Concepts from Chemical Reaction Kinetics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 234

TABLE 5.5
Equilibrium and Rate Constants for SiO 2 Dissolution Reactions at 298 K

ln k d (s −1 ) ln k p (s −1 ) Type ln K eq

Quartz − 9.11 − 30.81 − 21.70

α -Cristobolite − 7.71 − 29.41 − 21.70

β -Cristobolite − 6.72 − 28.44 − 21.70

Amorphous silica − 6.25 − 27.61 − 21.40

Source: From Stumm, W. and Morgan, J.M. 1981. Aquatic Chemistry , 3rd ed. NewYork, NY:
John Wiley & Sons, Inc.; Brezonik, P.L. 1994. Chemical Kinetics and Process Dynamics
in Aquatic Systems . Boca Raton, FL: Lewis Publishers/CRC Press, Inc.

It is obvious from the above equation that a plot of β versus t gives A s k prec /V w from the
time constant for the exponential fit. Thus k prec can be obtained, from which k diss =
k prec /K eq can be determined. In experimental systems, the initial stages of dissolution
aredominatedbythefastersolubilityoftheexposedsurfacesilicalayer.Theequilibrium
and rate constants for silica dissolution obtained from different sources for the various
silica forms is tabulated in Table 5.5.

5.7.5 A UTOCATALYSIS IN E NVIRONMENTAL R EACTIONS
In some environmental chemical reactions some of the products of the reaction act as
catalysts. A bimolecular autocatalysis reaction is represented as A + B → 2B. The

rate expression is r =− d [ A ] / d t = k [A][B]. Let us define the progress of the reaction

by ξ . If at any time [ A ] 0 −[ A ]=[ B ]−[ B ] 0 such that [ B ]=[ A ] 0 +[ B ] 0 −[ A ]=

[ ] 0 +[ ] 0 − ξ

A B ,

d d t =

− k ξ (( [ A ] 0 +[ B ] 0 − ξ ) . (5.153)

The above equation can be integrated to obtain

[ ] 0 +[ ] 0

A B

[ B ]=

e − k( [ A ] 0 +[ B ] 0 )t .

(5.154)

1 + ( [ A ] 0 / [ B ] 0 ) ·

Note from the above that at t = 0, [ B ]=[ B ] 0 . For [B] 0 , the only condition is that

[ 0, [B] will slowly increase; this is

termed the induction period. The value of [B] increases continuously and reaches its
maximumvalueof[A] 0 +[

B ]= 0 for all t . However, if [B] 0 = 0at t =

.ThecharacteristicS-shapedcurveshownin
Figure 5.14 is characteristic of autocatalytic reactions in the environment. Oscillatory
reactions such as the oxidation of malonic acid by bromate and catalyzed by cerium
ions (otherwise called the Belousov-Zhabotinsky reaction ) are classic examples of
autocatalysis.

B ] 0 as t →∞