Formation of complexes: thermodynamics

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1 LN08-1 Formation of complexes: thermodynamics Or, How to think about making and using transition metal complexes Its important to always consider, and distinguish between, stability and inertness of complexes. When discussing the stability of a metal complex, it s important to establish: stable (or unstable) with respect to what? e.g. relative to the reagents you used to make it? e.g. relative to possible further reaction products? Decomposition products Combustion products Constituent elements in their native form?

2 LN08-2 Formation of complexes: thermodynamics For example: making a new coordination complex often involves taking a simple metal halide salt (MX n (s)) from a bottle and dissolving it in water before adding ligand(s) One measure of the stability of your aqueous M n+ reagent is relative to the solid precursor: MX n (s) G (or H) M n+ (aq) + nx (aq) ( G lattice or H lattice ) Born Haber cycle M n+ (g) + nx (g) ( G hydration ) Free energy (or enthalpy) of dissolution = G lattice + G hydration

3 LN08-3 Orbital occupation effects Experimental lattice energies for MCl 2 (M = 3d metal); the point for d 0 corresponds to CaCl 2. Data not available for Sc, where the stable oxidation state is 3. Fig 20.35, p.708 Absolute enthalpies of hydration of the M 2 ions of the first row metals; the point for d 0 corresponds to Ca 2. Data are not available for Sc 2, Ti 2 and V 2 (+2 O.S. unstable to oxidation) Fig 20.36, p.708

4 LN08-4 Orbital occupation effects A ligand field stabilization energy (LFSE) is associated with any given Oh complex of d n configuration, based on its t 2g and e g orbital occupancies. By convention, negative LFSE is more stable. e.g. for Oh HS d 4 ion:

5 LN08-5 Orbital occupation effects LFSEs as a function of oct for high-spin Oh and Td systems. Compare these spectroscopic energies with experimental thermodynamic energies on previous slide. Fig 20.34, p.708 These spectroscopic and thermodynamic stabilization energies are not equivalent! But they are related and give similar trends.

6 LN08-6 Stability constants Review: H&S 7.12 Typically discuss the stability of coordination complexes with respect to their formation from aquated metal ions [M(H 2 O) 6 ] n+. e.g. Consider the equilibrium arising from addition of an excess ( 6 equivalents) of ligand L (where L is a neutral donor, like NH 3 ) to an aqueous solution of M n+ e.g. [Fe(H 2 O) 6 ] NH 3 > [Fe(NH 3 ) 6 ] 3+ (aq) + 6H 2 O < The product-favouredness of this equilibrium is described by G = RTln K; The size of the equilibrium constant directly represents the thermodynamic stability of the product relative to the aqueous metal lion and free ligand in water. K = [[Fe(NH 3 ) 6 ] 3+ ] [H 2 O] 6 [[Fe(H 2 O) 6 ] 3+ ] [NH 3 ] 6

7 LN08-7 Review: H&S 7.12 Stepwise stability constants, K x, reported. These correspond to the individual steps in the replacement of coordinated H 2 O by L. e.g. for the first step in the formation of the above hexaammineiron(iii) complex: [Fe(H 2 O) 6 ] 3+ + NH 3 Stability constants > [Fe(H 2 O) 5 (NH 3 )] 3+ (aq) + H 2 O < Similarly, for the substitution of the second H 2 O by NH 3 : [Fe(H 2 O) 5 (NH 3 )] 3+ + NH 3 > [Fe(H 2 O) 4 (NH 3 ) 2 ] 3+ (aq) + H 2 O <

8 LN08-8 Stability constants We can arrive at an overall equilibrium constant ( 2 ) for the substitution of two water ligands by two ammine ligands: [Fe(H 2 O) 6 ] NH 3 > [Fe(H 2 O) 4 (NH 3 ) 2 ] 3+ (aq) + 2H 2 O < 2 = K 1 x K 2 = [[Fe(H 2 O) 5 (NH 3 )] 3+ ] x [[Fe(H 2 O) 4 (NH 3 ) 2 ] 3+ ] [[Fe(H 2 O) 6 ] 3+ ] [NH 3 ] [[Fe(H 2 O) 5 (NH 3 )] 3+ ] [NH 3 ] Important to keep in mind the difference between K x and β x

