The amount of paramagnetism for a first-series transition metal complex is related approximately to its spin-only magnetic moment. The spin-only value of the magnetic moment in units of Bohr magnetons (BM) is given by sqrt(n(n + 2)), where n is the number of unpaired electrons. Calculate the spin-only value of the magnetic moment for the 2+ ions of the first-series transition metals (except Sc) in octahedral complexes with (a) weak-field ligands and (b) strong-field ligands. For which electron configurations can the magnetic moment distinguish between high-spin and low-spin electron configurations?

Video transcript

Welcome back, everybody. Let's look at our next problem. The spin only magnetic moment of a transit transition metal complex in bore magneton or BM is calculated as the square root of N multiplied by in parentheses, N plus two, where N is the number of unpaired electrons, it is proportional to the amount of paramagnetism in the metal. What is the spin only magnetic moment of manganese three plus a first series transition metal when it forms an octahedral complex with strong and weak filled light ligands can the magnetic moment distinguish between the electron configurations of MN three plus with a weak field and strong field ligand. And then we have four answer choices that give us different values for the spin only magnetic moment and have us choose whether it can or cannot distinguish between the two electron configurations. So my diagrams here are not all going to fit, I'm going to scroll down past our problems while we figure out what would these electron configurations look like with a weak and strong field ligand, would they look the same or different? And then we will calculate our spin only magnetic moment. So first of all, we have to start with figuring out the electron configuration of our cion. So let's start with elemental manganese. Its atomic number is 25. So the closest noble gas is argon, argon is 18 electrons. So that means 25 minus 18 manganese has seven valence electrodes. So it's electron configuration is argon written in brackets. Then we start filling in it's row four. So we have the four S orbitals. So four S two and then we have five more electrons that would go into the 3d orbitals, 3d 5. So that's neutral elemental manganese, but we have manganese three plus. So we lose three of those electrons. So the electron configuration of our CAV in here is going to be argon and brackets and we first will lose the outer fourth shell s electrons. So those are gone and then that's two and then we lose one of our D electrons. So we have argon and then 3d 4 is our electron configuration that we're dealing with. So let's think about our strong and weak field ligands. So we recall, and I'm gonna scroll down to make room for this diagram that we have the R five D orbitals in the case of a strong field ligand. That means that our crystal field splitting value are delta will be large. So we recall that our D orbitals get split with two orbitals at a higher energy level and three at a lower energy level. So this is a large delta with a weak field ligand, our delta is small. So there is very little energy difference between the two levels of de orbitals. We have four D electrons that we need to fill in. So in the strong field situation with a large delta, we're going to completely fill the lower energy D orbitals before we go up to the upper energy D orbitals. So we have 123 electrons in our three lower orbitals. But that fourth electron is going to stay in the lower three. So we'll have a set of paired electrons in one of those lower level, the orbitals and then two unpaired electrons. So we end up with two unpaired electrons total. In the case of a strong field ligand. In the case of the weak filled ligand, we have very little energy difference between our lower and upper energy levels. So as we fill in our four electrons, we fill in 123 in a lower level. But that fourth one can go up to the upper energy level since again, there's not much difference. So here we have four unpaired electrons. So right away, we can say we will be able to distinguish between weak field and strong field because our value for spin, only magnetic moment depends on the number of unpaired electrons. So let's scroll back to our answer choices. And I'm going to jot on the side that my strong field has two unpaired and my weak field has four unpaired. So I can do my equation up above. So scroll back up and I know that I can distinguish. So I'm going to go ahead and eliminate my answer choices that say I cannot distinguish. And that is choice C which says cannot distinguish and choice D which is cannot distinguish. So now we just need to calculate that spin only magnetic moment. So for the strong field, my calculation again, we have under a square root sign our N is two. So we have two multiply by the parenthesis two plus two. So that will equal the square root of two multiplied by four. So the square root of eight and that's going to equal 2.83 for the weak field under the square root sign I have four. And then in parentheses multiplied by four plus two. So I have the square root of four multiplied by six square root of 24 which equals 4.90. So let's look to match these up in our answer choices. Choice A says the strong field ligand is 2.83 and the weak field ligand is 4.90 and that matches what we have. So choice A will be our answer. When we look at choice B, it has flipped those values. So that is incorrect. So once again, we've calculated the spin only magnetic moment of that MN three plus with a strong filled ligand. It's 2.83 with a weak filled ligand. It's 4.90 and it can distinguish between the two electron configurations. See you in the next video.