Chemical Bonding: Fundamental Concepts Resonance Structures and Formal Charge Formal Charge [Page 1 of 2] Let Me Set the Stage for You

Home , Formal charge

Chemical Bonding: Fundamental Concepts Resonance Structures and Formal Charge Formal Charge [Page 1 of 2] Let me set the stage for you. We’ve talked about the idea of resonance structures and how you might need multiple resonance structures to complete the picture of a molecule. We’ve also talked about the idea that resonance structures for a particular molecule are not necessarily equivalent, meaning that they don’t necessarily contribute equally to our picture of reality. So what we need now is a tool to allow us to choose, or at least rank, the relative importance of resonance structures. That tool is something called “formal charge,” and that’s what I’m going to show you here. Here we have our nitrous oxide molecule. These are the three Lewis dot structures I showed you previously. They all satisfy the octet rule, and that’s really important. Now do the octet rule, and then we’re going to go beyond the octet rule. You can see that they’re inequivalent. By the way, nitrous oxide, in addition to being laughing gas, which you may have gotten in the dentist’s office, is also available to you in whipped cream cans, and I’ll let you figure that one out for yourself.

Let’s talk about formal charge. Formal charge, again, is going to be a way to choose between inequivalent resonance structures. As an aside, I’m also going to show you that we can use it to begin to predict connectivity, or how the atoms are connected to each other. Formal charge, first of all, is a process. It’s a way of counting electrons and sort of keeping track of them. All you have to do is a two-step process, the first step of which is: assign all of the loan pairs and one-half of the bonding electrons to the atom to which they are attached. I’ve done that for one of the resonance structures of nitrous oxide, which is here. For the nitrogen on the left, we give this nitrogen the lone pair electrons that are attached to it, plus one-half of the bonding electrons, and there were six bonding electrons here because we had a triple bond, so three of them go with the left-hand nitrogen, then three of them go with the center nitrogen. The center nitrogen doesn’t have any lone pairs, but it also gets one of the electrons from the bond between the nitrogen and the oxygen. And finally, the oxygen gets its six lone pairs plus one of the electrons from the bond. So this is how we’re going to divvy up the electrons.

Step two is to calculate formal charge, where the formal charge is defined to be the number of electrons in the isolated atoms. In other words, the number of valence electrons that an atom has when it’s neutral, minus the number of electrons assigned to it in the Lewis dot structure, based on the procedure that we used in step one. So here’s our same Lewis dot structure for nitrous oxide, and we’ve divided it up the same way. The nitrogen on the left has 5 electrons, and it also starts out with 5 electrons in the isolated atom. In other words, it starts with 5 valence electrons; this is a neutral nitrogen. So we say that its formal charge is 5 – 5, or 0. In the case of the nitrogen in the middle, we still have the first term here as a 5 but now we’re only going to give the middle nitrogen 4 electrons based on the Lewis dot structure in dividing up our electrons. 5 – 4 is +1. For the oxygen, it starts out with 6 in the isolated atom. It has 7, as we’ve divvied them up, and 6 – 7 is –1. So we have formal charge of 0 on this nitrogen, +1 on this one, and –1 on the oxygen. It’s important to understand that formal charge refers to individual atoms in individual Lewis dot structures, so in a different Lewis dot structure the atoms are going to have different formal charges.

All right, so how do we use formal charge? It turns out that if you can draw a Lewis dot structure where the formal charges for all the atoms are zero, that’s the best. And the reason is, if you think about it, having formal charge be zero on each of the atoms says that, roughly speaking, the number of electrons around the atom in the molecule is equal to the number of electrons around the atom when it’s a neutral atom. In other words, we’re not taking a whole lot of electrons away from a particular atom, or we’re not trying to put a bunch of extra electrons onto the atom when we turn it into a molecule.

Now, if 0 is best, plus or minus 1 is sort of second best. On the previous example, we had an example of +1 and –1. Formal charges of plus or minus 1, those are still okay. But if we have a Lewis dot structure where we calculate that the formal charges are greater than plus or minus 1, like plus or minus 2, or plus or minus 3, what we say is that those Lewis dot structures are not significant contributors. What do I mean by this? The idea is that all these Lewis dot structures, they’re perfectly legitimate. They all contribute in principle to our picture of reality, but some of them contribute more than others, and those with formal charges that are really low are a better reflection of reality. How do we measure reality? We measure reality in bond lengths. In other words, the predictions based on formal charge are reflected in when we go to measure bond length. We haven’t actually talked about measuring bond length, but in principle, you can at least buy that idea. Similarly, bond shape: we haven’t talked about bond shape yet, either, but our model, the Lewis dot theory, makes predictions. And those predictions reflect reality best when we choose those Lewis dot structures that have small formal charges.

