Equilibrium constant reverse reaction

Without further refinement, the value of the equilibrium constant for reaction (7-73) seemingly would depend on [H+]. Clearly, that supposition violates a very fundamental precept of thermodynamics. With the help of microscopic reversibility, the dilemma is resolved. It specifies that the equilibrium constant is separately realized for each pathway ... 

Aldol condensations are reversible and slightly exothermic reactions. The values of equilibrium constants and reaction enthalpies of some aldol reactions reported in the literature are listed in Table 17. 

To obtain the equilibrium constant, Kn, we multiply known equilibrium constants for reactions that add to give the net ionic equation for the neutralization reaction. Because CH3C02H is on the left side of the equation and CH3C02- is on the right side, one of the reactions needed is the dissociation of CH3C02H. Since H20 is on the right side of the equation and OH - is on the left side, the other reaction needed is the reverse of the dissociation of H20. Note that H30+ and one H20 molecule cancel when the two equations are added ... 

For the p-meLhoxybenzyl cation the equilibrium constant for reaction with the sulfur nucleophile is more favorable than that for the chloride ion by a factor of 107. As already discussed on p. 73 (cf. Table 6) this is a normal reflection of the greater carbon basicity of sulfur than chlorine. However in the case of the quinone methide the relative magnitudes of the equilibrium constants is reversed, with Me2s/ ci = 0.008. Toteva and Richard attribute this to the unfavorable steric and electrostatic interactions between the CF3 groups of the quinone methide adduct and the positively charged sulfonium ion. 

Reactions 17.5, 17.6, and 17.7 illustrate the gasification of char by reaction with various gases. The carbon-steam Reaction 17.5 is an endothermic reversible reaction. Steam undergoes a side reaction, Reaction 17.8, called the water-gas shift reaction. This reaction, which is very rapid, is catalyzed by various impurities and surfaces. The carbon-C02 reaction, Reaction 17.6, is favored at high temperatures and low pressures, whereas the carbon-H2 reaction, Reaction 17.7, is favored at low temperatures and high pressure. Since only three of Reactions 17.5-17.9 are independent, if the equilibrium constants for Reactions 17.6, 17.7, and 17.8 are known, the... 

The equilibrium constant for reaction (2), 3.9 x 10"5 M, was obtained from the rates of the forward and reverse reactions. (Note that in many discussions the concentration of water is included in the equilibrium constant.) Thus AfG° for e"q is 55 kJ/mol greater than for H. Reaction (3) was estimated to have AG° = 0. The other data are available in standard... 

Note that the equilibrium constant for reactions 3 and 4, namely Ks 4, may be calculable from spectroscopic and thermal data, so that hi = kz/Ks 4 may be calculated. This permits us to calculate kb = kA/kt and also the rate constant for reaction 6 (the reverse of h) from kb == kb/Kb e, where 7v is the cahiulable equilibrium constant. All of these data are given in Table XII.5. 

Use the following terms to create a concept map chemical equilibrium, equilibrium constant, solubility product constant, reversible reactions, and Le Chdtelier s principle. 

A revised, updated suinmary of equilibrium constants and reaction enthalpies for aqueous ion association reactions and mineral solubilities has been compiled from the literature for common equilibria occurring in natural waters at 0-100 C and 1 bar pressure. The species have been limited to those containing the elements Na, K, Li, Ca, Mg, Ba, Sr, Ra, Fe(II/III), Al, Mn(II,III,IV), Si, C, Cl, S(VI) and F. The necessary criteria for obtaining reliable and consistent thermodynamic data for water chemistry modeling is outlined and limitations on the application of equilibrium computations is described. An important limitation is that minerals that do not show reversible solubility behavior should not be assumed to attain chemical equilibrium in natural aquatic systems. 

The net overall equilibrium constant for the reaction in solution (Kna) and the internal equilibrium constant for reaction at the active site (/fmi) can be measured most easily using radiolabeled substrates. Thus the problem becomes one of separating substrate and product chromatographically and then quantitating the ratio of /fnet = P]/[S] following incubation of the substrate with a trace of enzyme for a time sufficient for the reaction to come to equilibrium. The equilibration time can be estimated from the magnitude of kcJKm in the forward and reverse reactions. If the substrate and product concentrations are below their Km values, then the rate of approach to equilibrium can be approximated by... 

According to the principle of microscopic reversibility ki/k.i can be equated to the equilibrium constant for Reaction I, which in turn can be expressed in terms of the electron affinity through the statistical thermodynamic expression for an ideal gas (24). 

Another advantage of kinetic methods is that they permit a larger number of chemical reactions to be used analytically. Many chemical reactions cannot be employed analytically in equilibrium or thermodynamic-based techniques the reactions attain equilibrium too slowly, side reactions or subsequent reactions of the products occur as the reaction proceeds to completion, or the reactions are not sufficiently quantitative (equilibrium constants are too small) to be applicable. However, kinetic-based techniques can be employed in many of these cases. For example, complications arising from an unfavorable equilibrium constant, slow reaction, side reactions, reverse reactions, and so forth are circumvented by measuring the reaction rate during the initial 1-2% of the overall reaction (where the mechanism is usually straightforward). Thus, virtually any chemical reaction whose initial rate can be measured can be employed in a kinetic-based method. 

