M.Sc. (Previous) Chemistry
Paper – I :
INORGANIC CHEMISTRY
BLOCK – III
UNIT – 8 : Metal Ligand Equilibria in Solution
Author – Dr. Purushottam B. Chakrawarti
Edtor – Dr. M.P. Agnihotri
Unit - 8
METAL-LIGAND EQUILIBRIA IN SOLUTION
Structure
8.0
Introduction.
8.1
Objectives.
8.2
Step-wise and Overall Formation Constants.
8.2.1
8.3
8.4
Thermodynamic Importance of Stability Constants.
Factors Affecting Stability.
8.3.1
Factors related with Metal.
8.3.2
Factors related with Ligands.
8.3.3
Chelate effect and its Thermodynamic Origin.
Methods of Determination of Stability Constants.
8.4.1
pH-metric method.
8.4.2
Spectrophotometric method.
8.5
Let Us Sum Up
8.6
Check Your Progress: The Key
8.0
INTRODUCTION
Generally complexes are designated as stable or unstable. The
general meaning of stability is supposed to be related with the concept,
whether a particular complex can be converted into other easily or not. As
a matter of fact, this is kinetic aspect of stability; which deals with the rate
of the reaction and its mechanism. The other aspect of stability is
thermodynamic aspect. In which stability of a complex is related with the
amount of energy released during its formation or the amount of energy
required to break it.
In this unit we describe complex forming equilibria in solution and
the various factors affecting it. We will also discuss the various factors
affecting stability constants for the formation of complexes in solution. In
the end of the unit we shall describe the method used for determining
stability constants of the complexes formed in solution. Which involves
quantitative characterisation of the complex-forming reaction in solution.
You may recall what you have already studied about the basic
concept of chemical equilibria in solution.
8.1
OBJECTIVES
The main aim of this unit is to study the complex formation equilibria
in solution. After going through this unit you should be able to:
 describe stepwise and overall formation constants;
 explain thermodynamic importance of stability constants;
 discuss factors affecting stability of complexes; and
 describe methods of determining stability constants for binary
complexes in solution.
8.2
STEP-WISE AND OVERALL FORMATION CONSTANTS.
The term stability is a loose term, when the term stability is used
without qualification, it means that the complex exists and under suitable
conditions, it may be stored for a long time. The term can not be
generalised for complexes. A complex may be quite stable to one reagent
and may decompose readily in presence of another reagent.
In studying the formation of complexes in solution, two types of
stability of complexes is found:
1.
Thermodynamic Stability
This is a measure of the extent of which the complex will form or
will be transformed into another species under certain conditions,
when the system has reached in equilibrium. When we are
concerned with this type of stability, we deal with metal-ligand
bond energies, stability constant etc.
2.
Kinetic Stability
This refers to the speed with which transformation leading to the
attainment of equilibrium will occur. When we are interested in
kinetic stability for complex ions in solutions, we deal with rates
and mechanism of chemical reactions. These reactions may be
substitution, isomerisation, recemisation and electron or group
transfer reactions. In the kinetic sense, it is more proper to call the
complexes inert or labile complex rather than stable or unstable
complex. The complexes in which the ligands are rapidly replaced
by others are called labile, while those in which substitution occurs
slowly are called inert complexes.
Stepwise and Overall Formation Constants
According to J. Bjerrum (1941) the formation of a complex in solution
proceeds by the stepwise addition of the ligands to the metal ion. Thus
the formation of the complex MLn may be supposed to take place by
the following n consecutive steps.
where
M
=
central metal cation
L
=
monodentate ligand
n
=
maximum co-ordination number for the metal
ion M for the ligand
( ML)
M + L  ML K1 = [ M ][L]
ML  ML2 K2 =
ML2  ML3 K3 =
Thus
( ML2 )
[ ML][ L]
( ML3 )
[ ML2 ][ L]
MLn-1 + L  MLn Kn =
( MLn )
[ MLn1 ][ L]
The equilibrium constants, K1, K2, K3, ..........Kn are called stepwise
stability constants.
The formation of the complex MLn may also be expressed by the
following steps and equilibrium constants.
B
M + L 
ML,  =
1
( ML)
[ M ][ L]
B
M +2L 
ML2,  2 =
( ML2 )
[ M ][ L]2
B
Thus M + nL 
MLn,  n =
( MLn)
[ M ][ L]n
2
n
................(8.1)
The equilibrium constants,  1,  2,  3, ..........  n are called overall
formation or overall stability constants.  n is called as nth overall (or
cumulative) formation constant or overall stability constants.
The higher the value of stability constant for a complex ion, the
greater will be its stability. Alternatively 1/k values sometimes are called
instability constant.
Stepwise and cumulative stability constants are also expressed as
log10K1, log10K2................log10Kn and log10n respectively.
Relationship or Interaction Between n and K1, K2, K3, ..........Kn
K's and 's are related to one another consider for example, the
expression for  3 is:3=
( ML3 )
[ M ][ L]3
On multiplying both numerator and denominator by [ML] [ML2] and
on rearranging we get:
3
=
[ ML3 ]
[ ML ][ ML2 ]

3
[ ML ][ ML2 ]
[ M ][ L]
=
=
Thus  n
=
=
[ ML ]
[ M ][ L]

[ ML3 ]
[ ML2 ]

[ ML ][ L] [ ML2 ][ L]
K 1 x K2 x K3
[ ML ]
[ M ][ L]

