Diffusion-Controlled Fast Reactions

In this section, we turn to chemical reactions that take place faster than a few milliseconds, often faster than microseconds. The most common example is the reaction of acid and base other good examples are the combustion of methane and the action of the enzyme urease. These reactions occur so quickly that in industrial situations they are always diffusion controlled. However, they are of scientific interest. 

To see how these fast reactions can be studied, we turn to the specific example of the temperature-jump apparatus shown in Fig. 17.4-1. In this apparatus, a cell containing perhaps 0.3 cm of conducting solution is suddenly heated by discharging a capacitor through the solution. This heating, typically about 10 °C, shifts any reactions in the cell away from equilibrium. These reactions then move to a new equilibrium at the new, higher temperature. The speed with which they reach this new state is measured with a spectrophotometer attached to an oscilloscope. 

One reaction studied with this temperature-jump apparatus is 

In the remainder of this section, we shall describe how the oscilloscope trace can be related to the rate constant and how the rate constant varies with the diffusion coefficient. 

The experimental signal found on the oscilloscope is rarely a smooth, exactly defined curve. Far more frequently it contains considerable noise, more than that shown in Fig. 17.4-1(b). One method of reducing this noise is to repeat the experiment and to average electronically the various signals obtained. Even so, the signal remains inexactly 

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In a study of the reaction of Ps and iodine in various solvents [Ta 70], it was found that the rate constant of the reaction varied linearly with the reciprocal of the viscosity of the solvent. The reaction is thus a diffusion-controlled fast reaction, similarly to the reaction between Ps and dissolved paramagnetic (and therefore strongly quenching) oxygen [Po 54]. 

Real reasons due to (a) the occurance of very fast (and therefore in most cases diffusion controlled) catalytic reactions on the electrode surface, (b) Formation of non-conducting carbonaceous or oxidic layers on the catalyst electrode surface. 

Figure 2-4 Typical concentration profiles of instantaneous reaction between the gas A and the reactant C, based on film theory, ids Diffusion controlled - slow reaction, (fcl kinetically controlled-slow reaction, (c) gas-film-controlled desorption - fast reaction, 0 liquid-film-controlled desorption-fast reaction, (e) liquid-film-controlled absorption -instantaneous reaction between A and C, (/) gas-film-controlled absorption-instantaneous reaction between A and C, (g) concentration profiles for A, B, and C for instantaneous reaction between A and C-both gas- and liquid-phase resistances are comparable.1 2...

Deviations from Eqs. (29), (30), and (33) occur when the effective double layer at the metal-gas interfaces is destroyed [140]. This is the case for (1) very low temperatures (<250 °C for YSZ, <100 °C for )8"-Al203) where ion spillover-backspillover is kinetically frozen, or (2) very high temperatures (>500 °C for YSZ, >400 °C for P"-A 203) where the effective double layer desorbs (3) fast diffusion-controlled catalytic reactions, which again destroy the double layer (4) formation of insulating carbonaceous or oxidic deposits at the metal-gas interface which allow for the storage of electric charge [140]. 

Transport is an integral component of all reaction systems. In well-mixed homogeneous solutions, the concentrations of all reactants and products are the same throughout the system, and there is no net movement of chemicals in space. The role of mass transport becomes evident only when chemical reactions are extremely fast. Diffusion determines the encounter frequency of reacting molecules and sets an upward limit on overall rates of reaction. (For example, for a diffusion-controlled bimolecular reaction in water the reaction rate constant is on the order of 1010 to 1011 M 1 s"1.) Mass transport plays a pronounced role in surface chemical reactions, since net movement of reactants (from solution to the surface) and products (from the surface to solution) often takes place. 

Finally a word on rates of acid-base reactions. All the protons in water are undergoing rapid migration from one oxygen atom to another, and the lifetime of an individual HsO+ ion in water is only approximately 10 13 sec. The rate of reaction of HsO+ with a base such as OH" in water is very fast but also diffusion-controlled.13 Reaction occurs when the solvated ions diffuse to within a critical separation, whereupon the proton is transferred by concerted shifts across one or more solvent molecules hydrogen-bonded to the base. 

The solvent effect on proton-transfer reactions is determined by two effects In cases of slow proton transfers, which are not diffusion-controlled, e.g. reactions between carbon acids and weak bases the solvent effect is determined by hydrogen-bonding and formation of ion pairs whereas tte viscosity of the solvent prevails in very fast diffusion-controll l reactions. 

Fig. 10. The complex impedance plot for several simple electrode processes at the electrode and their equivalent circuits (A) Ideally polarizable electrode. (B) Diffusion-controlled fast redox reaction. (C) Irreversible electrode reaction. (D) Quasi-reversible electrode reaction. Arrows indicate the increasing frequency.

It has been reported that ascorbic acid reacts with hydroxyl radical at a rate constant in the range of 7.2 x 10 -1.3 x 10 M- s at pH 1 (Nishikimi, 1975 Cabelli and Bielski, 1983), which shows that the reaction is fast and diffusion-controlled. The reaction proceeds either by an electron transfer or by the addition of hydroxyl radical to the double bond of ascorbic acid (Bielski, 1982). At physiological pH the reaction proceeds more slowly with a rate constant of 2.7 x 10 M- s-E This indicates that ascorbic acid is not a specific hydroxyl radical scavenger, since hydroxyl radical is so reactive that it can react with many other compounds at about the same rate. 