The sole difference between the advancing front and reversible reaction approach is the assumed size of the equilibrium constant for reaction 1. Advancing front models assume that reaction 1 is irreversible K is infinitely large. Finite values for K are assumed in the reversible reaction theory. 

Although the overall reaction is reversible with a measurable equilibrium constant, the reaction is probably virtually irreversible in vivo because of the ubiquitous pyrophosphatases. It is undoubtedly this step that prevents conversion of arginine to ornithine by reversal of the ornithine cycle and requires an arginase for arginine catabolism (see page 386). 

At equilibrium, both reversible reactions (3.20) and (3.31) come to a dynamic standstill, although the reaction has not stopped. An equihbrium constant for the overall process AP, for reaction (3.20), is equal to... 

The Equilibrium (Mass Action) Expression Gas Phase Equilibria Kp vs. Kp Homogeneous and Heterogeneous Equilibria Numerical Importance of the Equilibrium Expression Mathematical Manipulation of Equilibrium Constants Reversing the Chemical Equation Adjusting the Stoichiometry of the Chemical Reaction Equilibrium Constants for a Series of Reactions Units and the Equilibrium Constant... 

As written, these reactions are exothermic and, as ion-molecule reactions, can be expected to be very rapid, with rate coefficients 10 ml sec . In the temperature range 2000-2500°K, the equilibrium constant for reaction (46) is between 3 and 5 and for reaction (47) is between 27 and 42. Thus, for the reverse reactions, the rate coefficients will be > 10 ml sec These ion-molecule reactions are therefore faster than the reactions governing the neutral species concentrations H, H2, OH, O, and O2. The ions then are in equilibrium with the neutral species whether or not equilibrium among the neutral species has been established. Miller has measured the ratios of O , OH , and O2 downstream of low-pressure hydrocarbon-oxygen flames, from which he calculated, assuming equilibrium, the ratios of OH to H and of H2 to H. Comparison of the measured and equilibrium... 

Here we use the notation K(-2)xi to denote the equilibrium constant for the reaction obtained by multiplying reaction 1 by (—2).] Using Equation 10.7, the equilibrium constant for Reaction 3 is then given by the product of the equilibrium constant for Reaction 2 K2) and the equilibrium constant for the reaction that is twice the reverse of Reaction 1 ( T( 2)xi)- The equilibrium constant for the reverse of Reaction 1 is the reciprocal of the equilibrium constant for the forward reaction,... 

Six-co-ordinate low-spin iron(u) phthalocyanine complexes of the type L2pePc (L = imidazole, pyridine, piperidine, or 2-methylimidazole) reversibly bind carbon monoxide in toluene solution. The reaction has a dissociative mechanism and it is found that the limiting first-order rate constants for the dissociation of L parallel the equilibrium constants for reaction (8), viz. 2-MeIm > pip > py>Im. A substantial... 

In contrast to the relaxation technique, the flow methods can be used for reactions with large equilibrium constants (irreversible reactions) as well as with small ones (reversible reactions). The shortest half life that can be measured in flow systems depends on the mixing time. In shopped flow arrangements, the stopping time sets a barrier at 5.10 s. In a continuous flow system, only the mixing process is limiting. 

The free energy of solvation of the proton is the common reference for the equilibrium constant of both reactions 3 and 4. The reverse of reaction 4 is reaction 1, defining the redox potential of the XVX" couple (Equation 13.2). Expressing the equilibrium constant of reaction 3 in terms of the pK of XH, Hess law requires that... 

In a lower temperature range, the equihbrium constant Ky is larger, and the temperature has a marked effect on the reaction rate constant ki. However, as the temperature is gradually increased, the reversible exothermic reaction equilibrium constant Ky is decreased. The value in the square brackets in equation (8.5) is reduced, with the effect of temperature on reaction rate decreased too. When the temperature reaches a certain point, the effect of temperature on reaction rate becomes zero. Under continuously rising temperature, the impact of temperature on the equilibrium constant reverses, the reaction rate reduced when the temperature increases. That is, for a given composition of reactants, at a low temperature range )y > 0. When the temperature reaches a certain value with -)y = 0, the reaction rate reaches a maximum, which is the optimum temperature under this certain composition. After that, )y < 0 with the temperature continues increasing. 

For reaction 1 the forward and the reverse rate constants (fei and ki, respectively) could be determined. The rate of reaction was defined as the change in concentration of the toluene solution in reaction 2 (eqn [3]) over the time for ligand exchange in reaction 1. The equilibrium constant of reaction 1 determined as... 

The usual situation, true for the first three cases, is that in which the reactant and product solids are mutually insoluble. Langmuir [146] pointed out that such reactions undoubtedly occur at the linear interface between the two solid phases. The rate of reaction will thus be small when either solid phase is practically absent. Moreover, since both forward and reverse rates will depend on the amount of this common solid-solid interface, its extent cancels out at equilibrium, in harmony with the thermodynamic conclusion that for the reactions such as Eqs. VII-24 to VII-27 the equilibrium constant is given simply by the gas pressure and does not involve the amounts of the two solid phases. 

As seen in previous sections, the standard entropy AS of a chemical reaction can be detemiined from the equilibrium constant K and its temperature derivative, or equivalently from the temperature derivative of the standard emf of a reversible electrochemical cell. As in the previous case, calorimetric measurements on the separate reactants and products, plus the usual extrapolation, will... 

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