[ MLn ]
[ ML2 ]
.............
[ MLn1 ][ L]
[ ML][ L]
K1 x K2..........Kn
nn
or  n
=
K
n 1
n
From above relation, it is clear that the overall stability constant n is
equal to the product of the successive (i.e. stepwise) stability constants, K1,
K2, K3, ..........Kn. This in other words means that the value of stability
constants for a given complex is actually made up of a number of stepwise
stability constants.
8.2.1 Thermodynamic Importance of Stability
Constants
In order to reach accurate conclusions regarding the nature of the
forces acting within complex species during their formation in solution, the
energy changes accompanying the reaction in question i.e. a complete
thermodynamic characterisation of the reactions is necessary at the very
least, determination of enthalpy ( H ), entropy ( S ) and free energy
( G )changes accompanying complexation.
In the language of thermodynamics, the equilibrium constant of the
reaction is a measure of the change in free energy, heat content and
entropy. A more useful manner of stating equilibrium constant is in terms
of the standard free energy change G , i.e. the difference of free energy
between the products and the reactants in a standard state, which is
related to equilibrium constants by the thermodynamic expression:
- RT log K = G = H - T S .....................................(8.2)
The reactions tends to go in the direction written, when G is
negative.
Enthalpy change ( H ) gives the amount of heat either consumed or
liberated per mole of products and is related to the strength of the ligand
to metal bonds, compared to that of the metal to solvent bonds.
Entropy change ( S ) is related to the change in randomness (the
disorder) of a system. As is quite evident from the relation given above
(8.2), complex formation is most favoured by the negative enthalpy and
positive entropy changes (either of the two or both) as may be expressed
by the equation:
log K =
S  H / T
......................................................(8.3)
2.303 R
In many reactions both the heat and entropy changes favour complex
formation but their relative importance changes markedly with minor
variations from ML to M'L or ML'.
8.3
FACTORS AFFECTING STABILITY
8.3.1 Factors related with Metal
The nature of the metal ions and the effect of the different physical
properties of the metal ions on the stability of the complex are:
1.
Stability (or stability constant) increases with decreasing size of
metal ion. K generally varies are 1/r.
2.
Stability constants for a complex increase with the charge of the
central ion. The K for the Fe(II) complexes will be less then the K for
the corresponding Fe(III) complexes.
3.
The ions with high polarizability give complexes with higher stability
constants. Thus Cu(I) complexes have higher K values than the
similar sized Na+ complexes, similarly of Ca2+ and Cd(II) or Al (III) and
Ga(III) the former have low K values for the complex formation.
4.
Electronegativity increases the polarizing power and the ions with
higher electronegativity give stable complexes.
5.
Ionization Energies: The electronegativity, covalent nature and
ionic radii can be related to the ionization energies of the atoms. It
is found that the stability constants for the metal complexes with a
ligand increases with the ionization energies of the metallic species.
Observations of Bjerrum Niecilson and others show that although
most of the metals of the periodic table form complexes, this tendency is
the most with transition metals. The reason being that the chelate effect is
almost an entropy effect for the metal ions of nontransitional group, while
for the transitions metals it is partly an enthalpy effect which increases the
crystal field strength. The increase in crystal field strength increases the
points of attachment of the ligand to the metal ion imparting greater
chelating tendency to the latter (cf. CFS). Fig 8.1
Fig. 8.1: CFSE affecting stability of aquo-complexes
Chatt Ahrland classified the metals into a and b classes while a class
metals form stable complexes with ligands having the coordinating atoms,
N, O, F (second period elements), b class metals form stable complexes
with ligands in which donor atom is P, S, Cl (third or latter period elements).
The a class metals include H, alkali and alkaline earth metals; the
elements from Sc to Cr, Al to Cl, Zn to Br and lanthanides and actinides.
While amongst b class Rh, Pd, Ag, Ir, Pt, Au and Hg are included.
Elements from Mn to Cu, Tl to Po, Mo, Te, Ru, W, Re, Os, Cd are
border line metals.
It can be said with some approximation that increase in the ionic
charge of the metal ion and donor, will bring an increase in the chelating
tendency while the increase in ionic radius will decreases it. Thus small
cation size, comparatively large ionic charge and appropriate electronic
arrangements are responsible for the maximum ability of complex
formation by transition elements.
Mellor and Maley have shown that the stabilities of the complexes of
bivalent metal ions follow the order: Pd > Cu > Ni > Pb > Co > Zn > Cd > Fe >
Mn > Mg irrespective of the nature of the ligand. Irving and Williams from
the analysis of the data on stability constants of transition metal ions,
found that the order
Mn(II) < Fe(II) < Co(II) < Ni(II) < Cu(II) > Zn(II),
holds good. This order according to them follows logically from a
consideration of the reciprocal of ionic radius and second ionization
potential of the metal, and is known as 'Natural Order of Stability'.
Univalent ions have not been extensively studied but data on the
complexes of the univalent ions with dibenzol methanate ion shows the
order of the stability as:
Ag > Tl > Li > K > Rb > Cs
For tetravalent metals much less information is available, the greater
ease of hydrolysis of these ions making potentiometric titrations more
difficult. Irving and Williams suggest from a considerable limited number of
investigations that a rough order of stabilities be:
Ti > Fe > Ga > In > Al > Cr > Sc
8.3.2 Factors Related With Ligands
The properties of the ligands which affect the stability of the metal
complexes are as under:
1. Basicity of the ligands: The greater is the Lewis base strength, higher
is expected to be the stability constant of the complex. Thus K values
for the complexes are expected to change in a manner similar to the
changes in the proton association constant (BH) for the ligands.
2. Dipole moment and polarizability of the ligands: Due to the greater
electrostatic interactions between the metal ion and the ligands,
polarity and ploarizability of ligand results in higher K for the
complexes.
3. (ML)  -bonding always increases the stability of the complex.
4. Steric factor: It play an important rule in determining the stability
constants for the complexes. Thus the 2 methyl derivative of 3
hydroxyquinoline gives much less stable complexes then the parent
compound because of the steric hindrance caused by the methyl
group adjacent to the site of co-ordination.
In complex formation hydrogen behaves just like a metal ion.
Therefore, a ligand with a larger affinity for proton will show the same
behaviour towards the metal ions. According to Riley any factor which can
increases the localization of negative charge in the co-ordinating ligands
makes the electron more readily available and thus increasing the coordinating ability of a base. The correlation between the basic strength of
the ligand and the stability constant of the complexes was pointed our first
by Calvin and Wilson.
Ring Formation and Size of the Ring
Ring complexes or chelates are very stable due to reduced strain. The
number of ring formed, the size of the rings and stabilizing or interfering
resonance interactions are determined by the structure of the chelating
agent. The work of Ley on the chelates of amino-acids showed that five and
six membered rings are the most stable. Much evidence has accumulated
since then to prove that all chelates have either five or six membered rings.
Pfeiffer observed that in general the five membered rings is the more
stable when the ring is entirely saturated but when one or more double
bonds are present, the six membered rings is favoured. Schwarzenbach and
Co-workers have observed that there is a decrease in clate stability with the
increase in ring size. The stability of a five membered ring is not chiefly due
to entropy but rather to the enthalpy of formation; the example being 1, 2,
3 triamine- propane tetra chloroplatinum. Further the stability increases
with the increase in the number of rings in the molecule:
M(en) <
M(trien) < M(EDTA).
(one ring) (two rings) (five rings)
Steric Effect:
Steric hindrance can influence stability in many ways, e.g.
(i) Metal-ligand bonds are weakened due to the presence of bulky
group near the coordinating site.
(ii) The substituting group prevents the ligand from assuming the planar
configuration and hence introduce strain in the metal-donor bond.
(iii)Steric hinderacne is also due to strained structure of the chelated
ring, since it breaks the usual linear configuration of the complexes.
From the study of the copper complexes of substituted malonic acids
Riley concluded that ethyl and propyl groups had a larger effect then
methyl in reducing the stability.
Resonance Effects
The stability of a chelated ring will depend on the possibilities of
resonance in the ring and on how these will fit in with resonance in the
organic ligand itself. That resonance may affect the formation of a chelate
was first shown by Calvin and Wilson. The double bond resonance has been
attributed as a reason to be unusual stability of histamine cobalt chelate.
Orbital hybridisation
There are certain factors which serves to make a specific bonding
arrangement stable. As an example, the shape of , ', ''
triaminotriethylamine is such that the bonding atoms must be grouped
tetrahedral round a metal atom. The ligand will therefore tend to form a
stable complex with a metal such a zinc, which favours sp3 hybridisation in
its 4-co-ordinate compounds, rather than with one such as copper which is
limited to dsp2 (planar) hybridisation. Similarly, triethylene tetra amine
gives stable complex with metal ions having dsp2 hybridisation, rather then
sp3 hybridisation.
8.3.3 Chelate Effect And Its Thermodynamic Origin
The chief factor responsible for the stability of the chelate ring is the
entropy change which can be viewed statistically or as probability factor.
Considering the electronic effect of the donor atom to be the same in the
monodentate and the bidentatc ligands, it can be seen that the dissociation
of a monodentate from a complex will be higher than that in the chelating
bidentate. The dissociation of the M-L bond in monodentate will release
the ligand completely from the coordination sphere of the metal, so that it
can be easily swept off by the solvent. But the dissociation of one M-L bond
for the bidenate ligand does not release the ligand completely (for which
simultaneous dissociation at both ends is required). Hence the stability
constant for metal chelate must be higher. Consider the equilibrium
reactions (Fig. 8.4):
[Co(NH3)6]3+ + 3en  [Co(en)3]3+ + 6NH3 ...................(8.4)
Assuming that (i) Co-N bond strength in the two complexes is same
(the f value of ammonia and ethylendiamine are within 3%), and (ii) the
entropy changes due to structure making and structure breaking are
negligible due to the similar size of the complexes, it can be seen that the
S o will increase for the reaction as the number of moles of the products
are more than those for the reactants. This will help the reaction to go to
the right.
Check Your Progress-1
Notes : (i) Write your answers in the space given below .
(ii) Compare your answers with those given at the end of the
unit.
(i) Stability of metal complexes is primarily related with the
thermodynamic
stability.
Which
deals
with...........................
and....................
(ii) Overall stability constant, n for MLn complex is related with the
stepwise constants as- n = ..................................
(iii) The thermodynamic expression relating equilibrium constant is........................................
The reaction goes in the direction written when....................
(iv) CFSE results in the maximum increase in the stability of aquocomplexes of divalent metal ions in the first transition series at dn
configuration.......................and.........................
(v) The Irving Williams order of stability is..........................................
(vi) Chelate effect is primarily due to ............................ factor.
8.4
METHODS OF DETERMINATION OF STABILITY
CONSTANTS.
There are many physical and chemical properties which may be used
to detect the formation of complex in solution and to measure the stability
constants. The detection of the complexes and the determination of the
stability constants are very closely related. Most of the methods used for
the detection of complexes can also be used to determine their stability
constants.
The study of the complexes is supposed to be incomplete without
finding the stability or formation constants, because most of the properties
and utility of the complexes depend on it.
The value of stability constants may predict the conditions required
for complete formation of a given complex. This knowledge of the system is
essential for correctly interpreting its optical and kinetic properties of its
partition equilibria and its biological behaviour.
Further, it may also help in planning analytical and separation
procedures. For example in case where the species is highly coloured or
can be precipitated from solution, extracted into an organic solvent or
absorbed on an ion exchange or chromatographic column.
Stability constant is related with the thermodynamic parameters, as
-RT, Ink, = G = H - T S
Where, G , H and S are changes of free energy of enthalpy and
of entropy respectively.
The stepwise or overall stability constant, thermodynamic
equilibrium constant gives the value of free energy change, associated with
the reaction. The corresponding changes on entropy change of complex
formation may be obtained by combining the stability constants with the
enthalpy change of complex formation, which is obtained by determining
the stability constant at a series of temperatures. The knowledge of
entropy is essential for the full understanding of many factors such as size,
shape, electronic structure of the central metal and the ligand, the
temperature and the composition of the solvent, which influence the
stability of the complex.
Let us consider a reaction between a metal M and ligand L to form a
complex MmLn.
Mm + nL  MmLn
K=
[ Mm Ln]
[ M ]m [ L ]n
where 'K' is stability constant of the complex MmLn. The stability of
the complex is quantitatively expressed in terms of dissociation constant
1/k of the complex. The latter is the tendency of the complex to split up
into its components.
Some of the most important methods of determining the stability
constants are briefly described here.
8.4.1 pH - Metric Method
Bjerrum's Method
It is a potentiometric method for determining the stability constant
for complex formation. Although Bjerrum applied the method primarily to
the binding of simple molecules or negative ions to positive metal ions. It
may be used with equal success with chelating agents. The theoretical
relationship outlined by Bjerrum are not restricted to complex formation
but may be applied to any equilibrium process regardless of the nature of
the interacting substances. Thus, it has been used with success on acid
base, and redox equilibria. Although the reactions to be considered involve
ions that are more or less completely hydrated, rather than the simple
ions, but this fact does not affect the validity of the conclusions, provided
the activity of the water is maintained constant.
Formation or dissociation of a complex ion for molecule in the
solution always takes place in several steps, which can be easily
determined by measuring pH in this method.
Experimental Determination of Stability Constant by Bjerrum's Method
This is a potentiometric method. When the lignad is a weak base or
acid, competition between hydrogen ion and metal ions for ligand can be
used to the determination of the formation constant.
Let us consider the equilibrium in which an acid and metal ions are
added to a basic ligand in solution. Thus the following equation are
obtained:
Ka
L + H+ 
HL+, Ka =
[HL ]
[L][ H  ]
Basic Ligand Acid
[ML ]
L + M  ML , KF =
[L][ M  ]
+
KF
+
Basic Ligand metal ion
Here Ka and KF are the acid association constant of the ligand and
formation constant respectively.
Now if CH, Cm and CL are the total amounts in moles/litre of acid
(H+) , metal (m+) and basic ligand (L), we have
CH = [H+] + [HL+]
CL = [L] + [ML+] + [HL+]
Cm = [M+] + [ML+]
Solving the last three equations given above and using the acid
association constant of the ligand, Ka. Then we get
[ML+] = CL - CH + [H+] -
C H  [H  ]
Ka [H  ]
[M+] = Cm - [ML+]
[L] =
C H  [H  ]
Ka [H  ]
Thus on putting the values of [ML+], [M+] and [L] from the above
equation in
K1 =
[ML ]
[M  ][ L]
the value of K1 can be calculated. For the determination of [ML+],
[M+] and [L], the values of CH, CL, Cm, Ka and [H+], is generally determined
potentiometrically using a PH meter.
In order to get better results, the ligand must be a medium weak
acid or base and the formation constant, K1, should be within a factor of
105 of the value of the acid association constant of the ligand, Ka.
Irving Rossotti Method
Calvin-Bjerrum pH titration technique as adopted by Irving & Rossotti
is generally used for determining the proton-ligand and metal-ligand
formation constants. The procedure consists of:
(A) Determination of the formation curve of the system. This is

