Inorganic Chemistry Tutorial Work Hilary Week 5
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Inorganic Chemistry Tutorial Work – Hilary Week 5
1. Explain the classification of acids and bases as Class a (hard) or Class b (soft) and account for the observations that hard-hard and soft-soft interactions are so dominant in the compounds formed.
Experimental observations show very clearly that different acids and bases have varying affinities for one-another. We can quantify this by looking at a simple acid-base equilibrium:
A + :B ⇄ A-B Consider K = Kf = Formation constant = [AB] / [A] . [B] or consider Hf
Clearly, the more strongly bound a particular adduct (A-B), the higher Kf and the more exothermic Hf will be.
Let us look at a few values of Hf for the adducts (M Hal2):
-1 - - - - Hf,gas / kJmol F Cl Br I Be2+ -796.006 -360.2424 -229.2832 -64.0152 Ca2+ -784.5 -471.5368 -384.9284 -258.1532 Hg2+ -293.6545 -146.294 -85.45402 -16.12903
We can see that the behaviour of the cations is markedly different as we vary the corresponding anion. There are, broadly 2+ 2+ speaking two different sorts of behaviour. BeGraph and ofCa H aref,gas representativefor different adducts of the first type of behaviour, which we shall term “Class A”, while Hg2+ is representative of the second type of behaviour, which we shall term “Class B”. Anion - Clearly,-900 both class A and class B (Lewis) acids prefer to form an adduct with F in the gas phase, but while for the Class A acids this is very marked, it is much less pronounced for Class B acids. This means, that once we switch to a solvated environment, because of the loss of F-’s hydration energy on forming the adduct, the order of preference for ligands is reversed -800 to I- > Br- > Cl- > F- for Class B acids. More generally, this can be extended (as Pearson does) to call Class A “Hard acids” and Class B “Soft acids”. We can also label the anions as “Hard bases” (F-) and “Soft bases” (I-). Although the division is empirical and not-700 clear-cut, this is certainly broadly useful. What we observe is that hard acid – hard base and soft acid – soft base adducts are formed preferentially to the mixed hard – soft combinations. -600 1 - l o -500 m Be2+ J k
/ Ca2+
s a g
, Hg2+
f -400 H
-300
-200
-100
0 F- Cl- Br- I- Some examples:
Hard acids: H+, Group I and II metal ions, Al3+, Fe3+, Co3+ lanthanides. Early d-block metal ions in high oxidation states, e.g. Ti4+. As we shall see, they have a tendancy to be non-polarisable. Hence, small and highly-charged ions are good examples.
- - 2- 2- Hard bases: F , OH , NH3, CO3 , SO4 . As we shall see, they have a tendency to be non-polarisable. Ions based on the 2p elements are therefore good examples.
Soft acids: Late and heavier d-block elements and heavy p-block metal ions, particularly in low oxidation states. E.g. Cu+, + 2+ 2+ 2+ + 2+ 4+ Ag , Cd , Hg , Hg2 , Tl , Pt , Pt . As we shall see, larger and more-polarisable ions are good examples.
- - - Soft bases: I , CN , RS , PR3, CO. As we shall see, these are again larger and more-polarisable. They have a tendancy to involve elements from the 3p and lower rows.
Looking at these examples, we can see that HAHB interactions are expected to be largely Coulombic, while SASB interactions involve more polarisable less-higly-charged species and will therefore be more covalent in nature.
Obviously, it would be useful to get a more quantitative measure of hardness. This has been attempted by many researchers and a variety of different schemes have been proposed. Two of these can be outlined as follows:
valence Define the Ionic Potential, IP such that : IP radius (nm) I R Define the Misono softness parameter, Y 10 Z Z I Z 1
where R is the ionic radius in nm, Z is the valence, IZ is the ionization potential of the ion with valence Z.
