Thermodynamics and kinetics of
transformation reactions
Chapter 12
Chemical transformation reactions
bonds breaking and forming
3 types:
chemical
photochemical
biological
Questions
• Can a given compound be transformed in
the environment by one or more pathways?
• what are the reaction products?
• what are the kinetics?
• what is the influence of variables such as
pH, light intensity, redox condition, ionic
strength, etc, on products and kinetics?
Thermodynamics vs. Kinetics
• We have already discussed one type of
transformation reaction: proton transfer.
• Proton transfer was considered to be fast and
reversible, i.e. equilibrium was established.
• We could therefore ignore kinetics and deal only
with products and equilibrium.
• the reactions we will now discuss will generally be
under kinetic control, therefore focus on kinetics,
not equilibrium (although eqbm considerations
may be useful in predicting kinetics!)
Thermodynamics
• Use infinite dilution state in water as reference
i    RT ln
0'
i
 [i]
'
i
[i]0
   f G (aq)
0'
i
0
i
reference state,
o’i  1
General reversible chemical reaction
aA  bB  pP  qQ
where A, B, P, Q are chemical species
and a, b, p, q are stoichiometric coefficients
The free energy change of this reaction is equal to
the free energies of the products minus reactants:
 r G  a A  b B  p P  qQ
This is related to the standard free energies of
the product minus the reactants:
 r G  a A0 '  b B0 '  p P0'  q Q0 '  RT ln
( P' [ P]) p ( Q' [Q]) q
( A' [ A]) a ( B' [ B]) b
Reaction quotient, Qr
 r G  a A0 '  b B0 '  p P0'  q Q0 '  RT ln
( P' [ P]) p ( Q' [Q]) q
( A' [ A]) a ( B' [ B]) b
p
q
{
P
}
{
Q
}
 r G   r G 0  RT ln
{ A}a {B}b
 r G   r G  RT ln Qr
0
at equilibrium, rG = 0, and Q is equal to the equilibrium
constant:
{ P} p {Q}q
r
r
{ A}a { B}b
Q K 
Temperature dependence of K
as with ALL equilibrium constants, K is dependent on
temperature via the enthalpy of the reaction:
K rT 2  r H  1 1 
  
ln

K rT1
R  T1 T2 
enthalpies of chemical reactions can be MUCH larger
than those of phase transfer processes.
go through example 12.2 page 467
KINETICS
Rate law = a mathematical function describing the
turnover rate of the compound of interest as a function
of the concentrations of the various species
participating in the reaction
May or may NOT have a theoretical basis
For example:
dA
  k  [ A]a  [ B ]b  [C ]c
dt
a, b, c indicate the order of the reaction with respect to each
species
overall reaction order = a+b+c
First order reactions
dA
  k [ A]
dt
[ A]t  [ A]0  e
t1/ 2
 kt
ln 2 0.693


k
k
Pseudo first order reactions
• pseudo-first order: concentration of one reactant
remains essentially constant over time (often
because it is in large excess compared to the other
reagent)
A B  C  D
dA
 k[ A][ B]
dt
dA
 k '[ A] where k '  k[ B]
dt
ln[ A]  ln[ A]0  k ' t
t1/ 2
ln 2

k
First order reaction with back reaction
Example: conversion of aldehyde (A) to diol (D)
A D
d [ A]
 k1[ A]  k 2 [ D]
dt
d [ D]
  k1[ A]  k 2 [ D]
dt
At equilibrium
[ D ] k1

 Kr
[ A] k 2
For formaldehyde,
1
k1
10s
3
Kr 


2

10
k 2 5 10 3 s 1
thus at pH7 at equilibrium, formaldehyde is 99.8% in
the diol form
the time to steady state is the sum of the forward and
back rate constants:
t5%
ln( 0.05)
3


 0.3s
1
3 1
k1  k 2 10s  5 10 s
Catalyzed Reactions
Characterized by:
first-order kinetics at low concentration
zero-order kinetics at high concentration
Michealis-Menton kinetics
d [ A]
[ A]
 J
dt
[ A]  ( J / k ) Where J = max reaction rate = kE[E]tot
k = pseudo first order rxn rate constant
Michealis-Menton kinetics
d [ A]
[ A]
 J
dt
[ A]  ( J / k )
Where J = max reaction rate = kE[E]tot
k = pseudo first order reaction rate constant = kE[E]totKE
d [ A]
[ A]
 k E [ E ]tot
dt
[ A]  (1 / K E )
Reaction at a limited number of reactive sites (enzymes) [E]tot
which have affinity for binding the substrate of KE
Arrhenius Equation and
Transition State Theory
reactions occur as a sequence of elementary steps.
usually one of these steps is much slower than the
others  Rate Determining Step
empirically, the effect of T on the rate of this reaction
step (and therefore on the overall reaction rate) is
described by the Arrhenius equation:
k  Ae
 Ea / RT
pre-exponential factor or
“frequency factor”
Activation energy
describes collision frequency and
the orientation probability
describes the fraction of species
with energy greater than Ea
Temperature dependence of reaction rate constant is:
kT 2 Ea  1 1 
  
ln

kT 1
R  T1 T2 
Ea is therefore analogous to the H of a phase transfer process
Ea is usually 40 to 130 kJ/mol, i.e. usually bigger than H for
phase transfer processes.
Reaction rates are more sensitive to temperature than
partitioning
A = 1012 – 1016 for unimolecular reactions
A = 107 – 1012 for bimolecular processes
“Activated complex” or “transition state” theory:
B + C  BC‡  D + E
BC‡ is the activated complex or transition state
maximum energy barrier

 kT 
‡
rate  
 BC
 h 

‡
K‡ 
 kT  
rate    K [ B][C] = k [ B][C]
 h 
BC   e
‡
BC
 G ‡ 


 RT 


e
 H ‡ S ‡ 


 RT  R 


k = Boltzmann constant
h = Plank’s constant
 kT  S ‡ / R  H ‡ / RT
k 
e
e
 h 
Ea = potential energy of activation, H‡ is the total:
H ‡  Ea  RT
The well mixed reactor
aka The one-box model
aka The CSTR
Input I
Output O
Flow Q
Flow Q
volume V
mass M
mixing
concentration
C = M/V
Reaction
Rtot
lost
Rtot = total reaction
rate (sum of all
individual reactions)
Mass balance on the reactor
dM
 I  O  Rtot
dt
If volume is constant:
dC I O Rtot
  
dt V V
V
mass per time
Now we have to make some simplifying assumptions:
Assume 1: O  Q  C  Q M  k  M
w
V
kw = Q/V = flushing or dilution rate
Assume 2: all reactions are first order
Rtot   R j   k j M  ktot M
j
j
Mass balance becomes:
dM
 I  k w M  ktot M  I  (k w  ktot ) M
dt
steady state concentration:
I
M 
k w  ktot
C  M  / V
time to steady state:
t 5%
3

k w  ktot
If I = QCin
(Q / V )Cin  k w 
Cin
C 
 
k w  ktot
 k w  ktot 
Problem 12.1
Consider the transformation of hexachloroethane (HCA) to
tetrachloroethene (PCE) in an acidic (why acidic?) aqueous
solution at 25C containing 0.5 mM Fe2+ (aq), 5 mM Fe3+ (aq),
20 mM Cl- and 1 M HCA:
HCA + 2Fe2+  PCE + 2Fe3+ + 2Cl•What type of reaction is this?
•To what extent is HCA transformed to PCE?
fGº given in either aqueous or gas phase