expressed as a plot of n (formation function) against pL for metal

ligand system and a plot of n A against pH for a proton-ligand


system (Definitions of the terms n , n A and pL are given below).
(B) The calculation of the values of formation constants by solution of
the formation function of the system or otherwise.
(C) The
conversion
or
the
stoichiometric
constants
into
thermodynamic constants.

n term, was introduced by Bjerrum who called it the 'formation
functions' or 'ligand number ' and is defined as the average number of
ligand bound per metal atom or ion present in whatever form.

n = Total number of ligand ( L) bound to metal ( M )
Total number of M present in system
n
or

n
=
 . i [MLi ]
i o
n
.....................................(8.5)
 .[MLi ]
i o
which can be written using equation (8.1) as,
n

n
=
 . i .β[L]
i
[  = 1]................................(8.6)
i o
n
 .β
i o
1
[L]
i

A similar function for the proton-ligand sustems is n A, which defined
as the average number of protons bound per not complex bound ligand
molecule, and can be given by.
i

nA =
 . i .β
i o
i
 .β
i o
H
i
H
i
[H] i
[L]
[
H
o
= 1]........................(8.7)
i
whereas, pL gives the free ligand exponent and may be defined as.
pL = log .
(A)
1
[ L]
Construction of the Formation Curves:
In Irving Rossotti method, this involves pH-titration of the following
three sets of mixtures (keeping total volume constant) against a carbonate
free standard alkali:
(a)
Mineral acid
(b)
Mineral acid + Ligand solution
(c)
Mineral acid + Ligand solution + Metal ion solution.
The ionic strength in each set is kept constant by adding appropriate
quantities of a neutral electrolyte solution. The temperature of the solution
in each case is kept constant. On plotting the observed pH against the
volume of alkali, one obtains (a) and acid titration curve, (b) a ligand
titration curve and (c) a metal-complex titration curve, corresponding to
the above titrations. [Fig. 8.2(a)]
The calculation of

n
are made from the volume of alkali required to

produce the same pH value in the metal and ligand titrations. Similarly n A
values are calculated from the volume of alkali required to produce the
same pH value in the ligand and mineral acid titrations. According to Irving


and Ressotti, n A and n can be expressed as(V n  V 1 ) ( N  E  )
Y TLo 

(V   V 1 )
nA =
TLo
iii1
n
ο

n = (V  V ) (N  E )  TL o

(Vο  V 1 ) n
. TCM ο
....................(8.8)
....................(8.9)
Where Vo is the initial volume of the solution, Eo, TLo are the initial
concentrations of the mineral acid and the reagent respectively and V', V''
and V''' are the volume of alkali of a given normality, N, required during the
acid, the ligand and the metal titration respectively at a given pH (B). While
the term Y gives the number of titrable hydrogen ions arising from the
chelating agent and TMo gives the initial concentrations of the metal.
From the observed values of [L] for each

n
value, values of pL- are
calculated utilising the equation given by Irving and Rossotti:
n j
pL- log10

n o
 nH (
1
)n
anti log 

TCL0  n .TCM
0
.
V 0  V iii
Vo
....................(8.10)
Values of proton-ligand formation constants, K 1H , K 2H etc. obtained

from the proton-ligand formation curves plotted between values of n A and
pH [Fig. 8.2(b)].

The pH value at n A = 0.5 gives the value of log K 1H while the pH value

at n A = 1.5 gives the value of K H2 and so on.
Similarly, the values of stepwise stability constants of metalcomplexes are obtained from the formation curve plotted between the
values of n and pL- [Fig. 8.2(c)].
The value of formation constants are generally refined using least
square method.
Fig. 8.2: (a) pH - Titration Curves
(b) Proton-Ligand formation curve
(c) Metal-Ligand formation curve
8.4.2 Spectrophotrometric Method
1.
Job's Method
From the knowledge of stoichiometry of the complex, the value of K
(the stability constant) can be determined form the expression given
below, if the value of m and n are known:
K=
where, K
m n 1  n m1  ( P  1) m n 1 [n  (m  n) x]
m  n 1
C1
 P n 1 [ P (m  n) x 1 ]m n
=
Stability Constant
1/K
=
Dissociation Constant of the complex.
P
=
Ratio of the concentration of the ligand to the
concentration of metal.
C1
=
Molar concentration of metal solution.
X
=
Concentration of ligand for which the concentration
of complex is maximum.
m
=
The number of moles of a metal required to combine
with "n" moles of ligand.
for (1:1) Metal ligand ratio in the complex
m=n=1
K=
( P  1)(1  2 x)
C1  [ ( P  1)( x  1)]2
Vosburgh and Cooper as well as Katzin and Gebert have extended
Job's treatment to systems in which two or more complexes are formed.
The ratio of the concentration of metal should not be equal to 1 i.e. nonequimolecular solutions of ligand and metal should be used.
2.
Turner Anderson Method
Turner and Anderson have modified Job's method and have
successfully used for determination of stability constant. By plotting a
continuous variation curve for a given range of compositions and then
repeating the procedure for more dilute solutions. If the initial
concentrations of the metallic ions and ligands are 'a' and 'b' respectively,
then
K=
X
(a  x)(b  x)
where, K
=
Stability Constant
X
=
Concentration of the complex
It is assumed that Beer's Law is obeyed, i.e. the optical density of the
solution is proportional to the concentration of the complex in the given
range. If, therefore, any two solutions on the two curves have the same
optical density, as shown in the graph a1, a2 and b1, b2 represent the
concentrations of the metal and the ligand respectively on the two curves,
then:
K=
X
X
=
(a1  x)(b1  x) (a 2  x)(b2  x)
Where, the subscripts 1 and 2 refer to the reagent concentrations.
Thus K be calculated by solving the equation.
Molar Concentration
Fig. 8.3 :
Deskin has extended the method to the study of complexes formed
in the ration of 1:2, then:
M + 2L = ML2
K=
X
(a  x)(b  2 x) 2
Taking the concentration a1, a2 and b1, b2 for the same absorbance
i.e., the same value of x, we have
K=
X
X
=
2
2
(a1  x)(b1  2 x)
(a2  x)(b2  x)
The value of x is determined from the relation
4x2(a1-a2+b1-b2)-x(4a1b1-4a2b2+b 12 - b 22 )+ (a1b12-a2b22) = 0
i.e. AX2 + BX + C = 0
Where, A
=
4(a1 -a2 + b1 - b2)
-B
=
4(a1b1 - 4a2b2 + b 12 - b 22 )
or b1(4a1 + b1) - b2(4a2 + b2)
C
=
(a1b 12 - a2b 22 )
By solving the quadratic equation:
( B)  ( B 2  4 AC )
K=
2A
K=
( B)  ( B 2  4 AC )
2A
By knowing the value of X, the value of K can be calculated. Similarly,
if metal and ligand react in the ratio 2:1 then.
2 M + L = M2L
Taking the concentration a1, a2 and b1, b2 for the same absorbance
i.e., for the same value of X, we have
K=
X
X
=
2
(a1  2 x) (b1  x) (a 2  2 x) 2 (b2  2)
or 42(a1-a2+b1-b2)-(4a1b1-4a2b2+a 12 - a 22 + (a 12 b- a 22 b2) = 0
i.e. AX2 + BX + C = 0
Where, A
=
4(a1 -a2 + b1 - b2)
-B
=
(4(a1b1 - 4a2b2 + a 12 - a 22 )
or b1(4a1 + b1) - b2(4a2 + b2)
C
=
(a 1 b 1 - a 12 b 2 )
By solving the quadratic equation, the value of X is determined
( B)  ( B 2  4 AC )
K=
2A
or X =
( B)  ( B 2  4 AC)
2A
Mushran has modified this method so as to suit for 1:3 complexes.
3.
Mole Ratio Method
The you and jones method can also be utilised for determination of
the stability constants.
Fig. 8.4
The extrapolated value (A extp.) (fig. 8.4) near the "equivalence
point" on the plots correspond to the total absorbance of the complex. If
the complex formed is complete. Actually the complex is slightly
dissociated in this region, and the absorbance read is somewhat low. The
ratio of the true absorbance to the extrapolated absorbance is the mole
fraction of the complex actually formed.
A
[mx]

