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Lecture

ESS102H1 Lecture Notes - Ion Exchange, Enzyme, Abscissa And Ordinate


Department
Earth Sciences
Course Code
ESS102H1
Professor
John Ferris

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+
+
+
+=
=+
=+
+=
OHHOH
HCOHCO
HCOOHCO
COCaCaCO
2
3
2
3
32
2
3
2
3
3 Chemical Kinetics and System Dynamics
3.0 Introduction
The use of equilibrium mass action models in understanding chemical process in
aqueous systems permit a quantitative description of boundary conditions associated with
the attainment of equilibrium. A limitation to this approach is that it gives no information
concerning reaction pathways or the time needed to reach equilibrium. Instead, these
important problems are addressed by chemical kinetics and system dynamics.
Several key questions need to be answered in studies of reaction rates and system
dynamics. First, is the reaction sufficiently fast and reversible to be regarded as chemical
equilibrium controlled? Second, is the reaction homogeneous (occurring wholly within a
gas or liquid phase) or heterogeneous (involving reactants in a gas and a liquid, or a
liquid and a solid phase)? Slow reversible, irreversible, and heterogeneous reactions are
those most likely to require interpretation using kinetic models. Third, is there a specific
volume in which chemical equilibrium can be assumed to have been achieved for many
possible reactions? This may be called the local equilibrium assumption. Fourth, is the
system under consideration closed (only energy is exchanged with the surroundings) or
open (energy and matter are exchanged with the surroundings)?
3.1 Elementary and Overall Reactions
In kinetics a fundamental distinction is made between elementary and overall
chemical reactions. Specifically, an elementary reaction is one that describes an exact
reaction mechanism or pathway. Four examples include
(1)
(2)
(3)
(4)
Conversely, an overall reaction does not indicate the reaction mechanisms involved or the
pathway. In this case, an example would be the reaction arising from the combination of
Eqns. 1 to 4
+ +=++ 3
2
223 2HCOCaOHCOCaCO
(5)
1

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Rates of overall reactions can be predicted only if the rates of the component
elementary reactions are known. Rates of elementary reactions are often proportional to
the concentrations of reactants, but this may not always be the case for overall reactions.
3.2 Rate Laws
An implicit condition associated with chemical equilibria of reversible reactions
in closed systems is that concentrations of reactants and products do not change with
respect to time. This circumstance is satisfied when the forward and reverse reaction
rates are equivalent. In the case of a general reaction
BA
(1)
the equilibrium mass action relationship from chemical thermodynamics under dilute
conditions where activity coefficients are taken to be unity and square brackets indicate
molar concentrations is
][
][
A
B
K=
(2)
with forward
][
][ Ak
dt
Ad
f
=
(3)
and reverse
][
][ Bk
dt
Bd
r
=
(4)
rates of reaction written in differential form (i.e., change in concentration with respect to
reaction time) with forward kf and reverse kr rate constants, respectively. The
equivalency of the reaction rates satisfies the equilibrium mass action relationship
][][ BkAk rf =
(5)
such that
r
f
k
k
A
B
K== ][
][
(6)
2

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Example 3.1
The formation of the aqueous FeSO4+ complex is described by the reaction
++
+4
2
4
3FeSOSOFe
kf
kr
The equilibrium constant for the reaction is Keq = 205 L mol-1, and the forward rate
constant kf = 6.37 x 103 L mol-1 s-1 at 25 oC. Calculate the value of the reverse rate
constant kr.
1-
3
s 31
1037.6
205
=
×
===
r
rr
f
eq
k
kk
k
K
The concepts of molecularity and reaction order are important in the development
of rate expressions for stoichiometric reactions. Considering the general reaction
(7)
the expression for the forward reaction rate is
ba
ff BAk
dt
Bd
dt
Ad
R][][
][][ ===
(8)
In this instance, the forward reaction has a molecularity of two and an order equivalent to
the sum of the stoichiometric coefficients, (a + b). The reverse reaction is similar with a
rate expression
dc
fr DCk
dt
Dd
dt
Cd
R][][
][][ ===
(9)
and a molecularity of two, but different with a reaction order of (c + d). The total
reaction order is said to be the sum of the stoichiometric coefficients (a + b + c + d).
3
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