Chemical Bonding: Fundamental Concepts Resonance Structures and Formal Charge Formal Charge [Page 2 of 2] Let’s go back to the slide we came in on and calculate the formal charges for each one of these atoms. I’ve suddenly realized that I left out a lone pair, so let’s go ahead and do the procedure. I’m going to just do it for you on camera so you can see that it’s actually relatively straightforward. We’ve already done this one, and when we did this one, it was zero, +1, -1. For this one we’re going to divide the electrons—I left off a lone pair over here as well. So that’s step one, dividing the electrons. Now calculate formal charge. Remember, it’s the difference between the number of electrons that the atom comes in with minus the number of electrons it has when we assign them this way by our accounting scheme. So nitrogen starts with 5. In this picture it has 6. 5 – 6 is –1. 5 – 4 is +1. Oxygen starts out with 6 valence electrons. 6 – 6 is 0. So this one is pretty good, too, right? Zero and plus and minus ones. Nitrogen starts out with 5. Here it has 7, so that’s not so good. 5 – 7 is –2. 5 – 4 is +1. And 6 – 5 is +1.

Okay, what have we got? Well, we’ve improved the picture a little bit. We can say that both of these are significant contributors to reality, but this one where we have the triple bond between the nitrogen and the oxygen has an electron distribution—these are a reflection of electron distributions—that is really trying to put a lot of electrons around the nitrogen at the expense of the other two atoms, and that’s not so good. So this resonance structure doesn’t contribute significantly to our overall picture of what nitrous oxide ought to look like. These two are better, and we don’t have a tool yet to help us to choose between the relative importance of these two. We’re going to actually say that they both contribute significantly. One contributes more than the other, but we don’t have that tool yet. But we can certainly throw out this one as being not a significant contributor.

As an aside—and I have to bring in this here—the sum of the formal charges is equal to the overall charge. So when you’re doing these Lewis dot structures and calculating the formal charge, a thing to remember is that the sum of the formal charges is equal to the overall charge on the ion or molecule. How does that apply? For our nitrous problem, nitrous oxide is a neutral molecule, so the sum of the formal charges should be zero. Zero, meaning that that occurs when the sum of the formal charges is equal to the overall charge. Zero, meaning that it’s a neutral molecule. I’m sorry; I messed that up a little bit.

So we just add these numbers up: +1 plus –1 is 0, so that makes sense. –1 plus +1 plus 0 is equal to 0, so that makes sense. In other words, you can use this to double-check to make sure that you assigned formal charges correctly. And in the bottom one here, –2 plus +1 plus +1 is equal to 0, so it allows us to double-check to make sure we assigned formal charges correctly.

I also suggested that formal charge can be used to make predictions about connectivity. So you probably have wondered at some point how we know that carbon dioxide is O-C-O and not C-O-O. These are entirely different molecules. This one has the carbon in the middle; this one has the carbon on the left, so these are not resonance structures. And this one is reality. Carbon dioxide is the symmetrical molecule and not the asymmetric molecule. How do we use formal charge to rationalize that idea? Let’s go ahead and calculate the formal charges. Oxygen has 6 electrons in the valence shell as a neutral atom, so the formal charge is 0 in the molecule. Carbon has 4, so the formal charge is 0. Oxygen again has 6. And 6 – 6 is 0. Conversely, –2 plus +2 and 0—remember, plus and minus 2 is bad. So formal charge allows us to say why carbon dioxide should be the symmetrical molecule and not the asymmetric molecule. Again, it’s because, roughly speaking, the electron distribution around the atoms in the molecule is very similar to what it is in the free atoms.

Finally, let’s look at a possible resonance structure for carbon dioxide—so these now are resonance structures. But if we calculate the formal charges here, we get –1, 0, and +1. And it is true that [having] all zeroes is better than having plus or minus ones, so this is a more significant contributor to the overall picture of .

So, in summary, formal charges allow us to choose, or at least rank, inequivalent resonance structures according to their importance as to how they contribute to the big picture, to what our reality is. Similarly, formal charges allow us to make some at least rudimentary predictions about how the atoms ought to be connected together when they form molecules.