A extp
c

where
is the total analytical concentration (expressed in moles/litre) of
c

the metal or ligand, whichever has the limiting concentration at the point
in question. Therefore
[MX] = A/A extp. C
M = Cm - (mx) = Cm (A/A extp. ) C
X = Cm - (mx) = Cx - (A/A extp.) C
Stability constant K =

K=
[ MX ]
[ M ][ X ]
[( A / A extp . ) C]
[(Cm  A / A extp . ) C ][(Cx  A / A extp . )C ]
-
Where A
=
Absorbance at the metal ligand ratio.
A extp.
=
The extrapolated value of Absorbance.
Cm
=
Concentration of the metal at equivalence point.
Cx
=
Concentration of the ligand at equivalence
point.
C
=
Total analytical concentration of the ligand.
When metal ligand ratio and the ratio shown by extrapolation do not
be on the same ordinate, then the value Cx and C will not be the same. C is
calculated at the point of intersection of the extrapolated curve.
4.
Raghav Rao's Method
Subbarama Rao and Raghav Rao used job's method of continuous
variation and molar ratio method for determination of stability constants.
They used equimolar solutions of metal and ligand with optical density as
he index property. This method is also known as graphical method.
Reddy and Seshoish used the same graphical method using
conductance and optical density as the index property.
Check Your Progress-2
Notes : (i) Write your answers in the space given below .
(ii) Compare your answers with those given at the end of the
unit.
(i) Irving-Rossotti method is a modification of.......................method.

(ii) n is called.......................................and is defined as ...................
........................................................................................................
(iii) pL- = .........................................
(iv) Formation-curve is a plot between........................and.....................
(v) Turner Anderson method is a modification of ........................ method
used for determination of ................................. by plotting
............................... curve for a given range of .................
(vi) The extra plotted value in the mole ratio plot near the equivalence
point corresponds to ............................................. the complex.
8.5
LET US SUM UP

Stability of complexes in aqueous solutions is related with the
thermodynamic aspect, which deals with metal-ligand bond energy
and stability constants.

The formation of MLn complex in solution is supposed to take place
in n steps. In each step one mole of ligand is bound with the metal
ion replacing a mole of the coordinated water.

The equilibrium constants K1, K2, K3, ..........................Kn for the
reaction in each step of the complex formation are known as
'stepwise formation constants' and are related with the 'overall
stability or formation constant'  n , i.e. the equilibrium constant for
the overall reaction: M + nL  MLn,
as :  n = K1, K2, K3, ..........................Kn
nn
or n   K n
n 1

The equilibrium constant is related to the thermodynamic expression
as follows:
- RT log K =  G =  H - T  S .

The factors affecting stability of complexes are mainly related with
the metal ion and the ligands.

The factors due to metal are primarily related with the size of the
ion, its charge, possibility of  -bonding and CFSE gained.

Stability is proportional with the charge and ionic potential (e/r-ratio)
but is inversely proportional with the size of the metal ion.

ML,  -bonding increases it, while LM,  -bonding decreases it.

Similarly higher is the CFSE higher will be the stability.

a-groups metal form stable complexes with ligands N, O, F doner
atoms; while b groups metals give more stable complexes with the
ligands, having P, S and Cl donor atoms.

The Irving Williams order of stability is:
Mn (II) < Fe (II) < Co(II) < Ni(II) < Cu(II) > Zn(II).

Factors related with the ligands are mainly basicity, dipole moment
and polarizability of ligands, possibility of  -bonding and steric
factor.

Stability is proportional with the basicity, dipole and polarizability of
ligands.

ML,  -bonding (complexes with the unsaturated ligands) increases
the stability.

Shape of the ligand molecule also affects stability e.g. while
triethylene teramine gives complex with metal ions having dsp2
hybridisation(sq.
planar
geometry);
,
 I,

II
triamminotriethylamine gives stable complex with metal ions having
sp3 hybridisation (Tetrahedral geometry).

Chelates are more stable compared to non chelates.

Stability increases with the number of rings formed per mole of the
ligand e.g.
M(en) < M(trien) < M(EDTA)
(1 ring)

(2 ring)
(5 ring)
Higher stability of chelates is mainly related with the entropy factor.

The stability constants of metal complexes in solution are
determined generally using two methods: one the potentiometer
(pH) titration method due to Bjerrum and its modification by Irving
and Rossotti; and the other one spectrophotometer methods due to
job and its modification by Turner-Anderson.

In Irving Rossotti method stability constants are computed by

plotting formation curves, between n (the formation function) and
pL-.


n is the average number of ligand bound per metal atom or ion;
while pL is the free ligand exponent; log

I
[ L ]
According to half integral method:

The value of pL- at 0.5 n = Log K1

The value of pL- at 1.5 n = Log K2 and so on.

The values of stability constants are generally refined by least square
method.

Turner and Anderson method involves plotting a continuous
variation curve for a given composition and repeating the procedure
for more dilute solutions.
8.6
CHECK YOUR PROGRESS: THE KEY
1
(i)
Deals with M-L bond energy and stability constants.
n n
2
(ii)
Related as βn   K n
(iii)
- RT log K =  G =  H - T  S .
(iv)
 G is negative.
(v)
Mn (II) < Fe (II) < Co(II) < Ni(II) < Cu(II) > Zn(II)
(vi)
Entropy factor.
(i).
Bjerrums's method
(ii)
Formation function, defined as the average number of ligand
n 1
bound per metal or ion.
I
[ L ]
(iii)
PL- =
(iv)
Between n and PL-
(v)
Job's method used for determination of stability constants by