9 LN08-9 Overall stability constants For the formation of a new complex from [M(H 2 O) 6 ] n+ and ligand L, the overall stability constant is: [[M(H 2 O) 6-x L x ] n+ ] x = = K 1 K 2 K 3 K x [[M(H 2 O) 6 ] n+ ] [L] x e.g. 6 for the substitution of all six H 2 O ligands in [Fe(H 2 O) 6 ] 2+ with CN ligands is: = [[Fe(CN) 6 ] 4 ] = (or log = 35) [[Fe(H 2 O) 6 ] 2+ ] [CN ] 6 This is large! means collective equilibria heavily favour product. Stepwise (K) and overall (b) stability constants are often discussed as their log values. Larger log K n or log n for the formation of a complex indicates that the equilibrium concentration of the complex is larger. Log values are useful because: (i) x and K x can span many, many orders of magnitude; (ii) (ii) the relative stabilities of different complexes only become meaningful when their stability constants different by orders of magnitude.

10 LN08-10 Examples of stability constants M L log K 1 log K 2 log K 3 log K 4 log K 5 log K 6 log Ni 2+ NH Cu 2+ NH Too small to measure [M(H 2 O) 6 ] 2+ + xnh 3 > [M(H 2 O) 6-x (NH 3 ) x ] 2+ (aq) + x2h 2 O Normally see a steady decrease in log K n values as n increases. This is in part due to statistics: NH 3 is more likely to replace one of six water ligands in [Ni(H 2 O) 6 ] 2+ than one of five in [Ni(H 2 O) 5 (NH 3 )] 2+. This dependence is a function of the fact that the equilibria are all interrelated, and in the presence of a large excess of H 2 O.

11 LN08-11 Examples of stability constants M L log K 1 log K 2 log K 3 log K 4 log K 5 log K 6 log Ni 2+ NH Cu 2+ NH Why are log K n values for Ni 2+ and Cu 2+ for substitution of H 2 O by NH 3 different? Cu 2+ is d 9, which is prone to Jahn-Teller distortion ( Z-out ). regular octahedron: All Ni-O bonds 2.07 Å distorted octahedron: Red Ni-O bonds 1.95 Å Blue Ni-O bonds 2.38 Å

12 LN08-12 Examples of stability constants M L log K 1 log K 2 log K 3 log K 4 log K 5 log K 6 log Ag + NH Hg 2+ CN Hg 2+ I Deviations from a steady trend in successive log K n can indicate: (i) abrupt change in coordination number and geometry along the series of complexes (ii) abrupt change in the electronic structure of the metal ion (iii) special steric effects that become important only at certain degrees of coordination E.g. big drop from log K 2 to log K 3 for all 3 examples above. HgX 2 is very stable with CN=2, linear. So is silver. In the case of silver, actually causes an unusual increase for K 2 relative to K 1 The strong preference for low coordination numbers here offsets the usual trend of gradually diminishing K n for octahedral substitution.

13 LN Factors affecting stability of metal complexes G = RTlnK = H T S Enthalpy effects are important in determining the size of stability constants. We instinctively think of this in the context of M-L bond strengths. What are the relative M-L bond strengths? i) Is L a strong sigma donor? ii) Are additional, bond strengthening π-interactions possible/probable? e.g. Hg(CN) 2 (aq) versus Hg(I) 2 (aq): log 2 = vs 23.82

14 LN08-14 HSAB iii) Consider the match of M with L in terms of the Hard/Soft Acid/Base theory. In aqueous solution, hard Lewis acids (metal cations) form more stable complexes with hard Lewis bases (ligands), while soft acids (soft metal cations) preferentially bind soft Lewis bases (ligands) Table 7.9, p.235 Hard vs soft relates to polarizability Hard acids: small monocations with high charge density, or highly charged cations (again with high charge density) Hard bases: donor atoms that are not very polarizable, e.g. F Soft acids: large monocations of low charge density, low or zero-oxidation state metals Soft bases: contain donor atoms that are highly polarizable, eg. I (For bases, consider electronegativity of the donor atoms.)

