Chair Conformations of Cyclohexane - equivalent structures?

[Qube]

Homework Statement

Are these structures equivalent? Here's the professor's rendering:
http://i.minus.com/jnojtCx6wYvqD.png

The Attempt at a Solution

Here's my rendering. The molecule is 1-chloro-2-ethylcyclohexane.
I had projected the chlorine out of the page and the ethyl group into the page (opposite of the prof's rendering). And since the chloro is on the first carbon, and in my chair conformation, there are only two possible positions for any attachment to the first carbon - axial up or equatorial down - I made the chlorine axial up (because it's also up in the 2D drawing I made). Similarly, I made the ethyl group axial down (because it's projected into the page according to my 2D drawing, and the alternative is making it equatorial up, which doesn't match my 2D drawing).
Is my reasoning correct and is my drawing ultimately correct?
Here's my drawing.

 

[AGNuke]

No problem on my side.

 

[Qube]

Sweet, great to hear from a budding organic chemistry student! So in sum, if something is trans, then that just means the attachments are on opposite sides of each other right? Cis just means same side right?

Also is the chair flip of cyclohexane best described as creating a mirror image or is it something else?

 

[AGNuke]

Sweet, great to hear from a budding organic chemistry student!

Are you talking about me?

if something is trans, then that just means the attachments are on opposite sides of each other right? Cis just means same side right?

Fair enough.

Also is the chair flip of cyclohexane best described as creating a mirror image or is it something else?

I don't think that flipping of chair conformation affects the wedge-dash diagram. I tried making them and arrived at this conclusion, but it'd better if you wait for some confirmation.

 

[Qube]

Oops, I could have phrased that a lot more clearly. I meant what you said was great to hear for a new orgo student (that would be me).

 

[AGNuke]

The thing is, I haven't studied organic chemistry in about an year since I came in college for engineering, so I can't be exactly termed as Organic Chemistry student.

 

[Qube]

Probably still know more orgo than I do! So would it be correct to say that for each position on the cyclohexane chair conformation, there are one of two choices - up or down?

I ask because this is the process I have for converting between 2D projections and 3D conformations:

1) Number the carbons correctly (according to nomenclature rules).

2) Wedge: coming out the page. Up. So choose make that substituent up (be it equatorial up or axial up; doesn't matter - everything's relative). But since each carbon has only two "options" - i.e the first carbon above only has the option of having an axial up substituent or an equatorial down substituent, I just have to match the orientation).

3) Dash - going away from me (going into the page). Down. Make this substituent down (be it axial down or equatorial down).

Also are these directions alternating - i.e. one up and one down - because the angle between the substituents is about 109.5 degrees? I think I remember my book saying that the actual angle is 110.9 degrees (some compromise between angle and torsional strain).

 

[AGNuke]

So would it be correct to say that for each position on the cyclohexane chair conformation, there are one of two choices - up or down?

Yes.

I ask because this is the process I have for converting between 2D projections and 3D conformations:

Assuming you are handling "cyclohexane", you are correct.

Also are these directions alternating - i.e. one up and one down - because the angle between the substituents is about 109.5 degrees? I think I remember my book saying that the actual angle is 110.9 degrees (some compromise between angle and torsional strain).

I think you need to reframe this one.

 

[Qube]

What's wrong with the last statement?

 

[AGNuke]

I mean the way you are asking question, I'm not getting what you are actually asking (or telling).

"Are these directions alternating" - Are you referring to the adjacent carbons?

 

[Qube]

I mean the hydrogens or whatever substituents on the carbons - are they alternating up / down because of the angle between the attachments on the carbon?

 

[AGNuke]

And you mentioned the reason for your conclusion being the bond angle. All the substituents can be up or down.
(I think I saw Hexachlorobenzene that way), but that would cause a little bit of torsional strain I suppose.

 

[Qube]

True, all the substituents can be up or down but only on certain carbons are there say axial up positions. I.e. None of the carbons on the bottom of the chair would have axial up positions except the middle one.