Question
If B-Cl bond has a dipole moment, explain why $BCl_3$ molecule has zero dipole moment.

Answer

The dipole moment of any molecule is the vector sum total of each of the dipole moments. In $BCl_3$, molecule, although the B-Cl bonds individually are polar, the resultant dipole moment becomes zero.

We can see that the dipole moments of $B-^1Cl$ and $B-^2Cl$ produce a resultant which is equal in magnitude but opposite in direction to $B-^3Cl$ and hence cancels it out. That is why the net dipole moment of $BCl_3$, is zero.

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