 After we are familiar with the chemistry of the early actinides like uranium, neptronium, plutonium and amuricium. So, it is required now to have some discussion on the complexation of actinides which is very important in the nuclear fuel cycle applications. First, actinides form complexes with the ligands through electrostatic interactions like ion, ion as well as ion dipole interactions. At some cases covalency is playing also a role but to a very minor extent. This covalency becomes somewhat important in case of the earlier actinides and it is not that much important when we go for the heavy actinides. Now, coming to the actinide ions complexation, mostly we know these actinides are hard acids because of their high charge and they show preference for hard bases like the oxygen or fluorine type of donor atoms over the soft bases such as nitrogen, sulfur or phosphorus donor atoms. Again, due to the experimental participation, the affinity for soft donors is more in case of the actinides than that of the lanthanides and this has been the basis of the separation of trivalent actinides from the trivalent lanthanides which will be discussed in subsequent lecture. The complexation of actinides involves the replacement of water molecules from the inner coordination sphere as we know the actinides having very high charge that is either plus 3 plus 4 or in some cases in plus 5 and plus 6 charge. So, there is a tendency of strong hydration of these actinide ions as we know from the ionic species of the actinides the plus 5 and plus 6 ions they are undergoing hydrolysis to give the actinide ions. So, mainly when we are talking about the hydration of actinide ions we refer to the plus 3 and plus 4 oxidation rates of actinides. Then for the ions of the same charge the stability increases with the ratio of the effective charge to reduce that is the ionic potential that is the heavier actinides will have a stronger complexation than the lighter actinides. Now, when we are having different ionic species of the actinides that is the plus 3 plus 4 plus 5 and plus 6 oxidation states with ionic species of actinide 3 plus actinide 4 plus actinide O 2 plus or actinide O 2 2 plus respectively then the relative stability of these ions will be M 4 plus greater than that of M O 2 2 plus greater than that of M 3 plus which in turn is greater than that of M O 2 plus that is the actinide 5 ion. Relative order of the complexation for the ligands is given as below that is chloride ion forms a very very strong complex compared to nitrate which in turn forms a stronger complex compared to chloride which in terms forms a stronger complex compared to the perchlorate ion. So, these are the singlish charged anions and for the doubly charged anions like carbonate, oxalate and sulfate the order of complexation is carbonate forms a stronger complex than the oxalate which in turn forms a stronger complex than sulfate and these are for the inorganic ions I am discussing and for the organic ions again there will be a separate trend which I will be discussing in the subsequent part of the lecture. Now, before we go to the complex formation of the actinides let us discuss about the stability of the actinides of the how the stability constants are determined. What we are interested in is about the basic knowledge of determination of the stability constants. Now as we know because of the strong positive charge and the actinide ions they can form several complexes in the aqueous medium. Suppose we take M as the actinide ion it reacts with the ligand L to give the complex M L and this equilibrium reaction that is M plus L giving M L is given defined by a stability constant which is k1 which is defined as k1 equal to the concentration of M L which is the complex form divided by the product the concentrations of the metal ion as well as that of the ligand which is given in the denominator. Now if we are forming another complex with this particular complex that is M L is reacting with another ligand L in that case the complex form is M L2 and for this the equilibrium constant it is termed as k2 which is given as M L2 concentration divided by the product of the concentration of M L and the ligand concentration. So this is how the k1 and k2 are defined and similarly we can have for the nth complex of the metal ion the complex formation constant as kn. These complex formation constants are termed as the stepwise stability constants or the stepwise formation constants because here the complex session is taking place one step at a time that means first you have M L complex then you have M L2 complex then you have M L3 complex so and so on. Now if the complex formation is taking place where the metal ion is reacting with two ligands at the same time giving the complex M L2 then this is called the overall complex formation constants or it is defined as beta 2 in this case. You can appreciate here that the beta 1 is nothing but the same as the k1 where we have the same equilibrium but for the beta 2 is different than that of the k2 because in this