Thermodynamic stability-reaction of complex, Chemistry tutorial


The thermodynamic stability and reaction kinetics of coordination compound is a extremely significant feature of coordination chemistry and its application cut across all the disciplines comprising: catalyst deign in production industries, chemical analysis, pharmaceutical studies of drug design and biochemical studies of drug metabolism. This is due to the stability study and reaction mechanism of complexes determines their behavior in various environments that might comprise change in temperature or change in pH of reaction medium. This is significant to know that there is a line of separation between the kinetic and thermodynamic stability of complexes as at time the two terms are without conveying their real meaning.

Thermodynamic stability is the function of equilibrium constant. Higher the equilibrium constant points out greater stability of the complex. Though, kinetics is a function of the rate constant. The reaction having high rate constant is expected to carry on fast.    

Thermodynamic stability of complex compounds:

A metal ion in solution exists in the complex form, in combination by ligands (like solvent molecules or simple ions) or chelating groups. As noted prior, complexes might be neutral or cationic or anionic, based on the charges carried through the central metal ion and the coordinated groups. Stability of the complex in solution refers to the degree of association between the two species comprised in a state of equilibrium. Qualitatively, the greater the association, the greater is the stability of the compound. The magnitude of equilibrium stability constant for the association, quantitatively finds out the stability. Thermodynamic stability of a complex is the measure of extent to which this complex will be made up or be converted into the other complex under stated conditions on reaching equilibrium. If merely soluble mononuclear complexes are made up in a solution having metal ion, Mn+, and Monodentate neutral ligand, the system at equilibrium can be illustrated by the given expression;

[M]n+ + L ↔ [ML]n+          K1 = {[ML]n+}/{[M]n+}[L]

[ML]n+ + L ↔ [ML2]n+       K2 = {[ML2]n+}/{[ML]n+}[L]  

[ML2]n+ + L ↔ [ML3]n+      K3 = {[ML3]n+}/{[ML2]n+}[L]

[ML3]n+ + L ↔ [ML4]n+      K4 = {[ML4]n+}/{[ML3]n+}[L]

The reaction will carry on till a certain coordination number (N) is attained

[MLN-1]n+ + L ↔ [MLN]n+   KN = {[MLN]n+}/{[MLN-1]n+}[L]

The equilibrium constants K1, K2, K3, K4....... and KN are termed as stepwise formation or stability constants. Whenever combined altogether, the overall formation constant (βN) is derived

βN = K1 x K2 x K3 x K4........ KN or log βN = log k1 + log k2 + log k3 + log k4 +..... log kN

In most of the cases, the value of stepwise formation constant reduces as the coordination number rises. Illustration is the reaction between aqueous solution of Cd2+ and NH3

[Cd]2+ +  NH3 ↔ [Cd(NH3)]2+               K1 = {[Cd(NH3)]2+}/{[Cd]n+}[NH3] = 102.65

[Cd(NH3)]2+ + NH3  ↔ [Cd(NH3)2]2+     K2 = {[Cd(NH3)2]2+}/{[Cd(NH3)]2+} [NH3] = 102.10

[Cd(NH3)2]2+ + NH3 ↔ [Cd(NH3)3]2+     K3 = {[Cd(NH3)3]2+}/{[Cd(NH3)2]2+} [NH3] = 101.44

[Cd(NH3)3]2+ + NH3 ↔ [Cd(NH3)4]2+     K2 = {[Cd(NH3)4]2+}/{[Cd(NH3)3]2+} [NH3] = 100.93

βN = 107.12 or log βN = 7.12

The main reasons for the decrease in the K value are statistical factors, increased stearic hindrance whenever the incoming ligand is bigger than the leaving ligand and the columbic force whenever the ligand is charged. Provided acknowledged concentrations of metal ion and ligand react altogether to provide a complex whose composition is known, the stability constant can be found out for such reaction by measuring the concentration of the unreacted ligand, metal ion or the complex formed. This can be accomplished by monitoring change in one of the properties of a component in the system or use of ion-exchange, pH measurement, electronic or NMR methods.

The Chelate effect:

The word chelate effect is employed to illustrate special stability related by complexes containing chelate ring whenever compared to the stability of associated complexes with monodentate ligands. The chelate effect can be observed by comparing the reaction of a chelating ligand and a metal ion by the corresponding reaction comprising comparable monodentate ligands. For illustration, comparison of the binding of 2, 2'-bipyridine with pyridine or 1,2 diaminoethane (ethylenediamine = en) by ammonia.

