Lecture 12: Hybridization in Molecular Orbitals

Lecture 12: Hybridization in Molecular Orbitals Summary If multiple atomic orbitals within an atom have similar energy levels, they can hybridize, combining to form equal orbitals that have a lower average energy. Consider methane, CH4, as an example: the carbon atom has two 2s electrons and two 2p electrons. The 2s and 2p states hybridize, yielding four equal-energy, unpaired electrons that are ready to bond with hydrogen atoms. As hybridization occurs, carbon’s four electrons are redistributed so as to be maximally spaced apart, lowering the energy of the system and yielding the most stable state: a tetrahedral methane molecule. This kind of hybridization is called sp3 , because one s-orbital energy level combined with three p-orbital energy levels. For the case of ethane, C2 H4 , the hybridization process is slightly different, as shown here (this time as an energy level diagram). Each carbon forms only three bonds: two with hydrogen atoms, and one with the other carbon. The s-orbital energy level combines with two p-orbital energy levels to form three equal sp2 bonds; the remaining 2p electrons form a higherenergy π bond between the two carbon atoms and yield a double bond between the carbon atoms. The next logical molecule to consider is acetylene, C2 H2 . In this case, each carbon is only bonded to one hydrogen, so only one 2p energy level hybridizes with the 2s energy level to form a sp hybridized bond. The remaining 2p orbitals form two bonds, yielding a triple bond between the carbon atoms. In summary, hybridization occurs to lower the overall energy of the system: atomic orbitals combine with each other to form mixed states with a lower average energy. Knowing the hybridization of the molecule is equivalent to knowing the molecular shape: VSEPR gives the geometric name corresponding to the specific combination of bond angles that minimize the overall energy of the system. 16 Figures above by B.A. Averill and P. Eldridge in General Chemistry. License: CC BY-NC-SA. Source: Open Textbook Library. Why this matters More than 3 billion people on this planet live in water-stressed regions. 1.8 billion people drink fecally contaminated water. 600 million people boil their water to clean it. In places where water scarcity is a serious issue, by some estimates 70% of all disease and 30% of all death can be attributed to the lack of water or water quality. Fresh water makes up just 2.5% of all water on earth, but more than 2/3 of that is tied up in glaciers. This means that only 1% of all water on the planet is drinkable, and the balance of this precious resource is way offscale. Given the level of global crisis that access to freshwater has become, it makes a lot of sense to turn our attention to the other 97% of water on the planet, saltwater in the oceans. The problem, of course, being that it’s not drinkable (or useful in most agriculture), unless the salt is removed. The good news is that desalination is growing in terms of use and installed capacity, but the bad news is that it still costs far too much to become a ubiquitous substitute for groundwater. How can we work on lowering the cost and increasing efficiency in desalination? First of all, we need to know what the current cost breakdown is, and as you can see in the pie chart in this image, the major cost of desalination is in the energy it takes to pump water through the system. By “system” I mean a pretreatment facility where seawater is run through sand to filter out large impurities (shells, rocks, seaweed, etc.), followed by the actual “desal” part of desalination, where the water is run through a set of membranes (40,000 of them in the plant shown in the picture) that remove the salt and allow freshwater to pass. Pumping the saltwater through these membranes requires by far the biggest part of the plant’s energy consumption, so improving the membranes and making them more energy efficient is crucial. In fact, it’s not just that the membranes used today are energy inefficient, but it’s also that they get fouled up (bacteria and other organic matter grow on their pores) and are extremely delicate so can’t be cleaned very well. This means for most of the time the plant is paying higher energy costs than it needs to (by a factor of 2 or 3 sometimes!) because it has to pump water through membranes that are filthy and blocked and can’t be cleaned. Now that’s what I call a materials design opportunity! Make a better membrane for the salt removal step of desalination, and make the process cheaper. That’s how we come to our Why This Matters and connection to today’s lecture. We learned about the sigma and pi bonds that can form when the AOs of carbon atoms hybridize. 