Draw a potential energy diagram for rotation about the C¬C bon...

Question

Draw a potential energy diagram for rotation about the C¬C bond of 1,2-dichloroethane through 360°, starting with the least stable conformer. The anti conformer is 1.2 kcal/mol more stable than a gauche conformer. A gauche conformer has two energy barriers, 5.2 kcal/mol and 9.3 kcal/mol.

Accepted Answer

Hello everyone. Let's do this problem together. It says starting with the least stable conformer, draw an appropriate potential energy diagram for rotation about the carbon carbon bond of 12 di bromo ethane through 360 degrees. If a gauch conformer has two energy barriers, 5.4 kilocalories per mole and 9.5 kilocalories per mole. And the anti conformer is more stable than a gauch conformer by 1. kilocalories per mole. So let's start by simply drawing 12 di bromo Ethane. And then we can draw that or sorry, draw a new projection from that bond line structure. So Di bromo, Ethane, Ethane tells us we have a two carbon chain, 12 di bromo means we have one bromine atom on each carbon and to satisfy octet, that means each carbon will also have two hydrogens. So let's label this right-hand carbon one, the left-hand carbon two. And to draw our Newman projection, we are going to place our eyeball on the right hand side of the structure facing the left hand side. So looking down that carbon one to carbon two bond and that's how we are going to draw our new projections or our conformers. So there are two types of conformers, right? There are eclipsed and staggered. So eclipsed conformers, if you recall are, when the groups on each carbon are directly in front of one another, when we're looking down the carbon carbon bond and stagger is the opposite, right? They are in the windows of one another. So let's start with the eclipsed conformers and the front carbon carbon one is going to look the same for all of the conformers. We'll draw that Bromine atom at 12 o'clock hydrogen, one will be at four o'clock hydrogen two will be at eight o'clock. And I'm going to copy this so I can paste it for all of the other conformers. OK. So starting with conformer A, we'll call it, we will draw the least stable conformer which is zero degrees between the front and back bromine atom, right? Because that Bromine atom is the largest group on each carbon. So when those bromine atoms are directly in front of one another, that is a zero degree dihedral angle and it's very unstable. All right. So now we're going to rotate that back carbon 120 degrees to get conformer B. So now that bromine atom on carbon two will be behind the first hydrogen in the last eclipsed conformer conformer C, there will be a 240 degree dihedral angle between those bromine. So that bromine non carbon two is now behind hydrogen two. All right, let's look at the staggered conformers. So carbon one is still the same for all of these consumers. We're still only changing, oops, sorry about that. We are still only changing the back carbon. So we will call the first stagger conformer conformer D and that will have a 60 degree dihedral angle. So now that bromine will be in the window between the bromine and hydrogen on carbon one And this is called a Gaus conformer, which we saw that men in the problem, right, we'll get back to that in a little bit. The next conformer conformer E will have a 180 degree dihedral angle. So that bromine will be directly underneath right, 180 degrees away from that front bromine. And this is called an anti conformer, right. And lastly conformer F will be a degree dihedral angle. This is also called Gaus and that Bromine atom is in the window on the left hand side. Now, so those are our conformers. So let's draw our potential energy diagram and we will draw the energy of all of these conformers on the diagram. So we have our y axis labeled potential energy and that is increasing as we go up the y axis and our x axis is the dihedral angle that we mention. And that is also increasing as we go across. So starting at the left hand side, we start with zero degrees 60 degrees on the x axis, 120 degrees, 180 degrees, 240 degrees, 300 degrees and 360 degrees, right. The problem told us to start with the least stable conformer which is zero degrees and go all the way through 360 degrees. So a full rotation. So let's start with the least stable conformer, as I just mentioned. And that is the eclipse conformer with a zero degree dihedral angle, right? When those two large bromine atoms are right on top of one another. And that is going to have the same potential energy as the 360 degree conformer, right, a full rotation. So that will have high potential energy because it is the least stable, right? High energy less stability. So we will plot those points. I'll label them a all right, let's go to the least stable conformer which or sorry, the most stable conformer I meant the lowest energy. So if the least stable conformer is when those bromine atoms are close together, then the most stable conformer is when they will be furthest apart. So that will be the anti conformer conformer e most stable lowest energy. So we'll plot a point low on the y axis at 180 degrees. All right. What is the next most stable conformer? It's going to be the other two staggered conformers, right? And they are equivalent in energy because they are basically the same conformer. The bromine is just on the other side. So those gauch conformers at 60 degrees and 300 degrees are going to be higher energy than 180 degrees, but much lower than zero and 360 degrees. So we will draw those about one quarter of the way up our Y axis. And lastly, the other eclipse conformers conformers B and C are going to be higher energy than all of the staggered conformers, but lower energy than conformer A right, our zero degree conformer. So we will draw those in between. So about three quarters of the way up the Y axis at 120 degrees and 240 degrees. So now let's connect the dots, we plotted all our points. So starting with the Y axis go through zero degrees down to 60 degrees, back up to 1 20 down to 1 up to 2 40 down to up to 360. So it's almost like a sine wave situation, right? OK. So now we want to add the energy values that were given in our problem. So we have a Gauch conformer has two energy barriers, 5.4 kilocalories per mole and 9.5 kilocalories per mole. So as you might guess an energy barrier is sort of a high energy threshold that you have to pass to get to the gauch conformer. And as you might guess the visual represent who the visual representation of that energy barrier is going to be a peak, right, a maximum in energy. So if we have our gauch conformers down here at and 300 notice the peak right before that point. So we can draw a dotted line from our y axis horizontally to our gauch conformer. And I will continue that all the way to the other gauch conformer. I meant to write Gauch at degrees. So we have two values for the energy barriers. One is larger than the other. So we will assign the larger value to the larger peak, right? So this peak from point a down to the dotted line that we just drew that is a larger peak. So that is the larger energy barrier, which will have an energy value of 9. kilocalories per mole. And our hump right before the 200 or sorry, our hump at 240 degrees before the 300 degrees is equivalent to the hump at 120 degrees, right. So we will just label this first hump and that has a value of 5.4 kilocalories per mole. And there is one more value given to us. The anti conformer is more stable than a Gauch conformer by 1.4 kilocalories per mole. So the anti conformer noticed dips down below that dotted line where the gauch conformer is So that is the distance, the 1.4 kilocalories per mole is going to be the distance between the anti point and the point. So that is the 1.4 kilocalories per mole. So this is the potential energy diagram for 12 di bromo ethane for all of the dihedral angles from 0 to 360 degrees. That's it for this problem. I hope this video is helpful and thank you for watching.

Draw a potential energy diagram for rotation about the C¬C bond of 1,2-dichloroethane through 360°, starting with the least stable conformer. The anti conformer is 1.2 kcal/mol more stable than a gauche conformer. A gauche conformer has two energy barriers, 5.2 kcal/mol and 9.3 kcal/mol.

Key Concepts

Potential Energy Diagrams

Conformational Analysis

Energy Barriers

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