Equilibrium constants, list

Using the equilibrium constants listed in Table 13.2, arrange the following 0.1 M aqueous solutions in order of increasing pH (from lowest to highest). 

Figure 8.13. Equilibrium concentrations of biochemically important redox components as a function of pe at a pH of 7.0 (a) nitrogen (b) nitrogen, with elemental nitrogen N2 ignored (c) iron and manganese (d) sulfur (e) carbon. These equilibrium diagrams have been constructed from equilibrium constants listed in Tables 8.6a and 8.6b for the following concentrations Cr (total carbonate carbon) = 10 M [HjSCaq)) + [HS ] -I- [SOri = 10 M [NOj-] + [NOj"] + [NH ] = 10 M = 0.78 atm and thus [NjCaq)] = 0.5 x 10 M. For the construction of (b) the species NH4 , NOj, and NO are treated as metastable with regard to Nj.

For the pH values of leachate in these experiments (6.5 to 7.5), the As(V) species in reactions 6 and 7 predominate. Arsenate concentrations were below detection limits throughout the experiments however, after reactive organic carbon concentrations in the core decreased to the level where reduction of O2 was incomplete, geochemical modeling predicted oxidation of As(lll) to As(V). Because As(V) was not detected in core effluent, it was not possible to derive equilibrium constants for these adsorption reactions on this core material, and the equilibrium constants listed in Dzombak and Morel (1990) were used in the model. For reaction 6, the Log Kas(v)i was 23.51 and for reaction 7, the Log Kas(v)2 was 10.58. Arsenite adsorption was modeled by ... 

The equilibrium constants listed in Table V, measured by using 23Na and 133cs-NMR indicate that in the polymeriza-... 

Most tables of equilibrium constants list values for Kj, as obtained by extrapolation towards / — 0, but the spreadsheet calculation requires the uncorrected Ka s. Below we will indicate how to make the activity correction. 

Potentiometrically [16,17] determined first dissociation constant Ka (eqn 1) of ascorbic acid (H2A) under present experimental conditions is listed in Table 2. The stability constant Ki (eqn 2) of the Ru(III)-EDTA-ascorbate (1 1 1) complex computed spectrophotometrically [16,17] (Table 2) was obtained by observing the optical densities at 510 nm on varying the concentration of ascorbic acid at constant concentration of Ru(III)-EDTA. The other equilibrium constants listed in table 2 were evaluated kinetically. 

Each chemical reaction has a unique equilibrium constant value at a specified temperature. Equilibrium constants listed in the chemical literature are often reported at 25°C, to allow comparison of one system with any other. For any equilibrium reaction, the value of the equilibrium constant changes with temperature. 

The equilibrium constants listed in the Appendix C are for zero ionic strength that is, they are really thermodynamic equilibrium constants. Therefore, from Table C.3, K% = 1.0 X lO". ... 

It should be pointed out that most of the equilibrium constants listed in this table refer to solutions of constant ionic strength with the exception of Butler s data which have been corrected to zero ionic strength. The effect of ion association has also been neglected. The data of Pavarov et were obtained by radiotracer techniques at 18 2°C. 

Chemical composition of seawater in equilibrium with above minerals can be calculated using equilibrium constants listed in Table 4.2, mass balance equations and electroneutrality relation. The calculated results by Kramer (1965) are mostly... 

The extraction properties of the typical chelating agents discussed in Section 21.4.5 are well-illustrated by the equilibrium constants listed in Table 21.18. As to the / -diketones, the extraction always increases in the sequence AA < Benz A < TTA, generally quite strongly. The tropolone ITP is an even better extractant than TTA, espedally in the case of Th, which is remarkably poorly extracted by the /3-diketones as compared with other ions. Nor is oxine a good extractant for Th. This ligand extracts UOf" relatively well, however. 

The text listed below provides more details on how the potentiometric titration data may be used to calculate equilibrium constants. This text provides a number of examples and includes a discussion of several computer programs that have been developed to model equilibrium reactions. 

Many of the reactions listed at the beginning of this section are acid catalyzed, although a number of basic catalysts are also employed. Esterifications are equilibrium reactions, and the reactions are often carried out at elevated temperatures for favorable rate and equilibrium constants and to shift the equilibrium in favor of the polymer by volatilization of the by-product molecules. An undesired feature of higher polymerization temperatures is the increased probability of side reactions such as the dehydration of the diol or the pyrolysis of the ester. Basic catalysts produce less of the undesirable side reactions. 

Table 4-1 lists some rate constants for acid-base reactions. A very simple yet powerful generalization can be made For normal acids, proton transfer in the thermodynamically favored direction is diffusion controlled. Normal acids are predominantly oxygen and nitrogen acids carbon acids do not fit this pattern. The thermodynamicEilly favored direction is that in which the conventionally written equilibrium constant is greater than unity this is readily established from the pK of the conjugate acid. Approximate values of rate constants in both directions can thus be estimated by assuming a typical diffusion-limited value in the favored direction (most reasonably by inspection of experimental results for closely related... 