• For Y < 0.25 nm, metal ions form ionic bonds and are hard acids • For Y > 0.32 nm, metal ions form covalent bonds and are soft acids • For 0.25 Based on this Misono parameter, we can classify most common ions, as shown in this table (Stumm and Morgan, 1989): Much other work has been done to relate the HSAB concept to Frontier Orbital theory and generally to Quantum Mechanics. It is now possible to calculate ab-initio values for atomic hardness (which is a measure of hard/soft properties for individual atoms within a molecule). These allow us to plot surfaces for ligands or other species, showing where they will demonstrate hard / soft properties. This information is very useful in determining how things react. Atomic hardness in nitrobenzene. The ring is soft, while the nitro group is hard. Another way of looking at hard/soft properties is to consider equations such as this: (Drago) -HAB=EAEB + CACB where E are electrostatic (ionic) parameters for species A and B and C are covalent parameters for A and B. A stable adduct requires a large value for -HAB – this is equivalent to requiring that the HAHB or SASB matching occurs, because with a hard species, E will be large and C will be small, while with a soft species C will be large and E will be small. Therefore, we favour hard-hard and soft-soft interactions. This explains why such compounds are so dominant. (This effect is enhanced somewhat because in a SASB interaction, the increased polarisability means that the London forces also rise – this allows extra stabilisation of SASB adducts over and above that expected due to covalency.) It should be noted that in competition reactions / equilibria we expect to form the HAHB and SASB components. In this reaction, the driving force is the strong electrostatic bonding contributions in the HAHB adduct. The SASB forms mainly because it is what’s left behind – rather than because it is significantly stable in itself. This demonstrates that we must be careful to say what we are comparing to when we evaluate “stability”! 2. Discuss the basis of the Irving-Williams order, including such influences as effective nuclear charge, ionic radii, ligand field stabilisation, and the Jahn-Teller effect. The diagram below shows the Irving-Williams effect. Essentially this is the observation that for the +2 oxidation states of the first transition series, complexes get more stable as the size of the metal ion decreases, but, it is complicated by other effects arising from crystal / ligand field theory. We also see that as one moves across the d-block from left to right the ions get an increasing affinity for soft donors, while on the left they have the greatest affinity for hard donors. This series may be explained by considering the following factors: 1. Effective nuclear charge. As we move across the d-block from right to left, we are successively adding a proton and an electron at each step. The proton increases the nuclear charge by +1 e. The electron is added to one of the 3d orbitals. The d-orbitals are relatively diffuse and therefore they shield one-another very poorly. Hence, the effective nuclear charge will rise steadily over the d-block. This means that as one moves across we expect the attraction for the electrons in the metal – ligand bonds to increase, making them stronger and increasing the stability constant. This is in accordance with the broadly rising nature of the Irving-Williams plots. 2. Ionic radii. A similar argument reveals the presence of the d-block contraction. This is because as one moves across the d-block, the nuclear charge is rising steadily, but shielding is rising so fast. Also, each additional electron is still being added to the 3d orbitals. The extra effective nuclear charge increases the Coulombic attraction for each electron – which means that 3. Ligand field stabilization. This effect is a little more complicated to explain. First, we must introduce what is meant by a ligand field stabilization and explain how it works in these +2 octahedral complexes. If we look at a diagram of the d orbitals: We see that some of the d-orbitals come nearer to the ligand charges than the others. By examining the character table for the Oh point group, we can see that the dxy, dxz and dyz orbitals belong to the T2g irreducible representation while the dz2 and dx2-y2 belong to the Eg irreducible representation. If we imagine placing our metal ion into a uniform spherical field, of the same net charge as the ligands, we will raise all of the d orbitals in energy because of the increased Coulombic repulsion between the –ve electrons and the –ve field. They will, however, still be degenerate. If we now collapse the spherical field down to point charges at the ligand sites – we get a picture very much like the diagram above. Clearly, the different orbitals will experience different interactions with the ligand fields. We expect the orbitals which point towards