Control kinetic

The nonlinear current-voltage behavior associated with an electrochemical system is illustrated in Figiue 5.4(a). In the case shown here, the anodic (positive) current has an exponential dependence on potential whereas, the cathodic (negative) cvur-rent displays an influence of mass-transfer limitations. Regions are identified for which the current has a value equal to zero, the current is controlled by reaction kinetics, and the current is controlled by mass transfer. 

If the current corresponds to a single electrochemical reaction, a zero current is observed if the forward and backward rates for the reaction are equal. For example, if the forward (or anodic) reaction is given by 

If the zero current condition arises through a balemcing of different reactions, equilibrium is not achieved because the net rate for each reaction is not equal to zero. For example, if the corrosion of iron 

The potential at which the current for multiple electrochemical reactions is equal to zero is termed the mixed potential or, in the case of metal dissolution, the corrosion potential. Concepts of thermodynamics, kinetics, and transport must be applied to calculate values for the mixed or corrosion potential. 

The region of kinetic control of electrochemical reactions is characterized by current densities that are exponential functions of potential. For a single reversible reaction, the Butler-Volmer equation 

Often reactions or reaction steps in a network of reactions are at chemical equilibrium i.e., the rate of the forward reaction equals the rate of the reverse reaction. For instance, for the reversible reaction 

At chemical equilibrium the forward and reverse reaction rates are equal according to the principle of microscopic reversibility  

When a reversible reaction is not at equilibrium, knowledge of K, can be used to eliminate the rate constant of the reverse reaction by using Eq. (7-15) as follows  

When several reversible reactions occur simultaneously, each reaction ty is characterized by its equilibrium constant K. When the are known, the composition at equilibrium can be calculated from a set of equations such as Eq. (7-15) for each reaction. 

Conversion of a reactant is the number of moles converted per initial or feed moles of a reactant. Thus for component A 

The equilibrium constant (based on volumetric concentrations) is defined as the ratio of the forward and reverse rate constants and is related to the composition at equilibrium as follows  

can be calculated from the free energy change of the reaction. Using the van t Hoff relation, we obtain the dependence of on temperature  

Integrating with respect to temperature, we obtain a form similar to the Arrhenius expression of the rate constant for a narrow range of temperature  

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Experimental access to the probabilities P(E ,E) for energy transfer in large molecules usually involves teclmiques providing just the first moment of this distribution, i.e. the average energy (AE) transferred in a collision. Such methods include UV absorption, infrared fluorescence and related spectroscopic teclmiques [11. 28. 71. 72, 73 and 74]. More advanced teclmiques, such as kinetically controlled selective ionization (KCSI [74]) have also provided infonnation on higher moments of P(E ,E), such as ((AE) ). 

Hold U, Lenzer T, Luther K, Reihs K and Symonds A C 2000 Collisional energy transfer probabilities of highly excited molecules from kinetically controlled selective ionization (KCSI). I. The KCSI technique experimental approach for the determination of P(E, E) in the quasicontinuous energy ranged. Chem. Phys. 112 4076-89... 

Electrode processes are a class of heterogeneous chemical reaction that involves the transfer of charge across the interface between a solid and an adjacent solution phase, either in equilibrium or under partial or total kinetic control. A simple type of electrode reaction involves electron transfer between an inert metal electrode and an ion or molecule in solution. Oxidation of an electroactive species corresponds to the transfer of electrons from the solution phase to the electrode (anodic), whereas electron transfer in the opposite direction results in the reduction of the species (cathodic). Electron transfer is only possible when the electroactive material is within molecular distances of the electrode surface thus for a simple electrode reaction involving solution species of the fonn... 

The FMO coefficients also allow cpralitative prediction of the kinetically controlled regioselectivity, which needs to be considered for asymmetric dienes in combination with asymmetric dienophiles (A and B in Scheme 1.1). There is a preference for formation of a o-bond between the termini with the most extreme orbital coefficients ... 

Under the usual conditions their ratio is kinetically controlled. Alder and Stein already discerned that there usually exists a preference for formation of the endo isomer (formulated as a tendency of maximum accumulation of unsaturation, the Alder-Stein rule). Indeed, there are only very few examples of Diels-Alder reactions where the exo isomer is the major product. The interactions underlying this behaviour have been subject of intensive research. Since the reactions leadirig to endo and exo product share the same initial state, the differences between the respective transition-state energies fully account for the observed selectivity. These differences are typically in the range of 10-15 kJ per mole. ... 

Hthiated 4-substituted-2-methylthia2oles (171) at -78 C (Scheme 80). Crossover experiments at—78 and 25°C using thiazoles bearing different substituents (R = Me, Ph) proved that at low temperature the lithioderivatives (172 and 173) do not exchange H/Li and that the product ratios (175/176) observed are the result of independent metala-tion of the 2-methyl and the C-5 positions in a kinetically controlled process (444). At elevated temperatures the thermodynamic acidities prevail and the resonance stabilized benzyl-type anion (Scheme 81) becomes more abundant, so that in fine the kinetic lithio derivative is 173, whereas the thermodynamic derivative is 172. 

When the major product of a reaction is the one that is formed at the fastest rate we say that the reaction is governed by kinetic control Most organic reactions fall into this category and the electrophilic addition of hydrogen bromide to 1 3 butadiene at low temperature is a kmetically controlled reaction... 

