Calculating Energy Difference Between Chair Conformations
4. Alkanes and Cycloalkanes
Calculating Energy Difference Between Chair Conformations - Video Tutorials & Practice Problems
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For most classes all you will need to know how to do is use equatorial preference to predict the most stable chair conformation.
However, sometimes you will be required to use energetics to calculate the exact percentages of each chair in solution. This is a multistep process, so here I'm going to walk you through it from scratch.
Calculating Flip Energy
First we have to introduce the concept of an A-value, which is simply the energy difference between the equatorial (most stable) and axial (least stable) positions.
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concept
Explaining how A-Values are related to cyclohexane flip energy
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9m
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Video transcript
Alright guys, so in the next few videos I'm going to be going over a much more rigorous description of conformational analysis. Now, the reason that I'm even recording these to begin with is because your textbook goes through all this detail and I'm just trying to be as comprehensive as possible. All right. But this also happens to be an area of organic chemistry that many professors don't teach because they just find it too mathematical and too tedious. Okay, so you're gonna be responsible to talk to your professor or you know, look at old exams or whatever and determine if this is something that you need to know or not. Okay, I'm just teaching it just in case Now, as a side note, I'm going to need you to since it is mathematical, drop your iphone calculator, whatever and grab one of these because we're actually going to be doing equations with E and logarithms and stuff like that. Okay, so if you need to positive video to grab this by all means go for it. Let's go right into it. Okay. Okay, so the first thing that we're going to do is learn how to calculate flip energy. This has to do with cyclo hexane. Okay, sometimes we're going to be required to actually calculate these numbers in killing joules per mole and calculate the expense that it takes for a molecule to flip from equatorial to axial. Remember that I told you guys that equatorial preference states they are always trying to be in that more stable position. But how much energy does it actually take for the molecule to flip into that less stable position? Well, thankfully scientists have done that those scientific experiments for us and they developed something that we call a values. Okay now this term A values is a term that you're not going to find in your textbook. But it is found in more complicated texts. And obviously like if you look online you would see if this is called a values. Okay so you can Wikipedia later And but basically what is an A value? All it is is it's the sum of all of the energy expenses of the 13 di actual interactions that are created by going into the actual position. Ok so essentially in those parentheses, what I have is it's literally just the energy difference between the actual and equatorial positions in killed joules per mole. Okay now whenever you're measuring anything with energy you have to be aware that some texts and some professors like to use kila jewels per mole. And some professors like to use kilocalories per mole. Okay now I'm just gonna lower the screen for just one second. So you can see that there is just a really easy conversion here. Remember that one kilocalories per mole equals 4. kg joules per mole. So anything that I'm teaching you today in kila jules you can apply to kill a cow's you just have to do that simple dimensional analysis. Okay now personally I'm gonna choose to do everything in kilocalories per I'm sorry, exact opposite killer joules per mole. The reason is because all the equations that we're gonna use in the next few videos are in kilo jewels. So it doesn't make sense to go back and forth between kilocalories. That's just a waste of time. Okay, so now here are some of the most important A values in kilograms per mole. And these are not for you to memorize, but just you can see as a general trend that as your groups get bigger, the values get larger as well. So you can see that um like let's just look at an easy definition here, hydrogen has an A value of zero. Could you describe or kind of explain why it would have an A value of zero? Because guys if your substitution is hydrogen, all of the substitutions are hydrogen and that means there's no difference between actual and equatorial. That means that when you flip it, it's the same exact energy. So hydrogen is our standard. That's basically means that there's zero energy lost or or it costs zero energy to have it in one in one position versus another. Okay, now, if we all of a sudden make it into a methyl group. Now you can see the a value goes up significantly. Okay, because now what that's saying is that it costs 7.6 kg per mole to have a cycle hexen rest in the actual position versus the equatorial position. Okay, so you're gonna be expending 6.7 point six kg per mole to keep In that unstable position. Okay, and as you can see as the groups get bigger ethel tribunal, these values start to get really crazy high. Okay, just you guys know, 23 kg per mole is a large number in organic chemistry. Okay. As you can see, I've got the allergens interestingly, the halogen is don't change much notice that iodine, chlorine and bromine are all about the same and they're not really in the right order that you would expect. You would think that maybe as you get bigger, the harder it's gonna be to switch it to the