Inhibited rate dependence

Stable diaryl nitroxides such as 4,4 -dimethoxydiphenyl nitroxide (III) are somewhat better antioxidants than the dialkyl nitroxides. The III inhibited rate depends on both the oxygen pressure and the substrate... 

Figure 3. Inhibited-rate dependence on inhibitor concentration...

This is essentially a corrosion reaction involving anodic metal dissolution where the conjugate reaction is the hydrogen (qv) evolution process. Hence, the rate depends on temperature, concentration of acid, inhibiting agents, nature of the surface oxide film, etc. Unless the metal chloride is insoluble in aqueous solution eg, Ag or Hg ", the reaction products are removed from the metal or alloy surface by dissolution. The extent of removal is controUed by the local hydrodynamic conditions. 

Enzymatic reactions frequently undergo a phenomenon referred to as substrate inhibition. Here, the reaction rate reaches a maximum and subsequently falls as shown in Eigure 11-lb. Enzymatic reactions can also exhibit substrate activation as depicted by the sigmoidal type rate dependence in Eigure 11-lc. Biochemical reactions are limited by mass transfer where a substrate has to cross cell walls. Enzymatic reactions that depend on temperature are modeled with the Arrhenius equation. Most enzymes deactivate rapidly at temperatures of 50°C-100°C, and deactivation is an irreversible process. 

Figure 4. Concentration-dependent inhibition of electric eel AChE by ANTX-A(S). AChE and AhTrX-A(S) were incubated for 2 min. before inhibition rate was determined. Key (A) 0.079 ixg/mL ( ) 0.032 xg/mL (V) 0.016 lig/mL >) 0.0032 ig/mL ( ). 0016 tigjmL. NOTE Total inhibition occurs when 0.158 tiglmL ANTX-A(S) is preincubated with AChE for two minutes.

The aqueous ferricyanide oxidation of 2-mercaptoethanol to the disulphide is also complex kinetically" . In the pH range used (l.S. l) no complication from ionisation of the thiol is expected. Individual decays of oxidant concentrations are initially second-order but eventually become almost zero-order. For both second-and zero-order paths the rate depends on the first power of the thiol concentration and the former path is retarded by increasing the acidity, an approximately inverse relation existing above pH 3.2. Addition of ferrocyanide transforms the kinetics the rapid, second-order path is inhibited and the zero-order path is accelerated until, at 10 M ferrocyanide, the whole of the disappearance of oxidant is zero-order. Addition of Pb(C104)2, which removes product ferrocyanide, greatly enhances the oxidation rate and the consumption of oxidant becomes rs/-order. Two routes are considered to co-exist (taking due account of the acidity of ferrocyanic acid), viz. 

Calorimetric results demonstrate that the chain process is inhibited and terminated by oxygen. The inhibition period depends on oxygen, the light intensity and the type of photoinitiator. The measured values vary from 40 to 11 sec (variation of the light intensity (I0 = 4.15. .. 1.0 mW/cm2), p(air) = 1000 mbar), from 40 to 7 sec (variation of the air pressure (p(air) = 1000. .. 6 mbar, Ie = 1.0 mW/cm2)), and from 3 to 30 sec (variation of the initiator). Using values of the inhibition time and reaction rate one can estimate the relative efficiency of several radicals in the chain process. 

The mechanisms responsible for inhibited oxidation depend on the experimental conditions and particular properties of RH and antioxidant (see earlier). Let us assume that hydroperoxide is relatively stable, so that it virtually does not decompose during the induction period (kdr -c 1). Actually, this means that the rate of ROOH formation is much higher than the rate of its decomposition, / 2[RH] [RO]2 ] 3> d[ROOH]. For each of the mechanisms of inhibited autoxidation, there is a relationship between the amounts of the inhibitor consumed and hydroperoxide produced (see Tablel4.2). For example, for mechanism V with key reactions (2), (7), (—7), and (8), we can get (by dividing the oxidation rate v into the rate of inhibitor consumption) the following equation ... 

Equation (1) is generally used to estimate the rate constant, kin the micellar pseudophase, but for inhibited bimolecular reactions it provides an indirect method for estimation of otherwise inaccessible rate constants in water. Oxidation of a ferrocene to the corresponding ferricinium ion by Fe3 + is speeded by anionic micelles of SDS and inhibited by cationic micelles of cetyltrimethylammonium bromide or nitrate (Bunton and Cerichelli, 1980). The variation of the rate constants with [surfactant] fits the quantitative treatment described on p. 225. Oxidation of ferrocene by ferricyanide ion in water is too fast to be easily followed kinetically, but the reaction is strongly inhibited by anionic micelles of SDS which bind ferrocene, but exclude ferricyanide ion. Thus reaction occurs essentially quantitatively in the aqueous pseudophase, and the overall rate depends upon the rate constant in water and the distribution of ferrocene between water and the micelles. It is easy therefore to calculate the rate constant in water from this micellar inhibition. 

