i
n
t
PMA
PMA
MA kC
dt
dC
r =−= [2]
( )
, , (1 ) lag kt t CC C C e MA PMA o PMA PMA o
− − = −= − [3]
Under this condition, all PMA was hydrolyzed to malic acid with no detectable degradation
product, such as 3-oxopropanoic acid (Whitford 1925). The PMA hydrolysis rate or malic acid releasing
rate (rMA) is proportional to the concentration of PMA (CPMA) or the total molar concentration of malic
acid in the solution. In Eq. [3], k is the reaction rate constant (h-1) and tlag accounts for the delay in the
hydrolysis (h-1) possibly contributed by the time required for heating and diffusion of H+
to ester bonds.
CPMA,o is the initial PMA concentration, which should be equal to the final malic acid concentration when
all PMA has been hydrolyzed. In general, the model fits the data well, with R2
> 0.95. Table III lists the
best values for k, tlag and CPMA,o. As indicated by the k and tlag values, increasing the sulfuric acid
concentration from 1 M to 3 M also increased the rate and reduced the lag time of PMA hydrolysis.