How does the length of the z-component of the net dipole moment of ammonia relate to the actual length of the dipole moment vector?

1 Answer
Aug 20, 2017

Well, the length is identical. The dipole moment of ammonia is along its #z# axis, so the #x# and #y# components are zero, and only the #z# component contributes to the length.


The principal axis of rotation (#C_n#) requires the smallest angle of rotation #360^@/n# before coinciding with the original molecule.

For instance, the #C_n# axis of water requires a #180^@# rotation to bring it back to an orientation indistinguishable to how it was before. So, we call it #C_2# and point it along the #z# axis on the #yz# plane:

http://symmetry.otterbein.edu/

If you want to visualize this more, click on the image and try out the rotation yourself.

For ammonia, the #z# axis points vertically through the nitrogen atom, like the handle of an umbrella with the #"H"# atoms as the umbrella head.

http://symmetry.otterbein.edu/

The dipole moment of ammonia points exactly along the #z# axis. So, we write the dipole moment vector #vecmu# as:

#vecmu = << mu_x, mu_y, mu_z >>#

#= << 0, 0, 1.48 >>#

The length of the vector is given by the vector magnitude:

#color(blue)(|| vecmu ||) = sqrt(mu_x^2 + mu_y^2 + mu_z^2)#

#= sqrt(0^2 + 0^2 + ("1.48 D")^2)#

#=# #color(blue)("1.48 D")#