case we are considering the complex formation the metal ion reacting at one stage or at one time with the two molecules of the ligand forming the complex M L2. So in that case the overall complex formation constant beta 2 is given by M L2 concentration divided by the concentration of M multiplied by the concentration of L raised to the power 2. So this beta 2 is defined like this and similar way beta 3 up to beta n can be defined. Now the beta 2 is nothing but the product of k1 and k2 as you can see here if you multiply k1 and k2 you get the beta 2 and similarly beta 3 is the product of k1 into k2 into k3 and in case of stepwise stability constants always we have the k1 larger than that of the k2 which in turn larger than that of the k3 and so on so forth. That is because of the reason that once the one complex is formed that is you form a complex M L the charge on the metal ion is partially neutralized by the ligand and what the second ligand sees is relatively lower charge than that of the first ligand has seen and also there is a statistical factor because for the first ligand all the coordinating sites are available on the other hand for the second ligand all the coordination sites minus one is available for complex correlation. So in view of this the k2 is smaller than that of k1 and same way k3 is smaller than that of k2 and so on so forth. Now on the other hand for the overall complex formation constants the beta n which is the complex formation constant of the nth complex which is greater than that of the complex formation constant for the n minus 1 complex that is M L n minus 1 defined as beta n minus 1 and same way if you come to the fourth overall complex formation constant beta 4 is greater than beta 3 which is in term greater than beta 2 and this is greater than beta 1. So this is how the complex formation constants are defined. Now what are the methods to determine the stability constants or the complex formation constants there are general methods are there now one is called the potentiometric method which is also known as the Wehrm's method where you find out the average ligand number and as already mentioned here for the first stepwise formation constant that is the k1 value we have this equilibrium reaction given here and also there is a competing reaction with the ligand where the ligand also interacts with the proton which is there in the aqueous phase and this is called the proton association constants defined as the k a value of the ligand and the k is given as the concentration of h l plus divided by the product of the ligand concentration and hydrogen ion concentration as you know that ligand is a base so there is always a competition between the hydrogen ion and the metal ion to bind with the ligand now by potentiometric tradition the concentration of the metal ion the ligand and the ml species can be determined from which the complex formation constant in this case the k1 can be obtained similar way the complexation constants for the other complexes that is ml2 ml3 up to mln also can be obtained but for that we also need some software which will be doing the computation of the complex formation constants another method which is used for the complex formation very generally used is the spectrophotometry where we take the metal ion and mix with the ligand and here in this case this metal ligand complex should be forming a color complex and that is how when we measure the observance versus the lambda value we get some absorption spectra like this and by varying the ligand concentration keeping the metal ion concentration and constant or the vice versa we can find out different observance values and from which we can find out the complex formation constants now which are the factors which affect the stability constants the nature of the metal ion that is whether the metal ion is a soft metal ion or a hard metal ion so that matters a lot ionic size as I mentioned for similar charge of the metal ion the ionic size can be different because of the actinide contraction in our case particularly ionic charge the actinides can have different charge like plus 2 plus 3 plus 4 plus 5 and plus 6 then ionic species type what type of ionic species whether you have m o 2 plus m o 2 2 plus or the corresponding cations like m 5 plus or m 6 plus so that also matters a lot and that decides also on the stability of the complexes nature of the coordinating atom of the ligand that is whether you have a oxygen atom or a nitrogen atom or a sulfur atom or a halogen atom like fluoride fluoride etc this also decides the complex formation basically of the coordinating atom that is the electron donating power in a ligand then charge of on the ligand that is whether we have a singly charge like in fluoride or a double charged ligand like carbonate that also matters a lot so naturally carbonate forms a stronger complex because of 2 minus charge as compared to the fluoride which has the single minus charge and also the chelate effect that is whether the ligand is monodentate or bidentate for example