Equilibrium constant composite reaction

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 distribution of metals between dissolved and particulate phases in aquatic systems is governed by a competition between precipitation and adsorption (and transport as particles) versus dissolution and formation of soluble complexes (and transport in the solution phase). A great deal is known about the thermodynamics of these reactions, and in many cases it is possible to explain or predict semi-quantita-tively the equilibrium speciation of a metal in an environmental system. Predictions of complete speciation of the metal are often limited by inadequate information on chemical composition, equilibrium constants, and reaction rates. 

The composition of sodium polysulfide solutions saturated with sulfur of zero oxidation number (S°) has also been studied at 25 and 80 °C (solutions in contact with elemental sulfur) [76]. In this case the ratio 8° 8 per polysulfide ion increases with increasing alkahnity. The maximum average number of sulfur atoms per polysulfide molecule was obtained as 5.4 at 25 °C and 6.0 at 80 °C and pH values of >12. Equilibrium constants for reactions as in Eqs. (26) and (27) have been derived assuming various models with differing numbers of polysulfide ions present. 

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. 

Step 5 The equilibrium composition is entered into the equilibrium constant expression and the unknown quantity (equilibrium constant or reaction species concentration) is determined. 

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... 

Total pressure is one atmosphere. At the temperature of interest, the equilibrium constants of reactions (1) and (2) are respectively Ki = 8.26 X 10 and Kt = 7.9. What is the equilibrium composition of the system, expressed in mole fractions ... 

Methods of concentration-dependent distribution (CDD) utilizing reactions where products of unstable composition are formed, but in which the extent of reaction is determined by the corresponding equilibrium constant or reaction time. 

Furthermore, the values of the equilibrium constants for reactions 8-10 appear to depend upon the composition of the catalyst. For example, the methanecracking reaction 9 at 645°C has the following equilibrium constants ... 

When the equilibrium constants for reactions A and B are expressed in terms of the partial pressures of the various species (in atm), the equilibrium constants for these reactions have the values Kp = 0.046 and Kp = 0.034. Determine the number of independent reactions, and then determine the equilibrium composition of the mixture. 

Obtaining an Equilibrium Constant from Reaction Composition... 

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

Equilibrium constants for reactions (1) and (2) at selected temperatures are listed in Table 1. A complete list may be found in (Rostrup-Nielsen, 1984a). In principle, the equilibrium composition is determined by the atomic ratios 0/C, H/C, inert/C, pressure and temperature. 

In a neutral azole, the apparent rate of formation of an A-substituted derivative depends on the rate of reaction of a given tautomer and on the tautomeric equilibrium constant. For example, with a 3(5)-substituted pyrazole such as (199), which exists as a mixture of two tautomers (199a) and (199b) in equilibrium, the product composition [(200)]/[(201)] is a function of the rate constants Ha and fcs, as well as of the composition of the tautomeric mixture (Scheme 16) <76AHC(Si)l). 

Complex Clieinical-Reaction Equilibria When the composition of an equilibrium mixture is determined by a number of simultaneous reactions, calculations based on equilibrium constants become complex and tedious. A more direct procedure (and one suitable for general computer solution) is based on minimization of the total Gibbs energy G in accord with Eq. (4-271). The treatment here is... 

The equilibrium constant of a reaction is the product of compositions of reactants and products each raised to its stoichiometric coefficient. Hence, for the reaction described by Eq. (8.2) one may write... 

What Are the Key Ideas Instead of going tu cumpletiun, reactions proceed until the composition of a reaction mixture corresponds to minimum Gibbs free energy. This composition is described by an equilibrium constant that is characteristic of the reaction and depends on the temperature. 

Within experimental error, Guldberg and Waage obtained the same value of K whatever the initial composition of the reaction mixture. This remarkable result shows that K is characteristic of the composition of the reaction mixture at equilibrium at a given temperature. It is known as the equilibrium constant for the reaction. The law of mass action summarizes this result it states that, at equilibrium, the composition of the reaction mixture can be expressed in terms of an equilibrium constant where, for any reaction between gases that can be treated as ideal,... 

Each reaction has its own characteristic equilibrium constant, with a value that can be changed only by varying the temperature (Table 9.2). The extraordinary empirical result, which we justify in the next section, is that, regardless of the initial composition of a reaction mixture, the composition tends to adjust until the... 

The equilibrium composition of a reaction mixture is described by the equilibrium constant, which is equal to the activities of the products (raised to powers equal to their stoichiometric coefficients in the balanced chemical equation for the reaction) divided by the activities of the reactants (raised to powers equal to their stoichiometric coefficients). 

FIGURE 9.3 Whether we start with pure reactants or with pure products, a reaction mixture will always tend toward a mixture of reactants and products that has a composition in accord with the equilibrium constant for the reaction at the temperature of the experiment. 

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 ... 

A note on good practice Whether or not a reaction is spontaneous depends on the composition, so it is better to say that K > 1 for a reaction rather than that it is spontaneous. However, for reactions with very large equilibrium constants, it is very unlikely that the mixture of reagents prepared in the laboratory will correspond to 2 > K, and it is common to refer to such reactions as spontaneous. ... 

We have seen that the value of an equilibrium constant tells us whether we can expect a high or low concentration of product at equilibrium. The constant also allows us to predict the spontaneous direction of reaction in a reaction mixture of any composition. In the following three sections, we see how to express the equilibrium constant in terms of molar concentrations of gases as well as partial pressures and how to predict the equilibrium composition of a reaction mixture, given the value of the equilibrium constant for the reaction. Such information is critical to the success of many industrial processes and is fundamental to the discussion of acids and bases in the following chapters. 

The equilibrium constant of a reaction contains information about the equilibrium composition at the given temperature. However, in many cases, we know only the initial composition of the reaction mixture and are given apparently incomplete information about the equilibrium composition. In fact, the missing information can usually be inferred by using the reaction stoichiometry. The easiest way to proceed is to draw up an equilibrium table, a table showing the initial composition, the changes needed to reach equilibrium in terms of some unknown quantity x, and the final equilibrium composition. The procedure is summarized in Toolbox 9.1 and illustrated in the examples that follow. 

Step 1 Write the balanced chemical equation for the equilibrium and the corresponding expression for the equilibrium constant. Then set up an equilibrium table as shown here, with columns labeled by the species taking part in the reaction. In the first row, show the initial composition (molar concentration or partial pressure) of each species... 

To calculate the equilibrium composition of a reaction mixture, set up an equilibrium table in terms of changes in the concentrations of reactants and products, express the equilibrium constant in terms of those changes, and solve the resulting equation. 

FIGURE 9.10 These graphs show the changes in composition that can be expected when additional hydrogen and then ammonia are added to an equilibrium mixture of nitrogen, hydrogen, and ammonia. Note that the addition of hydrogen results in the formation of ammonia, whereas the addition of ammonia results in the decomposition of some of the added ammonia as reactants are formed. In each case, the mixture settles into a composition in accord with the equilibrium constant of the reaction. 

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. 

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