High-Acidity Rate Profiles

Use of the H0 acidity function in rate versus acidity profiles is purely arbitrary and is not meant to imply that the concentration of either the substrate or nitronium ion is a function of it. It is the most suitable acidity function, having been the most studied, with values available over a range of temperatures (69JA6654). 

Form of plots of log k2(obs.) versus H for (A) majority species and (B) free base minority species. 

A further analysis of rate profiles obtained for free base nitrations is possible. If allowance is made for the decrease in the concentration of the reactive species, the resulting rate profile should have a slope similar to that for a conjugate acid. Thefree base rate coefficient 2(fb) is defined by Eq. (3.9) and can be calculated by Eq. (3.10), in which m is the slope of the substrate protonation correlation. 

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For deactivated compounds this limitation does not exist, and nitration in sulphuric acid is an excellent method for comparing the reactivities of such compounds. For these, however, there remains the practical difficulty of following slow reactions and the possibility that with such reactions secondary processes might become important. With deactivated compounds, comparisons of reactivities can be made using nitration in concentrated sulphuric acid such comparisons are not accurate because of the behaviour of rate profiles at high acidities ( 2.3.2 figs. 2.1, 2.3). 

Metal-catalyzed hydrophosphination has been explored with only a few metals and with a limited array of substrates. Although these reactions usually proceed more quickly and with improved selectivity than their uncatalyzed counterparts, their potential for organic synthesis has not yet been exploited fully because of some drawbacks to the known reactions. The selectivity of Pt-catalyzed reactions is not sufficiently high in many cases, and only activated substrates can be used. Lanthanide-catalyzed reactions have been reported only for intramolecular cases and also sulfer from the formation of by-products. Recent studies of the mechanisms of these reactions may lead to improved selectivity and rate profiles. Further work on asymmetric hydrophosphination can be expected, since it is unlikely that good stereocontrol can be obtained in radical or acid/base-catalyzed processes. 

Even more efficient bimetallic cooperativity was achieved by the dinuclear complex 36 [53]. It was demonstrated to cleave 2, 3 -cAMP (298 K) and ApA (323 K) with high efficiency at pH 6, which results in 300-500-fold rate increase compared to the mononuclear complex Cu(II)-[9]aneN at pH 7.3. The pH-metric study showed two overlapped deprotonations of the metal-bound water molecules near pH 6. The observed bell-shaped pH-rate profiles indicate that the monohydroxy form is the active species. The proposed mechanism for both 2, 3 -cAMP and ApA hydrolysis consists of a double Lewis-acid activation of the substrates, while the metal-bound hydroxide acts as general base for activating the nucleophilic 2 -OH group in the case of ApA (36a). Based on the 1000-fold higher activity of the dinuclear complex toward 2, 3 -cAMP, the authors suggest nucleophilic catalysis of the Cu(II)-OH unit in 36b. The latter mechanism is comparable to those of protein phosphatase 1 and fructose 1,6-diphosphatase. 

Usually kH. and kOH can be determined at low and high pH, respectively, where only one form of catalysis is significant. For unreactive esters k0 is small, and can be neglected. The pH-rate profile, that is the plot of log ohs versus pH, then consists of two straight lines, of slope — 1.0 in the region of acid catalysis, and +1.0 in the alkaline region, which intersect at the rate minimum. This behaviour is illustrated by curve A of Fig. 13, which is the pH-rate profile for... 

The acidity constants of protonated ketones, pA %, are needed to determine the free energy of reaction associated with the rate constants ArG° = 2.3RT(pKe + pK ). Most ketones are very weak bases, pAT < 0, so that the acidity constant K b cannot be determined from the pi I rate profile in the range 1 < PH <13 (see Equation (11) and Fig. 3). The acidity constants of a few simple ketones were determined in highly concentrated acid solutions.19 Also, carbon protonation of the enols of carboxylates listed in Table 1 (entries cyclopentadienyl 1-carboxylate to phenylcyanoacetate) give the neutral carboxylic acids, the carbon acidities of which are known and are listed in the column headed pA . As can be seen from Fig. 10, the observed rate constants k, k for carbon protonation of these enols (8 data points marked by the symbol in Fig. 10) accurately follow the overall relationship that is defined mostly by the data points for k, and k f. We can thus reverse the process by assuming that the Marcus relationship determined above holds for the protonation of enols and use the experimental rate constants to estimate the acidity constants A e of ketones via the fitted Marcus relation, Equation (19). This procedure indicates, for example, that protonated 2,4-cyclohexadienone is less acidic than simple oxygen-protonated ketones, pA = —1.3. 

If sufficient rate data are unavailable for acidities below H0 -8.5, extrapolated rate coefficients may be obtained from the high-acidity region of the rate profiles by a different procedure. This latter may also be used for the extrapolation of data for compounds which show a mechanistic changeover [75JCS(P2)1600]. 

