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Thermodynamic and kinetic
aspects of metal complexes
We use terms to describe the Thermodynamic and Kinetic aspects of reactivity.
Thermodynamic. Stable or Unstable
Kinetic. Inert or Labile
An inert compound is not “inert” in the usual sense that no reaction will occur.
Rather, the reaction takes place slower than for labile compounds.
There
is
NO
connection
between
Thermodynamic
Stability/Instability of a complex and its Lability/Inertness toward
substitution.
For example:
Stable …but labile
[Ni(CN)4]2- + 413CN[Ni(CN)4]2Unstable but inert
[Co(NH3)6]3+ + 6H2O
[Ni(13CN)4]2- + 4CNNi2+(aq) + 4CN-(aq)
[Co(OH2)6]3++ 6NH4+
t1/2 ~ 30sec.
Keq = 1 x 10-30
t1/2 ~ days.
Keq = 1 x 1025
Stable complexes have a large POSITIVE GoRXN for ligand substitution and
Inert complexes have a large POSITIVE G‡ (activation).
Stability and Coordination Complexes ([MLn]x+)
Typically expressed in terms of an overall formation or stability constant.
(This is Kst on the Chemistry Data sheet you receive with exams)
[M]x+ + nL
[MLn ]x 
K st 
x
[M(aq)
][L]n
[MLn]x+
BUT, this does not occur in one fell swoop!!
Water molecules do not just all fly off and are immediately replaced by nL ligands.
[M] x+(aq) + L
[ML(n-1)]x+ + L

[ML]x+
[MLn]x+
K1
Kn
Ks are the stepwise formation constants and provide insight into
the solution species present as a function of [L].
These formation constants provide valuable information given that different species may
have VERY DIFFERENT properties…including environmental impact. Such information
provides selective isolation of metal ions from solution through reaction with ligands.
For formation of divalent alkaline earth
and 3d M2+ TM ions the IrvingWilliams Series holds true.
Ba<Sr<Ca<Mg<Mn<Fe<Co<Ni<Cu>Zn
What is contributing to this trend?
1.
2.
3.
Charge to radius ratio.
CFSE (beyond Mn2+)
Jahn-Teller Distortion
Hard-Soft Acids/Bases
See R-C p 450-451.
ML5X + Y
ML5Y + X
Step 1. Dissociation of X to yield a 5 coordinate intermediate.
K1
ML5X
ML5 + X
M-X bond is broken
L
L
L M L
L
L
L M L
L
L
Trigonal Bipyramidal
Slow and rate determining
The rate of D is only depends
on the conc. of ML5X
Square Pyramidal
Step 2. Coordination of Y to the ML5 intermediate.
ML5 + Y
K2
ML5Y
This mechanism is independent of [Y]
fast
The rate law for this process is rate = K1[ML5X] (the units of K1 are sec-1)
If we find a reaction follows this rate law we conclude it is dissociative.
ML5X + Y
ML5Y + X
Step 1. Collision of ML5X with Y to yield a 7-coordinate intermediate. (slow)
K1
ML5X + Y
ML5XY
(slow, rate determining)
X
Y
L
L
M
L
L
Capped
Octahedron
Pentagonal
Bipyramid
L
L
M
L
L
Y
L
L
X
Step 2. Cleavage of the M-X bond. (fast)
ML5XY
ML5Y + X
(fast)
The rate law for this process is rate = K1[ML5X][Y] (the units of K1 are sec-1Mole-1)
If we find a reaction follows this rate law we conclude it is associative.
Ligand substitution reactions
21.1 Rates of ligand substitution
21.2 The classification of mechanisms
Ligand substitution in square planar complexes
21.3 The shape of the transition state
Ligand substitution in octahedral complexes
21.5 Rate law and their interpretation
21.6 The activation of octahedral complexes
21.7 Base hydrolysis
21.8 Stereochemistry
21.9 Isomerization reactions
Redox Reactions
21.10 Classification of redox reactions
21.11 The inner sphere mechanism
21.12 The outter sphere mechanism
Substitution reactions
MLn-1L' + L
MLn + L'
Labile complexes <==> Fast substitution reactions (< few min)
Inert complexes <==> Slow substitution reactions (>h)
a kinetic concept
Not to be confused with
stable and unstable (a thermodynamic concept Gf <0)
Inert
Intermediate
d3, low spin d4-d6& d8
d8 (high spin)
Labile
d1, d2, low spin d4-d6& d7-d10
Mechanisms of ligand exchange reactions
in octahedral complexes
MLnY + X
MLnX + Y
Dissociative (D)
MLn Y
MLn X
X
Associative (A)
MLn
MLn Y
MLn X
Y
Y
MLn XY
Interchange (I)
MLn X
MLn Y
Y
Ia if association
is more important
[ML n]°
X
Y
X
Id if dissociation
is more important
X
Kinetics
of dissociative reactions
Kinetics
of interchange reactions
Fast equilibrium
K1 = k1/k-1
k2 << k-1
For [Y] >> [ML5X]
Kinetics of associative reactions
Principal mechanisms of ligand exchange in octahedral complexes
Dissociative
Associative
Dissociative pathway
(5-coordinated intermediate)
MOST COMMON
Associative pathway
(7-coordinated intermediate)
Experimental evidence for dissociative mechanisms
Rate is independent of the nature of L
Experimental evidence for dissociative mechanisms
Rate is dependent on the nature of L
Labile or inert?
L
L
L
M
L
L
Ea
L
L
L
L
M
L
L
M
L
L
L
X
L
X
G
LFAE = LFSE(sq pyr) - LFSE(oct)
Why are some configurations inert and some are labile?
Inert !
Substitution reactions in square-planar complexes
the trans effect
L
X
M
T
L
+X, -Y
L
Y
M
T
(the ability of T to labilize X)
L
effect is more pronounced for s donor
as follows:
OH-<NH3<Cl-<Br-<CN-,CO, CH3-<I-<PR3
• Trans effect is more pronounced for a ð
acceptor as follows:
Br-<Cl-<NCS-<NO2-<CN-<CO
 Trans
Synthetic applications
of the trans effect
Mechanisms of ligand exchange reactions in square planar complexes
L
L
X
L
S
+S
M
L
L
M
X
L
+Y
-X
Y
L
L
L
-d[ML3X]/dt = (ks + ky [Y]) [ML3X]
M
X
L
L
M
S
L
+Y
Y
L
-X
L
L
L
L
M
Y
-S
L
M
S
better
complementarity
Topological Effects
 The Chelate Effect
 Two donor atoms linked together = a chelate (claw)
 Chelate ligands form much more stable metal complexes
5
NH ligands (upHto
H2N
NH2than H
2N
monodentate
related
2N 10 times as
NH
NH2
NH
NH
stable)
trien
en
2,3,2
Ni2+ + L Formation Constants:
L =
NH3
en
trien
2,3,2
log b 8.12
13.54
13.8
16.4
B.
H2N
NH3
+
M
H2N
M
+
NH3
H2N
H2N
c) Thermodynamic Reasons for the Chelate Effect = Entropy
2 particles
3 particles
2 NH3
NH2
M
G
H
S
Ni(NH3)22+
-6.93
-7.8
-3
Ni(NH3)42+
-11.08
-15.6
-15
Ni(NH3)62+
-12.39
-24
-39
Ni(en)2+
-10.3
-9.8
Ni(en)22+
-18.47
Ni(en)32+
-24.16
OH2
+
k1
(G)
(H)
(S)
+4
-3.1
-1.2
+7
-18.3
+3
-7.4
-2.7
+18
-28.0
-10
-11.8
-4
+29
~1.3/ring
(small)
Largest
Effect
k2
OH2
L L
M
OH2
L
-1
d) Kinetics and thek Chelate
Effect
 Chelate complex formation
A
B
AB
L
k -2
L
M
L
C
dC k1k 2 [A][B] k -1k -2 [C]


