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polarity is intricately tied with electronegativity and dipole moment is (in this example) tied with the positioning of the Cl. Think cis- and trans- molecules in this scenario. The largest dipole moment would come from the Cl atom whose dipole moments do not cancel, b and c both cancel because the positioning of Cl are in opposite/ kind of opposite directions. a has the largest dipole moment.
Dipole moments occur in polar molecules, so because in 3, the dipoles in the C-Cl bonds are equal (as they are the same) and directly opposite to each other, they completely cancel out leaving the molecule non polar. Therefore, 3 is out. In 2, while the dipoles are pointing in different directions, they are not completely opposite to each other and therefore do not completely cancel; however, their dipole moment is relatively small as a result of some cancellation, as one points up while the other points down and to the right. 1 has the largest dipole moment because it has the least cancellation. The dipole of one points straight up while the other points up and to the right. Overall, they combine to point up, and this combination leads to the largest dipole moment of the three.
In order to find the polarity and the molecule with the strongest dipole moment, you have to add the vectors of the most electronegative atoms, in this case the chlorine. When you do this you find out that the first structure has the largest dipole moment vector pointing upwards and to the right.
You look at the electronegativity in each of the atoms (Cl are the more electronegative ones), then determine where the charge is being pulled. If the atom is uneven like it is in 1, the less the pull cancels out, leading to a larger dipole moment :) Hope this helps
The molecule with the largest dipole moments added up is the answer. The third one cancels out and has the least dipole moment, the second one has a dipole moment but is weaker than the first one because they are farther apart. The first one has the largest dipole moment because the two c-cl bonds are the closest and add up to a point right in between the two c-cl bonds.
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