Constant Buffer Concentration

The experimental detection of general acid catafysis is done by rate measurements at constant pH but differing buffer concentration. Because under these circumstances [H+] is constant but the weak acid component(s) of the buffer (HA, HA, etc.) changes, the observation of a change in rate is evidence of general acid catalysis. If the rate remains constant, the reaction exhibits specific acid catalysis. Similarly, general base-catalyzed reactions show a dependence of the rate on the concentration and identity of the basic constituents of the buffer system. 

An effective experimental design is to measure the pseudo-first-order rate constant k at constant pH and ionic strength as a function of total buffer concentration 6,. Very often the buffer substance is the catalyst. Let B represent the conjugate base form of the buffer. Because pH is constant, the ratio (B]/[BH ] is constant, and the concentrations of both species increase directly with 6 where B, = [B] -t-[BH"]. 

Throughout this section the hydronium ion and hydroxide ion concentrations appear in rate equations. For convenience these are written [H ] and [OH ]. Usually, of course, these quantities have been estimated from a measured pH, so they are conventional activities rather than concentrations. However, our present concern is with the formal analysis of rate equations, and we can conveniently assume that activity coefficients are unity or are at least constant. The basic experimental information is k, the pseudo-first-order rate constant, as a function of pH. Within a senes of such measurements the ionic strength should be held constant. If the pH is maintained constant with a buffer, k should be measured at more than one buffer concentration (but at constant pH) to see if the buffer affects the rate. If such a dependence is observed, the rate constant should be measured at several buffer concentrations and extrapolated to zero buffer to give the correct k for that pH. 

These are rate constants for the hydrolysis of cinnamic anhydride in bicarbonate-carbonate buffers. The pK of bicarbonate is 10.22. Find the rate constant for hydrolysis, at each pH, at zero buffer concentration. Analyze the data to determine if the acid or base component of the buffer, or both, are responsible for catalysis, and give the catalytic rate constant(s). 

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. 

These rate constants are for the hydrolysis of cinnamic anhydride in carbonate buffer, pH 8.45, total buffer concentration 0.024 M, in the presence of the catalysts pyridine, A -methylimidazole (NMIM), or 4-dimethylaminopyridine (DMAP). In the absence of added catalyst, but the presence of buffer, the rate constant was 0.005 24 s . You may assume that only the conjugate base form of each catalyst is catalytically effective. Calculate the catalytic rate constant for the three catalysts. What is the catalytic power of NMIM and of DMAP relative to pyridine ... 

FIGURE 16.11 Specific and general acid-base catalysis of simple reactions in solution may be distinguished by determining the dependence of observed reaction rate constants (/sobs) pH and buffer concentration, (a) In specific acid-base catalysis, or OH concentration affects the reaction rate, is pH-dependent, but buffers (which accept or donate H /OH ) have no effect, (b) In general acid-base catalysis, in which an ionizable buffer may donate or accept a proton in the transition state, is dependent on buffer concentration. 

The kinetics of decarboxylation of 4-aminosalicylic acid in some buffer solutions at 50 °C were studied. The first-order rate coefficients increased with increasing buffer concentration, though the pH and ionic strength were held constant (Table 217). This was not a salt effect since the rate change produced by substituting potassium chloride for the buffer salt was shown to be much smaller. It follows from the change in the first-order rate coefficients (kx) with... 

Hydration of compounds 2, 3, 4, 5 was found to be first order both in substrate and in hydronium ion (4-10). Furthermore, a careful kinetic study of compounds 2c-g and the sulfur analog 4 revealed that the hydration rate at constant ionic strength was dependent on the buffer concentration and hence was general acid catalyzed. 