For hydrogenation to take place, the substrate usually needs to bind to the metal complex, although exceptions are known to this rule [25]. Substrate inhibition can occur in a number of ways, for example if more than one molecule of substrate binds to the metal complex. At low concentration this may be a minor species, whereas at high substrate concentration this may be the only species. One example of this is the hydrogenation of allyl alcohol using Wilkinson s catalyst. Here, the rate dependence on the substrate concentration went through a maximum at 1.2 mmol IT1. The authors propose that this is caused by formation of a complex containing two molecules of allyl alcohol (Scheme 44.1) [26],... 

In the case of M(CO)6 catalysts, where M = Cr, Mo, or W, the kinetics were quite different than observed for Fe(CO)5, exhibiting an important approximately first order rate dependency on the concentration of base, relative to the zero order in concentration of base observed for the Fe(CO)5 system. Furthermore, instead of a zero order rate dependency for Pco, as observed for Fe(CO)5, the M(CO)6 catalysts displayed an inverse first order dependency (/.< ., inhibiting effect). 

At the cellular level, the major electrophysiological effect appears to be rate-dependent blockade of sodium channels [22]. The onset for this Class I effect (64 + 9% of the final depression of between the first and second beat of the train) was similar to that for Class IB agents [23]. The offset rate (recovery of from rate-dependent depression) for amiodarone was 1.48 s. This value falls between those seen for Class IB agents (200-500 ms) and lA agents (2.3-12.2 s) [23]. Amiodarone inhibited the binding of pH]ba-trochotoxinin A 20a-benzoate to the sodium channel, suggesting that it binds to inactivated sodium channels [24]. 

For kinetic experiments that are designed to determine the rate dependence of an enzyme-catalyzed reaction on nucleotide concentration, care must be exercized to maintain a constant free metal ion concentration under all experimental conditions. Too low a metal ion concentration allows uncomplexed nucleotides to inhibit an en-... 

The most notable feature about the data is the acetaldehyde rate, which increases with decreasing methanol conversion. For example, a rate of 17.5 K/hr is obtained at a conversion of 38%. There are numerous explanations for this trend, including product inhibition of the catalyst or rate dependence on methanol concentration. However, the important point is that when comparing any data dealing with this reaction, the conversions must be similar in order to draw meaningful conclusions. 

As with all members of its class, propafenone has its major effect on the fast inward sodium current. The IC agents depress over a wide range of heart rates and shift the resting membrane potential in the direction of hyperpolarization. The 1C agents bind slowly to the sodium channel and dissociate slowly. Therefore, they exhibit rate-dependent block. Inhibition of the sodium channel throughout the cardiac cycle will result in a decrease in the rate of ectopy and trigger ventricular tachycardia. 

The direct slowing of sinoatrial rate and atrioventricular conduction that is produced by muscarinic agonists is often opposed by reflex sympathetic discharge, elicited by the decrease in blood pressure (see Figure 6-7). The resultant sympathetic-parasympathetic interaction is complex because muscarinic modulation of sympathetic influences occurs by inhibition of norepinephrine release and by postjunctional cellular effects. Muscarinic receptors that are present on postganglionic parasympathetic nerve terminals allow neurally released acetylcholine to inhibit its own secretion. The neuronal muscarinic receptors need not be the same subtype as found on effector cells. Therefore, the net effect on heart rate depends on local concentrations of the agonist in the heart and in the vessels and on the level of reflex responsiveness. 

Both reactions are considered to be substrate-inhibited and hydrogen-ion rate-dependent. This leads to a nonmonotonic dependence of the reaction rates on both the substrates and pH. 

Another important issue is the permanence of the catalyst inhibition or poisoning. The permanence of catalyst inhibition is dependent on the mechanism of the chemical interaction of the poison with the catalyst. Catalyst inhibition and the resulting reduction in reaction rate could result from competition between the poison and the preferred reactant at the catalytic site, either because of a high affinity of the poison for the catalyst site or because of its slow reaction once on the catalyst site. If the affinity is too high, as when the poison actually reacts with the catalyst to form a new compound, the catalyst is permanently poisoned. If the inhibition is only related to a slow rate of reaction, it may be possible to remove the poison from the catalyst surface and restore catalyst activity. 

Equation (7) indicates that the relative effectiveness of Mg2+ and Ca2+ in inhibiting the limestone dissolution rate depends on the ratio of Mg2+ concentration to Ca2+ concentration. On the other hand, the sensitivity of limestone dissolution rate to the Mg2+ concentration is determined by the Ca2+ concentration. As indicated by Equation (7), when the minimum ratio ( Mg/0Ca) 0 5 is required... 

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