dt
k -1  k 2
k -1  k 2
ii.
The Steady-State Approximation yields:
k 1k 2
k -1k -2
dC
kf 
and k d 
 k f [A][B] - k d [C]
k -1 dissociation
 k 2 (k ) constants:k -1  k 2
dt
Or rewriting with formation (k ) and
f
d
k 1k 2
kf 
 k1a chelate
(the effect,
samekas>>kfor monodentat e ligands)
iii. Assuming
k -1  k 2
2
-1
k -1k -2
k -1k -2
kd 

k -1  k 2
k2
iv.
kf is not the source of the chelate effect. It is the same as other
ligands
NH3+
N
M
N
H+
Ni(trien)(H2O)22+
Ni(Htrien)(H2O)23+
H+
H+
H+
v.15ksd-1must be the source of 4the
effect
s-1 chelate
2 s-1
2 s-1
(dissociation is slow!)
k-1 is the same as for monodentate ligands
+
H4trien4+
k-2 (ring opening) is the same as for monodentate ligands:
N
N
Pt
N
Ni(H2O)62+
N
+
NH2
ka
Cl
NH
kb
N
Pt
N
3
+ k (ring closing)
Data
2
Pt(NH
) Clfor
3 3
N
2+
ka = 0.73 s-1
N
Pt(NH3)4+2
kb = 5.4 x 10-4 M-1s-1
ka
0.73 s 1
3


