The membrane and diffusion-media modeling equations apply to the same variables in the same phase in the catalyst layer. The rate of evaporation or condensation, eq 39, relates the water concentration in the gas and liquid phases. For the water content and chemical potential in the membrane, various approaches can be used, as discussed in section 4.2. If liquid water exists, a supersaturated isotherm can be used, or the liquid pressure can be assumed to be either continuous or related through a mass-transfer coefficient. If there is only water vapor, an isotherm is used. To relate the reactant and product concentrations, potentials, and currents in the phases within the catalyst layer, kinetic expressions (eqs 12 and 13) are used along with zero values for the divergence of the total current (eq 27). [Pg.463]

A remarkable achievement of statistical mechanics is the accurate prediction of gas-phase chemical reaction equilibria from atomic structures. From atomic masses, moments of inertia, bond lengths, and bond strengths, you can calculate partition functions. You can then calculate equilibrium constants and their dependence on temperature and pressure. In Chapter 19, we will apply these ideas to chemical kinetics, which pertains to the rates of reactions. Reactions can be affected by the medium they are in. Next we will develop models of liquids and other condensed phases. [Pg.248]

The traditional apparatus of statistical physics employed to construct models of physico-chemical processes is the method of calculating the partition function [17,19,26]. The alternative method of correlation functions or distribution functions [75] is more flexible. It is now the main method in the theory of the condensed state both for solid and liquid phases [76,77]. This method has also found an application for lattice systems [78,79]. A new variant of the method of correlation functions - the cluster approach was treated in the book [80]. The cluster approach provides a procedure for the self-consistent calculation of the complete set of probabilities of particle configurations on a cluster being considered. This makes it possible to take account of the local inhomogeneities of a lattice in the equilibrium and non-equilibrium states of a system of interacting particles. In this section the kinetic equations for wide atomic-molecular processes within the gas-solid systems were constructed. [Pg.370]

Experimental determination of Ay for a reaction requires the rate constant k to be determined at different pressures, k is obtained as a fit parameter by the reproduction of the experimental kinetic data with a suitable model. The data are the concentration of the reactants or of the products, or any other coordinate representing their concentration, as a function of time. The choice of a kinetic model for a solid-state chemical reaction is not trivial because many steps, having comparable rates, may be involved in making the kinetic law the superposition of the kinetics of all the different, and often unknown, processes. The evolution of the reaction should be analyzed considering all the fundamental aspects of condensed phase reactions and, in particular, beside the strictly chemical transformations, also the diffusion (transport of matter to and from the reaction center) and the nucleation processes. [Pg.153]

Several points are worth emphasizing. The first point is mass balance. The total amount of each element is conserved in the chemical equilibrium calculations. Thus the abundances of all gases and all condensed phases (solids and/or liquids) sum to the total elemental abundance - no less and no more. The second point is that chemical equilibrium is completely independent of the size, shape, and state of aggregation of condensed phases - a point demonstrated by Willard Gibbs over 130 years ago. Finally, the third point is that chemical equilibrium is path independent. Thus, the results of chemical equilibrium calculations are independent of any particular reaction. A particular chemical reaction does not need to be specified because all possible reactions give the same result at chemical equilibrium. This is completely different than chemical kinetic models where the results of the model are critically dependent on the reactions that are included. However, a chemical equilibrium calculation does not depend on kinetics, is independent of kinetics, and does not need a particular list of reactions. This point may seem obvious, but is often misunderstood. [Pg.351]

© 2019 chempedia.info