15 LN08-15 Example: HSAB [M(H 2 O) 6 ] n+ + X- > [M(H 2 O) 5 X]( n-1)+ (aq) + x2h 2 O Log K 1 F- Cl- Br- I- Fe Hg

16 LN08-16 G = RTlnK = H T S Both H and S are at play in the formation of complexes between highly charged cations and anions. [M(H 2 O) 6 ] n+ + yx- > [M(H 2 O) 6-y (X) y ] (n-y)+ (aq) + y2h 2 O Enthalpy: cancellation of (isolated) charges gives a negative change (heat released reaction is favoured). Entropy: the water molecules on M are highly ordered around the charged M n+ and around the X- (via hydrogen-bonding).

17 LN08-17 The chelate effect Complexes of polydentate ligands are more stable than complexes with the corresponding number of comparable monodentate ligands (e.g. similar donor atoms, Lewis basicities). [M(H 2 O) 6 ] 2+ + xnh 3 > [M(H 2 O) 6-x (NH 3 ) x ] 2+ (aq) + x2h 2 O [M(H 2 O) 6 ] 2+ + x en > [M(H 2 O) 6-2x (en) x ] 2+ (aq) + 2x2H 2 O M L log K 1 log K 2 log K 3 log K 4 log K 5 log K 6 log Cu 2+ NH Ni 2+ NH Cu 2+ en Ni 2+ en Compare log K 1 for the addition of en to M 2+ (aq) to log 2 for addition of two NH 3 : for Cu 2+ : NH 3 log β 2 = ( ) = 7.70 en log K 1 = for Ni 2+ NH 3 log β 2 = ( ) = 5.04 en log K 1 = 7.45

18 LN08-18 The chelate effect Consider the equilibrium [Co(NH 3 ) 6 ] en < > [Co(en) 3 ] NH 3 3 = 18.7 G = RTlnK = H T S The chelate effect is an entropically driven phenomenon

19 LN08-19 Chelate effect The chelate effect is amplified for ligands capable of forming multiple chelate rings Ethylenediamine tetraacetate (EDTA) M Log K 1 Ag Ca Cu Ni Fe Fe Co Co V V

20 LN08-20 The macrocyclic effect The there is a distinct difference between chelating ligands and macrocyclic ones macrocyclic effect L 4 ligand cyclam ligand Log K 1 Ni(L 4 ) Ni(cyclam) Consider the following reaction [Ni(L 4 )] 2+ + cyclam > [Ni(cyclam)] 2+ + L 4 <

21 LN08-21 The macrocyclic effect The free ligand L4 does not adopt the orientation shown. floppy ends. The binding of L4 involves a significant loss of entropy (conformational degrees of freedom) This effect counters the entropy increase incurred by the release of NH 3 molecules. The cyclam free macrocycle has fewer degrees of freedom: preorganization diminishes loss of entropy upon complex formation

22 LN08-22 The macrocyclic effect Enthaply can also be important in macrocyclic ligand binding. (and not always favouring the macrocycle- because the macrocycle is already somewhat restricted/constrained, it cannot as easily accommodate the steric/electronic requirements of the metal (and other ligands) G = RTlnK = H T S kj/mol Log K 1 ΔH TΔS

Chapter 25 Transition Metals and Coordination Compounds Part 1

Chapter 25 Transition Metals and Coordination Compounds Part 1 Introduction The transition elements are defined as: those metallic elements that have a partially but incompletely filled d subshell or easily