How does NH3 have 2 rotation axes?

[ampakine]

According to the character table for the C3v point group there are 2 C3 rotation axes along the z axis. How are there 2 of them? There is only 1 listed in the C2v point group table which makes sense but I can't see how a molecule like NH3 has more than one rotation axis along the z axis.

 

[SpectraCat]

According to the character table for the C3v point group there are 2 C3 rotation axes along the z axis. How are there 2 of them? There is only 1 listed in the C2v point group table which makes sense but I can't see how a molecule like NH3 has more than one rotation axis along the z axis.

You can rotate around the axis in either direction.

 

[DrDu]

There is only one axis, but two (or in reality 3) rotations (=symmetry elements): rotations by 0, 120 and 240 degrees.

 

[SpectraCat]

There is only one axis, but two (or in reality 3) rotations (=symmetry elements): rotations by 0, 120 and 240 degrees.

That is correct, but it is also the same as my answer. A rotation by 120 degrees is equivalent to a rotation by -120 degrees. Of course rotation by 0 degrees is equivalent to the identity element, E.

 

[Silex7]

who said that ammonia has 2 rotations axes? it has only one rotation axis which is C2 axis,

check here :
http://www.chemeddl.org/labs/avisualdatabase/index.php

and look for ammonia, and see symmetry properties.

 

[ampakine]

There is only one axis, but two (or in reality 3) rotations (=symmetry elements): rotations by 0, 120 and 240 degrees.

What about BrF₅ then. It belongs to the C_4v point group and according to here:
http://www.webqc.org/symmetrypointgroup-c4v.html
it has 2 C₄ rotations and a C₂ rotation. SpectralCats explanation works better here because if a 270 degree rotation can be considered a C₄ rotation then why couldn't a 180 degree rotation?

 

[ampakine]

who said that ammonia has 2 rotations axes? it has only one rotation axis which is C2 axis,

check here :
http://www.chemeddl.org/labs/avisualdatabase/index.php

and look for ammonia, and see symmetry properties.

who said that ammonia has 2 rotations axes? it has only one rotation axis which is C2 axis,

How can a 180 degree rotation of a trigonal pyramidal molecule be a symmetry element?

 

[Silex7]

How can a 180 degree rotation of a trigonal pyramidal molecule be a symmetry element?

look if you have a type of AB3 molecules with similar 3 atoms like NH3 then you have one rotation improper axis which is C2 this axis is passing through each H atom hence you have only one C2 axis since the 3 atoms are the same, but how does this axis process 180 symmetry?..this needs a bit visualization from you..

if you have a planar NH3 (that is a molecule drawn on planar paper with no 3D dimensions) and keeps in your mind the image of the C2 passing through one of the H atom, if you turn the paper to 180 degree (turn the paper to other side) you will have the left H atom in the right position and versa. and this is also with other atoms.

Notice also that NH3 has also C3 axis but this once passes through Nitrogen atom perpendicular to it (axis goes from the paper to out), that is if you rotate the molecules around the inner axis by 120 degree(that is the angel between 2 H atoms) you will actually have the same H positions which is another symmetry.
got it?

 

[SpectraCat]

look if you have a type of AB3 molecules with similar 3 atoms like NH3 then you have one rotation improper axis which is C2 this axis is passing through each H atom hence you have only one C2 axis since the 3 atoms are the same, but how does this axis process 180 symmetry?..this needs a bit visualization from you..

if you have a planar NH3 (that is a molecule drawn on planar paper with no 3D dimensions) and keeps in your mind the image of the C2 passing through one of the H atom, if you turn the paper to 180 degree (turn the paper to other side) you will have the left H atom in the right position and versa. and this is also with other atoms.

Notice also that NH3 has also C3 axis but this once passes through Nitrogen atom perpendicular to it (axis goes from the paper to out), that is if you rotate the molecules around the inner axis by 120 degree(that is the angel between 2 H atoms) you will actually have the same H positions which is another symmetry.
got it?

Except that NH3 is not planar .. you are describing D3h symmetry .. NH3 has C3v symmetry, and the OP is correct that it has no C2 axes.

 

[Silex7]

Except that NH3 is not planar .. you are describing D3h symmetry .. NH3 has C3v symmetry, and the OP is correct that it has no C2 axes.

Yes the trigonal pyramidal structure has only the C3 axis but there is no C2 axis, i mentioned the trigonal planar structure in my previous discussion.
http://www.chemeddl.org/labs/avisualdatabase/index.php?molecule=1&sort=name&kind=all&molecule2=-1&sort2=name

 

[SpectraCat]

Yes the trigonal pyramidal structure has only the C3 axis but there is no C2 axis, i mentioned the trigonal planar structure in my previous discussion.
http://www.chemeddl.org/labs/avisualdatabase/index.php?molecule=1&sort=name&kind=all&molecule2=-1&sort2=name

My point is that you are confusing the OP, because he asked about NH3 specifically, which is non-planar with C3v symmetry. Answering a question about another structure with another symmetry is not really relevant to his question.

Also you did NOT mention trigonal planar geometry in your initial response to the OP:

who said that ammonia has 2 rotations axes? it has only one rotation axis which is C2 axis,

check here :
http://www.chemeddl.org/labs/avisualdatabase/index.php

and look for ammonia, and see symmetry properties.

That response is just as wrong for a trigonal planar structure with D3h symmetry, which has one C3 xis and 3 C2 axes perpendicular to C3 axis.

What was the point of linking that website? It shows NH3 as non-planar with C3v symmetry also ... which is good, because otherwise it would be (very) wrong.

 

[SpectraCat]

What about BrF₅ then. It belongs to the C_4v point group and according to here:
http://www.webqc.org/symmetrypointgroup-c4v.html
it has 2 C₄ rotations and a C₂ rotation. SpectralCats explanation works better here because if a 270 degree rotation can be considered a C₄ rotation then why couldn't a 180 degree rotation?

Yes, that is correct. There are 4 permutations around the central 4-fold axis of symmetry corresponding to rotations of 90, 180, 270 (or -90) and 360 (or 0) degrees. The 180 degree rotation is equivalent to a C2 operation, while the rotations of 90 & -90 correspond to the two C4 operations.