Gaseous phase homogeneous equilibria

Gas molecules are considered as indistinguishable molecules the canonical partition function is therefore given by relation [5.25], By applying this relation and by using Stirling s first approximation [4.1], relation [6.105] becomes  

We are going to use molar variables. For this, we define a molar partition fraction given by  

In the calculation of the translational partition function, this definition replaces the volume Fby the molar volume 

Under standard conditions, at temperature T, the Gibbs energy in n moles of component i, which is considered to be an ideal gas (P,F = ,R7), becomes  

This relation is valid let us note this for gas-phase equilibria, when ideal gases are involved. 

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We are going to consider three types of equilibrium gaseous phase homogeneous, liquid phase homogenous and solid phase homogenous equilibria. 

The purpose of this chapter is to outline the simplest methods of arriving at a description of the distribution of species in mixtures of liquids, gases and solids. Homogeneous equilibrium deals with single phase systems, such as electrolyte solutions (e.g., seawater) or gas mixtures (e.g., a volcanic gas). Heterogeneous equilibrium involves coexisting gaseous, liquid and solid phases. 

The equilibria we have discussed so far have all been homogeneous that is. the reactants and [voducts have all existed in the same phase—either gaseous or aqueoas. In these cases, the equilibrium expressicm consists of writing the product of the product concentrations at equilibrium over the product of the reactant concentrations at equilibrium, with each concentration raised to a power equal to its stoichiometric coefficient in the balanced chemical equation (Equation 15.2). When the species in a reversible chemical reaction are not all in the same phase, the equilibrium is heterogeneous. 

In the reactions described so far, all the reactants and products have been gaseous the equilibrium systems are homogeneous. In certain reactions, at least one of the substances involved is a pure liquid or solid the others are gases. Such a system is heterogeneous, because more than one phase is present. Examples include... 

There are numerous possibilities for using equation (29) in conjunction with interface or gas-phase conditions to determine both m and T-. For example, the condensed product of equation (14) conceivably might experience the rate process of equation (1) as soon as Y = 1, so that equations (6) and (29) become two independent expressions for m and 7]. Alternatively and somewhat less unlikely, surface equilibrium may occur so that equation (12) determines T- in equation (29) in this case, a gas-phase analysis is generally needed to find Pi, j. It appears that in most real homogeneous propellants, the products of the exothermic condensed-phase reactions are mainly gaseous, so that considerations of dispersion or possibly of gas-phase reactions are most relevant for determining in equation (29), and equations (6), (11), or (12) are not directly useful. 

We briefly extend the preceding discussion to systems in which one or more pure condensed phases coexist with an ideal homogeneous mixture in gaseous, liquid, or solid form. It is now expedient to distinguish between pure condensed phases, subscript 5, and species involved in the solution, subscript i. For the reaction, written as -f- v,-A,- = 0 we write out the equilibrium condition as... 

A catalyst is a substance that increases the rate at which a chemical reaction approaches equilibrium without, itself, becoming permanently involved in the reaction. The key word in this definition is permanently since there is ample evidence showing that the catalyst and the reactants interact before a reaction can take place. The product of this interaction is a reactive intermediate from which the products are formed. This substratexatalyst interaction can take place homogeneously with both the reactants and the catalyst in the same phase, usually the liquid, or it can occur at the interface between two phases. These heterogeneously catalyzed reactions generally utilize a solid catalyst with the interaction taking place at either the gas/solid or liquid/solid interface. Additional phase transport problems can arise when a gaseous reactant is also present in the liquid/solid system. 

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