Excess acidity equation

A long series on acid-catalysed hydrolysis of bridged bi- and tri-cyclic compounds has continued in a study of the kinetics of the hydrolysis of exo- and cndb-2-methoxy-norbornanes. A high exolendo rate ratio (8850 at 308 K in 7 m perchloric acid), positive entropies of activation, the parameters of the excess acidity equation, and the products are in agreement with hydrolysis by the A-1 mechanism. 

Hydroxyalkyl sulphoxides 515 can be dehydrated either by treatment with phosphoric acid (equation 315) or by the alkylation with Mel in the presence of an excess of sodium hydride611 (equation 316). For other dehydration reactions see References 475 and 505 (Section IV.A.2.d). For elimination of amines see References 164 and 529 (Section IV.A.2.e). 

Ross and Chiarello (1979) have described a method for denitrosation of nitrosamines, such as dlalkylnitrosamines e.g. N-nitrosodimetl laminer etc., and complex aryl-alkyl nitrosamines, e.g. N-nitroso-N-(l-ethylpropyl)-3,4-dimethyl-2,6-dinitroaniline. The products of nitration and amination containing nitrosamlne as a substantial impurity are treated with an aldehyde or ketone in the presence of strong acids such as hydrochloric or hydrobromic acid. Under pressurized conditions at 105-110% for cme to two hours, the nitrosamlne is destroyed. The desired product can be recovered after neutralization of the excess acid. The equation shows the denitrosation of pendimethalin ... 

Sodium hydrogen carbonate is a common ingredient in antacid remedies. Using information from the equation for the reaction, explain how this chemical could relieve a stomach that contains excess acid. 

The action of excess cyclopentanecarboxylic acid on a CDCI3 solution of the cyclopentane drum, 1, causes its signal at -485.8 ppm to disappear and gives rise to four other peaks which correspond to formation of the ladder and an intermediate. These NMR experiments have shown that the hydrolysis process given in Equation 3 is reversible, i.e., a drum forms from a ladder composition and, in the presence of excess acid, the drum can be opened up to yield the ladder formulation. 

Equation (17) is the heart of the excess acidity method for the determination of unknown p bh+ values in strongly acidic media. Without going into detail (which is tedious) polynomial coefficients have been calculated that enable the calculation of X for 0-99.5 wt% H2SO4 and 0-80 wt% HCIO4. These are used with equation (18) and are given in Table 1. The form of equation (18) was... 

Fig. 4 Excess acidity plots according to equation (17) for some secondary amines in aqueous sulfuric acid at 25°C. Open circles, A-ethyl-4-chloro-2-nitroaniline closed circles, 4-nitrodiphenylamine open triangles, 2-nitrodiphenylamine closed triangles, N-ethyl-2,4-dinitroaniline open squares, 5-chloro-2-nitrodiphenylamine. Data from ref. 60 numbers to the right of the dashed lines are log/values.

For protonation-dehydration processes, such as trityl cation formation from triphenylcarbinols, equation (24), the water activity has to be included if the formulation of the activity coefficient ratio term is to be the same as that in equation (7), which it should be if linearity in X is to be expected see equation (25). The excess acidity expression in this case becomes equation (26) this is a slightly different formulation from that used previously for these processes,36 the one given here being more rigorous. Molarity-based water activities must be used, or else the standard states for all the species in equation (26) will not be the same, see above. For consistency this means that all values of p/fR listed in the literature will have to have 1.743 added to them, since at present the custom... 

By analogy with equation (12), the assumption made regarding the linearity of activity coefficient ratios is equation (45) (slope parameter j), and the resulting Bunnett-Olsen equations that apply to kinetic measurements are equations (46) and (47) for unprotonated and protonated substrates, respectively.156 These apply to the A1 and A-SE2 mechanisms for the A1 and A2 mechanisms they may require correction for partial substrate protonation as in equations (25) and (26) above. For A2 reactions an additional term such as the log water activity has to be added as in equation (33). These equations have been widely tested and work quite well.155-160 The difference between the Bunnett-Olsen and the excess acidity kinetic methods (discussed below) is that the Bunnett-Olsen method features an additive combination of the slope parameters e and , whereas the excess acidity method features a multiplicative one. There seems to be no theoretical justification for the former. Also the Bunnett-Olsen method still uses H0, whereas acidity functions are not needed for the excess acidity approach see above. 