For 5-chloro-4-aminopyridine (9.25) and its N,)V-dimethyl derivative (9.26), exchange at 158°C took place predominantly on the free base at lower acidity and on the conjugate acid at higher acidity (the changeover point occurs at a higher acidity for 9.26 than for 9.25). The rate-acidity profile became horizontal (i.e., zero slope) at very high acidity for 9.25 due to second protonation, but this was not observed for 9.26 ]71JCS(B)2363]. 

The effects of substituents on the form of the substrate reacting is nicely shown by comparison of the rate profiles for 9.27 and 9.33. 4-Pyri-done (9.27) exchanges as the free base even at H0 -10, whereas for its 2,6-dimethyl derivative (9.33), the reaction takes place mainly via the conjugate acid at // -— 3.5. 1,2,6-Trimethyl-4-pyridone (9.35) shows the changeover at even lower acidity (H0 -— 2.7). At high acidity, 9.33, 9.35, and 4-methoxy-2,6-dimethylpyridine (9.36) all react at similar rates and show similar dependence of rate upon acidity. This indicates that all react as the conjugate acids of type 9.37, and excludes the unlikely alternative 9.38. [In [68JCS(B)866], curve C of Fig. 3 refers to 4-methoxy-2,6-dimeth-ylpyridine, and not as stated]. At lower acidity the similarity in rate persists for 9.33 and 9.35, but 9.36 is much less reactive. Hence, the 4-pyridone 9.33 reacts as such and not as the 4-hydroxypyridine tautomer. 

At high acidity, 2,6-dimethyl-l-hydroxy-4-pyridone (9.34) reacted as the conjugate acid [68JCS(B)866] with a rate similar to that of 4-methoxy-2,6-dimethylpyridine N-oxide, so both must then react as conjugate acids of the structure type 9.39. In the intermediate acidity range pD +1 to H0 -2.5, the rate-acidity profile slope was zero for 9.34, indicating reaction on a neutral form. Since 4-methoxy-2,6-dimethylpyridine N-oxide (9.40) was much less reactive, the neutral form reacting must be 9.34 and not 9.41. 

Figure 5 shows a comparison of U(IV) concentration profiles realized experimentally for the mixer settler and the pulsed column. The U(IV) profile in the columns shows an inventory of about a tenfold stoichiometric excess for the aqueous phase, relative to the Pu profile to be expected from LWR fuel. The U(IV) production rate in the column can easily be increased to an extent higher than the feed rates of externally produced U(IV) normally required in the conventional reduction column. Therefore one can at least expect equally good results for the U/Pu separation with the electro-reduction column as with the normal procedures. This is also confirmed by experiments in the USA which resulted in the installation of an electro-reduction column in the AGNS Plant at Barnwell. In these experiments even with high acid concentrations (2 M HNO in the aqueous strip, BXS) high plutonium decontamination factors have been achieved (17). 

The effect of a change in acidity or basicity of a solvent on the reactivity of a substrate has importance in the catalysis of many reactions. The pH-dependence of a rate (a plot of log/ versus pH) is a free energy relationship because pH is proportional to a free energy much useful information can be obtained about the mechanism of a reaction from its pH-profile. At high acidities the concept of pH is not useful and acidity functions can be determined for solvent mixtures by examining the dissociation constants of standard acids as a function of the solvent composition (Equation 55) assuming that the ratio of the activity constants (Ya/Yha) is independent of structure for a series of structurally related acids (HA). 

Figure 2.1. pH rate profiles for the intramolecular general acid catalyzed hydrolysis of a typical substrate, for example an acetal (with no other ionizing group). Curve A describes the specific acid catalyzed reaction at sufficiently high pH reaction becomes pH-independent and a spontaneous, "water-... 

Consequently the change in the acidity profile has been linked to a fundamental change in the rate-determining step. Thus unlike the situation at lower acidities, where the initial A-nitrosation is always rate controlling, the slow step at very high acidities may be proton loss from the intermediate nitrosamine ion (14) as shown in Scheme (16) °. ... 

The rate constants for the nucleophilic addition of KCN to o ,Al-diphenyl nitrone and its derivatives (p-OCHs, p-CHs, p-Cl, and P-NO2) were detected by UV spectroscopy at 25 °C and rate equations, applied over a wide pH range, were obtained. On the basis of pH-rate profile, adduct analysis, general base catalysis, and substituent effect, a plausible mechanism for this addition reaction was proposed At high pH, the CN ion addition to the C=N bond was rate controlling, but in acidic media, the reaction proceeded by the addition of HCN to the C=N bond after protonation at oxygen of Q ,V-diphenyl nitrone. In the range of neutral pH, these two reactions occurred competitively. " ... 

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