How do you prove mathematically that the dipoles cancel in a carbon tetrachloride molecule?

Answer 1

You know that all the bond angles are 109.5 degrees, so the molecule is symmetrical under rotation by 109.5 degrees. If there is nothing asymmetrical that distinguishes one side of the molecule from the other, it follows that there is no dipole moment.

Answer 2

Stephen,

There are a couple ways to do this. The first way is to use the known geometry of the CCl4 molecule to express each dipole as a vector. You will need to define x, y, and z axes and then use the tetrahedral geometry to express the dipole of each C-Cl bond as a 3-D vector. Once you've done this, you can add the four vectors, and you will find that the sum is exacly <0,0,0>.

The second way will sound harder because it involves higher level math, but is actually much shorter. It involves the use of group theory, which is all about the symmetry that molecules contain. A "group" consists of all of the symmetry operations that one can perform on a molecule (or any other object) that will keep it looking exactly the same. The CCl4 molecule belongs to a group labelled "Td". This group posesses cubic symmetry, which means that it has a combination of symmetry elements that makes it impossible for the molecule to have a nonzero dipole. So if you know group theory, you can invoke this rule and make the claim simply based on the symmetry of the molecule.

I hope that helps with whatever you're doing. There are fascinating books and websites out there on symmetry, and I would encourage you to look at them if you find this problem interesting.

Answer 3

if u definitely need a mathematical proof do the following. dipoles are vectors. u have 4 vectors, all th same size, at 109.6 from one another. make a vectoral sum of all 4 of them, one after the other. you should end up with the 0 vector.

Answer 4

6.25 carbon tetrachloride to 1.26 dipoles.