Now we make the excess acidity assumption that activity coefficient ratios such as that in equation (49) are linear in one another. The best assumption to make is that the term with the activity coefficient of the transition state is linear in the activity coefficient ratio for the same substrate S,162,163 since this is as closely similar as possible to the one in equation (49), see equation (50). We already know that the latter terms are linear in X. Thus for unprotonated substrates the relevant rate equation becomes equation (51).145,161... 

The excess acidity method can also be used to obtain the protonation correction terms, if needed, in equations (51) and (54) dividing by Cs shows them to be log(l/(/+ 1)) and log(1/(1+ 1)), for the unprotonated and protonated cases, respectively, and log/values are available from equation (17). 

Thus for these reactions m is necessarily less than unity, a result that has now been widely observed in practice,117,118,120,161,180,181 and thus the m1 value offers a clear distinction between the A1 and A-SE2 mechanisms, which is not the case with the H0 correlations discussed above. A number of different excess acidity plots according to equation (56), covering a wide reactivity range, are shown in Fig. 9. These are for the hydration of oc-methylstyrene,120 equation (58), and the mechanistically similar hydration of phenylacetylene 118 for the isomerization of m-stilbene 120 and for the detritiation of tritiated benzene, equation (28) above."7 As can be seen, all four plots are good straight lines the references cited may be consulted for the details. The slopes look steep, but m values for carbon protonation approximate 1.8,36 and the nfi values are all calculated to be... 

The mechanism is given in equation (41) above, and the corresponding derived excess acidity rate equations are equations (59) and (60) for substrates that are predominantly unprotonated and protonated, respectively, under the reaction conditions.145,161... 

Plots of the left-hand side of these equations against X are curved, allowing easy distinction of an A2 mechanism. Excess acidity plots using equation (59) are shown for some ester hydrolyses in sulfuric acid at 25°C in Fig. 10, for 1-butyl acetate,29 and for methyl 2,6-dimethylbenzoate and methyl benzoate.41 The first ester (leftmost line in Fig. 10) clearly undergoes an A1 hydrolysis, specifically AAil 29 the parameters of the line are slope 1.552 + 0.027 intercept... 

Now a very useful feature of the excess acidity method comes into play likely nucleophiles or bases can be tested by subtracting their log activities or concentrations from the left-hand side of equations (59) and (60), and the species reacting with SH+ is uniquely identified when linearity of the result against X is achieved.145,161 For instance, subtraction of twice the water activity is required to attain linearity in ester hydrolysis processes such as equation (42), as shown in Fig. 11 for methyl benzoate41 and ethyl benzoate.210 The water activities given in Table 3 were used. The parameters of the lines in Fig. 11, obtained by curve-fitting, are methyl benzoate, slope 0.921 + 0.010, intercept... 

N-nitro amines, RNHN02, decompose to alcohols and nitrous oxide in strong acid media. Rate constants obtained for R = methyl in sulfuric acid222 224 are illustrated as excess acidity plots in Fig. 12.119 This shows multiple curvature, but analysis according to equation (59) shows that one water molecule is involved in the reaction up to about 80 wt% H2S04, and one bisulfate ion above this point, see Fig. 13. The proposed mechanism is shown in Scheme 2. 19... 

However, it has since been found that the curvature observed in these excess acidity plots is an artifact, caused by insufficiently effective halogen scavenging in the original experiments,247 and that when corrected for this the excess acidity plots of log - log Ch+ against X for these reactions are linear, not curved. This is a very interesting result, as it means that the base, B in Scheme 6, does not appear in the rate law, unlike the nucleophile in equation (42), see Figs 10 and 11. Why this should be is, at present, not clear further work seems necessary. 