This has been established for many years that keeping the coordination number of the metal ion similar, the complex resultant from coordination by the chelating ligand is much more thermodynamically stable than that formed by monodentate ligand. This can be established from the stability constant of the complexes made up adding two monodentate ligands compared by adding one didentate ligands, or adding four monodentate compared to two didentate, or adding six monodentate compared to three didentate. The complex formation of Ni2+ by ammonia or 1, 2-diaminoethane, can be deduced by the given equations:

[Ni(H2O)6]2+ + 6NH3 → [Ni(NH3)6]2+ + 6H2O     β6 = 108.76

[Ni(H2O)6]2+ + 3en → [Ni(en)]2+ + 6H2O            β6 = 1018.28

The overall stability constant value for Ni2+ complex having three chelate rings (en) is around 1010 greater than that made up by six monodentate ligands (NH3). The main factors responsible for the special stability of chelate can be attributed to rise in entropy as the reaction leading to the formation of the chelate yields in increase in pollution of product species whenever compared to the reactant species. Though, by monodentate ligand, the reaction yields in no change in population.

The other factor could be based on the understanding of how the reactions may carry on. To form a complex by 6 monodentate ligands needs 6 separate favorable collisions between the metal ion and the ligand molecules. In contrast, the tris-bidentate metal complex needs an initial collision for the first ligand to link by one arm; the other arm is for all time going to be nearby and merely needs a rotation of the other end to let the ligand to form the chelate ring. Therefore in the procedure of dissociation, whenever a monodentate group is displaced, it is lost into the bulk of the solution. On the other hand, when one end of a bidentate group is displaced the other arm is still linked and it is merely a matter of the arm rotating around and it can be re-attached again. Such conditions favor the formation of the complex by bidentate ligands instead of monodentate ligands. 

649_Formation of complex with bidentate ligands.jpg

Fig: Formation of complex with bidentate ligands

One ligand which forms extremely stable complexes is the anion ethylenediaminetetraacetate (EDTA4-). This ion can bond at six sites, so one EDTA4-ion replaces six water molecules when the reaction is taken out in aqueous solution. The result is the formation of complexes that encompass very high stability constants. This ligand is broadly utilized in analytical chemistry in the Complexometric titrations to find out the concentrations of metal ions. As it holds metal ions so securely, EDTA4- (in the form of Na4EDTA, Na2CaEDTA or Ca2EDTA) is added to salad dressings. The traces of metal ions catalyze oxidation reactions which lead to spoilage, however whenever EDTA4- is added, it binds to the metal ions so efficiently that they can't act as catalysts for the undesirable oxidation reactions. Most of the metal ions are efficiently complexed (or sequestered) via EDTA4- or H2EDTA2-, comprising the main-group ions like Mg2+, Ca2+ and Ba2+

This is not only the formation of chelate rings that affects the stability of complexes, however as well ring size is significant. Studies have illustrated that chelate rings having five or six members are usually more stable than those of the other sizes. For illustration, whenever the series of ligands having the formula H2N(CH2)nNH2 (here n   = 2, 3 or 4) forms complexes by the similar metal ion, the most stable complex is with ethylenediamine (n = 2) that results in a 5-membered chelate ring. Whenever n = 3 that corresponds to 1, 3-diaminopropane, the complexes made up have 6-membered rings and are less stable as compare to those of en. The complexes with the ligand having n = 4 (1,4-diaminobutane) are even less stable. The similar situation exists for complexes of the anions of dicarboxylic acids, -OOC-(CH2)n-COO- (here n = 0, 1, ...).

1991_Complexes of the anions of dicarboxylic acids.jpg

Fig: Complexes of the anions of dicarboxylic acids

Kinetics and mechanisms of complexes:

The kinetics of complex reaction is the speed at which transformations leading to attainment of equilibrium will take place. Most often, complexes experience reaction in which the composition of their coordination sphere changes via substitution of one ligand by the other. The method through which this substitution takes place in complex reactions is termed to as liability. Complex that experience liability very fast stated to be labile whereas others that experience similar reaction at slow rate are known as inert. It is significant to note that a complex can be inert and yet be thermodynamically not stable. Typical illustration is [Co(NH3)6]3+ that will persists for days in acid medium however yet unstable thermodynamically. On the other hand,[Fe(H2O)5F]2+ is labile and yet thermodynamically stable. The complexes of d3, low spin d4, d5 and d6 and also d8 square planar are chemically inert. The complexes of d1, d2 high spin d4, d5 and d6 and also d7, d9 and d10 are labile.

