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Topic: Planes and Axes of Symmetry (Beginner's Question)  (Read 24342 times)

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teiubesc53

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Planes and Axes of Symmetry (Beginner's Question)
« on: January 29, 2006, 11:35:02 AM »
Hello, I need clarification on the following, please help.

Is it possible to have the axes or plane of symmetry in the middle of the molecule (without dissecting any atoms at all) like ethane for instance?

If so, I'm I right to say the following:

- the staggered conformation of ethane has 3 planes of symmetry (each passing the corners of one
  methyl group) and that it has 2 axes of symmetry -- one in the middle of C-C bond with 180
  degrees of (left to right) rotation and the other disects both carbon atoms with 120 degrees of (up and    
  down) rotation

- the conformation of propane with one C-C bond staggered and the
  other C-C bond eclipsed has only 1 plane of symmetry that cuts the 3 carbon atoms in the middle and
  it has no axes of symmetry






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Re:Planes and Axes of Symmetry (Beginner's Question)
« Reply #1 on: January 29, 2006, 03:06:18 PM »
Yeah, I think that's correct.

Staggered ethane also has an inversion center.  Have you learned about that yet?

teiubesc53

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Re:Planes and Axes of Symmetry (Beginner's Question)
« Reply #2 on: January 29, 2006, 09:05:48 PM »
Yeah, I think that's correct.

Staggered ethane also has an inversion center.  Have you learned about that yet?


Hi movies, thanks for the reply. We've just started our Organic Chem last week so I'm pretty new to all of this.. umm.. would the term "inversion center" the same as "center of symmetry"? I think the inversion center/center of symmetry of ethane is also located in the middle of the bond between two carbon atoms. If I draw a line from the center towards the corresponding hydrogens on both sides it will have equal distance. Am I correct?

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Re:Planes and Axes of Symmetry (Beginner's Question)
« Reply #3 on: January 30, 2006, 08:22:58 PM »
Yeah, it sounds like they refer to the same thing.

teiubesc53

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Re:Planes and Axes of Symmetry (Beginner's Question)
« Reply #4 on: January 31, 2006, 01:10:14 AM »
Yeah, it sounds like they refer to the same thing.

All right, thanks for your time  ;D

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Re:Planes and Axes of Symmetry (Beginner's Question)
« Reply #5 on: February 01, 2006, 07:10:30 PM »
A little bit more. For the staggered conformation, it has an improper rotation symmetry as well, a S6.

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Re:Planes and Axes of Symmetry (Beginner's Question)
« Reply #6 on: February 01, 2006, 07:50:31 PM »
A little bit more. For the staggered conformation, it has an improper rotation symmetry as well, a S6.

Nice!!

So what is the point group then??

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Re:Planes and Axes of Symmetry (Beginner's Question)
« Reply #7 on: February 01, 2006, 11:56:34 PM »
If i'm not wrong, it's D3v.

teiubesc53

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Re:Planes and Axes of Symmetry (Beginner's Question)
« Reply #8 on: February 02, 2006, 04:57:55 AM »
A little bit more. For the staggered conformation, it has an improper rotation symmetry as well, a S6.

Hi, maxyoung, thanks for pointing that out. Actually, we haven't discussed that in class yet, but I researched it. From my understanding you got the S6 from rotating the staggered ethane 6 times (360/60) and since they're not mirror images of each other it's called an 'improper' rotation. However, I'm not sure what you guys mean by point group and D3v. Can you guys explain it please. That would be greatly appreciated.

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Re:Planes and Axes of Symmetry (Beginner's Question)
« Reply #9 on: February 02, 2006, 02:14:27 PM »
An improper rotation axis is defined by a rotation around an axis followed by a reflection across a plane perpendicular to that axis.  The subscript in S6 means that you rotate by 360/6 = 60 degrees, and then apply the mirror.  I'm not sure where the S comes from, but it is the symmetry symbol used for improper rotation symmetry.  Also notice that there is no such thing as S2 symmetry because that is the same as i, which is the symbol for an inversion center.

As for point groups, they are symbols that define the overall symmetry of a molecule depending on the symmetry elements that are present (rotation axes, mirror planes, etc.).  You usually don't study them until you get to inorganic chemistry or some higher level math classes.  They have implications for some of the physical properties of compounds as well as bonding.

Don't confuse these point groups with crystallographic point groups or space groups, which are different.

Here is a flowchart for how to arrive at the various point groups: http://www.poshusta.chem.wsu.edu/GroupTheory/FlowChart.htm

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Re:Planes and Axes of Symmetry (Beginner's Question)
« Reply #10 on: February 03, 2006, 12:54:33 PM »
If you are also wondering what a group is:

a group is an algebraic structure. the main idea is that you link two elements of a set and get a third one. For example the whole numbers with + <Z, +> are be a group. you link two elements, e.g. 4 + 3 and you get 7.

with symmetry operations linking two operations means that you do both of them after each other and you get a third symmetry operation.

anyway, symmetry groups are the reason why chemists have group theory in their math classes. for example there is an effective way to calculate the number of isomeric structures with Burnside's Lemma. in some cases it works at least. I don't know if it has many practical purposes, but it's kind of cool.
Math and alcohol don't mix, so... please, don't drink and derive!

teiubesc53

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Re:Planes and Axes of Symmetry (Beginner's Question)
« Reply #11 on: February 04, 2006, 03:16:10 AM »
Thanks for the explanations. I understand it now a bit especially with the flow chart. Many thanks ;D

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