a. Draw the two chair conformations of cis-1,3-dimeth...

Question

a. Draw the two chair conformations of cis-1,3-dimethylcyclohexane, and label all the positions as axial or equatorial.

b. Label the higher-energy conformation and the lower-energy conformation.

c. The energy difference in these two conformations has been measured to be about 23 kJ (5.4 kcal) per mole. How much of this energy difference is due to the torsional energy of gauche relationships?

d. How much energy is due to the additional steric strain of the 1,3-diaxial interaction?

Accepted Answer

All right. Hi, everyone. So this question reads as follows. Persist 13 di ethyl Cyclohexane part one draw and label the Axio and equatorial confirmations. Part two, determine which configuration would have the higher and lower energies. And part three calculate the energy difference due to the torsional energy of the Gauss relationship given that the energy difference of ax equatorial confirmation is approximately 17.2 kilojoules per mole. Lastly, for part two or excuse me, part four, calculate how much energy is due to the additional ster strain of the 13 di axial interaction. All right. So first, let's go ahead and get a sense for the structure of cy 13, diethyl Cyclohexane FBO Hexane is a six member ring. And here we have Ethyl substituents abbreviated here as C two H five on carbons one and three of the ring. Now, the cysts designation means that these ethel groups are going to be on the same side of the ring, whether they both point upwards or downwards. So from here, let's go ahead and group together parts one and two. And let's start by drawing out our chair confirmations, but actually let's go ahead and showcase stereo chemistry in the original structure by having both of our ethel groups on a wedge. However, you could also put them on a dash so long as they both point in the same direction. Alright. So now lets go ahead and talk about the cheer confirmation first. We're going to go ahead and draw out our six member ring as a chair confirmation. So for the purposes of clarity in my chair confirmation, I'm going to say that carbon number one is on this top right corner and I'm going to go ahead and keep labeling my carbons going in a counterclockwise direction. So on carbon number one, I would replace the equatorial hydrogen with my first EO group that's C two H five. And then on carbon number three, I would go ahead and do the same thing. So this is R equatorial confirmation and now let's go ahead and draw the axial. So now the Axio confirmation is obtained by flipping the first confirmation in this case, the equatorial. So now after a cheer flip, recall that substituents originally on equatorial positions are moved to axial positions and also position numbers should be rotated by one unit, whether that's clockwise or counterclockwise. Here, I'm going to rotate my position numbers one unit clockwise. Earlier, I mentioned that my ring was being labeled from one through six going in a counterclockwise direction, but I actually meant clockwise. So apologies for that. But here both Ethel groups would end up on Axio positions. So that concludes part one. Now, let's talk about part two, which is determining which config sorry, which confirmation has higher and lower energy. Recall that in this context, we talk about a concept known as equatorial preference. But what does that actually mean? Well, when we discuss equatorial preference, what that means is that chair confirmations in which bulkier or bigger substituents are on the equatorial position tend to be more stable. This is because larger substituents in the equatorial position experience less hysteric hindrance. And this translates to the equatorial conformer generally being more stable than the Axio conformer. And this example is no exception because recall that more stable confirmations have less energy. So here our equatorial conformer is going to have lower energy since it would be more stable in the Axio conformer would have higher energy. All right. So from here, we've completed part two. So now I'm going to scroll down to open up some space for some calculations in parts three and four. Now, as for part three were going to calculate the energy difference due to the torsional energy of the Gauss relationship. Recall that each Gaus interaction raises the energy of the compound by 4.2 kilo joules per mole. So in this particular case, we have two ethel groups and each ethel group would interact with another ethel group. So from this, we can calculate the energy difference due to that torsional energy because we have two ethel groups multiplied by two interactions, each or two interactions per ethel group multiplied by those 4.2 keto jules per m. So 4.2 multiplied by four, that's two multiplied by two. Here equals 16.8 kilo jewels promote. And that would be our answer to part three. All right. So from here, we can go ahead and scroll down to make some more space for part four, which is to calculate how much energy is due to the additional STAIC strain of the 13 di axial interaction. Now, the stric strain that comes from the 13 di axial interaction, specifically between the two ethel groups is the difference between the total energy and the energy due to that portion energy of the Gau interaction. So if I scroll up once more, we have already calculated the torsional energy of the Gauss relationship in part three. So we're going to subtract this quantity 16.8 kg joules per mole by our 17.2 kg joules per mole. So here part four thats 17.2 kilojoules per mole subtracted by 16.8 kilo jules per m and this equals 0.4 kilo Jules promo, which would be our final answer and there you have it. So here we have the answers to or it's one through four. So if you watch this video all the way through, thank you so very much for doing so. And I hope you found this helpful.

Key Concepts

Chair Conformation of Cyclohexane

Gauche Interaction

1,3-Diaxial Interaction

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