One of the molecular orbitals of the H2- ion is sketched below:

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Question

One of the molecular orbitals of the H2- ion is sketched below:

(d) Compared to the H¬H bond in H2, the H¬H bond in H2- is expected to be which of the following:
(i) Shorter and stronger, (ii) longer and stronger, (iii) shorter
and weaker, (iv) longer and weaker, or (v) the same length
and strength?

Accepted Answer

hey everyone in this example, we're going to be comparing the bonds between a helium two plus Catalan and a helium plus one carry on. Now. In order to compare the bonds here, we want to recall the concept of bond order. So we should recall that to calculate bond order, we're going to have one half multiplied by the number of electrons in our bonding molecular orbital. And then subtracted from this, we would have our number of electrons in our anti bonding molecular orbital. So the brackets would end here. And what we're going to do is draw out our molecular orbital diagram For our helium plus one carry on. Before we can do so we want to go ahead and recall the total valence electrons Within our molecule here or ion. And we should recognize that our HE two plus one cat ion is a diatonic molecule because it has two helium atoms bonded to one another recognize that helium has two electrons total and so we would say that we have two from one atom of helium added to two electrons from our second atom of helium to give us a total of four electrons. However, because we have this plus one charge here, we have this plus one charge here which is a caddy on charge. We would recognize that this means we will lose one electron. So we would say -1 electron and this is going to leave us with three electrons total for our valence electrons and this is what we will include in our molecular orbital diagram. So to draw out our orbital diagram, we would recognize that because helium is in the first period of the periodic tables, we're going to begin with the sigma one s bonding molecular orbital. And here we will fill in our first two electrons of our three total. So we would have one electron here in the upward direction and then an electron with the opposite spin. Now moving on to our next orbital. We want to fill in our anti bonding molecular orbital which is going to be the sigma, a strict one s anti bonding molecular orbital. And here we're going to fill in our last electron. So right now we have three total to use, we filled in two. So we're going to fill in our third electron here. It can be in any direction spin that you choose. And so this would be our molecular orbital diagram for our helium Plus one Cat eye on And now we're able to calculate bond order for our helium plus one caddy on. We would see that we would have one half, we would take the numbers of electrons in the bonding molecular orbital. So we have two electrons in the bonding molecular orbital and then we're going to subtract from this, Our electrons in the anti bonding molecular orbital, which we just counted one here, so -1 electron anti bonding molecular orbital and what we're going to get is a value for our bond order Equal to we would have 2 -1, which is one and so that would leave us with one half times one, which is going to give us one half. And so now we want to compare this to our bond order for a helium two plus cat ion molecule. So what we should have is 1/2 now for the number of electrons in the bonding molecular orbital. We want to think of the total Valence electrons here for our two plus Kati on of helium And because we recognize that a 2-plus canton means we lose two electrons from our three total electrons. We would say so for HE 2, 2 plus We would say now we have to take -2 electrons. So rather what we should do is have Sorry about that. So what we should do, we're going to erase this. So for 82 2 plus we would have originally four electrons from each atom. But because we're losing Two electrons based on that too plus charge would have -2 electrons. And so this is going to leave us with two electrons total. So just so everything is visible. So what that means is that our molecular orbital diagram for 82 2 plus is still going to have these two electrons here in the sigma one s bonding molecular orbital. So we would fill this in for our calculation we have two electrons in our bonding molecular orbital and now counting the number of electrons in our anti bonding molecular orbital Because we know we only have two electrons total for the two plus Catalan of helium, we won't have any electrons filled in our anti bonding molecular orbital for the two plus cat eye on here. And so we would say minus zero electrons in the anti bonding molecular orbital. So we would finish off the brackets here and what we would get here now is one half times two, which is just going to give us one. And so now what we can do is conclude that therefore the bond order of our helium two plus catalon is greater than our bond order of our helium Plus one Cat eye on and because we know that our two plus Catalan of helium has a bond order of one we can say because one is greater than one half this forms a stronger bond for the two plus Catalan of helium. And so therefore it's going to be a shorter bond or it's going to have a shorter bond length because we recall that bond strength and bond length have an inverse relationship. So as bond strength increases, our bond length will decrease. And so what that means is that we can confirm that the best answer choice to complete this example are actually going to be two choices where we would say a not only is the bond for helium two plus as a Catalan shorter, but it's also d stronger and so a and d are our final answers to complete this example. So I hope that everything I reviewed was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

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