Kinetic Study:

Kinetic study can be taken out with various forms of methods based on the rate of the reaction to be studied. Experimental methods have been building up to monitor reactions over time scales differing from as low as 10-15s to hours or days. As it is relatively simple to monitor the kinetics of a slow reaction taking place in few minutes or hours, highly specialized methods are needed in order to study the fast reactions.

Usually, kinetics study comprises methods necessarily comprises of mixing the reactants and initiating reaction on a time scale that is negligible relative to that of the reaction and then monitoring the concentration(s) of one or more reactants and/or products as the function of time. As rate constants differ with temperature, it is as well significant to find out and control precisely the temperature at which the reaction takes place. The methods usually employed to study reaction kinetics can be grouped into:

1) Static methods (for reaction with half-life more than one minute)

2) Flow or rapid mixing methods (1 min.≥ half-life ≥ 10-3sec.)

3) Relaxation methods (if half-life is less than 10-1 sec.)

Static methods of Kinetic study:

The static methods are employed for studying the inert reactions that take place over minutes to hours. The reaction is generally initiated simply by mixing the reactants altogether by hand or by a magnetic stirrer or other mechanical device and the growth of the reaction can be monitored over a time frame via observing a change in physical or chemical properties of one of the reactants or product. pH change, colour change, gas evolution, isotopic exchange can be the change being noticed. 

Flow or rapid mixing techniques of kinetic study:

Flow methods are employed to study the reactions taking place on timescales of seconds to milliseconds. In the simplest flow technique reactants are mixed at one end of a flow-tube, and the composition of the reaction mixture is monitored at one or more positions further all along the tube. Whenever the flow velocity all along the tube is known, then measurements at various positions give information on concentrations at dissimilar times after initiation of reaction. The progress of the reaction can be monitored by employing the physical and chemical changes illustrated static methods.

Continuous flow methods encompass the drawbacks that comparatively large quantities of reactants are required, and very high flow velocities are needed in order to study the fast reactions. Such problems might be avoided by employing a stopped flow method. In this process, a fixed volume of reactants are rapidly flowed to a reaction chamber and mixed via the action of a syringe fitted by an end stop. The composition of the reaction mixture is then monitored spectroscopically as the function of time after mixing at a fixed position in the reaction chamber.

Relaxation methods of kinetic study:

Such methods comprise producing a disturbance or perturbation on a state of equilibrium over a short time range. The disturbance might be temperature or pressure jump. The relaxation of the perturbated system is monitored to a new state of equilibrium via spectrophotometric and fast electronic devices. Radiofrequency and ultrasonic waves can as well be employed to induce the disturbance and the relaxation can be monitored by Nuclear Magnetic Resonance (NMR).

Methods used for monitoring concentrations:

For slow reactions, the composition of reaction mixture can be found out whereas the reaction is in progress either via withdrawing a small sample or through monitoring the bulk. This is termed as a real time analysis. The other option is to make use of the quenching process, in which reaction is stopped a certain time after initiation in such a way that the composition might be analyzed at leisure. Quenching might be accomplished in a number of manners like sudden cooling, adding a large quantity of solvent, rapid neutralization of an acid reagent, elimination of a catalyst or addition of a quencher. The key necessity is that the reaction should be slow enough (or the quenching process fast enough) for little reaction to take place throughout the quenching procedure itself. Often, the real time and quenching methods are combined via withdrawing and quenching small samples of the reaction mixture at a series of times throughout the reaction.

The composition of the reaction mixture might be followed in any one of a variety of dissimilar manners by tracking any chemical or physical change that takes place as the reaction carries on example:

A) For the reactions in which at least one reactant or product is a gas, the progress of reaction might be followed via monitoring the pressure or perhaps the volume change.

B) For the reactions involving ions, conductivity or pH measurements might often be used.