the ligands to be most destabilised, while the ones pointing between the ligands will be less destabilised. This introduces a splitting pattern, which is quite familiar. (The orbitals on the LHS of this diagram are the d orbitals in a spherically-symmetric field of the same charge as the ligand field.) The complexes on the Irving-Williams series all have the metal ion in a high spin configuration, so we will add three electrons to the t2g, then two to eg. Next we pair up the electrons in t2g by adding three more, then finally we pair up the electrons in eg by adding two more. Hence we must consider contributions from the exchange energy (which is proportional to the number of pairs electrons having parallel spins) and also from the splitting. We get a sort of double-humped graph for the stabilisation CFSE 0 0 2 4 6 8 10 12 -2 -4 -6 E S F C -8 -10 -12 -14 Number of d electrons energy as we move across the d-block, which is a characteristic of many d-block properties. This is a result of adding together these two factors. This effect helps to explain why the Irving-Williams series does not just increase steadily and why it turns down at the end. However, it doesn’t adequately explain copper’s position. This analysis also has an effect on the ionic radius of the metal ions. As we populate the antibonding (eg) orbitals, we expect the ionic radius to rise a bit. This effect, in combination with the varying nuclear charge, gives ionic radii like this: This may also help to get the series to turn down for Cu Zn. 4. Jahn-Teller effect. As mentioned above, the CFSE argument for the Irving-Williams series fails to position copper correctly. The reason for this is probably simply that copper does not exist as octahedral complexes – which means that the CF analysis does not hold in the form given above. This is because the Jahn-Teller theorem tells us that copper ions are stabilised by allowing a tetragonal distortion. This amounts to stretching two opposite metal-ligand bonds in the copper. The extreme version of this distortion is the square planar geometry. With this tetragonally-distorted geometry, we get different splitting patterns – so copper is anomalously stable in the series. Hence, we get a steady rise – with copper complexes being stabilised and then falling to zinc. It is also worth noting that as we move across the d-block, we get an increasing number of electrons. This tends to make the polarisability of the atoms rise – increasing the contributions of covalent and London forces to their bonding. Hence, as we go across the d-block and the series, we get an increasing affinity for soft ligands. 3. Explain, in detail, the principles of the chelate effect and macrocyclic effect, discussing such factors as entropy, enthalpy, ring strain, and interesting or unusual applications. The term chelate was first applied in 1920 by Sir Gilbert T. Morgan and H.D.K. Drew [J. Chem. Soc., 1920, 117, 1456], who stated: "The adjective chelate, derived from the great claw or chela of the lobster or other crustaceans, is suggested for the caliperlike groups which function as two associating units and fasten to the central atom so as to produce heterocyclic rings." The chelate effect is another interesting empirical observation from the chemistry of metal complexes. There is an extra stability associated with forming chelates compared to forming the most similar complex, but with unidentate ligands. For exmaple, consider the following equilibria: 2+ 2+ Ni (aq) + 6NH3(aq) ⇄ [Ni(NH3)6] (aq) + 6H2O log =8.61 2+ 2+ Ni (aq) + 3en(aq) ⇄ [Ni(en)3] (aq) + 6H2O log =18.28 The chelated complex (with ethylenediamine) is significantly (nearly 1010 times!) more stable than the equivalent complex with ammonia. Since the bonding with ammonia and ethylenediamine is very similar (they both donate through an amine nitrogen – so we expect a similar field effect – their f-factors differ by only 3%, etc…) we can expect the H terms for these two reactions to be about the same. This means that we must explain the difference in stabilities as being mainly due to the entropy term in this case. If we look at the metathesis reaction which is the “difference” between the two given above: 2+ 2+ [Ni(NH3)6] (aq) + 3en(aq) ⇄ [Ni(en)3] (aq) + 6NH3(aq) log =9.67 H = -12.1 kJmol-1 -TS0=-55.1kJmol-1 The enthalpy change is very close to the –11.5kJmol-1 estimated for the change in CFSE of Ni2+ from spectroscopic data, so presumably it can be explained that way. The entropy term dominates here. Consider the following data for cadmium ions. Reaction of ammonia and 1,2-diaminoethane with Cd2+. # of ligands G / kJmol-1 H / kJmol-1 S / JK-1mol-1 log b 2 NH3 (1 en) -28.24 (-33.30) -29.79 (-29.41) -5.19 (+13.05) 4.95 (5.84) 4 NH3 (2 en) -42.51 (-60.67) -53.14 (-56.48) -35.50 (+13.75) 7.44 (10.62) In this case, we can see that there is almost no difference in the H terms, so that in this case, the chelate effect is