as ethyl acetate, follows pseudo-first-order kinetics when conducted in
aqueous solution (Equation 3.11).
CH 3 COOCH 3 + H 2 O ! CH 3 COOH + CH 3 OH
(3.11)
3.1.3 A note on reversible reactions
All spontaneous reactions eventually reach a state of equilibrium. Consider the following reversible reaction:
A + B⇌
k f
k r
P
(3.12)
k f and k r represent the rate constants for the forward and reverse reactions, respectively, and the corresponding rate laws governing the two
processes are given by Equations 3.13 and 3.14:
n f t
ð Þ = k f A
½ Š B
½ Š  for  A + B ⟶
k f P
(3.13)
n r t
ð Þ = k r P
½ Š  for  P ⟶
k r A + B
(3.14)
The forward and the reverse rates will be equal to each other (n f (t) = n r (t))
when the reaction reaches equilibrium, and when this happens the
apparent concentrations [A], [B], and [P] will not change with time. Thus
k f A
½ Š eq B
½ Š eq = k r P
½ Š eq
(3.15)
We have used the subscripts eq in Equation 3.15 to emphasize equilibrium concentrations. Figure 3.3 shows changes in concentrations of
species A, B, and product P as a function of time. Reactant concentrations
decrease as product concentration increases. At time t eq , the reaction
reaches equilibrium and all concentrations become constant over time.
Rearranging Equation 3.15 gives,
k f
k r
=
P
½ Š eq
A
½ Š eq B
½ Š eq
= K
(3.16)
Thus, according to Equation 3.16 we see that for a reaction at equilibrium,
the ratio of the forward and reverse rate constants is numerically equal to
the thermodynamic equilibrium constant, K. We will make use of this
relationship from time to-time, especially when we discuss adsorption
isotherms in Chapter 7.
CHAPTER 3: Kinetics and Transport in Nanoscience
70