Equilibrium constant gases, reactions involving

Besides the second law method, there is another way of extracting reaction enthalpies from gas-phase equilibrium constants. This alternative involves the determination of a single value of an equilibrium constant at a given temperature and the calculation of the reaction entropy at the same temperature. From equations 2.54 and 2.55, we obtain... 

The usual situation, true for the first three cases, is that in which the reactant and product solids are mutually insoluble. Langmuir [146] pointed out that such reactions undoubtedly occur at the linear interface between the two solid phases. The rate of reaction will thus be small when either solid phase is practically absent. Moreover, since both forward and reverse rates will depend on the amount of this common solid-solid interface, its extent cancels out at equilibrium, in harmony with the thermodynamic conclusion that for the reactions such as Eqs. VII-24 to VII-27 the equilibrium constant is given simply by the gas pressure and does not involve the amounts of the two solid phases. 

It is possible to detemiine the equilibrium constant, K, for the bimolecular reaction involving gas-phase ions and neutral molecules in the ion source of a mass spectrometer [18]. These measurements have generally focused on tln-ee properties, proton affinity (or gas-phase basicity) [19, 20], gas-phase acidity [H] and solvation enthalpies (and free energies) [22, 23] ... 

In an earlier section, measurements were described in which the equilibrium constant, K, for bimolecular reactions involving gas-phase ions and neutral molecules were detennined. Another method for detemiining the proton or other affinity of a molecule is the bracketing method [ ]. The principle of this approach is quite straightforward. Let us again take the case of a proton affinity detemiination as an example. In a reaction... 

One word of warning when using the van t Hoff equation for reactions involving gases, the equilibrium constants must be K, not K(.. If we want a new value for Kc for a gas-phase reaction, we convert from K(. into K at the initial temperature (by using Eq. 12), use the van t Hoff equation to calculate the value of K at the new temperature, and then convert that K into the new Kc by using Eq. 12 at the new temperature. 

One of the earliest measurements of the gas-phase equilibrium acidity of propene involved measuring the rates of reaction of propene with hydroxide ion in both directions33. The resulting equilibrium constant gave A//acid = 391 1 kcalmol-1. In the case of ethylene, the acidity and independently measured electron affinity of vinyl radical were used to determine the bond dissociation energy, a quantity difficult to obtain accurately by other means8. 

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. 

All reactions involved in polymer chain growth are equilibrium reactions and consequently, their reverse reactions lead to chain degradation. The equilibrium constants are rather small and thus, the low-molecular-weight by-products have to be removed efficiently to shift the reaction to the product side. In industrial reactors, the overall esterification, as well as the polycondensation rate, is controlled by mass transport. Limitations of the latter arise mainly from the low solubility of TPA in EG, the diffusion of EG and water in the molten polymer and the mass transfer at the phase boundary between molten polymer and the gas phase. The importance of diffusion for the overall reaction rate has been demonstrated in experiments with thin polymer films [10]. 

Transesterification is the main reaction of PET polycondensation in both the melt phase and the solid state. It is the dominant reaction in the second and subsequent stages of PET production, but also occurs to a significant extent during esterification. As mentioned above, polycondensation is an equilibrium reaction and the reverse reaction is glycolysis. The temperature-dependent equilibrium constant of transesterification has already been discussed in Section 2.1. The polycondensation process in the melt phase involves a gas phase and a homogeneous liquid phase, while the SSP process involves a gas phase and two solid phases. The respective phase equilibria, which have to be considered for process modelling, will be discussed below in Section 3.1. 

The study described above for the water-gas shift reaction employed computational methods that could be used for other synthesis gas operations. The critical point calculation procedure of Heidemann and Khalil (14) proved to be adaptable to the mixtures involved. In the case of one reaction, it was possible to find conditions under which a critical mixture was at chemical reaction equilibrium by using a one dimensional Newton-Raphson procedures along the critical line defined by varying reaction extents. In the case of more than one independent chemical reaction, a Newton-Raphson procedure in the several reaction extents would be a candidate as an approach to satisfying the several equilibrium constant equations, (25). 

The influence of temperature on the reversible potential of MCFCs depends on several factors, one of which involves the equilibrium composition of the fuel gas (20,59,60,61). The water gas shift reaction achieves rapid equilibrium at the anode in MCFCs, and consequently CO serves as an indirect source of H2. The equilibrium constant (K)... 

Figures 1 to 3 present calculated equilibrium molar ratios of products to reactants as a function of temperature and total pressure of 1 and 100 atm. for the gas-carbon reactions (4), (7), and (5), (6), (4), (7), respectively. Up to 100 atm. over the temperature range involved, the fugacity coefficients of the gases are close to 1 therefore, pressures can be calculated directly from the equilibrium constant. From Fig. 1, it is seen that at temperatures above 1200°K. and at atmospheric pressure, the conversion of carbon dioxide to carbon monoxide by the reaction C - - COj 2CO essentially is unrestricted by equilibrium considerations. At elevated pressures, the possible conversion markedly decreases hence, high pressure has little utility for this reaction, since increased reaction rate can easily be obtained by increasing reaction temperature. On the other hand, for the reaction C -t- 2H2 CH4, the production of methane is seriously limited at one atmosphere pressure and practical operating temperatures, as seen in Fig. 2. Obviously, this reaction must be conducted at elevated pressures to realize a satisfactory yield of methane. For the carbon-steam reaction.

By writing molar component balances for gas and crystallite phases, assuming Henry s law equilibrium between these phases and applying exponential rate decay, the equilibrium model (model a) is obtained (13). All parameters in the model can be measured or estimated, independent of reaction studies, with the exception of Mi and M2y which are obtained from the observed rate decay. The Henry s law constant H was estimated from a liquid-phase equilibrium study. A model involving diffusional limitations within the crystallites has been developed by Tan and Fuller (6) and is not discussed here. 

The reactions with which we are mostly concerned in chemistry take place in solution rather than in the gas phase. The majority of them moreover involve reactants, products, or transition states carrying electric charges. In such cases the entropies of solvation are extremely large, and these entropies cannot be estimated at present. This immediately rules out any possibility of estimating absolute values of equilibrium or rate constants for reactions of this kind. If we are concerned with absolute calculations of rates and equilibria, we must confine ourselves either to gas-phase reactions, or to reactions of non-polar type. Even here we will usually be forced to make estimates of entropies that are of dubious significance chemical theory has not yet progressed to a point where problems of this kind can usefully be discussed. 

An aerogel is a solid with a density comparable to a gas. In a reaction involving an aerogel as reactant, should a term involving the aerogel be included in the equilibrium constant ... 

Intermolecular interactions in the gas phase have been measured in a series of cases using mass spectrometry 134-147). From the temperature dependence of the equilibrium constants, besides the free energies, the enthalpies and the entropies of the involved reactions were evaluated. The corresponding data are useful for comparison with the results of theoretical calculations (see Table 3). In order to compare the calculated interaction energies with the measured reaction enthalpies, a series of contributions has to be taken into account. Concerning these correction terms some inconsistencies arise in the literature. Therefore the list of them is given here in detail according to Ref. 148) ... 

As with any other chemical reaction, the formation of a metal complex from a metal ion and a set of proligands can be described by an equilibrium constant. In its simplest form, a complexation reaction might involve the reaction of unsolvated metal ions in the gas phase with gas phase proligands to form a complex. In practice it is difficult to study such reactions in the gas phase and complex formation is normally studied in solution, often in water. This introduces the complication that the solvent can also function as a ligand, so that complex formation will involve the displacement of solvent from the metal coordination sphere by the proligand. 

---