caused entirely by the entropy term. A further example may be given where the entropy effect outweighs an unfavourable enthalpy. Consider: 2+ 2+ [Ni (en)2 (H2O)2] (aq) + tren(aq) ⇄ [Ni (tren) (H2O)2] (aq) + 2 en(aq) log =1.88 tren = N(CH2CH2NH2)3 In this case, H0=+13.0kJmol-1 and –TS0=-23.7kJmol-1. The positive enthalpy term can be explained as a result of the increased steric strain with tren because there are three fused chelate rings, as well as being a result of the weaker M-N bonds in tren because it is a tertiary amine rather than a secondary amine. However, the entropy effect of having three chelate rings vs two is enough to outweigh the enthalpy effect – so that the formation of the tren complex is favourable. Probably the main cause of this significant entropy term in each case is the increase in the number of molecules on the right of each equation. For example, in the first metathesis, we go from four molecules on the left to seven on the right. Similarly in the equation above, we go from two molecules on the left to three on the right. As entropy is a measure of the disorder of the system – having more separate species means that the entropy increases significantly. Another way of looking at the effect is to consider the stepwise addition of the two co-ordinating sites on the chelating ligand. Initially, we expect the attack by the chelate or by the corresponding unidentate ligand to be equivalent – because from the point of view of the metal ions, they look the same. However, the second addition becomes very different. For the unidentate ligand, there is little difference in the probability of adding a second ligand compared to adding the first. However, with a chelating ligand, one end is already held by the metal. This means that the other end is moving around in the vicinity of the metal’s co-ordination site. Hence, the effective concentration is much greater and it is significantly more likely that the chelate ring will close. This also explains the decreasing magnitude of the chelate effect as the ring size increases. For example: 2+ 2+ [Cu (en)2] (aq) + 2 tn(aq) ⇄ [Cu (tn)2] (aq) + 2 en(aq) log =-2.86 The chelate formed with tn (H2N (CH2)3 NH2) is less favoured than the equivalent one formed with ethylenediamine. Of course, as the ring gets large (seven-membered or more), it is more likely that the ligand will act as a bridge – bonding to two different metal ions at its different sites. Although “the chelate effect” normally refers to these entropy effects, there are additional secondary effects that tend to favour the stabilisation of complexes by certain ligands. As an example, we consider two “phosphene” chelates of the type (R2P)HC=CH(PR2) and the saturated diphosphine analogue R2PCH2-CH2PR2. King reports that the latter, although they can form chelate rings, often act as bridging ligands to form binuclear complexes e.g. L5Mo R2PCH2-CH2PR2 MoL5. In contrast the unsaturated analogues form cheltes of the type (OC)2Mo(R2PCH=CHPR2)2. Two effects are important here. First, the phosphene ligands are sterically restricted from effective bridging, while the more flexible saturated analogues can do so easily. Second, there is an entropy advantage for the unsaturated analogue to form a chelate ring, because it already has restricted rotations within the molecule – so it doesn’t lose so many degrees of freedom upon the formation of a chelate ring. Another interesting class of ligands are derivatives of acetylacetone, which acts as a ligand through the acidic enol form. We get neutral complexes with trivalent metals such as [Ti(acac)3], [Cr(acac)3], [Co(acac)3]. These complexes contain symmetrical rings, with the two M-O bonds equal in length, the two C-O bonds equal and the two C-C bonds equal. This is a result of aromatic resonance in the six-membered chelate hetero-ring. The resonance gives extra stabilisation to these complexes. Carrying this concept further, we can see that by using cyclic ligands – it is possible to “use up” the rotational degrees of freedom in the chelate ring before we perform the complexation reaction (in an extended version of the phosphene case above). Such chelates are called macrocycles and the entropy term is even more favourable than with non-macrocyclic chelating ligands. Generally, a macrocycle consists of a large planar (or nearly planar) ring encircling the metal atom. A good example is cyclic polyethers (or “crown” ethers) where all the oxygen atoms point inward toward the metal atom. Crown ethers have the unusual property of forming stable complexes with alkali metals. The exceptional stability of these complexes seems to arrive from the close-fitting of the alkali metal ion into the hole in the middle of the ligand. This means that the crown ethers are very selective. For example: crown-4 (i.e. 4 oxygen atoms in the ring) selectively complexes Li+, crown-5 complexes best with Na+ and crown-6 with K+. These