FIGURE 10 8 Energy dia gram showing relationship of kinetic control to thermo dynamic control in addition of hydrogen bromide to 1 3 butadiene... 

Chloro 1 3 butadiene (chloroprene) is the monomer from which the elastomer neoprene IS prepared 2 Chloro 1 3 butadiene is the thermodynamically controlled product formed by addi tion of hydrogen chloride to vinylacetylene (H2C=CHC=CH) The principal product under conditions of kinetic control is the allenic chlonde 4 chloro 1 2 butadiene Suggest a mechanism to account for the formation of each product... 

On reaction with acyl chlorides and acid anhydrides phenols may undergo either acylation of the hydroxyl group (O acylation) or acylation of the ring (C acylation) The product of C acylation is more stable and predominates under conditions of thermodynamic control when alu mmum chloride is present (see entry 6 m Table 24 4 Section 24 8) O acylation is faster than C acylation and aryl esters are formed under conditions of kinetic control... 

Kinases (Section 28 3) Enzymes that catalyze the transfer of phosphate from ATP to some other molecule Kinetically controlled reaction (Section 10 10) Reaction in which the major product is the one that is formed at the fastest rate... 

The presence of a time limitation suggests that there must be a kinetically controlled interference, possibly arising from a competing chemical reaction. In this case the interference is the possible precipitation of CaCOs. 

Plot of signal versus time for an analytical system that is under (a) thermodynamic control and (b) under kinetic control. 

The composition of the products of reactions involving intermediates formed by metaHation depends on whether the measured composition results from kinetic control or from thermodynamic control. Thus the addition of diborane to 2-butene initially yields tri-j iAbutylboraneTri-j -butylborane. If heated and allowed to react further, this product isomerizes about 93% to the tributylborane, the product initially obtained from 1-butene (15). Similar effects are observed during hydroformylation reactions however, interpretation is more compHcated because the relative rates of isomerization and of carbonylation of the reaction intermediate depend on temperature and on hydrogen and carbon monoxide pressures (16). 

Alkylation of pyrazinones and quinoxalinones may be carried out under a variety of conditions and it is usually observed that while O-alkylation may occur under conditions of kinetic control, to yield the corresponding alkoxypyrazines or alkoxyquinoxalines, under thermodynamic control the A-alkylated products are formed. Alkylation using trialkyl-oxonium fluoroborate results in exclusive O-alkylation, and silylation under a variety of conditions (75MI21400) yields specifically the O-silylated products. Alkylation with methyl iodide or dimethyl sulfate invariably leads to A-methylation. 

With pteridine (1) the covalent hydration is a complex matter since the general acid-base catalyzed reaction provides a good example of a kinetically controlled addition to the... 

A parallel exists between the results of protonation and alkylation of pyrazolones since there is an alkyl derivative for each tautomer. The main difference is that the percentage of the different tautomers is thermodynamically controlled whereas that of alkyl derivatives is kinetically controlled. One has to remember that the alkyl derivatives thus obtained are the fixed compounds used in tautomeric studies. 

Under these conditions 2-methoxypropene reacts to form the kinetically controlled 1,3-O-isopropylidene, instead of the thermodynamically more stable 1,2-O-isopropylidene. ... 

Baker, D., Sohl, J.F., Agard, D.A. A protein-folding reaction under kinetic control. Nature 356 263-265, 1992. 

Product composition may be governed by the equilibrium thermodynamics of the system. When this is true, the product composition is governed by thermodynamic control. Alternatively, product composition may be governed by competing rates of formation of products. This is called kinetic control. 

Let us consider cases 1-3 in Fig. 4.4. In case 1, AG s for formation of the competing transition states A and B from the reactant R are much less than AG s for formation of A and B from A and B, respectively. If the latter two AG s are sufficiently large that the competitively formed products B and A do not return to R, the ratio of the products A and B at the end of the reaction will not depend on their relative stabilities, but only on their relative rates of formation. The formation of A and B is effectively irreversible in these circumstances. The reaction energy plot in case 1 corresponds to this situation and represents a case of kinetic control. The relative amounts of products A and B will depend on the heights of the activation barriers AG and G, not the relative stability of products A and B. 

In case 2, the lowest AG is that for formation of A from R, but the AG for formation of B from A is not much larger. System 2 might be governed by either kinetic or thermoifynamic factors. Conversion of R to A will be only slightly more rapid than conversion of A to B. If the reaction conditions are carefully adjusted, it will be possible for A to accumulate and not proceed to B. Under such conditions, A will be the dominant product and the reaction will be under kinetic control. Under somewhat more energetic conditions, for example, at a higher temperature, A will be transformed to B, and under these conditions the reaction will be under thermoifynamic control. A and B will equilibrate, and the product ratio will depend on the equilibriiun constant determined by AG. 

Because the product composition is kinetically controlled, the isomer ratio will be governed by the relative magnitudes of AG, AGI, and AG, the energies of activation for the ortho, meta, and para transition states, respectively. In Fig. 4.7 a qualitative comparison of these AG values is made. At the transition state, a positive charge is present on the benzene ring, primarily at positions 2, 4, and 6 in relation to the entering bromine. 

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