Orgo Concept question (cyclohexane chair angles)

[MBHockey]

I seem to have a good grasp on O-Chem to this point (only four weeks in though 🙂) but I'm curious about this one thing that I can't seem to wrap my head around.

In the chair confirmation of cyclohexane, I don't understand how you can measure angles between C atoms -- angles between H atoms branched off of carbons make sense since you can easily compare the "branch" that is the bond with other atoms -- but two C atoms, where's the frame of reference for two spheres?

For example, there's a sentence in my text which states that the C1 and C4 carbons of cyclohexane are gauche to each other. I don't understand see how they are at 60 degree angles to each other like the hydrogen atoms on C2 and C3 are to each other. Since C1 and C4 are not directly bonded...which bond do you "look down" to make this determination?

I have constructed a model of cyclohexane and have been staring at it for the past hour trying to figure out how you come to the conclusion that C1 and C4 are gauche. Similarly, how is an axial hydrogen on C1 gauche to C3? Again, I am confused which bond to "look down" to easily see this relationship.

I just don't see the frame of reference used when comparing anything to just a C atom.

Thanks

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[BerkReviewTeach]

I seem to have a good grasp on O-Chem to this point (only four weeks in though 🙂) but I'm curious about this one thing that I can't seem to wrap my head around.

In the chair confirmation of cyclohexane, I don't understand how you can measure angles between C atoms -- angles between H atoms branched off of carbons make sense since you can easily compare the "branch" that is the bond with other atoms -- but two C atoms, where's the frame of reference for two spheres?

For example, there's a sentence in my text which states that the C1 and C4 carbons of cyclohexane are gauche to each other. I don't understand see how they are at 60 degree angles to each other like the hydrogen atoms on C2 and C3 are to each other. Since C1 and C4 are not directly bonded...which bond do you "look down" to make this determination?

I have constructed a model of cyclohexane and have been staring at it for the past hour trying to figure out how you come to the conclusion that C1 and C4 are gauche. Similarly, how is an axial hydrogen on C1 gauche to C3? Again, I am confused which bond to "look down" to easily see this relationship.

I just don't see the frame of reference used when comparing anything to just a C atom.

Thanks

Gauche and anti do not refer to a bond angle. The book likely used the term dihedral angle. It's basically the angle of rotation away from perfectly eclipsed substituents on a C-C bond.

In that case, the are looking directly down the C2-C3 bond in such a way that C3 is eclipsed from view by C2. If C1 is sticking straight down, then in a two-dimensional perspective, C4 would have to be rotated by 60 degrees to become eclipsed by C1.

That terminology basically refers to a two-dimensional perspective of a three-dimensional molecule.

 

[MBHockey]

Gauche and anti do not refer to a bond angle. The book likely used the term dihedral angle. It's basically the angle of rotation away from perfectly eclipsed substituents on a C-C bond.

In that case, the are looking directly down the C2-C3 bond in such a way that C3 is eclipsed from view by C2. If C1 is sticking straight down, then in a two-dimensional perspective, C4 would have to be rotated by 60 degrees to become eclipsed by C1.

That terminology basically refers to a two-dimensional perspective of a three-dimensional molecule.

Yeah, I'm aware of that -- the angles I was talking about were with respect to a Newman projection (something I should have stated.)

 

[BerkReviewTeach]

Yeah, I'm aware of that -- the angles I was talking about were with respect to a Newman projection (something I should have stated.)

The dihedral angle of 60 degrees is from the Newmann projection of cyclohexane.