1.4
x
10
M  Effective Concentrat ion
4
1 1
k b 5.4 x 10 M s
Huge Concentration!
NH3
NH2
k2, the formation of the second M—L bond, has been shown to
be extremely large compared to a second monodentate
M toNH
ligand
binding.
This is due
the3 large “effective
M NH
2
concentration” of the second donor atom of a chelate
chelate
monodentate
IfM
k2+ is large, kd must
L be small;
kf
kd
Very fast bond reformation after the first donor dissociates
Feis2+the kinetic HCO
7 x 103effect
10
source
2 of the chelate
Fe2+
vi.
Data
C2O42-
2 x 104
3 x 10-3
2)
The Macrocycle Effect
 Macrocyclic chelate complexes are up 107 times more stable than noncyclic chelates with the same number of donors
Ni(trien)2+ + H+
Ni2+ + H4trien4+
t½ = 2 seconds
2+
+
2+
4+
Ni(cyclam)
+ H
Ni
+ H4cyclam
t½ = 2 years
Connecting all of the donors (having no end group) makes k-2 important
N
 Breaking
the first M—L bond requires major ligand deformation
NH2
 The increase in Ea required greatly slows down k-2
N
N
N
N
N
N
M
M
M
b)
N
N
N
N
N
N
N
chelate
macrocycle
c) A macrocycle is still a chelate, so it still has
the k2 chelate effect going
d)
M
The result is a very stable complex as kd becomes miniscule
N
R
a)
3)
b)
N
The Cryptate Effect
NH HN HN
N
 Additional connections between donor atoms
in a macrocycle
M
M
further enhance complex stability by making dissociation even more
N
difficult
NH HN HN
N
R

My own research and others’ seek to take advantage of this stability

Data
Cu(H2O)62+ water substitution t½ = 1.4 x 10-9 s
Cu(Me4Cyclam) in 1 M H+ t½ = 2 s
Cu(Bcyclam)Cl+ in 1 M H+ t½ > 6 years = 1.9 x 108 s
d)
Usefulness of such stable complexes
 Oxidation catalysis in harsh aqueous conditions (H + or OH-)
 MRI Contrast agents that must not dissociate toxic Gd 3+
M
2+
C. RigidityCu
Effects


L
t½
en
0.006 s
difference
2+
bipy
0.025 s
x 3 more
More Cu
rigid
ligands (assuming
complementarity)
make
stableCucomplexes
2+
spartiene
295 min
x 106
Data 2+
Ni
dien
0.07 s
Ni2+
tach
7 min
x (6 x 103)
Ni2+
TRI
90 days
x 108
H2N
NH2
en
N
N
N
N
bipy
spartiene
N
NH2
H2N
NH
dien
N
NH2
NH2
NH2
tach
N
TRI
a) Retention of configuration with
a square pyramidal intermediate
B.
Substitution in trans complexes
1) 3 possible substitution reactions for trans-[M(LL)2BX] + Y
b) Trigonal bipyramidal intermediate
with B in the plane gives a mixture
of products
c) Trigonal bipyramidal intermediate
with B axial leads to cis product
2)
Experimental Data
 Many factors determine the mixture of isomers in the product
 Example: Identity of X

C.
Prediction is very difficult without experimental data on related
complexes
Substitution in cis complexes

The same 3 possibilities exist as for trans

The products are just as hard to predict
D. Isomerization


of Chelate Complexes
One mechanism is simple dissociation and reattachment of
one donor of the ligand. This would be identical to any
other substitution reaction
Pseudorotation
 “Bailar Twist” = Trigonal twist = all three rings move
together through a parallel intermediate
Bailar Twist
Tetragonal
Twist
 Tetragonal
Twists = one ring stays the same and
the others
move
Tetragonal Twist
Bailar Twist
Electron transfer (redox) reactions
-1e (oxidation)
M1(x+)Ln + M2(y+)L’n
M1(x +1)+Ln + M2(y-1)+L’n
+1e (reduction)
Very fast reactions (much faster than ligand exchange)
May involve ligand exchange or not
Very important in biological processes (metalloenzymes)
Outer sphere mechanism
[Fe(CN)6]3- + [IrCl6]3-
[Fe(CN)6]4- + [IrCl6]2-
[Co(NH3)5Cl]+ + [Ru(NH3)6]3+
[Co(NH3)5Cl]2+ + [Ru(NH3)6]2+
Reactions ca. 100 times faster
than ligand exchange
(coordination spheres remain the same)
A
B
"solvent cage"
r = k [A][B]
Ea
Tunneling
mechanism
A
+
B
A'
G
+
B'
Inner sphere mechanism
[Co(NH3)5Cl)]2+ + [Çr(H2O)6]2+
[Co(NH3)5Cl)]2+:::[Çr(H2O)6]2+
[CoIII(NH3)5(m-Cl)ÇrII(H2O)6]4+
[CoII(NH3)5(m-Cl)ÇrIII(H2O)6]4+
[CoII(NH3)5(H2O)]2+
[Co(NH3)5Cl)]2+:::[Çr(H2O)6]2+
[CoIII(NH3)5(m-Cl)ÇrII(H2O)6]4+
[CoII(NH3)5(m-Cl)ÇrIII(H2O)6]4+
[CoII(NH3)5(H2O)]2+ + [ÇrIII(H2O)5Cl]2+
[Ço(H2O)6]2+ + 5NH4+
Inner sphere mechanism
Ox-X + Red
k1
Ox-X-Red
k2
Reactions much faster
than outer sphere electron transfer
(bridging ligand often exchanged)
k3
k4
Ox(H2O)- + Red-X+
Ox-X-Red
Tunneling
through bridge
mechanism
r = k’ [Ox-X][Red] k’ = (k1k3/k2 + k3)
Ea
Ox-X
+
Red
Ox(H2O) - + Red-X +
G