to -98°C they determined not only the equilibrium constant but all the thermodynamic and kinetic parameters = 0.55 kcal mol (CD2CI2) and 1.60 kcal moU (toluene-ds),... 

In discussing the experimental data, we shall wish to make use of the equilibrium constants that are to be found in the literature. We must therefore inquire into the relation that the thermodynamic treatment bears to the treatment that has been given above. When the expression for any reaction, such as (66) for example, has been written down, the species that have been written on the left-hand side are called the reactants, and those on the right-hand side are called the products. The... 

Appendix 1 includes a review of SI base units as well as tables of thermodynamic data and equilibrium constants. 

Reactions 1 and 3 are highly exothermic and therefore have equilibrium constants that decrease rapidly with temperature. Reaction 2 is moderately exothermic, and consequently its equilibrium constant shows a moderate decrease with temperature. Reaction 4 is moderately endothermic, and its equilibrium constant increases with increasing temperature. The relationship between temperature and equilibrium constant for these four reactions is depicted in Figure 1 where carbon is assumed to be graphite. Thermodynamic data were taken from Refs. 1 and 2. 

We are free to choose either K or Kc to report the equilibrium constant of a reaction. However, it is important to remember that calculations of an equilibrium constant from thermodynamic tables of data (standard Gibbs free energies of formation, for instance) and Eq. 8 give K, not Kc. In some cases, we need to know Kc after we have calculated K from thermodynamic data, and so we need to be able to convert between these two constants. 

Some of the thermodynamic data and equilibrium constants that are required follow. 

Equation (7.28) may not provide a good fit for the equilibrium data if the equilibrium mixture is nonideal. Suppose that the proper form for Kkmetic is determined through extensive experimentation or by using thermodynamic correlations. It could be a version of Equation (7.28) with exponents different from the stoichiometric coefficients, or it may be a different functional form. Whatever the form, it is possible to force the reverse rate to be consistent with the equilibrium constant, and this is recommended whenever the reaction shows appreciable reversibility. 

Examples 7.12 and 7.13 treated the case where the kinetic equilibrium constant had been determined experimentally. The next two examples illustrate the case where the thermodynamic equilibrium constant is estimated from tabulated data. 

These four equations are perfectly adequate for equilibrium calculations although they are nonsense with respect to mechanism. Table 7.2 has the data needed to calculate the four equilibrium constants at the standard state of 298.15 K and 1 bar. Table 7.1 has the necessary data to correct for temperature. The composition at equilibrium can be found using the reaction coordinate method or the method of false transients. The four chemical equations are not unique since various members of the set can be combined algebraically without reducing the dimensionality, M=4. Various equivalent sets can be derived, but none can even approximate a plausible mechanism since one of the starting materials, oxygen, has been assumed to be absent at equilibrium. Thermodynamics provides the destination but not the route. 

Equation is extremely important because it links thermodynamic data with equilibrium constants. Recall that Equation makes it possible to use tabulated values for A Gj to calculate the value for A G ° for many reactions ... 

C16-0063. Using standard thermodynamic data from Appendix D, calculate the equilibrium constant at 298 K for each of the following chemical equilibria ... 

Later we shall see how fundamental quantities such as /i can be estimated from first principles (via a basic knowledge of the molecule such as its molecular weight, rotational constants etc.) and how the equilibrium constant is derived by requiring the chemical potentials of the interacting species to add up to zero as in Eq. (20). The above equations relate kinetics to thermodynamics and enable one to predict the rate constant for a reaction in the forward direction if the rate constant for the reverse reaction as well as thermodynamic data is known. 

To calculate the equilibrium composition of a mixture at a given temperature, we first need to calculate the equilibrium constant from thermodynamic data valid under the standard conditions of 298 K and 1 bar, as in Tab. 2.2. Differentiating Eq. (22) and using AG° = A - TAS° we obtain the Van t Hoff equation ... 

The rate model contains four adjustable parameters, as the rate constant k and a term in the denominator, Xad, are written using the Arrhenius expression and so require a preexponential term and an activation energy. The equilibrium constant can be calculated from thermodynamic data. The constants depend on the catalyst employed, but some, such as the activation energy, are about the same for many commercial catalysts. Equation (57) is a steady-state model the low velocity of temperature fronts moving through catalyst beds often justifies its use for periodic flow reversal. 

From thermodynamic data it is possible to evaluate the equilibrium constant and all of the equilibrium concentrations in the above equation, reducing it to the following form. 

Needless to say, an analysis which will finally allow one to nail down all rates, activation parameters, and equilibrium constants requires a large amount of precise and reliable kinetic data from appropriate experiments, including the determination of isotope effects and the like, as well as a rather sophisticated treatment and solution of the complete kinetic scheme. Then a comparison is necessary between various organosilanes with different types of C-H and C-Si bonds as well as the comparison between the dtbpm and the dcpm ligand systems, not to speak of model calculations in order to understand the molecular origin of the kinetic and thermodynamic numbers. We are presently in the process of solving these problems. 

Are the equilibrium constants for the important reactions in the thermodynamic dataset sufficiently accurate The collection of thermodynamic data is subject to error in the experiment, chemical analysis, and interpretation of the experimental results. Error margins, however, are seldom reported and never seem to appear in data compilations. Compiled data, furthermore, have generally been extrapolated from the temperature of measurement to that of interest (e.g., Helgeson, 1969). The stabilities of many aqueous species have been determined only at room temperature, for example, and mineral solubilities many times are measured at high temperatures where reactions approach equilibrium most rapidly. Evaluating the stabilities and sometimes even the stoichiometries of complex species is especially difficult and prone to inaccuracy. 

In the broadest sense, of course, no model is unique (see, for example, Oreskes et al., 1994). A geochemical modeler could conceptualize the problem differently, choose a different compilation of thermodynamic data, include more or fewer species and minerals in the calculation, or employ a different method of estimating activity coefficients. The modeler might allow a mineral to form at equilibrium with the fluid or require it to precipitate according to any of a number of published kinetic rate laws and rate constants, and so on. Since a model is a simplified version of reality that is useful as a tool (Chapter 2), it follows that there is no correct model, only a model that is most useful for a given purpose. 

We employ the LLNL thermodynamic data for aqueous species, as before, omitting the PbC03 ion pair, which in the dataset is erroneously stable by several orders of magnitude. The reactions comprising the surface complexation model, including those for which equilibrium constants have only been estimated, are stored in dataset FeOH+.dat . 

Table 5 lists equilibrium data for a new hypothetical gas-phase cyclisation series, for which the required thermodynamic quantities are available from either direct calorimetric measurements or statistical mechanical calculations. Compounds whose tabulated data were obtained by means of methods involving group contributions were not considered. Calculations were carried out by using S%g8 values based on a 1 M standard state. These were obtained by subtracting 6.35 e.u. from tabulated S g-values, which are based on a 1 Atm standard state. Equilibrium constants and thermodynamic parameters for these hypothetical reactions are not meaningful as such. More significant are the EM-values, and the corresponding contributions from the enthalpy and entropy terms. 

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