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4. Alkanes and Cycloalkanes

Now that we know how to calculate the difference in flip energy, we can plug that information into the famous Equilibrium Constant equation to determine exact K_{e} of the reaction.

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Calculating Chair Equilibrium

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Alright, guys. So in these videos, I'm going to teach you how to use free energy in killing joules per mole to calculate the exact percentages of each confirmation that you would get of a cyclo hexane again, These videos might be beyond the scope of what your professor wants you to know for your test. So I'm gonna leave it up to you to decide if you need to know this or not. All right, so you've been warned, so it's time to get into this. All right, So it turns out that we can use that delta G value that we get from our A values to calculate those exact, um, percentages at any given temperature. Okay, Now, the way we do this is through the Gibbs free energy equilibrium. Constant equation. Okay, now, just so you guys know if this equation looks familiar, it's not unique to this type of problem. In fact, pretty much any process that you could describe a free energy difference in can be, um, you can determine an equilibrium through this equation. So this is a There's a very important equation for all of chemistry, not just for cyclo Hexane is okay. now, as you can see, what it says is that let's just go through one term at a time says that the Delta G or the change in free energy is equal to the negative are now remember that our is the gas constant that we used to use in general chemistry. And there were two different values of our that we used to use. We'll just note that the one we're using is in jewels per most. That's 8.134 Okay, that's gonna be important in a second. Okay, then temperature temperatures in Calvin. Remember that? Um I mean, it's been a while since we dealt with temperature, but remember that zero degrees Celsius is equal to 0.15 degrees Kelvin. Okay, so it's gonna be a conversion that we have to use in a little bit. Then you're gonna multiply that by the natural log of the equilibrium. Constant. Well, in order to solve any of these problems for percentages, we need to know the value of the equilibrium constant because equilibrium constant by definition, tells you what's your products over your reactant? I need to know that fraction Okay, so if we go ahead and we saw for K E, I did the math for you. Don't worry. What we get is that the K E is equal to the negative Delta G over the R times, the tea all to the eat. OK? And if we can just plug in these variables, we're going to get the equilibrium constant. Now we know what our is. We know what t is. Your calculator tells you what he is. All we need is negative. Delta Jeep. Do we have a way to find that? Yes, guys, that through our A values are a values. Tell us what the free energy changes as we go Axial. Alright, Awesome. So now I do want to make one note of the Delta G notice that this is negative Delta G, but everything that we, um everything that we solved when you're doing a values we were actually solving for positive Delta G because we were actually looking at the less stable one. We're looking at how much energy they have to put into the system to go to Axl. So when we use this equation, we're actually gonna be in putting the positive Delta g here, and that's fine. Okay, So we're gonna be getting is a number that describes basically how we're going to that less stable. Um, that less stable value. Okay, so then over here we have is that then we get that Katie. And now we can solve for the percentages using the definition products Overreacting. Okay, so now, once we get that positive K e number, that positive Katie number means that we're actually going towards the favorite direction. I'm not sure if you guys remember, but if you have a k e over one, Okay, that means you're going to the more favorite direction. Okay, So I'm just telling guys right now, if we use a positive number for Delta G, we're going to get also a positive number, or I mean, I'm sorry. We're gonna get a number. That's above one for K E. We're gonna get this greater than one. It's gonna be equal greater than one. So what that means is that our definition of e has to be the products over the reactant meaning the more favored confirmation over the less favored. Okay, So just letting us know that the way that we've arranged this equation. And the way that your textbook does it is that it always does the more favored over the less favorite. Okay, meaning that when you get this positive value, it's gonna tell you what percentage you're gonna have of the equatorial, and then the that minus 100 will be your axial. Okay, now, here it says that K E is equal to X over one over X and guys, that just has to do with the definition of equilibrium. Constant help K is what your ex is what you're making, right? That's your product. So then one minus. Whatever you whatever you made would be you're reacting. Okay, then we don't really want k e here. We want X because we're really trying to figure out how much of this product we're going to get, right? So if we solve for X, I did that for you. What you're finally going to get is that X is equal to K E over K E plus one, and if you want to put it in a percentage term, it's times 100. Okay, now, that was a ton of words that I just said a lot of numbers and symbols. I do not need you guys to perfectly understand this as much as I just need you to memorize it and know how to understand and know how to use it. Okay, If you're Professor wants you to solve this on your exam, then thes equations should be in your mind. You should have memorized this equation. You should have memorized the definition of K e or how to solve for X. Alright, so now we're gonna focus on the actual working part on the actual part that we determine percentages, which is so cool, I personally am a huge or go nerd, as you guys know. So this is fun getting to determine the exact percentage of each cyclo hexane. So this first one will be a worked example, and we'll go ahead and start off with this first one. So I'm just going to pause the video and then we'll come back and we'll solve this one together.

Gas Constant correct number:8.**314**

Once we have the Ke of the equilibria, we can solve for x, which will be the percentage of my most favored chair.

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Problem

Estimate the equilibrium composition of the chair conformers of cis-1,3-diethylcyclohexane at room temperature.

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Did you remember to use the correct Gas Constant number?! (*8.314)*

3

Problem

Estimate the equilibrium composition of the chair conformers of trans-1-methyl-3-phenylcyclohexane at room temperature.

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*Note:* The correct value for methyl should be **7.6**, not 4.2

With that, the correct answer should be closer to __88__% / __12__% for the percentage of both chairs using the correct value for R (8.314). Hope that makes sense!

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