we have this ligands like amine coordinating site is the nitrogen and also we have ethylene diamine this is ethylene diamine and this case also the coordinating site is the nitrogen atoms but this is this can form a chelate complex this ethylene diamine so if I have a metal here so this can bind like this and this is a chelate complex and similarly if I have amine complex of the metal so this is how these two nitrogens are coordinated with two amines and for the ethylene diamine also I have two nitrogen atoms coordinating but the chelate formation in case of the ethylene diamine gives a stronger complex as compared to the two amine complexes shown here next is the ring size and the number of rings here we have got a five membered ring for ethylene diamine some cases we may have a four membered ring some cases we may have a six membered ring so the stability of the complex again depends on the ring size of the chelates then there is something called a macrocyclic effect so we have this crown ethyl type ligands so for example I take this 12 crown 4 if this forms a complex with a metal ion say lithium plus so in this case it is stabilized because of the macrocyclic effect and lithium forms a very strong complex with a 12 crown 4 there are also steric factors if the ligand is having some functional groups which are binding and also some side chains which are affecting the stereochemistry or the approach of the binding donor atom in that case there are steric factors which are affecting the complex formation constants so that is how the complex formation constants can be lower in such cases where the steric factors are hindering the complexation now the affinity of the sulfur in the aqueous solution is almost not there or we can say there is no affinity for sulfur that is why we do not study many of these sulfur donor ligands in the aqueous solution there is moderate affinity for the nitrogen donor ligands and generally the complexation reactions are endothermic as the stability is due to the large gain in the entropy that is the water release as we have already mentioned before these actinides are having relatively high charge and they are strongly hydrated so when the complex is formed in that case the ligands are to replace the water molecules in the inner coordination sphere and that is leading to very strong entropy gain because the water molecules are released then soft metal ions prefer heavier donors and here the stability is from the enthalpy term heavier donor means compared to oxygen and sulfur naturally sulfur will have a difference for the soft metal and compared to oxygen hard actinide ions which are strongly hydrated prefer hard anions like fluoride now coming to the inorganic ligands like halides some of the most prominent complexes of actinides are the hydrates or hydroxides this is very important in view of the very hydration energies of the actinide ions which are in the plus three or plus four oxidation states and the hydroxide complexation is reflected in the hydrolysis constants this will be discussed in a separate chapter so I will not go into very deep into this now coming to the halides the fluoride ion is readily replaces the water but not the higher highlights like the chlorides or bromides so the highlights are monatomic anions and form complexes without any steric constraint now here this table which is given below it gives a complexion of highlights such as fluoride chloride and bromides the first column gives the metal ions the second column the ionic strength the third fourth and fifth and sixth column gives the log k1 k2 k3 and k4 values for fluoride the last but one column is for the chloride ion complex formation and the last column is about the bromide complex formation now we'll just see how this complex formation constants with fluoride chloride and bromide is there for the actinide ions first let us take the trivalent actinide ions that is americium 3 plus and curium 3 plus for a simplicity we have taken data for a particular ionic strength which is constant that is 0.5 molar ion strength and you see the log k values there is no clear trend here though we expect that the curium 3 plus should have higher stability constant as compared to americium 3 plus so it is not the case on the other hand the log k2 value for curium is higher than that of the americium 3 plus same also is the trend for the log k3 so overall we can say that the complex formation constants of americium and curium in the trivalent oxidation state are nearly comparable now we come to the tetravalent oxidation state that is thorium 4 plus iranium 4 plus and neptinium 4 plus for comparison purpose we have taken the ionic strength constant for them as 4 molar and you can see here that the thorium value is 8.12 for the log k1 which increases significantly for iranium that is 8.98 but for neptinium 4 plus it decreases so the increase of the log k1 value for from thorium 4 plus to iranium 4 plus is understandable because of the higher ionic potential but for the neptinium 4 plus there is a strong