actual position. But remember halogen are unique because their bond lengths also get longer. So look at iodine, it's in an interesting position where it happens to be the biggest one. So you would think, oh heck, that thing does not want to move axial, but it also has the longest bond length. So it doesn't really have a lot of interactions with the hydrogen that are next to it. Okay, now, really quick and I know I'm kind of jumping around but this is exactly a diagram of those 13 die actual interactions. So imagine that I'm gonna erase this, but imagine that this is my target molecules. So imagine that that's my iodine, right? Or whatever the 13 die actual interactions are the interactions experienced with the hydrogen that are also actually correct? Well, what I'm trying to say is that iodine for example, has a super long bond. So it's almost out of the way from those hydrogen. Okay, so just kind of exception again. Please don't memorize it. It's just interesting. And then we've got some other weird substitue ints that I just thought were interesting and I thought might be relevant. So I have a cyanide, I have an al kind alcohol. Very important. And then a final group write a final group. I'm sorry, a final group. Okay, so let's move ahead to this diagram here. So here I have my equatorial position. As you can see, I'm just looking at an example of methyl cyclo hexane. Okay, it's in the equatorial position. Now it's going to take energy for it to move to the actual position. How much energy? Well, for that. We have to look at our values and our values say 7.6. That's what I would write here that the actual is going to cost me 7. kg joules per mole. Now, according to what we learned in the past, we would have easily been able to say that over 50% of the molecule is going to be Equatorial and less than 50% is going to be axial. Why? Because we know that equatorial preference states that you favor the equatorial site. So favor means that more than half is that and less than half is this perfect. But in this exercise by the end of these videos we're gonna be able to calculate the exact percentage is not just this one's better, this one's worse. I'm gonna be able to say that 95% of it is going to be equatorial and only 5% will be actual. How do we get there through these calculations? Okay, so now I just have to go over a few more terms. Remember that K. E is your equilibrium constant? It's defined by the products over the reactant. Okay, so I would expect that my K E. Would go to the left in this in this case. Okay. That my K. E. Would have a value that would favor the equal. Okay, the equatorial molecule. Okay, now remember that K. E. Is products over reactant? Okay, that's what it's defined as. So when we do calculations with Katie later, we're always going to use this definition of products Overreacting where products is your axle and reactant is your equatorial. Now you might be asking me johnny why is products axial? Because that's the thing we're trying to make we're trying to get it to go axial. So I'm saying what amount of this is going to go to the axial position. Okay, what amount of this is going to go to the equatorial position. Perfect. Alright. So now I want to just make a quick note here guys of that 7.6 number. Um it seems random. But it's actually related to something that we've learned in the past because if you took, let's say an eyeball, let's say you're trying to make a Newman projection and you were trying to see how these you know how this bond looked. What you would actually find is that the hydrogen are actually in a Gosh confirmation to the methyl group. So, see here, I've got this um I've got this methyl group, right, And then I've got this hydrogen that's coming off of the gauze gauze position. Okay, so do you guys recall what was the energy that it took to move a hydrogen into the Gosh position for a methyl group? It was actually 3.8 kg joules per mole. Okay, now you can't see it in this diagram because I'm kind of splitting it down the middle. But you would have the same exact confirmation over here. You have the same exact interaction over there. It's just you have to rotate the molecule. So what's crazy is that these 13 di actual interactions are just accumulation of these Gosh interactions that we had talked about. Four Newman projections. So, a Gosh confirmation cost 3.8 for a methyl and a hydrogen? Well, what if you have two of them, then that's going to equal, you're a you're a value. So a value is really just to some of these gauche interactions that are happening on a new and projection kind of interesting. Again, you don't need to calculate this. I just find it interesting that you can actually somewhat derive or approximate these A values just from learning your confirmation of values from new and projections, so these concepts are related.
We can use these values to calculate how much energy it is going to take to flip a chair into its least stable form.
Note:The above chair flip in the video is slightly off. Remember that the direction of the groups (up vs. down) should not change when going from axial to equatorial or vice versa.
All the math is still correct here, but I should have drawn the groups down instead of up on the second chair.:)
[Refer to the videos below for examples of this]
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Problem
Problem
Calculate the difference in Gibbs free energy between the alternative chair conformations of trans-4-iodo-1-cyclohexanol.
A
6.1 kcal/mol
B
1.5 kcal/mol
C
2.3 kcal/mol
D
3 kcal/mol
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Problem
Problem
Calculate the difference in Gibbs free energy between the alternative chair conformations of cis-2-ethyl-1-phenylcyclohexane.