complexes have the unusual property of allowing alkali metals to dissolve in organic solvents when they are present. They do this by complexing the alkali metal cation. The resulting complex is soluble as a result of the large hydrophobic groups present on the crown’s ring. For example: + - K + crown-6 [K(crown-6)] + [e(solvent)] This is an example structure of a crown-ether – alkali-metal complex (specifically K(18-crown-6)), produced using Chem3D and an energy-minimised configuration: Similar stabilisation can be used to allow the crystallisation (and therefore characterisation) of Zintl salts by complexing the metal cations. Another use of the macrocyclic effect is to increase the nucleophilicity of fluoride salts. For example, KF in benzene is not very soluble and not very nucleophilic because it tends to exist as ion-pairs. Adding crown-6 ether increases the solubility ten-fold and raises the nucleophilicity of the fluoride ion (by solvating the potassium cation and therefore breaking up the ion-pairing). If a macrocycle is sufficiently large and flexible, it is possible for it to wrap completely around a metal ion – bonding to all the octahedral positions. This completely seals up the metal in a “cage” of ligand. Such a complex is called a clathro-chelate or a cryptate. Ligands which form these types of complex are highly selective and give very stable complexes (there is very favourable entropy and enthalpy). An example of a 222 cryptand. 4. Describe, with examples, how different ligands can control the preferred oxidation states of transition metal ions. The control of preferred oxidation states is a result of a broader result – that it is possible to tune the redox potentials of a transition metal ion by changing the ligands co-ordinated to it. There are two principal mechanisms for this control. These are steric and electronic effects. We shall deal with steric effects first. The basis for steric control is that very often a metal ion in a given oxidation state prefers a particular geometry. A classic example is given by copper compounds. These have a variety of geometries, but they exist largely as tetrahedral cuprous (CuI) or Jahn-Teller distorted octahedral cupric (CuII) compounds. This CuI/CuII redox potential is critically important in biology, chemistry and materials science – so it has been well-investigated. An example of this steric effect was investigated by Williams and James in 1962. They studied the redox potentials for [Cu 2+ / + 2+ / + (phen)2] and [Cu (dmp)2] . N N N N H3C CH3 phen dmp Clearly, we cannot explain this difference based on electronic effects, because both ligands donate through the N lone pairs – which are practically identical in position and environment. When X-ray structure data became available, it was clear that the methyl groups in the cupric dmp complex are in an unfavourable geometry, this stabilises the cuprous state with respect to the oxidised state. For the phen complexes, this interaction is minimised – so that the cupric state is the more stable. Thus, we can control the oxidation state of copper in these complexes by varying the ligand. There are also electronic effects, which arise because different ligands have their and * orbitals at different levels relative to the metal HOMO / LUMO levels in the various oxidation states. Ligands that are good p-acceptors stabilise low oxidation states, because back-donation is more significant, due to a closer energy match of the metal orbital and ligand p* orbitals. For example: 3+ - 2+ 0 [Fe (o-phenanthroline)3] + e ⇄ [Fe (o-phenanthroline)3] E =+1.10V 3+ - 2+ 0 [Fe (bipyridyl)3] + e ⇄ [Fe (bipyridyl)3] E =+0.96V Conversely, ligands which are good s-donors (or maybe p-donors) will have good overlap between the metal orbital and the ligand s or p donor orbital. This stabilises the high oxidation states. EDTA is a good example of this. [Fe EDTA]- + e- ⇄ [Fe EDTA]2- E0=-0.12V A further important example of this comes from cobalt chemistry. 3+ - 2+ 0 [Co (H2O)6] + e ⇄ [Co (H2O)6] E =+1.84V 3+ - 2+ 0 [Co (NH3)6] + e ⇄ [Co (NH3)6] E =-0.10V III 6 6 II In both Co complexes, we have a low spin d t2g configuration, while in both Co complexes, we have a high-spin configuration. Hence the difference is not attributable to the spin states per se. The best explanation is that the energy mismatch is least between the high energy donor orbitals of ammonia and the relatively low acceptor orbitals of CoIII – so that CoIII is stabilised by ammonia. In aqueous solution, in the absence of strongly donating ligands, we have the opposite situation and the overlap is best with the CoII species. Hence CoII is dominant in water, but it can easily be oxidised to CoIII by ammonia or similar ligands – which give a vast array of co-ordinated complexes because of the kinetic stability to ligand substitution shown by CoIII which means that they survive long enough to react and be isolated.