plotting continuous variation curve.............of composition.
(vi)
The total absorbance of.
Unit - 9
METAL CLUSTERS
Structure
9.0
Introduction.
9.1
Objectives.
9.2
Boranes and Higher Boranes.
9.2.1
Wade's Rule.
9.2.2
Closo-Boranes.
9.2.3
Nido-Boranes.
9.2.4
Arachno-Boranes.
9.2.5
Structural Interrelation.
9.2.6
Synthesis.
9.2.7
9.3
9.4
Reactions.
Carboranes.
9.3.1
Synthesis.
9.3.2
Properties.
9.3.3
Structures.
Metalloboranes and Metallocarboranes.
9.4.1
Properties.
9.5
Metal Carbonyl Halides.
9.6
Compounds with metal-metal multiple bonds.
9.7
Let Us Sum Up.
9.8
Check Your Progress: The Key.
9.0
INTRODUCTION
Closed polyhedrons play important part in the synthesis of clustermolecules in inorganic chemistry. These cluster-molecules include
polyhedral boranes, carboranes and metalloboranes and metallo
carboranes; organometallic clusters and metal halide clusters.
The definition of metal clusters includes those molecular complexes
in which metal-metal bonds form a triangular or a large closed structure.
This definition does not include linear M-M-M bonded compounds or those
cage like structures in which metal atoms, in closed structures are
interlinked through ligands, forming M-L-M bonds.
Presence of metal-metal (M-M) bond in these molecules may be
ascertained with the help of data of bond lengths and also the stability of
compounds. As amongst d-block groups, metal-metal bond strength
gradually increases moving down a group, hence d-block metal in fourth
and fifth periods of the periodic table form M-M bonded compounds in
large number.
9.1
OBJECTIVES
The main aim of this unit is to study the nature, methods of
preparation and structures of metal-clusters. After going through this unit
you should be able to:
 describe boranes and higher boranes with reference to their
classification, synthesis reactions and structures;
 discuss carboranes and explain their synthesis and properties in the
light of their structures;
 describe metalloboranes and metallocarboranes in relation with
carboranes;
 explain structures of metal carbonyl halides; and
 identify compounds with metal-metal multiple bonds and their
structures.
9.2
BORANES & HIGHER BORANES.
Boron hydrides are known as Boranes. These are named boranes in
analogy with alkanes. These are gaseous substance at ordinary
temperatures.
It is expected that boron would form the hydride BH3, but this
compound is unstable at the room temperature. However, higher hydrides
like
B2H6(diborance).
B4H12
(tetraborane),
B6H10(hexaborane),
B10H14(decaborane) etc. are known. The general formula of boranes are
BnHn + 4 and BnHn + 6 (Proposed by stock). In addition to these is one,
recently discovered series of closed polyhedral structures with the formula
[BnHn]2-. Higher boranes have different shapes, some resemble with nests,
some with butterfly and some with spider's web.
The modern explanation of the structure of boranes is due to
C.L.Higgins, who proposed the concept of three centred two electron bond
(  -bond) Fig. 9.1. He also proposed the concept of completely delocalised
molecular orbitals to explain structures of boron polyhedrons. He
established icosahedral structure of [B12H12] Fig 9.2.
Fig. 9.1: 3C, 2e bond in B2H6
Fig. 9.2: B12H12 Icosahedron
In higher boranes, in addition to two centred two electron (2c, 2e)
and
the three centred two electron bond (3c, 2e bond) present in
diborance, B-B 2C, 2e and B-B-B (3c, 2e) bonds are also important. In B-B-B
bonds, three atoms of boron with their sp3 hybridisation are placed at the
corners of a equilateral triangle (Fig. 9.3).
Fig. 9.3: B-B-B bond
9.2.1 Wade's Rule
In 1970 K. Wade gave a rule relating the number of electrons in the
higher borane molecules with their formulae and shapes. Using these rules
one can predict the general shapes of the molecules from their formulae.
These rules are also applicable on carboranes and other polyhderal
molecules called 'Deltahedral's Deltahedrons are so called, as they are
composed of delta,  , shaped triangular faces.
According to Wade's rule, the building blocks of deltahedrons are BH
units, which are formed by sp-hybridisation of boron atom. Out of the two
sp hybrids one is used in the formation of 2c, 2e B-H exo bond of the
deltahedron and the other sp hybrid is directed inside as a radial orbital.
Remaining two unhybridised p orbitals of each boron atoms are placed
perpendicular to the radial orbitals and are known as tangential orbitals.
These radial and tangential orbitals combine by linear combination method
to form skeleton or framework of the deltahedron. To fill all bonding
molecular orbitals of the skeleton, necessary number of electrons are
obtained form the radial orbitals of BH units and s orbitals of the extra
hydrogen atoms. These electrons are called Skeletal electrons. For example
in B4H10, four BH units contribute 8 electrons (4x2 = 8) and six extra
hydrogens give six electrons thus B4H10 has total 14 skeletal electrons Fig
9.4 gives the molecular energy diagram of [B6H6]2-. This molecule has seven
pairs of skeletal electrons (six boron atoms and one pair from two negative
charges). These are used to saturate seven skeletal molecular orbitals (a1g,
t1u and t2g).
tui
eg
t2g
t2u
t2g
t1u
a1g
Fig. 9.4: Skeletal molecular energy diagram of [B6H6]2-
Classification:
On the basis of structures, molecular formula and skeletal electrons
higher boranes are classified into Closo, Nido, Arachno and Hypo (Table
9.1):
Table 9.1
Name
Formula
Skeletal
Electron Pair
Examples
Closo
[BnHn]2-
n+1
[B5H5]2- to [B12H12]2-
Nido
[BnHn+4]
n+2
B2H6 , B5H9, B6H19
Arachno
[BnHn+6]
n+3
B4H10 , B5H11
Hypo
[BnHn+8]
n+4
Only derivatives are known.
9.2.2 Closo Boranes
These are closed structured (Closo, Greak, meaning cage) boranes
with the molecular formula [BnHn]2- and skeletal electrons = n+1 pairs (=
2n+2 electrons). In this structure, there is one boron atom placed at each
apex and there are no B-H-B bonds present in the molecule. All the
member of the series from n=5 to 12 are known. [B5H5]2- is trigonal
bipyramidal, [B6H6]2- is octahedral and [B12H12]2- is icosahedral. All are stable
on heating and are
quite inert.
9.2.3 Nido-Boranes
These boranes have nest (Nido, Latin, meaning Nest) like structure.
Their general formula is BnHn+4 and have (n+2) pairs = 2n+4 skeletal
electrons on removing one boron atom from an apex of closo structure,
nido structure is obtained. Because, of the lost boron atom, these boranes
have extra hydrogens for completing the valency. The polyhedra in this
series have B-H-B bridge bonds in addition to B-B bonds. They are
comparatively less stable than 'Closo', but more than 'Arachno' on heating.
9.2.4 Arachno-Boranes
These boranes have the general formula (BnHn+6) and skeletal
electrons = (n+3) pairs = 2n+6 = electrons. These molecules are obtained by
removing two boron atoms from two apexes of the closo structure and
have spider-web like structure. They have B-H-B bridge-bonds in their
structures and are very reactive and unstable on heating.
9.2.5 Structural Inter-relation
The structural interrelation between closo, nido arachno species is
shown in Fig. 9.5.
Arachno B4H10
Fig. 9.5:
This is based on the observation that the structures having same
number of skeletal electrons are related with one another by the removal
of BH unit one by one and the addition of suitable number of electrons and
hydrogen atoms, e.g. by removing one BH unit and two electrons from
octahedral closo. [B6H6]2- ion and adding four hydrogens, we get square
pyramidal nido- B5H9 borane. On repeating same process on nido B5H9 (i.e.
removing one BH unit and adding two hydrogen's), we get butterfly shaped
arachno. B4H10. Each of these three boranes have 14 skeletal electrons, but
due to removal of BH unit, the resulting structure becomes more open
gradually (Fig. 9.5). The most symmetrical closo structure has (n+1) skeletal
molecular orbital, which requrie 2n+2 electrons. Similarly, nido-boranes
have (n+2) molecular-orbitals and need 2n+4 skeletal electrons; while for
(n+3) molecular orbital, arachno boranes require 2n+6 skeletal electrons
(see fig 5.6 for comparison between these classes of boranes).
9.2.6 Synthesis
The simplest method for synthesis of higher boranes is the controlled
pyrolysis of diborance, B2H6 it is a gas phase reaction, BH3 formed in the
first step reacts with borane to give higher boranes:
B2H6(g)

2BH3(g)
B2H6(g) + BH3(g)

B3H7(g) + H2(g)
B3H7(g) + BH3(g)

B4H10(g)
B2H6(g) + BH3(g)

B3H9(g)  [B3H8]-(g) + H+
5[B3H6](g)

[B12H12]2-(g) + 3[BH4]-(g) + 8H2(g)
2[BH4](g) + 5B2H6(g)

[B12H12]2- + 13H2
Closp
Nido
Arachno
Fig. 9.6: Interrelation between closo, nido and arachno-boranes
9.2.7 Reactions
The important reactions of higher boranes are with Lewis bases,
which involve removal of BH2 or BHn from the cluster, growth of the cluster
or removal of one or more number of protons:
1.
Decomposition by Lewis-bases:
B4H10 + 2NH3  [BH2(NH3)2] + [B3H8]
The reaction is analogous to the reaction of diborane with ammonia.
2.
Deprotonation :
Higher boranes give deprotonation reaction easily rather than
decomposition:
B4H10 + N(CH3)3 [HN(NH3)3] + [B10H13] This deprotonation takes place from 3c, 2e BHB-bond. The
bronsted acidity of boranes increases with their size:
B4H10 < B5H9 < B10H14
For deprotonation of B5H9 strong-base like Li4(CH3)4 is required:
B5H9 + Li(CH3)  Li+[B5H8]- + CH4
3.
Cluster Building:
Reactions of borane with borohydride are important with
respect to synthesis of higher boranes:
5K[B9H14] + 2 B5H9  5K[B11H14] + 9 H2
4.
Electrophilic displacement of proton:
Electrophilic displacement of proton by the catalytic activity of
Lewis acids like AlCl3 is the basis of alkylation and halogenation of
boranes:
AlCl
B5H9 + CH3Cl 
 [CH3B5H8] + HCl
3
Check Your Progress-1
Notes : (i) Write your answers in the space given below .
(ii) Compare your answers with those given at the end of the
unit.
A(i) Metal Clusters include those molecular complexes in which
..............bonds form a....................or large ...............................
(ii) Higher boranes may have different shapes resembling (a)
(b)
(c)
(iii) The various types of bonds present in higher boranes are mainly(a)
(b)
B(i) Wade's rule relates (a)
(b)
and (c)
(ii)
Main
polyhedral
structure
of
higher
boranes
is
called
............................. which have ....................... units as the building
blocks.
(iii) Main classes of higher boranes with their general formula and
skeletal electrons pairs are Name
Formula
Skeletal electron pairs
(a) ......................... ...............................
.............................
(b) ......................... ...............................
.............................
(c) ......................... ...............................
.............................
9.3
CARBORANES
Carboranes are mixed hydrides of carbon and boron, having both
carbon and boron atoms in an electron - deficient; skeletal framework.
There are two types of carboranes:
1. Closo-Carboranes: These have closed cage structrues in which
hydrogen bridges are structurally analogous to the Bn Hn-2 anions
with B- replaced by isoelectronic carbon. These carboranes have the
general formula. C2Bn+2 (n=3) to 12. The important member is
C2B10H12 (Fig. 9.7). Which is isoelectronic with [B12H12]2- similarly
B4C2H6 is isoelectronic with [B6H6]2-.
(A) 31, 2, C2 B10 H12
(B) C2B4H6
Fig. 9.7
2. Nido Carboranes: They are having an open case structure in which
some framework members are attached likely by hydrogen bridges.
These are derived formally from one or other of several borones.
These contain one to four carbon atoms in the skeleton.
In addition to the above types of carboranes, there are a
number of carboranes with an additional heteroatom such as
phosphorus built into the basic structure and a family of metallo
carboranes, some of which are similar to ferrocene. One peculiar
feature common to all carboranes is that to date no compound has
been synthesized with either carbon bridging two boron atoms in a
three centre two electron bond or acting as one end off a hydride
bridge.
First carborane was obtained in 1953 when mixtures of
diborane and acetylene were ignited with a hot wire. Since that time,
many new carboranes have been isolated.
Nomenclature:
Rules for naming carboranes are as follows:
i. First of all, give the positions and number of carbon atoms, then the
type of carborane (either closo or nido) and finally the name of the
borane from which the carborane is formally derived and the number
of hydrogen atoms shown in bracket. For example CB5H9 is name as
monocarbonido hexaborane (9). Similarly, the three isomers of
C2B10H12 are named as 1, 2; 1, 7 and 1, 12 dicarbo-closododecaborane (12).
ii. Number of atoms in these structure are counted by starting the
numbering from that in the apical position and proceeding through
successive rings in a clockwise direction.
This rule is important in naming the isomers.
Closo-Carboranes or Closed Cage Carboranes
These carboranes are having general formula C2BnHn+2 (n=3 to 10) in
which the constituents are only terminal. These are isoelectronic
with the corresponding [BnHn]2- ions and have the same closed
polyhedral structures, with one hydrogen atom bonded to each
carbon and boron. No bridging hydrogen atoms are present in the
C2Bn skeleton. They are considered in three groups.
a.
small, n = 3 - 5
b.
large, n = 6-10 and
c.
dicarbo-closo-dodecaborone
9.3.2 Preparation:
I(a)
The Small Closo Carboranes (C2BnHn+2 where n = 3 to 5)
C