C) If the reaction is slow adequate, the reaction mixture might be titrated.

D) Whenever one of the components is colored then Colorimetry might be suitable.

E) Absorption or emission spectroscopy is common (that is, more on these later).

F) For reactions comprising chiral compounds, polarimetry (that is, measurement of optical activity) might be helpful.

G) Other methods comprise mass spectrometry, gas chromatography, NMR/ESR and lots of more.

Reaction mechanism in complexes:

Reaction mechanism is basically the pathway leading to the manufacture of the product or attainment of equilibrium in a particular reaction. There are two severe cases in reaction mechanisms of complexes; SN1 (substitution Nucleophilic Unimolecular reaction) and SN2 (substitution Nucleophilic bimolecular reaction).

In SN1 mechanism, just one species takes place at the transition state. In such a reaction, the departing ligand will leave prior to the attachment of the incoming ligand, leading to the reduction in coordination number at the transition state. An example is illustrated below, where X symbolizes the leaving group and Y the entering group.

1112_Reaction mechanism in complexes.jpg

Fig: Reaction mechanism in complexes

The first phase is the rate determining step as it is slow. The expression for the rate law can be represented as R = k {[L5MX]n+}  in which 'k' is the rate constant and not equilibrium constant. In SN2 mechanism, the two species appear at the transition state. The incoming ligand gets attached prior to the departure of the leaving group leading to the increase in coordination number at the transition state. The rate of the reaction is based on the concentrations of both the reacting complex and the incoming ligand. The expression for rate law can be represented as R = k {[L5MX]n+}[Y-]

2161_Expression for rate law.jpg

Fig: Expression for rate law

Most frequently, complex reactions don't really fall to such two (SN1 and SN2) extremes as the transition states in most of the cases are very hard to recognize (or might not be detected). Though, mechanisms of reactions in complexes are between such extremes. Whenever the contribution of the incoming group to the transition state is small the reaction mechanism can be approximated to be SN1 however if the contribution is important, the reaction is approximated to SN2. 

Factors which affect the rate of complex reactions are solvent intervention, ion-pair formation and the conjugate-base formation.

Solvent Intervention:

As most of the reactions of complexes are studied in aqueous system where water can acts as the ligand and rich in extremely high concentration, a possible reaction path is illustrated below here X and Y are the neutral ligands.

[L5MX] + H2O → [L5MOH2] + X   slow

[L5MOH2] + Y → [L5MY] + H2O   fast

As the concentration of water is constant, the reaction can be taken as SN1

Ion-Pair formation:

In a reaction comprising positively charged complex and negatively charge ligand, the two reactants will be attracted altogether via their electric charges. The greater the charges, the greater the attractive force among the reactant. This will lead to the equilibrium.

[L5MX]n+ + Ym- ↔ {[L5MX]Y}n-m 

K = [{[L5MX]Y}n-m]/{[L5MX]n+}[Ym-]

{[L5MX]Y}n-m = K {[L5MX]n+}[Ym-]

Whenever the reaction carries on with speed by formation of the ion pair, the rate of reaction can be deduced as R= k K{[L5MX]n+}[Ym-] =k" {[L5MX]n+}[Ym-], here k" as both kinetic and thermodynamic contributions. This reaction can be taken as SN2 after further investigation on the transition state composition.

Conjugate base formation:

There are mainly two possibilities having a pH dependent reaction, these possibilities are described below:

The rate law might comprise [OH-] in such a way that the hydroxyl group attacks the metal complex leading to SN2 reaction.

The [OH-] might be comprise interaction in such a manner that it reacts fast to eliminate a proton from a protonated ligand in the reacting metal complex making a conjugate base (CB) that then reacts slowly to replace the leaving group.

[Co(NH)5X]2+ +  OH- → [Co(NH3)4(NH2)X]+ + H2O

[Co(NH3)4(NH2)X]+ + Y- → [Co(NH)5Y]2+

In the presence of protonic hydrogen (ionisable), this proposed reaction pathway is favorable and the rate law follows SN1 (CB), this means that the reaction is based on the concentration of the reacting complex in the presence of OH-.

In the absence of protonic hydrogen or if the elimination of proton in the above reaction is slow, the SN2 is most appropriate reaction mechanism.

R = {[Co(NH3)5X]2+}[OH-]

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