[Rutherford]

Why does the left compound have a net dipole moment and the right not? I thought that both have zero moments, as both chlorine atoms are in the same plane and oppositely oriented.

[mkurek]

The compound on the left has two chlorine atoms concentrated on the same side of the molecule. This gives it a partial negative charge towards that end of the molecule.

[Rutherford]

Why? How don't the dipole moments of C-Cl cancel out?

[mkurek]

That's what causes the dipole moment. Look at the electronegativity values for carbon and for chlorine.

Which is more electronegative?

Chlorine is. That's why there's a dipole moment.

[Rutherford]

I know, but I couldn't figure out why don't they cancel out, the two C-Cl dipoles, but now I see, thanks.

[Rutherford]

How to calculate the net dipole moment of the left molecule if the dipole moment of C-Cl bond is marked as x?

[Corribus]

Put the cartesian origin at the center of the molecule, with the y-axis parallel to the line drawn between the two chlorines. Now consider dipole moment vectors. There is no dipole moment in the y-direction because there is a line of symmetry (the x-axis) between the two chlorines. What about the x-direction?

[Rutherford]

It looks like in the image I uploaded.  The intensity of a is 1, of b is 1 but in opposite direction, so their sum in y direction is 0. In the x direction, projection of vector a: a₁=a·cos90°=0, projection of vector b is b₁=b·cos90°=0, but this is surely wrong. Where is the mistake?

[Rutherford]

Oops. I see the mistake, the vector begin starts from the cartesian origin. Then the vectors should be divided into two components x and y, y cancels out, x adds. What's the value of angle alpha?

[Corribus]

Right. The total displacement vector in the x direction will be double whatever the distance between one of the chlorine atoms and the y axis is (double, because there are two chlorines). There is no z axis to worry about here because the molecule is flat. The dipole moment will be the magnitude of the displacement vector times the charge density of chlorine.

EDIT: Doesn't really matter what the angle alpha is. The y components cancel out, so all that matters is the x-components, which you can get without alpha. Remember, it's the total displacement vector that counts, not the individual vectors.  If you add your two vectors, you'll see you get a total vector lying exactly on the x axis (alpha disappears).

[Rutherford]

But, to calculate the x component and the net dipole moment I need the angle alpha. How to calculate x without the angle?

[Corribus]

You do not necessarily need alpha. All you need is coordinate information from either a good computation or an experiment (e.g., crystal structure). Calculating an actual magnitude for the dipole moment is a fair bit more difficult than just determining whether it is zero or nonzero, because you also need the charge density of chlorine.

[Rutherford]

Okay, thanks very much .