Equilibrium constants from reaction compositions

Obtaining an Equilibrium Constant from Reaction Composition... 

Obtaining an equilibrium constant from reaction composition Given the equilibrium composition, find Kc-(EXAMPLE 15.3)... 

Changes in free energy and the equilibrium constants for Reactions 1, 2, 3, and 4 are quite sensitive to temperature (Figures 2 and 3). These equilibrium constants were used to calculate the composition of the exit gas from the methanator by solving the coupled equilibrium relationships of Reactions 1 and 2 and mass conservation relationships by a Newton-Raphson technique it was assumed that carbon was not formed. Features of the computer program used were as follows (a) any pressure and temperature may be specified (b) an inert gas may be present (c) after... 

The solvation of chromium(llI) ion in certain mixed-solvent systems has been studied in experiments which are relatively free of ambiguity. The exchange of solvent molecules between the mixed solvent and the solvated species Cr(OH2)w (So)n3+ (So = organic solvent component) is a very slow process. The species with solvation shells having different compositions can be separated from one another by column ion-exchange procedures. Analytical procedures based upon such separations allow evaluation of equilibrium constants for reactions involving replacement of coordinated water by the polar organic component. These equilibrium constants are reviewed in this chapter with attention focused upon the dependence of the equilibrium constants upon solvent composition, and the relationship of relative values of the equilibrium constants to the statistically expected values. 

Reaction (2) is basically the production of hydrogen from carbon gasification followed by Reaction (1). The water-gas shift reaction may provide additional hydrogen. At 427°C, the equilibrium constant calculated from thermodynamic information in the JANAF tables (JL6) is K2 = 2.6 x 10 2 atm, where K2 is the equilibrium constant for Reaction (2). Assuming unit solid activities and typical retort gas compositions, we find that... 

Example 9.4 deals with a system at equilibrium, but suppose the reaction mixture has arbitrary concentrations. How can we tell whether it will have a tendency to form more products or to decompose into reactants To answer this question, we first need the equilibrium constant. We may have to determine it experimentally or calculate it from standard Gibbs free energy data. Then we calculate the reaction quotient, Q, from the actual composition of the reaction mixture, as described in Section 9.3. To predict whether a particular mixture of reactants and products will rend to produce more products or more reactants, we compare Q with K ... 

The effect of temperature on the equilibrium composition arises from the dependence of the equilibrium constant on the temperature. The relation between the equilibrium constant and the standard Gibbs free energy of reaction in Eq. 8 applies to any temperature. Therefore, we ought to be able to use it to relate the equilibrium constant at one temperature to its value at another temperature. 

Hamilton [13] assumed the presence of all ions with n ranging from 1 to 8 in aqueous polysulfide solutions which is by far the most acceptable model but since there is insufficient experimental data available this model cannot be worked out quantitatively without additional assumptions. The general idea is that those species are most abundant which are close to the average composition of the particular solution, e.g., 84 and 85 for a solution of composition Na284.5, and that the larger and smaller ions are symmetrically less abundant. Equilibrium constants for the various reactions... 

The kinetic equilibrium constant is estimated from the thermodynamic equilibrium constant using Equation (7.36). The reaction rate is calculated and compositions are marched ahead by one time step. The energy balance is then used to march enthalpy ahead by one step. The energy balance in Chapter 5 used a mass basis for heat capacities and enthalpies. A molar basis is more suitable for the current problem. The molar counterpart of Equation (5.18) is... 

In this example the exit gas stream composition from a converter will be determined for a given inlet gas composition and steam ratio by assuming that in the outlet stream the gases reach chemical equilibrium. In practice the reaction is carried out over a catalyst, and the assumption that the outlet composition approaches the equilibrium composition is valid. Equilibrium constants for the reaction are readily available in the literature. 

To construct such a diagram, a set of defect reaction equations is formulated and expressions for the equilibrium constants of each are obtained. The assumption that the defects are noninteracting allows the law of mass action in its simplest form, with concentrations instead of activities, to be used for this purpose. To simplify matters, only one defect reaction is considered to be dominant in any particular composition region, this being chosen from knowledge of the chemical attributes of the system under consideration. The simplified equilibrium expressions are then used to construct plots of the logarithm of defect concentration against an experimental variable such as the log (partial pressure) of the components. The procedure is best illustrated by an example. 

A. System NH3 H S-H20. The dissociation of water (re-action 9) and the second dissociation of H2S (reaction 6) are neglected at given temperature and total molalities of NHo and H2S there remain four unknown molalities in the liquid phase (e.g. NH3, NH4+, H2S and HS ), the composition of the vapor phase and the total pressure, which are calculated from 8 equations The dissociation constants of ammonia and hydrogen sulfide (eqs.I and III) together with the phase equilibrium for hydrogen sulfide (eq. XII) are combined resulting in a equilibrium constant K 2... 

The interpretation of slopes also requires meaningful rate data. When the reaction consists of a series of elementary steps (and this is always so with heterogeneous catalytic reactions), the rate coefficients obtained from a superficial treatment of a limited set of measurements may be composites of several rate and equilibrium constants for individual steps, in favorable cases constituting a product. As every step may be influenced by the substituents, the resulting effect can be easily attributed to a false elementary step. 

In Eq. 2.36, kf is the forward rate constant, and the composition of the transition state is H4ASO4I, although it could contain additionally (or be short of) the elements of one or more water molecules, since we cannot determine the order with respect to the solvent. Equation 2.36 cannot be arrived at from reaction 2.35, but consideration of the concentration factors in the two equations tells us at once the rate law for the reverse reaction (Eq. 2.38, rate constant kT), since, according to reaction 2.35, the equilibrium expression has to be... 

Because we can calculate E° from standard potentials, we can now also calculate equilibrium constants for any reaction that can be expressed in terms of two half-reactions. Toolbox 12.2 summarizes the steps involved, and Example 12.7 shows the steps in action. Equation 6 also shows that the magnitude of E° for a cell reaction is an indication of the equilibrium composition. It follows from the equation that a reaction with a large positive E° has a very large K. A reaction with a large negative E° has a K much less than 1. 

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