The activity coefficient term in equation (66) contains an extra /s term, so exact linearity of the left-hand side in X would not be expected. Nevertheless, the resulting plot was almost linear, with a correlation coefficient of 0.999,246 meaning that the excess acidity treatment does in fact apply. Note that the water molecule in equation (63) is acting as a base. For the k3 step in Scheme 8, log — log Ch+ against X was found to be linear, and for the k-- step log k — log Ch+ - logaH2o was linear here the water molecule is acting as a nucleophile.246... 

Having seen that the excess acidity method works for second-order as well as for first-order acid-catalyzed processes, it is of interest to see whether it extends to reactions that are not acid catalyzed. The hydrolysis of acylimidazoles, equation (68), takes place in aqueous acids the substrate is protonated on the ring nitrogen in the pH range, and in acid media the reaction rate constants decrease steadily with increasing acidity.251,253... 

This all seemed very reasonable at the time, but subsequent work was not consistent with it. A small but measurable amount of 180 exchange was reported for some amides in reasonably concentrated HC1 media,277,278 and for at least one amide the amount of exchange decreased with increasing acidity,277 which is the opposite of what would be expected with the Scheme 14 one-water-molecule mechanism taking over from the equation (74) three-water-molecule mechanism as the acidity increased. Also, the solvent deuterium isotope effect was found to be close to unity for at least one amide,278 a result that has since been confirmed,279 which is not what would be expected on the basis of either a three- or a one-water-molecule process.280 Because of this it was decided to reexamine the lactam hydrolysis data subsequent to the publication of the excess acidity analysis of the H NMR results for these,268 a new study appeared with rate constant data for four of these molecules in aqueous H2S04 media obtained by UV spectroscopy at several temperatures,281 and this was included too.282... 

Fig. 16 Excess acidity plot against X according to equation (60) for the hydrolysis of methyl benzimidate at several temperatures, showing the involvement of two water molecules. Data from ref. 253.

The reaction between ethyl acetate (A) and aqueous sodium hyroxide (B) (present in slight excess) was followed by withdrawing 10 cc samples of the reaction mixture, pipetting into an excess of 0.01 N HC1 and back titrating the excess acid with alkali. The tabulated results are of the volume, V, of 0.01 N acid necessary to neutralize the NaOH in 10 cc of reaction mixture at the time, sec, shown. The rate equation is to be found. 

A modification of the Bunnett-Olsen equation concerned with solvent acidity in which log([SH+]/[S]) - log[H+] = m X -h p/ sH where [S] and [SH+] are the solvent and protonated solvent concentrations, and X is the activity function log[(7s7H+/ysH+)] for an arbitrary reference base. In practice, X = - (Ho + log[H+]), called the excess acidity (where Ho is the Hammett acidity function, m = 1- (f), and 4> represents the response of the S + H+ SH+ equilibrium to changes in the acid concentration). See Acidity Function Bunnett-Olsen Equation... 

In the present experiment, you will determine the amount of HC1 neutralized by two different commercial antacid tablets. To do so we use a technique called back-titration. We add an excess amount of 0.2 N HC1 to the antacid tablet. The excess acid (more than is needed for neutralization) helps to dissolve the tablet. Then the active ingredients in the antacid tablet will neutralize part of the added acid. The remaining HC1 is determined by titration with NaOH. A standardized NaOH solution of known concentration (0.2 N) is used and added slowly until all the HC1 is neutralized. We observe this end point of the titration when the added indicator, thymol blue, changes its color from red to yellow. The volume of the excess 0.2 N HC1 (the volume not neutralized by the antacid) is obtained from the titration equation ... 

Commercial bleach is used to prepare 5-chlorouracil from uracil798. Br2/NaOH and I2/Na2C03 are used for the bromination and iodination of 3-hydroxypyridine799 Cl2/NaOH in excess hydroxide is applied for an efficient chlorination of 2-hydroxynico-tinic acid (equation 107)800. 

---