Rates of approach to equilibrium

The ketone is added to a large excess of a strong base at low temperature, usually LDA in THF at -78 °C. The more acidic and less sterically hindered proton is removed in a kineti-cally controlled reaction. The equilibrium with a thermodynamically more stable enolate (generally the one which is more stabilized by substituents) is only reached very slowly (H.O. House, 1977), and the kinetic enolates may be trapped and isolated as silyl enol ethers (J.K. Rasmussen, 1977 H.O. House, 1969). If, on the other hand, a weak acid is added to the solution, e.g. an excess of the non-ionized ketone or a non-nucleophilic alcohol such as cert-butanol, then the tautomeric enolate is preferentially formed (stabilized mostly by hyperconjugation effects). The rate of approach to equilibrium is particularly slow with lithium as the counterion and much faster with potassium or sodium. 

Adsorption is invariably an exothermic process, so that, provided equilibrium has been established, the amount adsorbed at a given relative pressure must diminish as the temperature increases. It not infrequently happens, however, that the isotherm at a given temperature Tj actually lies above the isotherm for a lower temperature Ti. Anomalous behaviour of this kind is characteristic of a system which is not in equilibrium, and represents the combined effects of temperature on the rate of approach to equilibrium and on the position of equilibrium itself. It points to a process which is activated in the reaction-kinetic sense and which therefore occurs more rapidly as temperature is increased. 

This is the expression we need. It has been plotted in Figure 1.3 for three concentrations of A. Note how the rate of approach to equilibrium increases as [A] becomes greater. This is because the time course is determined by (, + A, [ A ). This quantity is sometimes replaced by a single constant, so that Eq. (1.22) can be rewritten as either ... 

The treatment of chemical reaction equilibria outlined above can be generalized to cover the situation where multiple reactions occur simultaneously. In theory one can take all conceivable reactions into account in computing the composition of a gas mixture at equilibrium. However, because of kinetic limitations on the rate of approach to equilibrium of certain reactions, one can treat many systems as if equilibrium is achieved in some reactions, but not in others. In many cases reactions that are thermodynamically possible do not, in fact, occur at appreciable rates. 

Propagation problems. These problems are concerned with predicting the subsequent behavior of a system from a knowledge of the initial state. For this reason they are often called the transient (time-varying) or unsteady-state phenomena. Chemical engineering examples include the transient state of chemical reactions (kinetics), the propagation of pressure waves in a fluid, transient behavior of an adsorption column, and the rate of approach to equilibrium of a packed distillation column. 

At low hydroxide-ion concentrations, the rate of approach to equilibrium after a temperature jump decreases as the hydroxide-ion concentration increases. At higher concentrations the reaction becomes first order in hydroxide ion. The value of the kinetic solvent deuterium isotope effect on the reaction shows little variation over the range of hydroxide-ion concentrations studied as shown in Fig. 19. The ratio t-1(H20)/t 1(D20) at a particular concentration of OL (L = H or D) remains within the range 2.0 to 3.0 for OL" concentrations of 0.001 to 0.100 mol dm - 3 and provides little mechanistic information. Similar results were obtained in the original work (Perlmutter-Hayman and Shinar, 1978). 

Since water is normally present in large excess, the reaction can be characterized by two first-order velocity constants, for hydrate dissociation, and k for hydration. Any method which measures the rate of approach to equilibrium will give an overall rate constant k = k kJ, ... 

The complex kinetic dependence on hydroxide-ion concentration was explained by the mechanism in (27). Proton removal from the phenylazo-resorcinol monoanion by the hydroxide ion to give the dianion occurs by two different routes. One route is first order with respect to the hydroxide ion with rate coefficients and and is assumed to consist of a direct attack by the hydroxide ion on the hydrogen-bonded proton. The other route leads to a complex dependence of the rate of approach to equilibrium on the hydroxide-ion concentration, and involves prior opening of the hydrogen bond (rate coefficients kj and followed by proton removal (rate coefficients and k j). Equation (28) is derived from the mechanism... 

The aquation of the various CoCCN -3 complexes must occur by a reaction path which is merely the reverse of that followed in the anation. If the proposed mechanism for the anation reaction is valid, the reverse of Reactions 1 and 2 may be used to describe the equation. In any given experiment the rate of approach to equilibrium may be characterized by a first-order rate constant k which is related to the other kinetic parameters by Equation 3. When krfa/kz k (X ), as it is in... 

The phenomenon under consideration was studied systematically in the beginning of the 19th century. In 1815, Davy performed experiments that dealt with catalytic combustion on platinum gauzes. The term catalysis , however, was introduced by Berzelius in 1836. He first defined a catalyst (Berzelius, 1836) as a compound, which increases the rate of a chemical reaction, but which is not consumed during the reaction. This definition was later amended by Ostwald (1853-1932) in 1895 to involve the possibility that small amounts of the catalyst are lost in the reaction or that the catalytic activity is slowly decreased A catalyst is a substance that increases the rate of approach to equilibrium of a chemical reaction without being substantially consumed in the reaction. It was more than a century after Berzelius first definition that Marcel Prettre s introduced the notion of yield The catalyst is a substance that increases the rate of a chemical transformation without modifying the yield, and that is found intact among the final products of the reaction. ... 

