In the current study, aspartame degradation was used as a model acid-base catalyzed reaction to evaluate the effect of nonionic polyols on its kinetics in phosphate buffer solutions. These aqueous solutions of phosphate buffer exist as an equilibrium mixture of several different species (that is, the acid [H_{3}PO_{4}], the monobasic anion [H_{2}PO^{−}_{4}], the dibasic anion [HPO^{−2}_{4}], and the tribasic anion [PO^{−3}_{4}]), present in varying proportions depending on the pH of the medium (Christian 1980). Of phosphoric acid's 3 pK_{a} values, the equilibrium concentrations of the monobasic and dibasic anions are governed by the 2nd pK_{a} value (pK_{2}) between approximately pHs 4.5 and 9. Because buffer type and concentration influence the rates of aspartame degradation (Tsoubeli and Labuza 1991; Bell and Wetzel 1995), it is important to take into account the catalysis by the buffer salts when evaluating the effect of pH and pK_{a} on the rate constant.

Based on the above-mentioned degradation pathways, the pseudo-1st-order rate constant for aspartame degradation, *k*_{obs}, can be expressed using the following equation for an acid-base catalyzed reaction

- (1)

where *k*_{o} (rate constant for the uncatalyzed reaction) equals 1 × 10^{−7} min^{−1}, *k*_{[H+]} (rate constant for catalysis by hydronium ions) equals 0.00146 M^{−1} min^{−1}, and *k*_{[OH−]} (the rate constant for catalysis by hydroxyl ions) equals 79.8 M^{−1} min^{−1}, as previously determined at 25 °C by Bell and Wetzel (1995). In addition, [H^{+}], [OH^{−}], [H_{2}PO^{−}_{4}], and [HPO^{−2}_{4}] are the molar concentrations of hydronium ions, hydroxyl ions, monobasic phosphate ions, and dibasic phosphate ions, respectively. Using the measured pH, [H^{+}] and [OH^{−}] are calculated, assuming an activity coefficient (γ) equal to one. Because pH actually measures hydrogen ion activity (a_{H}), γ is required to convert these into hydrogen ion concentrations ([H^{+}]= a_{H}/γ) for the kinetic expressions. From the pH and the apparent pK_{a} value of phosphate buffer, [H_{2}PO^{−}_{4}] and [HPO^{−2}_{4}] can be calculated using the Henderson–Hasselbach equation. The terms *k*_{A1} and *k*_{A2} are the rate constants for the formation of α-AP catalyzed by the monobasic and dibasic phosphate ions, respectively, while *k*_{D1} and *k*_{D2} are the rate constants for the formation of DKP catalyzed by the monobasic and dibasic phosphate ions, respectively. The term *f*_{NH2} is the fraction of aspartame having the amine group unprotonated (the required molecular conformation leading to DKP formation). This term is calculated using the pK_{a} value of 7.9 for aspartame's amine group (Skwierczynski and Connors 1993) and the measured pH of the system; algebraic rearrangement of the Henderson–Hasselbach equation yields the following equation

- (2)

As mentioned previously and verified experimentally, DKP was the only measurable degradation product in the dibasic phosphate buffer solutions (pH > 7). This finding is consistent with those reported in the literature for solutions having alkaline pH values (Prudel and others 1986; Gaines and Bada 1988; Pattanaargson and Sanchavanakit 2000). The amount of α-AP was negligible, so *k*_{A2}, the rate constant for the formation of α-AP catalyzed by the dibasic phosphate anion, was taken as zero and omitted from Eq. 1. Thus, the kinetic equation for aspartame degradation in dibasic phosphate buffer becomes

- (3)

Defining *k*′ as (*k*_{o}+*k*_{[H+]}[H^{+}]+*k*_{[OH−]}[OH^{−}]), substituting into Eq. 3, and rearranging the equation, one arrives at

- (4)

A plot of (*k*_{obs}−*k*′) as a function of (*f*_{NH2}[HPO^{−2}_{4}]) gave a straight line with a slope of 0.271 (that is, *k*_{D2}= 0.271 M^{−1} min^{−1}) and an *R*^{2} value of 0.999. The standard error associated with *k*_{D2} was 2.0 × 10^{−5}.

Similarly, the rate constants for the formation of α-AP (*k*_{A1}) and DKP (*k*_{D1}) catalyzed by monobasic phosphate buffer were determined using the following equation

- (5)

Using nonlinear regression to fit the experimental data to Eq. 5, the values of *k*_{A1} and *k*_{D1} were determined to be 3.98 × 10^{−5} and 2.33 × 10^{−2} M^{−1} min^{−1}, respectively. The *R*^{2} value for this nonlinear regression model was 0.995. The standard errors associated with *k*_{A1} and *k*_{D1} were 3.4 × 10^{−6} and 6.7 × 10^{−3}, respectively.

Substituting the values of the rate constants for catalysis by dibasic and monobasic phosphate buffer into Eq. 1, the final mathematical equation for modeling aspartame degradation in phosphate buffer at 25 °C becomes

- (6)

It should be pointed out that this equation is unique to aspartame degradation in phosphate buffer at 25 °C. Equation 6 is not applicable to the reaction occurring in a different buffer type or at a different temperature. The above-mentioned kinetic model will be used to evaluate how the polyol-induced changes in buffer pK_{a} and pH values affect aspartame degradation, an acid-base catalyzed reaction; this discussion will be presented in detail subsequently.