Hydrolysis kinetics

 

The rate law for hydrolysis is usually defined by a simple pseudo-first order reaction.

                        

where  [RX] is the molar concentration of the chemical,

k_h is the observed pseudo-first order rate constant for hydrolysis at a given pH,

k_B is the alkaline second order rate constant,

k_A is the acid-catalyzed second order rate constant, and

k_N' is the neutral second order constant. 

 

By taking into account the acid-catalyzed, neutral, and alkaline hydrolysis reaction, we can express the observed pseudo-first order reaction as:

                                                    (4)

and since [H₂O] generally remains constant, we can simplify equation 4 to;

                                                           (5)

In this equation, k_A, and k_B are the second-order reaction rate constants for acid-catalyzed, alkaline-hydrolysis, respectively, and k_N is the first order rate constant for neutral hydrolysis (the alkaline and acid-catalyzed rate constants have the dimensions of M^-1s^-1 and the neutral rate constant has the dimensions of s^-1) (11).

At equilibrium,                            

K_w       =        [H⁺ ] [OH^-]                                  (6)

               thus,            [OH^-]   =        K_w/[H⁺]                                      (7)

Substituting equation 7 into equation 5 yields,

                                                                    (8)

Equation 8 shows how the pH affects the overall rate of hydrolysis.  At high or low pH (high OH^- or H⁺) one of the first two terms is usually dominant, while at pH 7 the last term may be the most important.  However, the detailed relationship of pH and rate constant depends on the specific values of k_A, k_B, and k_N.  Each separate rate constant indicates a stoichiometric relationship between the compounds to be hydrolyzed and the reactants (acid, base, or water), but it does not indicate the detailed mechanism or pathway, which may change from one class to another (11).

As can be seen from equation 8, the hydrolysis reaction is strongly dependent on the pH.  A slight change in pH causes a large change in the rate of reaction and/or the hydrolysis half-life. When a reaction follows first-order kinetics, the concentration decreases exponentially with time.  According to equation 2, a plot of the natural log of concentration (ln[RX]_t) versus time will vary linearly with a slope of -k_h.  This slope and the rate are dependent on the concentration.  The hydrolysis half-life, the time required for 50% of the compound to disappear, will be determined for first-order and pseudo-first order reactions by (12):

                                                (9)

The larger the overall rate of reaction, the smaller the half-life will be obtained.