Solvated electrons can be obtained in concentrations up to 10" moldm . Reactions with solvated electrons are very fast second-order reactions, with rate constants between 10 to 5x10 mor dm s", which means that their rates are close to the diffusion control. A reaction is diffusion-controlled when the reaction rate is dependent upon the rate at which reactants diffuse toward one another. A diffusion-controlled reaction must have a small activation energy, because if is high (EJRT 1), then the reaction rate is controlled by the number of molecules with energy higher than the activation energy, not by the diffusion rate. Reactions with high E are activation-controlled. 

Similarly to the response at hydrodynamic electrodes, linear and cyclic potential sweeps for simple electrode reactions will yield steady-state voltammograms with forward and reverse scans retracing one another, provided the scan rate is slow enough to maintain the steady state [28, 35, 36, 37 and 38]. The limiting current will be detemiined by the slowest step in the overall process, but if the kinetics are fast, then the current will be under diffusion control and hence obey the above equation for a disc. The slope of the wave in the absence of IR drop will, once again, depend on the degree of reversibility of the electrode process. 

Manufacture and Processing. Mononitrotoluenes are produced by the nitration of toluene in a manner similar to that described for nitrobenzene. The presence of the methyl group on the aromatic ring faciUtates the nitration of toluene, as compared to that of benzene, and increases the ease of oxidation which results in undesirable by-products. Thus the nitration of toluene generally is carried out at lower temperatures than the nitration of benzene to minimize oxidative side reactions. Because toluene nitrates at a faster rate than benzene, the milder conditions also reduce the formation of dinitrotoluenes. Toluene is less soluble than benzene in the acid phase, thus vigorous agitation of the reaction mixture is necessary to maximize the interfacial area of the two phases and the mass transfer of the reactants. The rate of a typical industrial nitration can be modeled in terms of a fast reaction taking place in a zone in the aqueous phase adjacent to the interface where the reaction is diffusion controlled. 

Up to the present the principal interest in heteroaromatic tautomeric systems has been the determination of the position of equilibrium, although methods for studying fast proton-transfer reactions (e.g., fluorescence spectroscopy and proton resonance ) are now becoming available, and more interest is being shown in reactions of this type (see, e.g., references 21 and 22 and the references therein). Thus, the reactions of the imidazolium cation and imidazole with hydroxyl and hydrogen ions, respectively, have recently been demonstrated to be diffusion controlled. ... 

The result of the fast reactions in the ion source is the production of two abundant reagent ions (CH5+ and C2H5+) that are stable in the methane plasma (do not react further with neutral methane). These so-called reagent ions are strong Brpnsted acids and will ionize most compounds by transferring a proton (eq. 7). For exothermic reactions, the proton is transferred from the reagent ion to the neutral sample molecule at the diffusion controlled rate (at every collision, or ca. 10 9 s 1). 

The reaction rate is very fast indeed (ti = 10-3 sec), but this is stated to be many orders of magnitude less than the speed at which diffusion control would be expected109. 

Revisions of the continuous-flow method have been made to allow observations along the length of the flow tube rather than at right angles.5 This method, fast continuous flow, eliminates the dead time during which the reaction cannot be observed. Kinetic data can be extracted to a time resolution of nearly 10 p,s, but the mathematics is more complicated in this limit, because the mixing and chemical reaction occur on the same time scale. Rate constants nearly as large as the diffusion-controlled value have been determined in favorable cases.6... 

In an aqueous solution, solute molecules or ions require a certain amount of time to migrate through the solution. The rate of this migration sets an upper limit on how fast reactions can take place, because no reaction can take place faster than the ions can he supplied. This limit is known as the diffusion-controlled rate. It has been found that the diffusion rate for hydrogen ions is about three times as fast as that for other ions in aqueous solution. Explain why this is so. 

It is appropriate to differentiate between polymerizations occuring at temperatures above and below the glass transition point(Tg) of the polymer being produced. For polymerizations below Tg the diffusion coefficients of even small monomer molecules can fall appreciably and as a consequence even relatively slow reactions involving monomer molecules can become diffusion controlled complicating the mechanism of polymerization even further. For polymerizations above Tg one can reasonably assume that reactions involving small molecules are not diffusion controlled, except perhaps for extremely fast reactions such as those involving termination of small radicals. 

If the reaction is diffusion controlled, i.e. the charge transfer is fast compared to reactant transport, the value of A i/2 is equal to k. ... 

Proton transfers between oxygen and nitrogen acids and bases are usually extremely fast. In the thermodynamically favored direction, they are generally diffusion controlled. In fact, a normal acid is defined as one whose proton-transfer reactions are completely diffusion controlled, except when the conjugate acid of the base to which the proton is transferred has a pA value very close (differs by g2 pA units) to that of the acid. The normal acid-base reaction mechanism consists of three steps ... 

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