 1,5 - C2B3H5 + 1,6 - C2B4H6 +2,4 - C2B5H7
B5H9 + C2H2 490
o
Example - The closo hexaborane isomers, C2BnH6,
(b)
The Large Closo Carboranes (C2B2Hn+2 where n = 6 to 9)
The first three members of this group of carboranes are
obtained by the thermolysis of 1,3 - C2B7H13 and 1,3 - C2B2H12.
Example
:
C2B6H8
is
made
from
hexaborane
(10)
and
dimethylacetylene. The structure of 1,7 - Me2C2B6H6 is based on the
bicapped triangular prism. The carbon atoms are present one on the
prism and the other above the face opposite.
(c)
Dicarobo-closo-dodecaborone:
Preparation: The orthocarborane is the only isomer which can
be synthesized directly. However, it is synthesized by the base
catalysed reaction of acetylenes with decarborane (14) or via
B10H12L2.
H
RC

 B10H12L2 
 R2L2B10H10 + H2 + 2L
B10H14 + 2L 
2
2
2
Example: C2B10H12 gives three isomeric structure - 1,2 (ortho), 1-7
(meta) and 1, 12 (para)
(II) Nido-Carboranes or Open Cage Carboranes
These structures are derived formally from one or other of
several boranes and contain from one to four carbon atoms in the
skeleton.
Examples: CB5H9, C2B4H8, C3B3H7, C4B2H6 etc.
Preparation: The smaller nido-carboranes are generally prepared by
reacting a borane with acetylene under mild conditions.
Example: B5H9and C2H2 undergo reaction in the gas phase at 215oC to
give mainly the nidocarborane 2,3 - C2B4H8 together with methyl
derivatives of CB5H9.
The preparation method described above does not yield a
single product but a mixture of several products whose separation is
not an easy task. However some smaller nidocaroranes are prepared
by the following specific methods:
i.
Mono carbo-nido-hexaborane (7) CB5H7 is formed by
passing
silent
electric
discharge
through
1-methyl
pentaborane (9).
ii.
The only example isoelectronic with B5H9 is 1,2-
dicarbonido
- pentaborane(7), C2B3H7, which is prepared as follows:
C
B4H10 + C2H2 50
 C2B3H7 (3 - 4 % yield)
o
iii. Monocarbonidohexaborane (9), CB5H9 is
formed from
ethyldifluoroborane and lithium.
The nido-carboranes are formally related to B6H10. All are having
eight pairs of electrons which are bonding the six cage atoms together.
Large Nido-Carborane:
Dicarbo-nido-undecaborane, C2B9H13, is the second member of
the class of nido-carboranes C2BnHn+4 (n =4 or 9),. The parent
carborane and its substituted derivatives can be prepared by the
base
degradation
of
ortho-carborane
(1,2-dicarbocloso-
dodecaborane (C2B10H12).

1
MeO
H
1,2 - C2H10H12 
 C2B9H12 
 C2B9H13
When C2B9H13 is heated, the closo-undeca-Borone (11) cage is
formed.
9.3.2 Properties
Properties of carboranes resemble with that of the corresponding
boranes closely. Thus, 1.2 dicarbo closo-dodecarborane-12 is stable in both
air and heat. On heating in inert atmosphere at 500oC, it is converted into 1,
7 isomer i.e. meta or neo isomer; while at 700oC it is concerted to 1, 12
isomer i.e. para-isomer (Fig. 9.8)
Fig. 9.5: (a) C2B10H12
(b) 1,7 C2B10H12
(c) 1,12 C2B10H12
Analogous to boranes, carboranes are also classified into closo, nido
and arachno structure.
The chemical reactions, in so far as they are known, are very similar
to those of C2B10H12, which are described below. Various substitution
reactions have been studied and the hydrogen atoms bonded to carbon are
weakly acidic.
All three of the icosahedral isomers are stable both to heat and to
chemical attack, and much more so than decaborane (14). They are white
crystalline solids which resist both strong oxidizing agents and strong
reducing agents and are also stable to hydrolysis. This is important because
it allows reactions to be carried out on substitutions, often under quite
drastic conditions, without destroying the cage structure, rather as the
chemistry of derivatives of an aromatic ring such as benzene can be
developed without destroying the ring.
Most chemical studies have been concerned with substituents on the
two carbon atoms. These may be introduced in the first place by employing
substituted acetylene in the carborane syntheses. Such groups as C-alkyl, haloalkyl, -aryl, -alkaenyl and -alkenyl may be introduced into the structure
in this way. Further reactions on the subsequents groups may then be
carried out by the usual synthetic methods of organic chemistry to give, for
example, carboxylic acid, ester, alcohol, ketone, amine or unsaturated
groups in the side chain.
The nido-carborane 2.3-C2B4H8 is converted to the closo-carboranes
C2B3H5, C2B4H6 and C2B5H7 on pyrolysis or ultraviolet irradiation.
Largely because of preparative difficulties, relatively little is known
about the reactions of the smaller nido-carboranes. They are only
moderately stable to heat and are less resistant to hydrolysis and oxidation
in air than the closo species. Halogen substitutions have been observed, as
has the formation of anions; for example,
diglyme
 Na+C2B4H7- + H2
C2B4H8 + NaH 
Similarly with LiC4H9, Lithium derivative is former:
B10C2H12 + 2LiC4H9  B10C2H10Li2 + 2C4H10
The Sodium derivative with FeCl3 gives Fe-derivative:
2Na2[B9C2H11] + FeCl3  2NaCl + Na2[Fe(B9B2C11)2]
9.3.3 Structures
Structural studies of carboranes have been done using X-ray analysis
and nmr studies.
The C2B3, C2B4 and C2B5 closo-carboranes, for example, have trigonal
bipyramidal, octahedral and pentagonal bipyramidal skeletal structrues
respectively, and positional isomers have been identified.
The icosahedra structure is similar to that of B12H122- (Fig. 9.8) and is
electron-deficient, with electron delocalization extending over the whole
framework. It is thus in effect a three-dimensional aromatic molecule, with
marked electron withdrawing character, the most important result of which
is to render the two hydrogen atoms bonded to carbon acidic. All the C-H
and B-H bonds are of the normal two-electron type and the electron
deficiency is associated with the framework, in which there are multicentre
bonds.
The Structure of nido C3B3H7 is shown in Fig. 9.9. In the diagram
hydrogen bridges are shown by curved lines, but terminal B-H and C-H
bonds are ommitted. It can be seen that the introductions of successive
carbon atoms to the framework involves the elimination of one bridge
hydrogen atom and one B-H (i.e. the replacement of BH2 by an isoelectronic
CH unit). Like all the carboranes these compounds are electron-deficient,
with multicentered bonds and delocalization extending over the entire
framework. In much the same way, C2B3H7 has a square pyramidal structure
that is formally derived from that of B5H9, with two BH2 replaced by 2CH.
Fig. 9.9
9.4
METALLO-BORANES AND METALLO CARBORANES
Borane-clusters, in which metals are present are know as
'Metalloboranes'. Many metalloboranes have been prepared. In some cases
metal atom is attached with the borohydride ion through hydrogen bridge.
The most common and important metalloborane group is one in which
direct metal boron bond is present.
An important example of main group element metallocarborane is
closo [B11H11AlCH3]2- (Fig. 9.10). It is prepared by the action of trim ethyl
aluminium [Al(CH3)3]2 with Na2[B11H13]:

