Combined equilibrium

You should be able to describe a system at equilibrium both qualitatively and quantitatively. Rigorous solutions to equilibrium problems can be developed by combining equilibrium constant expressions with appropriate mass balance and charge balance equations. Using this systematic approach, you can solve some quite complicated equilibrium problems. When a less rigorous an-... 

Increasing the subscripts in Eq. (13-47) by 1 and substituting for C dd in Eq. (13-48) gives the following combined equilibrium and material-balance relationship for component i ... 

In principle, one may combine equilibrium and critical data in one database for the parameter estimation. From a numerical implementation point of view this can easily be done with the proposed estimation methods. However, it was not done because it puts a tremendous demand in the correlational ability of the EoS to describe all the data and it will be simply a computational exercise. 

Bordwell129 developed a method of estimating relative bond dissociation energies (BDE) for families of acids, HA, by combining equilibrium acidity constants, pXeA, with the oxidation potential of their conjugated bases, A, both measured in DMSO ... 

THE COMBINED EQUILIBRIUM AND STEADY-STATE TREATMENT. There are a number of reasons why a rate equation should be derived by the combined equilibrium and steady-state approach. First, the experimentally observed kinetic patterns necessitate such a treatment. For example, several enzymic reactions have been proposed to proceed by the rapid-equilibrium random mechanism in one direction, but by the ordered pathway in the other. Second, steady-state treatment of complex mechanisms often results in equations that contain many higher-order terms. It is at times necessary to simplify the equation to bring it down to a manageable size and to reveal the basic kinetic properties of the mechanism. 

Cameron, D. R., and Klute, A. (1977). Convective-dispersive solute transport with a combined equilibrium and kinetic adsorption model. Water Res. 13, 183-188. 

Figure A.4 Combined equilibrium methane reformer and fuel cells for hydrogen and carbon monoxide at standard conditions, Pq and Tq...

Combining equilibrium iii with equilibrium ii, and [CH2(0H)2] (CH20(aq)l one obtains the equilibrium constant... 

Combine equilibrium constants for individual reactions to obtain net equilibrium constants for combined reactions (Section 14.4, Problems 17-20). 

Analytical solutions that cover both the intermediate and the final time regimes are also available. Equation 44 is independent of the initial conditions and can be integrated using the combined equilibrium relation a(ij + 1/0)p = 1. As for rjo = 0,16 this yields an implicit equation for the time dependence of rj, which leads to the approximate solution... 

Combining equilibrium expressions for these two dissociation reactions with equation 8.8, the following two expressions are obtained (assuming that molar concentrations of dissolved ions can be approximated to activities) ... 

The anion A can combine with protons to increase the solubihty of the precipitates. The combined equilibrium concentrations of A and HA make up the total analytical concentration, Cha, which will be equal to [M" ] from the dissolved precipitate (if neitl pr M or A is in excess). By applying the equilibrium constants for the equilibria involved, we can calculate the solubility of the precipitate at a given acidity. 

Macrosyneresis occurs after the gel point, when the crosslinks form a coherent network. The beginning of phase separation can be established by combining equilibrium effects that change in the system because of the conversion and the network swelling. 

The tunable solvent properties of NCW allow for facile separation of products upon cooling, but excess water imposes a too severe equilibrium limitation on this reaction. To address the equilibrium limitation in the presence of excess water, the acetylations of phenol and resorcinol were run in neat acetic acid. At 290°C, phenol was converted to 2-hydroxyacetophenone, 4-hydroxyacetophenone, and phenyl acetate with a combined equilibrium yield of 8 mol% (Fig. 9.50). By-products included 2-methylchromone and 4-methylcoumarine. Under the same conditions, resorcinol was successfully converted to primarily 2,4-dihydroxyacetophenone, with an equilibrium yield of more than 50% in less than 12 h. The yield of 2,4-dihydroxyacetophenone vs time is shown in Fig. 9.51. 

For a dew point problem, it is the vapor phase composition that is known, while the liquid phase composition is unknown. Rearranging the combined equilibrium and material balance equations as before will not provide any benefit in this case. However, let s return to Raoult s law. 

According to Le Chatelier s principle, we expect reaction (18.2) to be displaced to the right—that is, additional Mg(OH)2 would dissolve to replace OH ions drawn off by the neutralization reaction (18.3). The overall net ionic equation can be obtained by doubling equation (18.3) and adding it to equation (18.2). At the same time, we can apply the method of combining equilibrium constants (page 701). The result is... 

We have assessed the qualitative correctness of reaction (21.19). To calculate the quantitative extent of the dissolution of CaCOg(s) in rainwater is somewhat more difficult. The calculation centers on the combined equilibrium constant expression for reaction (21.19), X = 2.6 X 10 , and is affected by the partial pressure of atmospheric CO2 in equilibrium with rainwater. Typical data are given in Chapter 16, Practice Example A, page 782. 

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