## B

EXAMPLE 4.5 Calculation of the catalytic coefficients for buffer species

The following data were obtained for the hydrolytic rate constant k of codeine sulfate at 100°C in phosphate buffers of varying total concentration BT at pH values of 6 and 8:

107k (s01) at pH 6 6.1 11.2 16.3 21.4 107k (s01) at pH 8 12.9 25.0 37.0 49.0

If the fraction of [H2PO-] present in buffer solutions at pH 6 is 0.74 and at pH 8 is 0.23, determine graphically the catalytic coefficients for the buffer species (a) H2PO- and (b) HPO4-.

### Answer

From equation (4.46), a plot of kobs against BT has an intercept k0 and a gradient k,. Therefore plot kobs against BT from the given data at each pH and measure the gradient of the graph. From the graph:

where kH po- and kHPO2- are the rate constants for catalysis by H2 PO- and HPO4- ions respectively, and Bt is the total concentration of phosphate buffer. Notice that the terms for specific acid- and base-catalysis have little effect at this pH and we need not consider them in this treatment.

From equation (4.46), a plot of kobs against BT will have an intercept k0 and a gradient k,. To find values for the catalytic coefficients, we rearrange the equation into the following linear form:

We can now see that a second plot of the apparent rate constant k, against the fraction of the acid buffer component present, i.e.

k at pH 6 = 1.7 x 10-5 (mol dm-3)-1 s-1 k! at pH 8 = 4.0 x 10-5 (mol dm-3)-1 s-1

From equation (4.47), a plot of k' against the fraction of acidic buffer component, [H2PO-]/Bt, has an intercept of kHPO2-. Also when [H2PO-]/BT = 1, k' = kH2PO-

From the graph:

kHPO2- = 5.1 x 10-5 (mol dm-3)-1 s-1 kH PO- = 0.5 x 10-5 (mol dm-3)-1 s-1

The relationship between the ability of a buffer component to catalyse hydrolysis, denoted by the catalytic coefficient, k, and its dissociation constant, K, may be expressed by the Br0nsted catalysis law as kA = aKA

for a weak acid

for a weak base

where a, b, a and fi are constants characteristic of the solvent and temperature. a and fi are positive and vary between 0 and 1.

In our treatment of the degradation of codeine sulfate we have not yet considered any effect which changes in its ionisation might have on its stability. Codeine has a pKa of 8.2 at 25°C and so its ionisation state will change over the pH range 6-10. With this particular drug, the stability was not affected by any such changes. This is not the case with many drugs, however, and complex pH-rate profiles are often produced because of the differing susceptibility of the unionised and ionised forms of the drug molecule to hydrolysis.

By way of illustration we will look at the case of the hydrolysis of mecillinam (XII), which is an antimicrobially active amidopenicillamic acid. This amphoteric drug can exist as a cation, which we can write as MH+, as a zwitterion MH& or as an anion M0. Figure 4.10 shows the pH-rate profile at zero buffer concentration. The reason this plot is so much more complex than that of codeine sulfate is that each of the species present in solution can undergo specific acid-base catalysis to varying extents and so each contributes to the overall profile shown in Fig. 4.10.

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