PH -rate profile

Fig. 8.6. pH-Rate profile for release of salicylic acid fiom benz-aldehyde disalicyl acetal. [Reproduced firom E. Anderson and T. H. Fife, J. Am. Chem. Soc. 95 6437 (1973) by permission of the American Chemical Society.]... 

The pH-rate profile (see Fig. 8.6) indicates that of the species that are available, the monoanion of the acetal is the most reactive. The reaction is fastest in the intermediate pH range, where the concentration of this species is at a maximum. The concentration of the neutral molecule decreases with increasing pH the converse is true of the concentration of the dianion. 

The change in mechanism with pH for compound 1 gives rise to the pH-rate profile shown in Fig. 8.7. The rates at the extremities pH < 2 and pH > 9 are proportional to [H+] and [ OH], respectively, and represent the specific proton-catalyzed and hydroxide-catalyzed mechanisms. In the absence of the intramolecular catalytic mechanisms, the... 

Fig. 8.7. pH-Rate profile for compound 1. (Reproduced from Ref. 72 by permission of the American Chemical Society.)... 

Consider the alkaline pH region of the pH-rate profile in Fig. 8.4 (p. 459), which indicates a rate independent of pH. The rate-controlling reaction in this region is... 

Derive the general expression for the observed rate constant for hydrolysis of A as a function of pH. Assume, as is the case experimentally, that intramolecular general acid catalysis completely outweighs intermolecular catalysis by hydronium ion in the pH range of interest. Does the form of your expression agree with the pH rate profile given for this reaction in Fig. 8.6 (p. 489) ... 

This results in a pH-rate profile as shown in Fig. 8.P21, with the acetate catalysis being signifieant in the pH range 3-6. Discuss how this catalysis by acetate ion might oeeur. What are the most likely mechanisms for hydrolysis at pH < 2 and pH > 7, where the rates are linear in [H+] and [ OH], respectively ... 

Fig. 8.P21. pH-Rate profile for hydrolysis of A in buffered aqueous solution at 70 C.

Examine the stmcture of the reactants given and the pH-rate profiles (Figs. 8.P25a-d) of the reactions in question. Offer explanations for the response of the observed... 

Figure 8.P28 gives the pH-rate profile for conversion of the acid A to the anhydride B in aqueous solution. The reaction shows no sensitivity to buffer concentration. Notice that the reaction rate increases with the size of the alkyl substituent, and, in fact, the derivative with R = = CHj is still more reactive. Propose a mechanism which is... 

Assume that the steady-state approximation can be applied to the intermediate TI. Derive the kinetic expression for hydrolysis of the imine. How many variables must be determined to construct the pH-rate profile What simplifying assumptions are justified at very high and very low pH values What are the kinetic expressions that result from these assumptions ... 

Figure 8.P31 gives the pH-rate profile for hydrolysis of thioesters A-D and shows a dependence on the nature of the substituents in the alkylthio group. Propose a mechanism which would account for the pH-rate profile of each compound. 

Figure S-I2. pH-rate profile for the reaetion of hydroxylamine with aeetone in water at 25°C. Dashed line rate of acid-eatalyzed dehydration step solid line observed rate.

Except for those reactions whose characteristic rate constants vary linearly with the hydronium or hydroxide ion concentration, the most effective presentation of pH-rate data is a graphical one. Two kinds of plot pH-rate profiles) are commonly seen ... 

The initial goal of the kinetic analysis is to express k as a function of [H ], pH-independent rate constants, and appropriate acid-base dissociation constants. Then numerical estimates of these constants are obtained. The theoretical pH-rate profile can now be calculated and compared with the experimental curve. A quantitative agreement indicates that the proposed rate equation is consistent with experiment. It is advisable to use other information (such as independently measured dissociation constants) to support the kinetic analysis. 

If ki = ki, p7/min = U2 pA" . This is an unusual condition it has been observed in the hydrolysis of acetamide at 100°C. Since pA" = 12.32 at 100°C, the minimum rate in this reaction occurs at pH 6.16. For ester hydrolyses, ki is usually greater than ki, and the minimum is observed near pH 5-6 (at room temperature). Equation (6-57) is used in the construction of a calculated pH-rate profile, when it allows... 

Figure 6-8 is a pH-rate profile for the hydrolysis of p-nitrophenyl acetate. The slopes of the straight-line portions are —1,0, and -L 1, reading in the acid to base direction, and this system can be described by... 

An inflection point in a pH-rate profile suggests a change in the nature of the reaction caused by a change in the pH of the medium. The usual reason for this behavior is an acid-base equilibrium of a reactant. Here we consider the simplest such system, in which the substrate is a monobasic acid (or monoacidic base). It is pertinent to consider the mathematical nature of the acid-base equilibrium. Let HS represent a weak acid. (The charge type is irrelevant.) The acid dissociation constant, = [H ][S ]/[HS], is taken to be appropriate to the conditions (temperature, ionic strength, solvent) of the kinetic experiments. The fractions of solute in the conjugate acid and base forms are given by... 