The coefficients a, b, and c for hydrogenation were obtained from the literature [13] and those for nitrile and hydrogenated nitrile were calculated from a group contribution method reported by Rihani and Doraiswami [14]. All the necessary data are listed in Table 1. The integration constant / and AHq have been calculated by incorporating the values of AG° and AH° at 298 K in Eqs. (3) and (4). The equilibrium constant at atmospheric pressure and various temperature has been calculated according to the relationship ... 

The values of the equilibrium constant K listed in Table A are those obtained from data at low pressures, where the gases behave ideally. At higher pressures the mole percent of ammonia observed is generally larger than the calculated value. For example, at 400°C and 300 atm, the observed mole percent of NH3 is 47 the calculated value is only 41. 

The equilibrium constant Ka is called, logically enough, the acid equilibrium constant of the weak acid HB. The Ka values of some weak acids (in order of decreasing strength) are listed in Table 13.2. The weaker the acid, the smaller the value of Ka. For example, HCN (Ka = 5.8 X 10-10) is a weaker acid than HN02, for which Ka = 6.0 X 10-4. 

The add equilibrium constants of the oxoadds of the halogens are listed in Table 21.5. Notice that the value of K, increases with—... 

In Table 9-1V are listed some reactions along with the equilibrium law relation of concentrations and the numerical values of the equilibrium constants. First, let s verify the forms of the equilibrium law relation among the concentra-... 

Now look at the numerical values of the equilibrium constants. The K s listed range from 10+1 to 10 16, so we see there is a wide variation. We want to acquire a sense of the relation between the size of the equilibrium constant and the state of equilibrium. A large value of K must mean that at equilibrium there are much larger concentrations present of products than of reactants. Remember that the numerator of our equilibrium expression contains the concentrations of the products of the reaction. The value of 2 X 10,s for the K for reaction (19) certainly indicates that if a reaction is initiated by placing metallic copper in a solution containing Ag+ (for example, in silver nitrate solution), when equilibrium is finally reached, the concentration of Cu+2 ion, [Cu+2], is very much greater than the square of the silver ion concentration, [Ag+]2. 

Solubility equilibrium constants, such as (20) and (22), are given a special name—the solubility product. It is symbolized K,p. A low value of K,p means the concentrations of ions are low at equilibrium. Hence the solubility must be low. Table 10-11 lists solubility products for some common compounds. 

Calculation of the second-order rate constant of carbonylation, kg, and the equilibrium constant, K = [t-C4H9CO+]/[t-C4H ][CO] = A c/fcD> requires knowledge of the concentration of CO. The constant a in Henry s law Pco = [CO] was determined to be 5-3 litre mole atm in HF—SbFs (equimolar) and 53 litre mole atm in FHSOs—SbFs (equimolar) at 20°C. From the ratio [t-C4HBCO+]/[t-C4HJ"] at a known CO pressure, values for k and K were obtained. The data are listed in Table 1, which includes the values for the rate and equilibrium constants of two other tertiary alkyl cations, namely the t-pentyl and the t-adamantyl ions (Hogeveen et al., 1970). 

This is a qualitative problem. First identify the major species, and then list their equilibria. Values for equilibrium constants can be found in tables in this chapter and in Appendix E. 

We will list the elementary steps and decide which is rate-limiting and which are in quasi-equilibrium. For ammonia synthesis a consensus exists that the dissociation of N2 is the rate-limiting step, and we shall make this assumption here. With quasi-equilibrium steps the differential equation, together with equilibrium condition, leads to an expression for the coverage of species involved in terms of the partial pressures of reactants, equilibrium constants and the coverage of other intermediates. 

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

The columns of numbers given with each panel show the fraction of receptors in each condition at the particular concentration of A indicated by x on one of the curves. The values of the equilibrium constants used in the simulations are listed in Table 1.4. 

Table 1.3 sets out the relationships between the three primary and the nine other equilibrium constants that appear in Figure 1.28. Table 1.4 lists the particular values used to calculate the sets... 

Each differential equation contains a flow term identified by Q/V (flow rate/reactor volume) and also a reaction term which can be identified by a rate of reaction or equilibrium constant (k, K, k ). These reaction and equilibrium constants are functions of temperature which, in this study, was fixed. The viscosity dependence of the equilibrium constant (relating reactive species to total polymer) shown in Equations 6 and 7 was observed experimentally and is known as the Trommsdorf effect (6). Table I lists values and units of all parameters in Equations 1-7. 

A listing of thermodynamic properties determined by a full range of methods enables the ArG° values to be determined and hence the allowed reactions and equilibrium constants for all reactions. A tabulation of some thermodynamic quantities is found in Appendix C. 

The reaction favours the formation of ozone with a significant equilibrium constant. Appendix C also lists the enthalpies of formation and the standard enthalpy of the reaction ArH° can be calculated. The answer for the enthalpy calculation is ArH° = —106.47 kJ mol, showing this to be an exothermic reaction, liberating heat. The entropy change at 298 K can also be calculated because ArG° = ArH° — T ArS°, so ArS° = 25.4 Jmol-1 K-1, indicating an increase in the entropy of the reaction as it proceeds by creating one molecule from two. 

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