Rate constants bimolecular

The second-order rate law for bimolecular reactions is empirically well confinned. Figure A3.4.3 shows the example of methyl radical recombination (equation (A3.4.36)) in a graphical representation following equation (A3.4.38) [22, 23 and 24]. For this example the bimolecular rate constant is... 

Smoluchowski theory [29, 30] and its modifications fonu the basis of most approaches used to interpret bimolecular rate constants obtained from chemical kinetics experiments in tenus of difhision effects [31]. The Smoluchowski model is based on Brownian motion theory underlying the phenomenological difhision equation in the absence of external forces. In the standard picture, one considers a dilute fluid solution of reactants A and B with [A] [B] and asks for the time evolution of [B] in the vicinity of A, i.e. of the density distribution p(r,t) = [B](rl)/[B] 2i ] r(t))l ] Q ([B] is assumed not to change appreciably during the reaction). The initial distribution and the outer and inner boundary conditions are chosen, respectively, as... 

From these considerations we conclude that diffusion-limited bimolecular rate constants are of the order 10 -10 M s . If an experimentally measured rate constant is of this magnitude, the usual conclusion is, therefore, that it is diffusion limited. For example, this extremely important reaction (in water)... 

Bimolecular rate constants determined at temperatures giving conveniently measurable rates and calculated for the temperature given in parentheses. 

Bimolecular rate constants determined at temperatures giving conveniently measurable rates and calculated for the temperature given in parentheses, except for some of the catalyzed reactions (lines 1-4 and 14—19) which are third-order. 

Bimolecular rate constant in liter mole i sec i a value of lO i at 60° was given.i39... 

Biisslcr et ai [110-113] treated charge recombination in organic LEDs in terms of chemical kinetics. The probability of recombination depends on the ratio of recombination rate ynp-np (where y represents a bimolecular rate constant) and the transition time (itr=dlpE) of the charge carriers through the device. 

Table 1. A compilation of specific bimolecular rate constants (/tc) for the reaction of hydrated electrons with Li battery related materials (61,62]...

Iq/I — t — KgI0 [Q], in which Kg is the bimolecular rate constant of interaction of quencher Q with the excited states of the PCS, t is the lifetime of excited molecules with no quencher, I0 is the quantum yield of fluorescence in the absence of the quencher, and I is the quantum yield of fluorescence in the presence of the quencher. 

A minor component, if truly minute, can be discounted as the reactive form. To continue with this example, were KCrQ very, very small, then the bimolecular rate constant would need to be impossibly large to compensate. The maximum rate constant of a bimolecular reaction is limited by the encounter frequency of the solutes. In water at 298 K, the limit is 1010 L mol-1 s"1, the diffusion-controlled limit. This value is derived in Section 9.2. For our immediate purposes, we note that one can discount any proposed bimolecular step with a rate constant that would exceed the diffusion-controlled limit. 

The luminescence of an excited state generally decays spontaneously along one or more separate pathways light emission (fluorescence or phosphorescence) and non-radiative decay. The collective rate constant is designated k° (lifetime r°). The excited state may also react with another entity in the solution. Such a species is called a quencher, Q. Each quencher has a characteristic bimolecular rate constant kq. The scheme and rate law are... 

LRG ]) provides a preliminary estimate for the bimolecular rate constant of GTPyS binding ( 2 x 10 /ilf s ). This estimate is within an order of magnitude of the rates of GTP binding to another G protein (23). 

Figure lb shows the transient absorption spectra of RF (i.e. the difference between the ground singlet and excited triplet states) obtained by laser-flash photolysis using a Nd Yag pulsed laser operating at 355 nm (10 ns pulse width) as excitation source. At short times after the laser pulse, the transient spectrum shows the characteristic absorption of the lowest vibrational triplet state transitions (0 <— 0) and (1 <— 0) at approximately 715 and 660 nm, respectively. In the absence of GA, the initial triplet state decays with a lifetime around 27 ps in deoxygenated solutions by dismutation reaction to form semi oxidized and semi reduced forms with characteristic absorption bands at 360 nm and 500-600 nm and (Melo et al., 1999). However, in the presence of GA, the SRF is efficiently quenched by the gum with a bimolecular rate constant = 1.6x10 M-is-i calculated... 

