Organic Chemistry

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4. Alkanes and Cycloalkanes

Calculating Energy Difference Between Chair Conformations

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.



Explaining how A-Values are related to cyclohexane flip energy

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Alright, guys. So in the next few videos, I'm going to be going over a much more rigorous description of confirmation. All analysis. Now, the reason that we even recording these to begin with is because your textbook goes through all this detail on. 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 to mathematical and too tedious. OK, 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 gonna need you, Thio. Since it is mathematical, drop your iPhone calculator, whatever. And grab one of these because we're actually gonna be doing equations with e and logarithms and stuff like that. Okay, so if you need to pause the video to grab this, by all means, go for it. Let's go right into it. Okay, So the first thing that we're going to do is learn how to calculate flick energy. This has to do with cyclo. Hexane is okay. Sometimes we're gonna be required to actually calculate these numbers in kill a Jules per mole and calculate the expense that it takes for a molecule to flip from equatorial toe axial. Remember that I told you guys that equatorial preference states they're always trying to be in that more stable position. But how much energy does it actually take for the molecule toe 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 gonna find in your textbook, but it is found in mawr, 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 die actual interactions that are created by going into the actual position. Okay, So, essentially in those parentheses, what I have is it's literally just the energy difference between the axial and equatorial positions in killing 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 killing joules 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 1 kg cal promote equals 4. killer jewels. Permal. So anything that I'm teaching you today in killer jewels, you can apply tequila cows. You just have to do that simple dimensional analysis. Okay, Now, personally, I'm gonna choose to do everything in kilocalories. I'm sorry. Exact opposite killer jewels per mole. The reason is because all the equations that we're gonna use in the next few videos are in Kila 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 killing joules per mole and these air. 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, let's just look at an easy definition here. Hydrogen has an a value of zero. Could you describe or kind of explain why you would have a value of zero? Because, guys, if you're substitution, is hydrogen, all of the substitutions or hydrogen and that means there's no difference between actual in 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 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 toe. Have a cyclo hexane rest in the actual position versus the equatorial position. Okay, so you're gonna be expending 6.7 point 6 kg per mole to keep it in the unstable position. Okay. And as you can see as the groups get bigger, Ethel Turk beetle. 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 hell logins. Interestingly, the hell logins 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 going to be to switch it to the actual position. But remember halogen zehr 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. Is that air 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 interaction. So imagine that I'm gonna race this, but imagine that this is my target molecules. Imagine that. That's my iodine right or whatever. The 13 die actual interactions are the interactions experienced with the hydrogen? Is that air also actually correct? Well, what I'm trying to say is that I dine, 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 alkaline alcohol. Very important. And then a A final group, right? A federal group. I'm sorry, a federal 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 of metal cyclo hexane. Okay, it's in the equatorial position now. It's gonna 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 a value say 7.6. That's what I would right here that the axial is going to cost me 7. killer jewels 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 gonna 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 gonna 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 Is your equilibrium constant? It's defined by the products over the reactant. So 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 equilibrium. Okay. The equatorial, um molecule. Okay, now remember that K e is products overreacting. Okay, that's what it's defined as So when we do calculations with Katie later, we're always gonna use this definition of products. Overreact INTs where products is your axial 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 actual position? Okay, What amount of this is going to go to the equatorial position? Perfect. Alright, so now I wanna 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 it. So you're trying to make a human projection and you're 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 metal group. Right, And then I've got this hydrogen that's coming off of the KAOS gosh position. Okay, So do you guys recall what was the energy that it took to move ah, hydrogen into the gosh position for a metal group? It was actually 3.8 kg 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 gosh confirmation over here. You have the same exact gosh interaction over there. It's just you have to rotate the molecule. So what's crazy is that thes 13 die? Actual interactions are just accumulation of these gosh interactions that we had talked about. Four Newman projections, so Ah, gosh. Confirmation cost 3.8 for a meth Alana hydrogen. Well, what if you have two of them, then that's gonna equal. You're a valve. You're a value. So in a value is really just a some of these gosh 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 Newman 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]


Calculate the difference in Gibbs free energy between the alternative chair conformations of trans-4-iodo-1-cyclohexanol. 


Calculate the difference in Gibbs free energy between the alternative chair conformations of cis-2-ethyl-1-phenylcyclohexane.