Draw a crystal field energy-level diagram, and predict the number of unpaired electrons for each of the following: 

(a) [Mn(H2O)6]2+

Video transcript

All right. Hi everyone. So for this question, let's give the corresponding crystal field energy level diagram or FEC 63 positive and determine the number of unpaired electrons. Now recall that the crystal field theory is a theory that explains or attempts to explain the bonding scene in complexes by explaining its electrostatic interactions. In particular, the theory especially focuses on Liggins and the charges that they carry as well as the energies of D orbitals of the central metal aisle. So because of this importance placed on the energies of D orbitals, right, our first step is to find the number of D electrons on the charged metal center, which in this case is iron, right? So the first order of business is to calculate the oxidation state of iron in this complex. Now recall that the oxidation number of the metal when added to the oxidation numbers of all ligands must equal the overall charge of the complex, right. So if the oxidation state of iron is a variable X, then X added to the oxidation number of our carbonel ligand multiplied by their quantity should equal positive three, which is the overall charge of the ion and therefore the overall oxidation number now because the carbona ligand happens to be neutral, the oxidation number is going to be zero. So X here added to zero should equal positive three, which means that X which is the oxidation number of iron is equal to positive three, right? So with this in mind, we can go ahead and find the electronic configuration of iron with an oxidation state of positive three. So first we can go ahead and start with the electronic configuration of neutral iron. Recall that when an element is neutral, when an atom is neutral, the number of electrons is equal to the number of protons and the number of protons is indicated by the atomic number. So if iron having an atomic number of 26 or if iron has an atomic number of 26 then it is going to have 26 electrons when it is neutron. So based off the periodic table, the electronic configuration of neutral iron is argon four s two 3d 6. So in this case, to find the electronic configuration of iron with an oxidation state of three, therefore, a charge of positive three right three electrons must be removed from the highest energy orbitals. In this case, two electrons are going to be removed from the four s orbital, followed by one more from the 3d orbital, giving us an electronic configuration of argon 3d 5. This means that there are five D electrons that we have to distribute in the energy level diagram. Now, the energy level diagram depends on what type of complex it actually is, right. So recall that iron here is bonded to six Carboni ligands, all of which are Monod, meaning that each ligand attaches itself to the iron center via one donor atom. So because they all contribute a co-ordination number of one, the co-ordination number is equal to one multiplied by six which equals six. So a co ordination number of six indicates that this is going to be an octahedral complex. So at this point, we go ahead and we draw the diagram for an octahedral complex and then proceed to add our five D electrons. Now recall that for an octahedral complex, there are two higher energy D orbitals, namely DZ squared and DX squared subtracted by Y squared. And there are three lower energy orbitals namely DXY DXZ NDYZ. Now, in this case for the record, right, the carbona ligands are strong field and low spin, which means that there's going to be a relatively large splitting energy. And when it comes to distributing electrons recall that lower energy orbitals have to be filled before proceeding on to the higher energy one. And also if there are multiple energy levels or multiple orbitals of the same energy level, they all have to have one unpaired electron before they are subsequently paired. So because I happen to have three lower energy D orbitals, I'm first going to go ahead and place one unpaired electron in each of them. And then because I have five in total, right, the remaining two electrons remain in the lower energy orbitals, but I'm going to go ahead impair them. So this is my energy level diagram and we can see here that there is going to be one unpaired electron as evidenced by the unpaired electron in the orbital dyz. And there you have it right. So here is the energy level diagram for the octahedral complex. And based on the fact that it had five D electrons, it therefore had one unpaired electron. So with that being said, thank you so very much for watching and I hope you found this helpful.