Concepts from Chemical Reaction Kinetics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 232

0 50 100 150 200 250 300

0 0

pH = 5.69, Blank

0.2 0.2

0.4 0.4

pH = 5.71, 10.3 g/L alumina

0.6 0.6

0.8 0.8

1 1

0 50 100 150 200 250 300

time/h

FIGURE 5.14 Heterogeneous catalysis of MPT by alumina in the aqueous phase.
Thesquaresymbolrepresentsparticle-freesolutionandthetriangularsymbolrepresents
particle-laden solution. Reaction was conducted in 0.003 M acetate buffer. (From Stone,
A.T. 1989. Journal of Colloid and Interface Science 127, 429-441.)

on alumina surface enhanced the hydrolysis rate thus providing an additional pathway
for the reaction. The overall reaction rate can be written as

d [ MPT − ]
d t

= k base [ OH − ][ MPT − ]+ k r =− K ads Γ OH − Γ MPT − , (5.144)

Γ

where K ads is the adsorbed complex formation constant for MPT − on alumina, Γ OH
is the OH − concentration in the diffuse layer, and Γ MPT − is the adsorbed MPT −
concentration (obtained from the Poisson-Boltzmann equation, Section 3.5).

Γ OH − Γ MPT − =[ OH − ][ MPT − ] e (F( ψ s +ψ d )/RT) . (5.145)

Utilizing the above equation, we have the overall rate constant for hydrolysis, k H :

k Γ K ads e (F( ψ s +ψ d )/RT)

+ k base

k H = [ OH − ] .

(5.146)

Thus k H is substantially larger than k base . At a constant pH the exponential term
decreases with ionic strength. Similarly, due to competition from other ions in solution,
K ads for MPT − also decreases. Thus, k H will decrease with increasing I . The above
equation also predicts a maximum in the rate with pH. With increasing pH, Γ OH −
increases and Γ MPT − decreases. These opposing effects should cancel each other at
some pH where the maximum in rate is observed.