Several times in this discussion we have noted the importance of experimental conditions that permit as rapid an equilibration as possible. The implication of these remarks is that osmotic equilibrium is reached slowly. In some cases as much as one week may be required for equilibrium to be achieved. To shorten this time, procedures based on measuring the rate of approach to equilibrium have been developed. The osmometer of Figure 3.3b is especially suited for this procedure. 

If pure A is placed in a solution, its concentration will decrease until it reaches an equilibrium with the B which has been formed. It is easy to show that in this case [A] does not decay exponentially but [A] - [A]equil does. If log([A] - [A]equil) is plotted against time a first-order rate constant k, characteristic of the rate of approach to equilibrium, will be obtained. Its relationship to fcjand k2 is given by Eq. 9-11. 

For a-D-galactopyranose, under the conditions used, these were -pyra-nose, 19.9 minutes, / -pyranose, 20.3 minutes, and furanose, 16.2 minutes. Thus, the rate at which the furanoses approach equilibrium is somewhat, but not markedly greater than the rates for the pyranose tautomers. A similar treatment of the data for / -L-arabinopyranose gave a set of four straight lines from which it could be seen that the rates of approach to equilibrium were nearly identical for all the tautomers. The values were a-pyranose, 6.8 minutes -pyranose, 6.7 minutes a-furanose, 6.4 minutes and / -furanose, 7.2 minutes. 

Figure 6.1. Rate of approach to equilibrium of (a) carbaryl and (b) parathion on Ca-saturated soil humic material. [From Leenheer and Ahlrichs (1971), with permission.]...

There is no simple, direct relationship between elasticity and emulsion or foam stability because additional factors, such as film thickness and adsorption behaviour, are also important [204]. Nevertheless, several researchers have found useful correlations between EM and emulsion or foam stability [131,201,203], The existence of surface elasticity explains why some substances that lower surface tension do not stabilize foams [25]. That is, they do not have the required rate of approach to equilibrium after a surface expansion or contraction as they do not have the necessary surface elasticity. Although greater surface elasticity tends to produce more stable bubbles, if the restoring force contributed by surface elasticity is not of sufficient magnitude, then persistent foams may not be formed due to the overwhelming effects of the gravitational and capillary forces. More stable foams may require additional stabilizing mechanisms. 

How does a catalyst affect a chemical reaction If we maintain the restriction that a catalyst is not appreciably consumed in a chemical reaction, then it can be shown thermodynamically that its role in the reaction cannot be to change the ultimate equilibrium point. Its role is restricted to one of accelerating the rate of approach to equilibrium. However, in most chemical systems, there are many mctastable compositions intermediate in free energy between reactants and the state of ultimate equilibrium. We can describe the specificity of catalysts in terms of... 

In first order-first order reversible reactions, the rate of approach to equilibrium is proportional to the fractional distance from equilibrium, measured in terms of any quantity that is a linear function of the concentrations. The same rule holds true for any participant in reactions with first-order parallel steps. 

The question whether reaction (xxiii) is fairly rapidly equilibrated, i.e. whether the water gas equilibrium is rapidly established, in the recombination zones of any flames has received considerable attention. The equilibrium is certainly not rapidly established in lower temperature (Tb 1100 K), fuel-rich H2/N2/CO2/O2 or H2/N2/CO/O2 flames at atmospheric pressure. In such H2/N2/O2 flames with a trace of added CO2, Dixon-Lewis et al. [169] found that only about 12 % of the CO2 reacted in the flame, whereas for equilibration the final [CO] /[CO2] ratio should have been about unity. Further, in a similar H2/N2CO/O2 flame which contained about 20 % H2 and 8 % CO initially, Dixon-Lewis et al. [419] found the [C02]/[C0] ratio in the effluent gas to be only about In higher temperature flames the equilibrium is approached more rapidly. Fenimore and Jones [209], similarly using mass spectrometric probing of atmospheric pressure H2 /O2 /Ar flames containing a little CO2, found that at 1345 K the rate of approach to equilibrium was as rapid as could be followed conveniently . However, at 1605 K with a very lean, low pressure propane-air flame, Friedman and Cyphers [413] found the ratio [CO] /[H2 ] at distances up to 1.5 cm above the luminous zone to be two to three times higher than would be expected on the basis of equilibration. 

The kinetic method provides another way of obtaining equilibrium constants by the measurement of the rate of approach to equilibrium. It relies on the back reaction having a measurable effect on the forward electron-transfer reaction in a scheme comprising Eqs. 52 and 54 ... 

The chemical reaction step in adsorption of As(III) and As(V) by metal oxyhydroxides has been reported to be rapid, with greater than 90% adsorption occurring within a few hours (Anderson et al., 1976 Darland and Inskeep, 1997b Elkhatib et al, 1984b Fuller et al., 1993 Grossl and Sparks, 1995 Singh et al., 1988 Van der Hoek et al., 1994 Xu et al., 1988). This initial rapid adsorption step is followed by a slower approach to equilibrium which may take up to several days. The slow rate of approach to equilibrium... 

This intermediate survives several molecular collisions before passing through a second transition state to form the product [M(H20)(ra 1)L](m xA. Thus, the rate determining step (k is the bond making between Lx with Mm+ and the mechanism is termed associatively (a) activated and the mechanism associative, A. (In the back reaction the rate determining step is characterized by k 2). The rate of approach to equilibrium in the presence of excess [Lx ], characterized by kobs in Equation (8) is dependent on the nature of Lx ... 

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