Draw a potential-energy diagram for rotation about the C-2---C...

Question

Draw a potential-energy diagram for rotation about the C-2---C-3 bond of pentane through 360°, starting with the least stable conformer.

Accepted Answer

Hello everyone. Let's do this problem. It says for rotation about the carbon three to carbon four bond of hexane through 360 degrees. Draw an appropriate potential energy diagram. You should start the diagram with the least stable conformer. So first, let's draw hexane and we can point out the carbon three to carbon forward bond and see what groups are on that, those carbons, right? Because we want to draw the Newman projections to show that rotation. And in the Newman projections, we only draw these two carbons, the carbon three and carbon four bonds specified here and the three groups attached to each carbon. So let's draw out Hexane, which we know has six carbons because of that prefix hex. So 123456 carbons and a zigzag chain Adding our hydrogens to satisfy each carbon's octet from carbon one. And through carbon six, we'll have C H three C H two, C H two, C H two, C H two and C H three. So let's pick out the carbon three to carbon four bond towards the center of our structure. And I'll highlight that in yellow here. So we have three groups on each carbon two hydrogens and an ethyl group. And it's the same groups on carbon three and carbon four. So let's show all of the different Newman projections or conformers that we can draw for the rotation of 0 to degrees. So there are two different types that we can generalize these conformers under and that will be eclipsed structures, which is where those groups are overlapping each other. And that's going to be less stable. And then there are also staggered structures. And you guessed it, that is when the groups do not overlap. So groups not overlapping. And do you think that'll be more stable? Definitely because there will be less STAIC hindrance between those groups when they are not overlapping, they will have more space. All right. So let's draw these conformers. We'll start with 0°. So I can actually draw, there's going to be three eclipsed Newman projections and three staggered projections. And the front carbon is going to look the same for all of them. We have CH two CH 3 at the top and the hydrogens towards the bottom and we can leave this position the same. And then we'll simply rotate the groups on the back carbon on carbon four. All right. So if we're starting with 0° and we'll call this conformer a we're talking about zero degrees between the two largest groups. So those two ethyl groups on each carbon right, carbon three and carbon four. So if we have zero degrees between those groups, that will look something like this CH two CH 3, the EO groups are right in front of one another. All right, rotating 120°, we'll put that ethyl group in front of the bottom, right hand hydrogen, right. So all of these conformers, we want the groups directly in front of one another And that will be conformer B 120° in conformer C. It's going to be 240° and the group will now be in front of that or behind that bottom left hand corner, hydrogen CH two CH hydrogen behind the ethyl group on carbon three hydrogen In the bottom right hand corner on carbon four. So those are our three eclipsed Newman projections. Let's draw the three staggered projections. So again, we can draw the same front carbon or circle with the three bonds coming out of it. And we can put our ethel group on the top, center hydrogens on the bottom left and right bonds and then will rotate the back carbon to change the position of those groups. So the closest angle to zero we can get for a staggered confirmation is going to be 60°. So now basically in the windows of the front carbon groups, we're going to have the groups on the back carbon. So we'll have that ethyl group on carbon four at 60 degrees from the ethyl group on carbon three. And the hydrogens Also are 60° from the groups on the front carbon. So that is conformer D conformer E we keep rotating. So now that ethyl group will be 180 degrees from the carbon three ethyl group. So the carbon four ethyl group I should say and carbon three L group are 180°. And lastly conformer F Is going to be 300°. And the group On carbon four is now 60° counterclockwise from the front ethel group. And again, these three staggered confirmations are more stable than the eclipse confirmation. So when we draw our potential energy diagram, which we are going to do, now, we're basically alternating back and forth through eclipse staggered, eclipse staggered. So I'll show you what that looks like because we're going by angle. So we draw Y axis and X axis, the y axis is labeled potential energy increasing as we go up the y axis. And then we have the X axis labeled dihedral angle and those are those angles that we just discussed. So we'll have one tick mark for every angle. So starting with zero degrees up to 360 degrees, which would be the same structure, right. So halfway between that is 180 then we have 60 degrees, 120 degrees, 2 40 degrees And 300°. OK. So 0° is an eclipsed structure. So is that gonna be high energy or low energy? That would be very high energy, right? Because the two, not only are two groups right in front of each other, they are the largest groups. So that's going to be the highest energy out of the whole graph, right? So we'll plot our point towards the top of the graph will label that point a. Now going what's the lowest point on our, on our graph? Let's do that point next. So that'll be when the largest groups are furthest from each other. So which conformer is that, That'll be the staggered conformer E, right? They are 180° apart. So we'll plot a point low on the potential energy axis and label that point E And we can also mark the point for 360°, right? That'll be the same as 0° as we mentioned. All right. So now let's go back to the beginning and we'll go down to 60°. So 60° is a staggered conformer. So it'll be lower energy than the starting point of 0°. But Yes, it won't be as low as 180, but it won't be as high as the other eclipsed conformers either. OK. So we'll do it a little bit higher than point E and this structure is equivalent to the conformer at 300 degrees, right? Those ey groups are in the same relationship to one another on carbons three and four. So at 60 degrees, we have conformer E 300 degrees, we have conformer F And then similarly, just how those structures are equivalent. The conformers at 120° and 240° are also equivalent, right? They're just mirrors of each other. Those ethel groups are the same distance from on carbon three and carbon four, right, just the other side and those will be higher energy then conformers D E and F but just not quite as high as conformer A. So we'll draw them high energy but lower then conformer A. So we have point B at 1 20 degrees and conformer C at 240 degrees. So now we can connect our dots with these curved lines. So going from A down to D back up to B to our minimum at E Up to sea at 2 40° Down lower energy for 300° or staggered confirmation and back up to our maximum at our eclipsed confirmation. So this is the potential energy diagram for the carbon 3 to carbon four bond of hexane from 0 to 360°. And these are all the conformers that are represented in this potential energy diagram. And with that being said, that makes d the correct answer to this problem. That's it for this video. I hope this was helpful and thank you for watching.

Draw a potential-energy diagram for rotation about the C-2---C-3 bond of pentane through 360°, starting with the least stable conformer.

Key Concepts

Conformational Analysis

Potential Energy Diagram

Stability of Conformers

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