In the first group of studies, involving kinetic inhibition studies, comparisons of the uilibrium (K ), phosphorylation (IC), and inhibition constant (K.) for the inhibition of electric eel and human erythrocyte AChE by ANTX-A(S) and DFP were done (Table II). From Table II it is seen that ANTX- A(S) has a higher affinity for human erythrocyte AChE (K =0.253 fiM) than electric eel AChE (K j=3.67 aM). AN DC-A(S) also shows greater affinity for AChE than DFP (K =300 fiM). And finally the bimolecular rate constant, Kj, which indicates the overall rate of reaction, shows AChE is more sensitive toward inhibition by ANTX-A(S) (Kj=1.36 pM- min- ) than DFP (K, = 0.033 /iM- min ). These studies add information to the comparative activity of ANTX-A(S) and other irreversible AChE inhibitors but do not show the site of inhibition. 

A detailed treatment of the transport and kinetics at microheterogeneous electrodes was given by Albery and Bartlett The electron transfer of MV to Pt-particles can be described by a bimolecular rate constant kj ... 

Nosaka and Fox determined the quantum yield for the reduction of methyl viologen adsorbed on colloidal CdS particles as a function of incident light intensity. Electron transfer from CdS to MV " competes with electron-hole recombination. They derived a bimolecular rate constant of 9 10 cm s for the latter process. 

The rate of MV formation was also dependent on pH. The bimolecular rate constant, as calculated from the first order rate constant of the MV build-up and the concentration of colloidal particles, was substantially smaller than expected for a diffusion controlled reaction Eq. (10). The electrochemical rate constant k Eq. (9) which largely determines the rate of reaction was calculated using a diffusion coefficient of of 10 cm s A plot of log k vs. pH is shown in Fig. 24. 

The first estimations of for photoinduced processes were reported by Dvorak et al. for the photoreaction in Eq. (40) [157,158]. In this work, the authors proposed that the impedance under illumination could be estimated from the ratio between the AC photopotential under chopped illumination and the AC photocurrent responses. Subsequently, the faradaic impedance was calculated following a treatment similar to that described in Eqs. (22) to (26), i.e., subtracting the impedance under illumination and in the dark. From this analysis, a pseudo-first-order photoinduced ET rate constant of the order of 10 to 10 ms was estimated, corresponding to a rather unrealistic ket > 10 M cms . Considering the nonactivated limit for adiabatic outer sphere heterogeneous ET at liquid-liquid interfaces given by Eq. (17) [5], the maximum bimolecular rate constant is approximately 1000 smaller than the values reported by these authors. 

Red2 in phase 2, CR d, = 1.5mM, this corresponds to a bimolecular rate constant, kn of... 

Since the most direct evidence for specihc solvation of a carbene would be a spectroscopic signature distinct from that of the free carbene and also from that of a fully formed ylide, TRIR spectroscopy has been used to search for such car-bene-solvent interactions. Chlorophenylcarbene (32) and fluorophenylcarbene (33) were recently examined by TRIR spectroscopy in the absence and presence of tetrahydrofuran (THF) or benzene. These carbenes possess IR bands near 1225 cm that largely involve stretching of the partial double bond between the carbene carbon and the aromatic ring. It was anticipated that electron pair donation from a coordinating solvent such as THF or benzene into the empty carbene p-orbital might reduce the partial double bond character to the carbene center, shifting this vibrational frequency to a lower value. However, such shifts were not observed, perhaps because these halophenylcarbenes are so well stabilized that interactions with solvent are too weak to be observed. The bimolecular rate constant for the reaction of carbenes 32 and 33 with tetramethylethylene (TME) was also unaffected by THF or benzene, consistent with the lack of solvent coordination in these cases. °... 

Fig. 5. Effective bimolecular rate constants at 300 K for the M + C3H6 reaction for all three transition metal rows. Values taken from Refs. 89, 91, and 94. Missing points were either not studied or exhibited no reaction with propene.

Unimolecular and Bimolecular Rate Constants for the Different Elementary Steps Involved in the MB Photosensitized Degradation of Bixin in Acetonitrile Methanol (1 1) Solutions at 25°C... 

Bimolecular Rate constants for Electron Transfer between Carotenoid Pairs in Argon Saturated Hexane (CAR/- + CAR2 CAR, + CAR/-)... 

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