decrease we find and this is not explainable this all because of trace complexation behavior of the neptinium ion expectedly neptinium should have a higher complex formation constant than that of iranium 4 plus but we will see in the subsequent lectures that neptinium 4 plus behaves somewhat different manner compared to the other actinide ions and the same also for the neptinium 6 when you have NPO 22 plus come here for the next three ions with a plus 6 oxidation states at one molar the ionic strength we find that the iranilion complex function constant that the log k1 value is 4.54 which should have increased for neptinium ion neptinium 6 but the value has decreased to 3.86 which on the other hand has increased significantly for the plutonilion that is PO 22 plus to 5.06 same as the train for the log k2 values and also for the log k3 values for which the neptinium 6 data is not there but you can see that the iranium complex formation constant is significantly lower than that of the plutonilion complex formation constant which is explainable from the ionic potential now coming to the chloride ion complexion compared to the fluoride ion you find that the complex formation constants are significantly lower find that for the trivalent as well as the tetravalent ions and also the hexavalent ions you find that the complex formation constants are significantly lower compared to what is seen for the fluoride ion and with bromide ion again you find even lower complex formation constants only the log k1 values are given for the fluoride and bromide ion. Now we come to the other inorganic ligands like sulfate and nitrate. So the sulfate ions they form much stronger complexes as compared to the nitrate that is obvious because sulfate is having 2 minus charge as compared to the nitrate ion which is having a single charge. And also there are the number of donor atoms which are participating in case of the sulfate. Many times it is 2 compared to the nitrate. There are of course examples where the nitrate ion also acts as a bidentate ligand like you have this 3 oxygens attached to the nitrogen in case of the nitrate and sometimes this O minus is coordinating to the metal ion. Some cases you have even the metal ion is binding to 2 oxygens of the nitrate. So this type of scenario also is there. So you have both monodentate as well as bidentate complexes in case of the nitrate but the sulfate because of the 2 minus charge it forms many cases bidentate complexes. Now in case of nitrate sulfate the coordination is through the oxygen atoms and they have very high affinity for the actinide ions but compared to the nitrate ion sulfate has a greater affinity and here the log k1 and log k2 values for the sulfate ion is given for the actinide ions and the last column is about the nitrate ion. You can see that this nitrate ion complex formation constants are definitely much lower than that of the sulfate ion for americium 3 plus and curium 3 plus ion. You find again curium 3 plus is having lower complex formation constant for the log k1 value when the ionic strength is 2 molar but for 0.5 molar ionic strength the complex formation constants are more or less same that is 1.85 and 1.86 and the log k2 values for curium 3 plus is larger compared to that of americium 3 plus. On the other hand log k2 value for the curium 3 plus is lower as compared to that of americium 3 plus for the sulfate ion. So this is really intriguing the complex formation constants of americium and curium are more or less comparable we can say in many cases. Now coming to the tetravalent actinide ions thorium 4 plus, uranium 4 plus and leptinium 4 plus and plutonium 4 plus all cases the ionic strength has been kept as 2 molar and we see here in this case from thorium 4 plus to uranium 4 plus the log k1 values are increasing from 3.30 to 3.65 which decreases in case of the neptunium 4 plus as we have seen in case of the fluoride and the same observation was also seen for the plutonium 4 plus that the log k1 values increases as compared to that of uranium as well as neptunium. So the plutonium 4 plus complex formation constant is higher can be explained on the basis of its very high ionic potential but the neptunium 4 plus log k1 value is in between that of uranium 4 plus and plutonium 4 plus and this is some sort of an anomaly. Same is the train we can see for the log k2 values but the neptunium 4 plus complex formation constant is in between that of uranium 4 plus and plutonium 4 plus. Now coming to the hexavalent ions the uranil ion first complex formation constant which the sulphate ion is comparable to that of the neptunil ion on the other hand the second complex formation constant that is the log k2 value is significantly lower as compared to that has been reported for the uranil ion. The complex formation constants with the uranil ion with the nitrate is very very low compared to what we have seen for the sulphate ion and also it is lower than that of the halides like fluoride but it is comparable to that of the bromide ion for the log k1 values.