17 Figures above by B.A. Averill and P. Eldridge in General Chemistry. License: CC BY-NC-SA. Source: Open Textbook Library. In the examples in class we had carbon bonded to hydrogen and sometimes also to itself. If we only have sp2 hybridization and we only have C atoms and no H atoms, then we arrive at a very, very cool material: graphene. It’s bonded together in a honeycomb lattice sheet (a 2D sheet) with sp2 bonds, and those extra p electrons form pi bonds across the plane to give it a huge stability boost. It’s a very cool material and its isolation from graphite (which is just stacks of graphene) won the Nobel Prize in 2010. (The scientists who discovered graphene were able to separate it from a chunk of graphite using only run-of-the-mill tape! So remember, sometimes all you need for a Nobel Prize is pencil lead, tape, and determination). I can’t possibly go into all the details for why graphene is cool, but if you search online you’ll see right away. Another consequence of graphene is that it launched a whole field of “2D materials” where researchers have realized that so many other materials can be made into these sheets that are only one or a few atoms thick. It’s now even possible to make completely new stacks of 3D materials by mixing and matching 2D sheets (check out for example the paper by Geim and Grigorieva, “Van der Waals heterostructures,” Nature volume 499, pages 419–425 (25 July 2013). By the way, Geim was one of the two scientists who won the Nobel prize for graphene’s discovery. The other is Novoselov, but Geim is a bit special as he is the only person to ever have won both the Nobel and the IgNobel prizes, the latter for levitating frogs. But I digress. The point is that graphene may just be the ultimate membrane. It’s only 1 atom thick, so in terms of viscous loss it’s hard to beat. Plus, it’s much more resilient than today’s polymer membranes so it can be cleaned easily. It’s no wonder graphene’s been considered as a potential for desalination since 2012, even by people you might already know, for example, “Water Desalination across Nanoporous Graphene,” by Cohen-Tanugi and Grossman, Nanoletters volume 12, pages 36023608 (2012). Because of its massive potential in water desalination and also water treatement and purification in general, there are many research groups and even already a number of companies working towards commercializing graphene-based membranes (Via Separations, for example). This is all extremely exciting, but it’s also only possible because of the hybridization that occurs in carbon atoms, which combined with those pi bonds allows them to take the form of graphene. Why this employs This is a tough one since hybridization in chemistry is what enables so many molecules to exist at all, and this impacts nearly all job sectors, not to mention life itself. But since we covered graphene in Why This Matters let’s stick to graphene here in the Employment category too. There are companies directly manufacturing graphene and investing a lot of $$ into making it cheap, at large scales, and at high quality (meaning very few defects if possible), or with tailored functional chemistries. There are also different versions of graphene, from pure graphene to graphene-oxide to reduced graphene oxide and so on. Graphene Supermarket, ACS Material, or Graphenea are all examples of companies making graphene products and all of them have job openings for students who know about hybridization. 18 Diagrams above © sources unknown. All rights reserved. This content is excluded from our Creative Commons license. For information, see https://ocw.mit.edu/fairuse. But graphene production has been embraced in a big way by large companies, too. Toshiba has invested over $50M in manufacturing plants for new carbon materials, from graphene to other sp2 carbon nanostructures like carbon nanotubes and fullerenes. Other large chemical producers have joined the club, like Cemtrex, Mitsubishi Chemical, Cabot, or Aixtron, to name only a few examples. And these are all just companies thinking about making graphene, but then if we expand to ones that are using it to improve their technology, the list goes on and on. This is especially true in battery companies, both big and small, where the use of sp2 carbon nanostructures like graphene has tremendous potential. Applications involving catalysis and electronics are also fantastic candidates for the use of graphene. Extra practice 1. Look at a single carbon in the portion of a diamond lattice below. Convince yourself that the structure could keep growing outwards infinitely in all directions. Diamond lattice © source unknown. All rights reserved. This content is excluded from our Creative Commons license. For information, see https://ocw.mit.edu/fairuse. a) What is the formal charge on any one carbon atom? b) What is the hybridization of any one bond? How do you know? c) Is this a resonant structure? How do you know? 19 2. Look at a single carbon atom in the portion of a buckminsterfullerene molecule below (yes, it’s the logo for our class!) Model by Mstroeck. License: CC BY-SA. This is excluded from our Creative Commons license. For information, see https://ocw.mit.edu/fairuse. a) The formal charge on any one C atom is 0. How many sigma and pi bonds must each carbon be forming? b) Is VSEPR satisfied? Is it almost satisfied? c) What is the hybridization of any one sigma bond? How do you know? d) Is this a resonant structure? How do you know? 20 Solutions 1. a) 0, it’s forming 4 bonds b) C is forming 4 sigma bonds, so it must have 4 equivalent hybridized orbitals: it must have used all three p-orbitals and its s-orbital: sp3 c) No - the electrons are all forming sigma bonds, so there’s no other configuration of electrons allowed 2. a) There has to be a double bond associated with each carbon for it to be forming 4 bonds and have 0 formal charge, so each carbon is forming 3 sigma bonds and 1 pi bond b) Each sigma bond has to be sp2 hybridized, since three bonds are being formed total and they all lie in a plane c) Yes - There are different configurations in which the pi-bonds can be made over the whole fullerene molecule, so there are resonances. Also, we infer that the p-orbitals forming the pi-bonds can either add or subtract giving delocalized electron molecular orbitals - pointing to resonance 21