The horizontal part is due to the uncatalyzed rate constant, k+, in Eq. (43). A pH profile can be done at, for example, six pH values, and since there are two kinetic points (times) and two buffer concentrations at each, a total of 24 assays are needed, which is not insurmountable. This number may be minimized and optimized by careful selection of pH and buffer concentrations [60]. Later in the program the pH profile should be repeated but with multiple points and several buffer concentrations, but this is beyond the point of preformulation. An example of a full pH profile is one running from pH 1 to pH 11 [61-64]. 

Even for experimentally simple systems, a quantitative understanding of the dissolution of ionizable drugs is possible only if drug solubility, drug ionization constant, buffer concentration, buffer species, and buffer pH are known. 

Where D is the apparent Ca2+ diffusion coefficient, D is the true diffusion coefficient in water, Ks is the buffer dissociation constant, and B is the concentration of the buffer. For a detailed analysis of Ca2+ diffusion in the presence of fixed and mobile buffers, see Wagner Keizer (1994). 

H3 as reversible in the pH range of interest (4 to 8.5). Experiments where the buffer concentration was varied showed that reactions HI and H3 remain at equilibrium. The rate constant is thus related to the various steps of Scheme 5.2) according to... 

Figure 4.19. Torsion constant a versus buffer concentration for supercoiled M13mp7 DNA in different buffers. All samples except that in 10 mM Tris contain 10 raW NaCl, so all have between 10 and 12 mM univalent positive ions. The sample in the middle contains only 10 mM NaCl. The numbers (1, 2, and 4) in the sample label refer to the gel electrophoretic mobilities, which reflect different tertiary structures, as described in the text. The a samples all contain varying amounts of Tris, while the b samples all contain citrate.

Continuous systems use the same buffer, at constant pH, in the gel, sample, and electrode reservoirs. With continuous systems, the sample is loaded directly on the gel in which separation will occur. The sample application buffer is the same as the gel and electrode buffer, but at about half the concentration. The localized voltage drop that results from decreased conductivity in the sample solution helps drive sample proteins into the gel and sharpens protein bands. Once inside a gel, proteins are separated on the basis of their individual (gel-mediated) mobility differences. Bandwidths are highly dependent on the height of the applied sample... 

Overall, it is seen that the binding constants in presence of counterions (total buffer concentration of 20 mM) are lower by a factor of about 10 than in a plain methanolic medium without counterions (see Table 1.4). In contrast, the intrinsic enantioselecitivity is still in the same order of magnitude or even higher (A s/A r 17 by ITC and ca. 50 under CE conditions) because of a more proper balance of the otherwise dominating ionic interaction. 

EDTA is a low-molecular-weight organic molecule, ethylenediaminetetraacetate, that is commonly used as a proxy for marine DOM. It is acts as buffer, maintaining constant pH and/or metal ion concentrations in experimental solutions. 

Concerted acid-base catalysed enolizations of a range of simple aldehydes and ketones have been measured in water at 25 °C, using a range of substituted acetic acid-acetate buffers.The buffer plots yield rate constants for acid (A a) and base ( b) catalytic terms in the normal way at low buffer concentrations. Extension up to higher concentrations (as far as [total buffer] = 2 m, typically) yields the third-order term ( ab) via upward curvature of the plots. While ab does not have a simple correlation with either k or b, it does correlate with their product, i.e. 

Figure 3. Plot of log hex 3-amino-2-hydroxyinethylbenzamide (rate constant obtained by extrapolation to zero buffer concentration) vs. pH at 30° and p = 0 5 in 50% dioxane—H2O (v/v) 0 and 50% dioxane—D2O . The rate constants are for appearance of product (4-aniinophthalide).

The rate of a general acid-catalyzed reaction is equal to 2ha ha[HA] multiplied by some function of the substrate concentration(s) where [HA] is the general acid concentration and A ha is the corresponding catalytic rate constant. Experimentally, general acid catalysis can be distinguished from specihc acid catalysis by analysis of the effect of buffer concentration on the overall reaction rate. See also Specific Acid Catalysis Catalysis General Base Catalysis... 

---