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$ B-F $ bond has a dipole moment but $ B{{F}_{3}} $ molecule does not. Why?

Answer
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Hint: We know that the covalent compounds can be polar or nonpolar, depending upon the polarity of bonds involved in these compounds. In polar covalent compounds, the bonding present is of polar covalent bonding.

Complete answer:
Polar molecules result from an unequal/unsymmetrical sharing of valence electrons. While there may be unequal sharing of electrons in the individual bonds, in a nonpolar molecule, these bonds are evenly distributed and cancel out. There is no net dipole. Nonpolar molecules are symmetric with no unshared electrons; polar molecules are asymmetrical, either containing lone pairs of electrons on a central atom or having atoms with different electronegativities bonds. The bond is formed in two different atoms which have different electronegativity that means there is an unequal sharing of electrons during bond formation between two atoms.
The unequal sharing of electrons leads to the development of fractional positive and negative charge on the atoms in a bond and the bond is said to become polar. In non-polar compounds, the bonding is a nonpolar type that means the electrons are shared between bonded atoms equally. Usually, the electronegativity difference between two bonded atoms in a nonpolar bond is less than $ 0.5. $ The formation of nonpolar covalent bonds may take place if bonded atoms in a polar covalent bond cancel the charges on them by arranging accordingly.
Thus, the polarity and non-polarity of molecules depend upon their dipole moment. During covalent bond formation, when there is an unequal sharing of electrons between atoms, the separation of charges takes place between atoms resulting in a dipole moment.

Note:
Remember that the dipole moment is denoted as $ \mu $ and measured in the Debye unit. The shape of a molecule with a dipole moment and the polarity of its bonds are the determining factors for deciding the overall polarity of that molecule. The molecule may contain a polar bond but the molecule may not be polar.