Al2(CH3)6 + 2[B11H13]2- 
2[B11H11AlCH3]2- + 4CH4
Fig. 9.10: Closo [B11H11AlCH3]2-
The hydrogen attached with carbon in closo- B10C2H12 is slightly
acidic. This can be substituted by butyl lithium or Grignard's reagent to get
lithium or magnesium metallocarboranes:
2C4H9Li + C2H2B10H10  C2Li2B10H10
2RMgBr + C2H2B10H10  [CMgBr]2B10H10 + 2R-H
Similarly, [C2B9H11]2- ion, reacts with FeCl2, BrRe(CO)5 or BrMn(CO)5 to
give Fe, Re or Mn derivatives:
2[C2B9H11]2- + FeCl2  [(C2B9H11)2Fe]2- + 2Cl[C2B9H11]2- + BrRe(CO)5  [C2B9H11.Re(CO)3]- + Br- + 2CO
[C2BgH11]2- + BrMn(CO)5  [C2B9H11.Mn(CO)3]- + Br- + 2CO
There is a similar reaction with the hexacarbonyls of Cr, Mo and W
under the influence of ultraviolet light, and the air sensitive products are of
the type (C2B9H11)M(CO)32- (M = Cr, Mo, W). Closely related complexes of
other transition metals (Co, Ni, Pd, Cu and Au) have also been made,
including some with sub-substitutnts on the ion.
In the first place formation of  -bonded complexes based on
carborane structures is not restricted to the C2B9H112- ion; there are a
number formed on the same principle by CB10H113- and some of its aminesubstituted derivatives (e.g. [(CB10H11)2Cr]3- and C2B4H63-) also give
complexes, and it may be noted, some of these are nido-anions. Thus [1,6
C2B7H9)2Co]- has the structure shown below (Fig. 9.11), the ion being
derived from 1,3-C2B7H13.
(a)
(b)
(c)
Fig. 9.11: (a) Carbonyl metallocene
(b) Carbonyl Cyclopentadieny
(c) Carbolyl Carbonyl Compound
On the basis of Wade's rule, the structrues of these metal derivatives
may be known from their molecular formula and skeletal electrons. For
example in B3H7[Fe(CO)3]2, n=5 (3B + 2Fe) and skeletel electrons are 14.
Hence it has nido structure corresponding to square pyramidal (Fig. 9.12).
Fig. 9.12: Structure of [Fe(CO3)B4H8]
9.4.1 Properties
Just as the carboranes, lithio and Grignard's derivatives of metallo
carbones give substitution reactions of organometallics, which include:
(a) Formation of derivatives such as carboxylic acids, ester, alcohol,
ketone, amines etc.
(b) Synthesis of iodo and nitroso devivatives.
(c) Elmination of Lithium halidePCl3 + C2PhL2B10H10  (C2PhB10H10)2Pl
Ph3PAuCl + C2RLiB10H10  Ph3AuC(Cr)B10H10l
N ( CO ) i
2(C6H5)2PCl + C2Li2B10H10  (C6H5)2PC-CP(C6H5)2 

4
l l
- B10H10 OC
CO
Ni
Similarly, derivatives of mercury and other metals(  -bonded) have also
been obtained,
H Cl
 B10H10RC2HgC2RB10H10
RC2LiB10H10 
9
2
Ph3PAuCl + C2RLiB10H10  Ph3PAuC(CR)B10H10
9.5
METAL CARBONYL AND HALIDE CLUSTERS
As has been described earlier, metal carbonyl clusters are rarely
formed by earlier d-block metals; while that of f-metals are unknown, i.e.
these clusters are formed by group 6 to 10 elements.
An alternative method for counting skeletal electrons in these
compounds is due to D.M.P. Mingos and J. Lauher. This method is also
based on Wade's rule and is known as Wade-Mingos-Lauher rule. In this
method the total number of valence electrons in all the metal atoms
present in the complex are counted and then electrons donated by ligands
are added. Thus in Rh6(CO)166Rh
=
6x9
=
54 e-
16CO
=
=
32 e-
Total =
86 e-
16 x 2
Out of the total 86e-, twelve electrons per rhodium atom are used for
non framework bonding, and remaining 14e- are obtained for skeletal
bonding. These include seven bonding paris, equal to 2n+2 electron. Hence,
Rh6(CO)16 should have closo- structure
Some examples showing inter-relation between cluster-valency
electrons and structures are given in Table 9.2.
Table 9.2
No. of
Metal
Atoms
Geometry
Metal
Skeleton
Structure
Bonding
No. of
Molecular Cluster
Orbital
electron
Examples
1.
Monomer
9
18
Ni(CO)4
2.
Dimer
17
34
Fe(CO)9,
Mn2(CO)10
3.
Triangle
24
48
Os3(CO)12,
Co3(CO)9CH
4.
Tetrahedron
30
60
Co4(CO)12,
Rh4(CO)12
Butterfly
31
62
Re4(CO)162-,
[Fe4(CO)12C]2-
Square
32
64
Os4(CO)16,
Pt4(O2CMe)8
5.
TBP
36
72
Os5(CO)16
Octahedral
37
74
Fe5(CO)15C
No. of
Metal
Atoms
Geometry
6.
Metal
Skeleton
Structure
Bonding
No. of
Molecular Cluster
Orbital
electron
Trigonal
prism
7.
Examples
43
86
Ru6(CO)17C
45
90
[Rh6(CO)15C]3-
It is quite clear from table 9.2 in tetranuclear metal cluster three
structures, tetrahedral, butterfly and square planar, are seen, with 60, 62
and 64 cluster electrons respectively (Fig. 9.13).
Tetrahedron
Butterfly
Fig. 9.13
Synthesis:
1. Pyrolytic Synthesis:

