Resonance

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Take the carbonate ion. Its Lewis structure has carbon in the middle, a double bond to one oxygen, and single bonds to the other two. Now, a double bond is shorter than a single bond, right? So we expect one short bond and two long ones. But measure them, and all three carbon oxygen bonds come out exactly equal! So which oxygen really has the double bond? Strange, isn't it? Today, one beautiful idea called resonance settles this. And in JEE, questions on resonance and bond order come up often. So, let's begin.

0:41One Lewis structure is not enough

So, look at the figure. This is the carbonate ion: C O three, with a small three below for three oxygens, and two minus on top for its charge. One Lewis structure cannot describe it, so we draw three. These are called canonical structures, or resonance structures, okay? The little minus signs mark the oxygens with a negative charge, and the double-headed arrow between the structures means resonance, not a reaction. Now compare the three pictures. What changes from one to the next? Only the electrons, exactly! On paper, the double bond and the two minus charges sit on a different oxygen each time. But the atoms stay put: carbon in the middle, three oxygens around it, in the same positions every time. Clear? So now we have three pictures. Tell me, which one of them is the real carbonate ion? The first? The second? The third? None of them! The real ion is one single structure, the resonance hybrid, on the right of the figure. See the dashed lines? The double bond is shared out over all three bonds. Its caption says it: the two minus charge is spread over all three oxygens, and each C O bond, carbon to oxygen, has bond order one and one third. So all three bonds are equal. With me?

1:57The biggest trap: no flipping

Now, the biggest trap in this topic. Many students imagine the ion flipping very fast: the first structure, then the second, then the third, again and again. So, for a tiny instant, is it ever the first structure alone? No, never! This is important. Canonical structures are only pictures on paper. We draw several because no single Lewis structure can show the real ion. Okay? The ion never flips between them. It always has the hybrid structure, with three equal bonds. And none of the canonical structures can be isolated. Got it?

2:33How much more stable? Resonance energy

Now, one more fact about the hybrid. It is more stable than any of the canonical structures, even the best one. Right? So how much more stable? That is the resonance energy. Resonance energy equals E of the most stable canonical structure, minus E of the actual molecule. Here E simply means energy, okay? The actual molecule lies lower, so this difference is the extra stability that resonance gives. Clear?

3:00Bond order from resonance

Now, the most useful number here: the bond order. Bond order equals the total bonds between the two kinds of atom, over the number of such links. So, count the bonds in any one canonical structure, and share them equally over the links. Okay? Try it on carbonate. Take any one of its canonical structures. How many carbon oxygen bonds in total, and over how many links? Yes! The double bond counts two, and each single bond counts one. Two plus one plus one: four bonds, over three links. Four over three. That is the one and one third from our figure! More than single, less than double. Clear? Same way for the others. Nitrate, N O three minus: also four over three. Ozone, O three; nitrite, N O two minus; and formate, HCOO minus: three over two each. Okay? And three more. Phosphate, P O four three minus: five over four. Sulphate, S O four two minus: three over two. And the carbon carbon bond in benzene: three over two. No need to memorise this list: count bonds over links, and rebuild any of them. With me?

4:12Equal resonance, equal bond lengths

So now, back to our puzzle, with real numbers. Equal resonance gives equal bond lengths. In carbonate, every C O bond is one hundred and twenty nine picometres; that is the p m on screen, okay? No short bond, no long bond. Puzzle solved! Same story in benzene, the six-carbon ring. Every C C bond is one hundred and thirty nine picometres. Right? Now compare. On screen, C single bond C is one hundred and fifty four picometres, and C double bond C is one hundred and thirty four, with greater than signs between them. Benzene's one thirty nine sits in between, just as its bond order, three over two, sits between one and two. So, as the bond order goes up, does the bond get longer, or shorter? Shorter, correct! Higher bond order, shorter bond. Keep this rule ready, because both our examples need it. Got it?

5:03Example 1: O-O bond order and bond length in ozone

Alright, example one. Give the bond order, and the relative bond length, of the O O bonds in ozone. Pause the video and try it first. Done? Okay, let's check. Ozone has two equivalent structures. On screen: O, double bond, O, single bond, O; then the double-headed arrow; then the same chain with the double bond on the other side. So, three bonds over two O O links. What is the bond order? Two plus one, over two: three over two, that is one point five. Very good! Okay? Now the bond lengths. The two structures are equivalent, so both O O bonds are equal: one hundred and twenty eight picometres each. Right? Compare: an O O single bond is one hundred and forty eight, and a double bond is one hundred and twenty one. One twenty eight lies right between them. Intermediate, exactly as our rule says. Neat, isn't it?

6:00Example 2: N-O bond lengths in NO2+, NO2- and NO3-

Now a harder one, JEE level. Arrange the N O bond lengths in three ions: N O two plus, N O two minus, and N O three minus. The small numbers below count the oxygens, and the plus and minus on top are the charges. Pause and try. Hint: find the bond orders first. Done? Okay, let's check. Start with N O two plus and N O two minus. Same atoms: one nitrogen, two oxygens. So they have the same bond order, right? No, no, careful! The charges differ, so the electrons differ, and so does the bonding. N O two plus is drawn as O, double bond, N plus, double bond, O, okay? Both bonds are double, so the bond order is two. Clear? Now N O two minus. Its double bond can sit on either oxygen, just like ozone: two structures. Two plus one, over two: three over two. Right? And N O three minus? Three structures, just like carbonate. Two plus one plus one, over three: four over three. With me? So the bond orders fall: two, then three over two, then four over three. And higher bond order means a shorter bond. So which ion has the longest N O bond? N O three minus, yes, exactly! So the N O bond lengths: N O two plus, less than N O two minus, less than N O three minus. Two ions with the same atoms, two different answers. That is a classic trap. Got it?

7:33Quick revision: resonance hybrid, bond order, no flipping

So, quick revision. One: when one Lewis structure is not enough, we draw several canonical structures, but the real molecule is one resonance hybrid, more stable than all of them. Two: bond order is total bonds over links, and a higher bond order means a shorter bond. Three: canonical structures are only pictures on paper. The molecule never flips between them. Now go and try the practice problems on this page. All the best!