If k is much larger than k", Eq. (6-64) takes the form of Eq. (6-61) for the fraction Fhs thus we may expect the experimental rate constant to be a sigmoid function of pH. If k" is larger than k, the / -pH plot should resemble the Fs-pH plot. Equation (6-64) is a very important relationship for the description of pH effects on reaction rates. Most sigmoid pH-rate profiles can be quantitatively accounted for with its use. Relatively minor modifications [such as the addition of rate terms first-order in H or OH to Eq. (6-63)] can often extend the description over the entire pH range. 

The kinetic analysis of the sigmoid pH-rate profile will yield numerical estimates of the pH-independent parameters K, k, and k". With these estimates the apparent constant k is calculated using the theoretical equation over the pH range that was explored experimentally. Quantitative agreement between the calculated line and the experimental points indicates that the model is a good one. A further easy, and very pertinent, test is a comparison of the kinetically determined value with the value obtained by conventional methods under the same conditions. 

Figure 6-12. (A) pH-rate profiles plotted at l -pH and (B) log l -pH for the hydrolysis of phthalamic acid. ...

Figure 6-13. pH-rate profile for the hydrolysis of trimethylacelylsalicylic acid at 25°C (aqueous solution containing 0.5% ethanol) (60). 

The pH-independent plateau from about pH 5 to 9 represents reaction of the acylsalicylate anion. It is obvious from the pH-rate profile that k" is much larger than k. The theoretical equation for k, the observed first-order rate constant, is derived in the usual way from Eq. (6-71). 

A frequently encountered pH-rate profile exhibits a bell-like shape or hump, with two inflection points. This graphical feature is essentially two sigmoid curves back-to-back. By analogy with the earlier analysis of the sigmoid pH-rate curve, where the shape was ascribed to an acid-base equilibrium of the substrate, we find that the bell-shaped curve can usually be accounted for in terms of two acid-base dissociations of the substrate. The substrate can be regarded, for this analysis, as a dibasic acid H2S, where the charge type is irrelevant we take the neutral molecule as an example. The acid dissociation constants are... 

Figure 6-18 shows a bell-shaped pH-rate profile for the hydrolysis of monomethyl dihydrogen phosphate. Other examples are the hydrolysis of o-carboxyphenyl hydrogen succinate and the hydration of fumaric acid. ... 

A bell-shaped pH-rate profile can also be produced in a two-step reaction involving a single ionizable group if the rate-determining step changes when the pH is altered. An example, the oximation of acetone, is shown in Fig. 5-12. 

A collection of pH-rate profiles for drug decomposition reactions has been published. ... 

The following data are for the hydrolysis of cinnamic anhydride in (2-amino-2-hydroxymethyl-1,3-propane diol buffers. Extrapolate them to zero buffer concentration, and, together with data from Problem 9, plot the pH-rate profile. Determine the order with respect to hydroxide, and calculate the rate constant for hydrolysis. 

But pH-rate profiles suggest that k and k( are composite constants... 

In studies of the hydration and dehydration of pteridine and the methylpteridines, but not levelled out as solutions were made more acid. This was explained by assuming that hydronium ion catalysis of the reactions proceeded only by the formation of the cations of HY+ and HX+, respectively. This effect is strikingly shown by 1,3,8-triazanaphthalene, for which the pH-rate profile of is V-shaped between pH 6.82 and 10.29 but levels out and remains constant from pH 5.3 down to, at least, 2.4. ... 

The pH-rate profile for the hydration of 2-hydroxypteridine at 20° shown in Fig. 4 is typical for the heterocyclic acids listed in Table VI. Some representative values of and are given in Table VII. The function plotted in the figure follows from Eq. (18), and the deviations... 

Fig. 5. The pH-rate profiles at 20° and an ionic strength of 0.1 for the reversible hydration of (O) pteridine, (x) 2-methylpteridme, and ( + ) 7 -methy Ipteridine.

Figure 1 shows the pH-rate profiles of some active complexes. Both Ni2 + and Zn2 + ion complexes of 8 afford saturation curves with inflection at around pH s 6 and 8, respectively, which represent, most likely, the ionization of the hydroxyl group complexed with a Ni2+ or a Zn2+ ion. The pKa = 8.6 was assigned for the ionization of the hydroxyl group of the latter complex 12). The lower pH for the ionization of the Ni2+ ion complex in respect to that of the Zn2+ ion complex indicates that the ligand 8 coordinates to Ni2+ ion more tightly than to Zn2+ ion, which is in conformity with a larger K value (1120 M) for the Ni2 + ion than for the Zn2 + ion complex (559 M) at pH 7.05 (Table 2). 

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