2CO2(CO)8 
CO4(CO)12 + 4CO 
2. Redox Condensation:
Square Planar
Ni(CO)4 + [Ni5(CO)12]2-  [Ni6(CO)12]2- + 4CO 
3. Ston's Method: Condensation of meatl carbonyls with unsaturated
metal carbonyls:
(CO)5Mo = C(OMe)Ph + Pt(Cod)2  (CO)5Mo.Pt(Cod)(OMe)Ph
Cp.W(CO)2 (  C.tol) + Co2(CO)8  (Cp)(CO)2W.Co2(CO)6C.tol
Reactions:
1. Substitution Fragmentation:
Fe3(CO)12 + P.Ph3  Fe3(CO)11(Ph3) + Fe3(CO)10(P.Ph3)2 +
Fe(CO)5 + Fe(CO)4(P.Ph3) + Fe(CO)3(PPh3)2 + CO
2. Prolongation:
[Fe3(CO)11]2- + H+  [Fe3H(CO)11]3. Cluster Catalytic Ligand Transformation: eg. in Os cluster.
9.5
Metal Halide clusters
Although the first information of metal halide clusters was given in
12th Century in the form of calomel, but dimeric nature of mercurous ion
could be established in 20th Century only. But now number of metal halide
clusters are known.
Dinuclear Complexes:
Most important dinuclear species is [Re2X8]2- (Fig. 9.14).
Fig. 9.14: Structure of [Re2Cl8]2-
Analogous to [Re2X8]2- ion, in which very small M-M distance and
eclipsed configuration of chlorine atoms are present, is [Mo2Cl8]2- and
[W2Cl9]3- (Fig. 9.15).
Fig. 9.15: Structure of [W2Cl9]3-
The structures of these dinuclear complexes are either similar to
ethane or an edge-shared bioctahedron or a face shared bioctahedron (Fig.
9.15). or tetragonal prism (Fig. 9.14).
Trinuclear Cluster:
The well known examples of trianuclear cluster are rhenium
trichloride, [ReCl3]3 or Fe3Cl9 and their derivatives. Rhenium Chloride is a
trimer, and has been used for the preparation of other trimers as a starting
material. Its structure is shown in Fig. 9.16.
Fig. 9.16: Structure of [W2Cl9]3-
Tetra nuclear Clusters:
Only a few examples of tetranuclear clusters of halides and oxides
are known. Most important example is the dimeric [Mo2Cl8]4- cluster giving
a tetra nuclear molecule :
Hexanuclear clusters:
Hexanuclear Clusters or Mo, Nb and Ta halides are well known. Two
species are known, one with molecular formula M6X12 or [M6X8]X4 and the
other with molecular formula [M6X14]2-.
Molybdenum forms cluster of the type [M6X8]X4. [M6X8]4+ ion has an
octahedral skeleton of metal atoms, each face of which is coordinated with
a chloride ion (Fig. 9.17).
Fig. 9.17: Structure of [M6Cl8]4+
Niobium and tantalum give clusters of M6Cl12 type. In these each
edge of the octahedral structure of metal atoms is coordinated with a
chloride ion (Fig. 9.18).
Fig. 9.18: Structure of [M6X12]
Similarly, Nb, Ta and Zr give clusters of [Nb6Cl12L6]2+ type also. In
which 12 chloride ligands are present (one on each edge) on 12 edges of
the octahedral skeleton of metal atoms and the remaining six ligands are
attached to six metal atoms (one on each metal atom), e.g. Nb and Ta give
[M6X18]2+ type clusters (Fig. 9.19):
Fig. 9.19: Structure of [M6X18]2+
Solid [Mo6Cl14]2- species is derived from MoCl2 as its hexamer (Fig.
9.20).
Fig. 9.20
9.6
COMPOUNDS WITH METAL-METAL MULTIPLE BONDS
As has been shown earlier, the earlier metals in d-block series in their
lower oxidation states have tendency to form metal-metal multiple bonds.
These metal-metal bonds may be present in smaller molecules and also in
macro-chain solids.
Chevrel-phases :
Chevrel
phases
generally
involve
tertiary
molybdenum
chalcogenides, MxMoX6, polynuclear clusters, which have characteristic
properties (specially electrical and magnetic). Their structures are also
abnormal. An important example of these phases is a super-conducter
substance, PbMo6S8. Its structure consists of an octahedral cluster of
molybdenum atoms, which is surrounded by cubic cluster of sulphur atoms.
Then this whole structure is enclosed in to a cubic structure of lead atoms.
The internal Mo6S8 cubic structure rotates with respect to lead lattice. This
rotation is due to strong repulsion between sulphur atoms. Similarly, the
superconductivity
originates
due
to
overlapping
molybdenum (Fig. 9.21).
Fig. 9.21  = Mo, o = s, 0 = Pb
Zintle anions and cations:
of
d-orbital
of
In 19th century, it was seen that post transition metals in liquid
ammonia solution, in presence of alkali metals give highly coloured anions.
After 1930, polyatomic anions such as Sn94-, Pb74-, Pb94-,Sb73- and Bi33- were
discovered. In 1975 cryptate salts of these anions were also obtained.
Some cations, Bi95+, Te64+, etc were also prepared
These species were designated as Zintle anions and cations. These
are homopoly atomic species, which have no ligands attached with. (Fig.
9.22)
Fig.: 9.22 a. Pb52-, c. Bi95+, d. Te64+
Many compounds having metal metal multiple bonds show ethane
like structure. Important compounds with metal-metal quadruple-bond
include halide complex, [M2X8]2 and oxalate complexes of Cr, Mo and W.
(Fig. 9.23)
Fig. 9.23: structure of [Mo2(CH3COO)4]
Table 9.3 gives important informations about the complexes having metalmetal multiple bonds.
Table 9.3
Complex
Electronic
Configuration
Bond Order
Bond
Length
Check Your Progress -2
Notes : (1) Write your answers in the space given below.
(2) Complex your answers with those given at the end of
the unit.
(a) (i) carboranes are......................of carbon and boron having both
these atoms in an...........................skeletal frame work.
(ii) The important example of carboranes is........................which
is isoelectronic with..........................................
(iii) The isomeric compounds of 1, 2 dicarbocloso decabrone 12
are (i)
........................................
and (ii)
........................................
(iv) [C2B9H11]2- ion reacts with FeCl2 and BrRe(CO)5 to give(i)
........................................ and
(ii)
........................................ respectively.
(v) Rh6(CO)16 has total ............................. electrons ...................
electrons per rhodium atom are used for .................... bonding
and remaining ..................... electrons (=
) pair
electrons indicate......................structure.
(vi) In [Nb6Cl12L6]2+ crystals ..................... ligands are present on
....................... of the ........................... skeleton of metal
atoms
and remaining ........................ ligands are attached to ...............
atoms.
(vii) Compounds with metal-metal multiple bonds are given by
........................ in .......................... block series, in their
................ oxidation states.
(viii) Example of -
9.7
(i)
Chevrel phase is ........................................
(ii)
Zintle anion is .......................... and ....................
(iii)
Oxalate complex is ........................................
LET US SUM UP
 Closed polyhedrons play important part in the synthesis of cluster
molecules in inorganic chemistry. These cluster molecules include
polyhedral boranes, carboranes, metallo-boroanes and -carboranes
and metal halide crystals.
 Metal clusters include those molecular complexes in which metalmetal bonds from triangular or large closed structures.
 Higher boranes (boron hydrides) may be given general formula
[BnHn]2-, BnHn+4 and BnHn+6. They have different shapes; some
resemble nests, some with butterfly and some with spider's web.
 In higher boranes, in addition to 2c,2e and 3c, 2e bonds, B-B 2c,2e
and B-B-B 3c,2e bonds are also present.
 Wade's rule relates the number of electrons in the higher boranes
with their formulae and shapes. According to this rule the building
blocks are BH units (due to sp hybridisation of boron atoms).
 Out of the two sp-hybrids of B, one is used for 2c,2e B-H bonding and
the other one is directed inside as a radial orbital. Remaining two
unhybridised p-orbital of each B atom are placed perpendicular to
the radial orbitals and are known as tangential orbital. These radial
and tangential orbitals combine to form skeleton of the deltahedron.
To fill the bonding molecular orbitals of the skeleton, necessary
number of electrons are obtained from the radial orbitals of BH units
and extra hydrogen s-orbitals. These electrons are called skeletal
electrons.
 On the basis of structures, molecular formula and skeletal electrons,
higher boranes are classified in to four groups:
Closo, [BnHn]2-, with (n+1) skeletal electron pairs,
Nido, [BnHn+4], with (n+2) skeletal electron pairs,
Arachno, [BnHn+6], with (n+3) skeletal electron pairs,
and Hypo, [BnHn+8], with (n+4) skeletal electron pairs,
 Removal of one BH unit and 2 electrons from octahedral closed
[B6H6]2- ion and adding four hydrogen atoms gives square pyramidal
nido B5H9 borane. On repeating same process on nido B5H9, butterfly
shaped arachno B4H10 is obtained. Each of these three boranes has
14 skeletal electrons, but removal of BH unit gradually results in
more and more open structure.
 The bronsted- acidity of boranes increases with their size:
B4H10 < B5H9 < B10H14
 Carboranes are mixed hydrides of C and B having both these atoms in
an electron defficient skeletal framework. They are classified in to
closo and nido-carboranes accordingly.
 Important member of carboranes is B4C2H6 which is isomeric with
[B6H6]2-.
 Properties of Carboranes resemble with those of the corresponding
boranes. Thus 1,2-di-carbo closo dodecarborane -12 is stable in both
air and heat. Its meta and para isomers are 1,7 C2B10H12 and 1,12
C2B10H12 respectively.
 Borane and carborane clusters in which metals are present are
known as Metalloboranes and Metallo carboranes Closo- B10C2H12
reacts with butyl lithium or grignard's reagent to give lithium and
magnesium metallocarbornes.
Similarly
[C2B9H11]2-
reacts
with
FeCl2,
BrRe(CO)5
or
BrMn(CO)5 to give Fe, Re or Mn derivatives.
 On the basis of wade's rule the structures of these metal derivatives
may be known from their molecular formulae and skeletal electrons
e.g. B3H7 [Fe(CO)3]2 with n=5 (3B+2Fe) and skeletal electron 14 is
nido-metalloborane with square pyramidal geometry.

Skeletal electrons in metal carbonyl and halide clusters are counted
using Wade-Mingos-Lauher-rule. In this method the total number of
valency electrons in all the metal atoms present in the complex are
counted and then electrons donated by ligands are added. Thus in
Rh6(CO)16 6 Rh = 6 x 9
= 54e-
16 CO = 16 x 2
= 32e-
Total = 86eOut of these 86e-, 12 per Rh atom are used for the non-frame
work bonding and remaining 14e- are used for skeletal-bonding.
These include (n+1) e--pairs; hence it has closo-structure.
 Important examples of metal halide crystals are [ReCl8]2-, [W2Cl9]3-,
[ReCl3]3 dimeric [Mo2Cl8]4- and [Mo6Cl8]4+.
 In [Nb6Cl12L6] type clusters, 12 Cl- ligands are present on 12 edges of
the octahedral skeleton of metal atoms and remaining 6 ligands are
attached to six metal atoms.
 Compounds with metal-metal multiple bonds may be either chevrel
phases (e.g. PbMo6S8) Zintle anions or cations (e.g. Sn94-, Pb74-, Bi95+,
Te64+ etc) or metal-metal polybonded complexes.
9.8
CHECK YOUR PROGRESS: THE KEY
1(A) (i)
Metal-metal bonds.
Form a triangular or
Large closed structure.
(ii)
(iii)
(B) (i)
(ii)
(a)
Nest
(b)
Butterfly
(c)
Spider's web
(a)
2c, 2e bonds
(b)
3c, 2e bonds
(a)
Number of electrons in the molecule.
(b)
Their formula, and
(c)
Shapes.
Called Deltahedron
Which have BH units.
(iii)
2(i)
(ii)
Name
Formula
Skeletal electron-pairs
(a)
Closo
[BnHn]2-
(n+1)
(b)
Nido
[BnHn+4]
(n+2)
(c)
Arachno
[BnHn+6]
(n+3)
Mixed hydrides in an electron defficient.
C2B10H12
with B12H12
(iii)
(i) 1, 7 C2B10H12 (meta isomer)
(ii) 1, 7 C2B10H12 (para isomer)
(iv)
(i) [(C2B9H11)2Fe]2- and
(ii) [C2B9H11Re(CO)3]-
(v)
86 electrons.
12 electrons for
non frame work bonding
remaining 14 electrons (=n+1) pairs indicate closo structrue.
(vi)
12 ligands
on 12 edges of the
octahedral skeleton
to six metal atoms.
(vii)
Earlier metals in d-block
in their lower oxidation states.
(viii) (i)
(ii)
PbMo6S8
Sn94-, Pb74- and Sb73(iii)
[Mo2(CH3OO)4]