Bond lengths in Cycloocta - 1,3,6 - triene

[baldbrain]

Homework Statement

Which is the correct statement about the given compound?
(a) Bond length between C2 and C3 = Bond length between C5 and C6
(b) Bond length between C1 and C2 = Bond length between C6 and C7
(c) Bond length between C6 and C7 < Bond length between C3 and C4
(d) Bond length between C2 and C3 < Bond length between C3 and C4

The Attempt at a Solution

Well, since I can't predict anything about the inequalities, I think it's (a) as well as (b). But their answer is (c). But I don't understand how?

 

[mjc123]

Why can't you predict anything about the inequalities? Why do you assume untrue equalities?
What is the difference between the double bond between 6 and 7 and those between 1 and 2, and 3 and 4? What effect would this have on bond lengths?

 

[SammyS]

Homework Statement

Which is the correct statement about the given compound?
(a) Bond length between C2 and C3 = Bond length between C5 and C6
(b) Bond length between C1 and C2 = Bond length between C6 and C7
(c) Bond length between C6 and C7 < Bond length between C3 and C4
(d) Bond length between C2 and C3 < Bond length between C3 and C4

View attachment 204214

The Attempt at a Solution

Well, since I can't predict anything about the inequalities, I think it's (a) as well as (b). But their answer is (c). But I don't understand how?

What academic discipline is the source of this question?

In addition to knowing how bond length tends to differ for double bonds compared to single bonds in some qualitative way, it looks like you also need to take symmetry into account.

 

[baldbrain]

Why can't you predict anything about the inequalities? Why do you assume untrue equalities?
What is the difference between the double bond between 6 and 7 and those between 1 and 2, and 3 and 4? What effect would this have on bond lengths?

That bond is vertical (w.r.t to other double bonds).
So does that mean that there is min. repulsion between C6 & C7 (or min. strain on that bond) and hence that bond is shorter and stronger?

 

[baldbrain]

What academic discipline is the source of this question?

12th.
We've just done the Resonance theory, Hyperconjugation etc. & properties and reactions of benzene, phenol & haloarenes etc.
So I know nothing about cycloalkenes

 

[DrClaude]

So does that mean that there is min. repulsion between C6 & C7 (or min. strain on that bond) and hence that bond is shorter and stronger?

I don't think that repulsion is the way to go.

My guess is that you have covered π conjugation. There is something from that that you can apply here to get more information about the nature of the different double bonds in the molecule.

 

[SammyS]

That bond is vertical (w.r.t to other double bonds).
So does that mean that there is min. repulsion between C6 & C7 (or min. strain on that bond) and hence that bond is shorter and stronger?

That the bond is depicted as being vertical is not relevant.

Look at the two bonds in each direction from the bond of interest. Then answer:

What is the difference between the double bond between 6 and 7 and those between 1 and 2, and 3 and 4? What effect would this have on bond lengths?

.

 

[baldbrain]

Look at the two bonds in each direction from the bond of interest.

The p orbitals of C6 & C7 are the most conjugated, seeing the geometry of the molecule?

 

[baldbrain]

Sorry I have time to post recently. So, as I said, are the p orbitals of C6 & C7 most conjugated?

 

[mjc123]

What would they be conjugated with?

 

[baldbrain]

Hey everybody, sorry there wasn't any activity on this for quite long. I think that the extra ring strain caused due to the double bonds is the reason for unequal π bond lengths.

 

[DrClaude]

You need to draw resonance structures https://en.wikipedia.org/wiki/Resonance_(chemistry) and see how that can affect bond length.

 

[baldbrain]

You need to draw resonance structures https://en.wikipedia.org/wiki/Resonance_(chemistry) and see how that can affect bond length.

That didn't give me a clue. Of course, they affect bond lengths. But I couldn't predict anything.

 

[DrClaude]

That didn't give me a clue. Of course, they affect bond lengths. But I couldn't predict anything.

Then start by drawing the p orbitals. What π bonds are conjugated?

 

[baldbrain]

I got it. I looked up the compound's PubChem CID and looked at it's 3D conformer in different ways (Interact button). If we look fron the appropriate point of view, not only is C6=C7<C3=C4 but the C1=C2 bond length is equal to C3=C4 bond length.

 

[baldbrain]

Then start by drawing the p orbitals. What π bonds are conjugated?

C1=C2 & C3=C4.

 

[DrClaude]

the C1=C2 bond length is equal to C3=C4 bond length.

That you can figure out quickly by symmetry.

C1=C2 & C3=C4.

Yes. Since these bonds are conjugated, how does it affect bond length? (Hint: think effective bond order.)

 

[baldbrain]

Oh, I get it. The conjugated bonds have only partial double bond character while the C6=C7 has complete double bond character.
Hence, effective bond order greater, stronger and shorter is the bond.

 

[DrClaude]

Oh, I get it. The conjugated bonds have only partial double bond character while the C6=C7 has complete double bond character.
Hence, effective bond order greater, stronger and shorter is the bond.

Correct.

 

[baldbrain]

Correct.

Thanks.