Describe the structure of diborane (B₂H₆) and explain why the bridging B–H bonds are longer than the terminal B–H bonds.

Video transcript

Hi, everyone. Welcome back. Let's look at our next problem. The structure of tetra Bora 10, the 10 in parentheses is shown below. The bh terminal bonds are shorter than the bh bridge bonds. Explain why. And we have our tetra boring molecule consisting of two pentagonal rings with alternating boron and hydrogen atoms. The two middle boron atoms sort of joining the two pentagons are bonded together and each have a hydrogen bonded to them outside of the ring. And there are two boons sort of at the point of each pentagon that have two hydrogens bonded to them as well outside of the rinks. Our answer choices for explanations are a, the bh bridge bonds are longer than the terminal Bh bonds because they are weaker electron deficient bonds. Choice B it starts the same way that these bond that bridge bonds are longer than the terminal bonds because they have greater electron density and experience greater repulsion. Choice C the bridge bonds are longer than the terminal bonds because they are ordinary covalent bonds or choice D the bridge bonds are longer than the terminal bonds because they have lesser electron density and experience greater repulsion. Well, one answer. Choice, we can rule out right away just because it doesn't make sense. Choice D that says they have lesser electron density and experience greater repulsion. This just doesn't make sense, the more electrons you'd have packed together, the more repulsion they would have due to all the negative charge they all have. So choice D just doesn't make sense, we'll cross it right off. So we have as explanation that there are weaker electron deficient bonds, they have greater electron density or their ordinary covalent bonds. So let's look at our structure and think about what our bond natures will be in this structure. So first, let's start with, we know something is funny here because we've got hydrogens with two bonds. And when you do enough chemistry, you'll know, you only expect to see one bond with a hydrogen atom. So you've got these hydrogen atoms bridging two boron atoms. And that's just weird. So we know there's going to be something funny going on there. Let's first count up how many valence electrons we have given the way the structure is drawn if it were just a typical chemical structure that we'd see. Well, we'd start by saying how many valence electrons are provided by the atoms that are in this structure. So our boran, each one has three valence electrons multiplied by four boron atoms. So that equals 12 balance electrons coming from boron hydrogen, of course, has one valence electron and there are 10 hydrogen atoms in this structure. So that equals 10 electrons. So that gives us a total of 22 valence electrons available for bonding. Now, let's look at our structure under typical rules, we'd expect every bond in the structure to contain two electrons. So let's count all of our bonds. We have 12, 3456789, 1011, 1213, 1415, we have 15 bonds if they have two electrons each. So multiplied by two, that would say 30 electrons participating in bonds. Well, we only have 22 valence electrons. So this is not possible. So basically what that means is we don't have two electrons per bond in our structure. So some of our bonds must be electron deficient. So as we know, our normal bonds with two electrons would be what are called two center two electron bonds, we say equals normal. And when we look at our structure here, we can assume that our terminal hydrogens are all these typical two center, two electrons. They look like what we'd expect. They have just the one bond with their one valence electron. So let's label each of those terminal hydrogen bonds as being two electron bonds. So I've drawn two dots representing two electrons on each of these bonds. So that will give us 2468, 1012. So 12 valence electrons in these hydrogen boron bonds. And then in addition, we'd expect to see two electrons in the boron boron bond in the middle boron. Although it only has three valence electrons, it does have empty p orbitals and can participate in four bonds. So that would be two more. So two valence electrons, we know we have 22 valence electrons from the atoms participating in this structure. So we have eight electrons left to assign to our structure. So if we look, we have 12345678 bridging bh bonds. So if we assign one remaining electron and I'm going to do these in red to each of our bh bridging bonds, that gives me the proper number of electrons. And then that means that we have these electrons shared in three center, two electron bonds, each consisting of two boons with a hydrogen in between. So these would be in the re center, two electron bonds. So these are electron deficient. Well, if we think about electron deficient bonds, they have fewer electrons in them than the typical ones. They would be weaker. There's fewer electrons involved in the bond just in the way a single bond is weaker than a double bond, which has more electrons involved. So fewer electrons shared electron deficient would mean there's a weaker bond and a weaker bond will be a longer bond with a stronger bond, you have more attraction there and therefore, they are tighter together in a shorter bond. So our explanation here will be choice a the Bh bridge bonds are longer because they are weaker electron deficient bonds. They are three center, two electron rather than two center two electron. We look at our other answer. Choices. Choice B says they're longer because they have greater electron density. Well, they don't, they have smaller electron density since they have fewer electrons. So choice B is incorrect. And then choice C says that they're longer because they're ordinary covalent bonds. And again, this is not correct, they're not ordinary covalent bonds, they're these special type of bonds. So once again, our bh terminal bonds and tetra boring are shorter than the bh bridge bonds because choice A, the bh bridge bonds are longer than the terminal bh bonds because they are weaker electron deficient bonds. See you in the next video.