Formal charge on carbon

- To assign formal charge, you take the number of valence electrons in the free atom, or the number of valence electrons the atom is supposed to have, and from that, you subtract the number of valence electrons in the bonded atom, or the number of valence electrons the atom actually has in the drawing. So let's assign a formal charge to carbon in the methane molecule. Remember that each bond consists of two electrons, so I'm gonna draw in these electrons in these bonds, because it's gonna make it easier for us to assign a formal charge to carbon. So to find a formal charge for carbon, the formal charge is equal to the number of valence electrons in the free atom, or the number of valence electrons that carbon is supposed to have. We know that carbon is supposed to have four valence electrons, so I could write a four here, and from that, we subtract the number of valence electrons that carbon actually has in the drawing. Remember, when we drew our dot structures, we knew that each bond here came from one valence electron from hydrogen and one valence electron from carbon, so I could give that one valence electron back to hydrogen, and one valence electron to carbon, and so we're going to divide up all of our bonds that way, alright, give one valence electron to hydrogen, and the other valence electron to carbon, because that makes it easier for us to see that carbon has four valence electrons in our drawing, so let me highlight them here, one, two, three, four. So we're going to subtract four from four, so four minus four is equal to zero. So carbon has a formal charge of zero in methane. Let's do another example, this one down here. You can see it's different because this time we have three bonds. So let me draw in the electrons in those bonds, and let's find the formal charge on carbon. The formal charge on carbon is equal to the number of valence electrons that carbon is supposed to have, which we know is four, and from that we subtract the number of valence electrons that carbon actually has in our drawing. We divide up the electrons in our bonds, just like we did before, and we can see that carbon has only three electrons around it this time, so I'll highlight those, one, two, and three. So four minus three is equal to plus one, so carbon has a formal charge of plus one. So carbon's supposed to have four valence electrons, it has only three around it, so it lost one of its electrons, which gives it a formal charge of plus one. Let me go ahead and redraw that, so over here on the right, we have carbon with three bonds to hydrogen, and this carbon has a plus one formal charge, so we can represent that by putting a + charge here next to the carbon. Notice that carbon does not have an octet of electrons around it, it has only six electrons around it, and that's actually okay, carbon can never exceed an octet, but it's okay for carbon to have less than eight electrons. This is a carbon with a plus one formal charge, it's a positively charged carbon, we call those carbocations, so let me write down here, this is a carbocation. And carbocations come up a lot in organic chemistry mechanisms, so it's really important to understand them. Alright, let's think about the pattern that we see here, we have three single bonds around this carbon, let me go ahead and highlight them here, so here's one, two, and three, so we have three single bonds around our carbon, and we have zero lone pairs of electrons around that carbon, so three bonds plus zero loan pairs of electrons will give you a positively charged carbon, will give you a carbocation. What is the hybridization of this positively charged carbon? Well, there's one, two, three single bonds and zero loan pairs of electrons, and so from the videos on hybridization, you should know that this carbon is sp2 hybridized, and therefore this carbon will have trigonal planar geometry around it, and again, that's important when you do your organic chemistry mechanics, so carbocations are extremely important to understand. Let's look at some other examples of carbocations and analyze them a little bit too. So let's start with the carbocation on the far left. The carbon with the plus one formal charge is this one, in the center here, and what is this carbon in red bonded to? Well, the carbon in red is bonded to a CH3 group up here, which we call a methyl group in organic chemistry, the carbon in red is bonded to another CH3 group here, and another CH3 group here. So the carbon in red already has three single bonds with zero loan pairs of electrons, and so the carbon in red is a plus one formal charge. Let's look at this carbocation right here, let's highlight the carbon with the plus one formal charge, it's this one, so this carbon in red is bonded to a CH3 group on the left and CH3 group on the right, so we only have two bonds here, we only have two bonds at this point, but we know in order for that carbon in red to have a plus one formal charge, we need three bonds, like the example on the left, in the example on the left we have three bonds here to that carbon, and so where is the last bond? The last bond, of course, must be to a hydrogen, so we draw it in here like that, so the carbon in red is bonded to a hydrogen. Usually you leave off your hydrogens when you make these drawings, but it's important to understand what's actually there. Move on to the last example, this time the positive one formal charge is on this carbon in red, and that carbon in red is directly bonded to one other carbon, so that's one bond, but we know we need a total of three bonds, so the carbon in red must have two more bonds, and those two other bonds must be to hydrogen, so we draw in, there's one bond to hydrogen, and there's another bond to hydrogen, so it's important to recognize these patterns. Let's do another formal charge, let's assign formal charge to another carbon. Let's put in our electrons in our bonds, so we put those in, and our goal is find the formal charge on carbon, and so the formal charge on carbon is equal to the number of valence electrons that carbon is supposed to have, which we know is four, and from that, we subtract the number of valence electrons that carbon actually has in our drawing. So we divide up these electrons here in these bonds, and this time, carbon has a loan pair of electrons on it, so how many electrons are around carbon in our drawing? This time, there's one, two, three, and then two more from this loan pair, so four and five, so four minus five gives us a formal charge of negative one, so carbon is supposed to have four valence electrons, here it has five, so it's like it's gained an extra electron, which gives it a negative one formal charge. Let me go ahead and redraw that, we have carbon with three bonds to hydrogen and one loan pair of electrons on this carbon, a negative one formal charge, so we can represent that here with our negative sign next to that carbon. A carbon with a negative charge is called a carbanion, so this is a carbanion, and let's analyze the pattern that we have for our carbanion. We have one, two, three bonds, so let me write that down, we have three bonds, and this time we have one loan pair of electrons, so we have one loan pair, so three single bonds plus one loan pair of electrons for a carbon will give us a negative one formal charge on that carbon, we will have a carbanion. These also come up in mechanisms in organic chemistry, so let's analyze some carbanions, so down here, let's start with the carbanion on the left, and the negative one formal charge is on this carbon, which I just marked in red. So we should have three bonds and one loan pair of electrons on that carbon, well, let's analyze it, the carbon in red is bonded to a CH3, a CH3, and a CH3, so that takes care of our three bonds, and of course, here's the one loan pair of electrons. Let's move on to the next example, so the carbon with the negative one formal charge is this carbon, that I just marked in red, the carbon in red is directly bonded to a carbon here, and directly bonded to a carbon here, so that's two bonds, I need a total of three bonds. 'Cause I already have a loan pair of electrons, right here's my loan pair of electrons on that carbon, so I need one more bond, and that bond, of course, must be to a hydrogen, so I can draw in a hydrogen here, again, that hydrogen is usually left off when you're drawing dot structures, but it's important to realize that hydrogen is actually there. Finally, one more example. The negative one formal charge is on this carbon, and that carbon is directly bonded to one other carbon, it already has a loan pair of electrons, so so far, we have one bond and one loan pair, we need a total of three bonds, so we need two more bonds on that carbon in red, and so those last two bonds, of course, must be to two hydrogens. So it's important to be able to assign formal charge and to do the math, it's important to be able to do these calculations, but eventually you won't need to do the math anymore, eventually you'll be able to look at a carbon and come with a formal charge after you've done enough problems.