Zero.as , BF3 has trigonal planar structure ,the resultant moment of any two B-F dipoles is equal in magnitude but opposite in direction to the moment of the third one. So, they get cancelled and thus net dipole of the BF3 molecule becomes zero, so, it is non-polar....

The value of the dipole moment for the BF3 molecule can be determined by considering its molecular geometry and the electronegativity of its constituent atoms.

Dipole Moment:
The dipole moment (µ) of a molecule is a measure of the polarity of the molecule. It is a vector quantity that indicates the separation of positive and negative charges within the molecule. A nonpolar molecule has a dipole moment of zero, while a polar molecule has a nonzero dipole moment.

Molecular Geometry of BF3:
To determine the dipole moment of BF3, we first need to consider its molecular geometry. BF3 has a trigonal planar molecular geometry, where the central boron atom is surrounded by three fluorine atoms. The boron atom is sp2 hybridized, forming three sigma bonds with the fluorine atoms. The molecule is symmetric, with the fluorine atoms forming an equilateral triangle around the boron atom.

Bond Polarity:
To determine the polarity of the BF3 molecule, we need to analyze the polarity of its bonds. The polarity of a bond is determined by the difference in electronegativity between the atoms involved. In general, a bond between atoms with different electronegativities will be polar, while a bond between atoms with similar electronegativities will be nonpolar.

The electronegativity of boron is 2.04, while the electronegativity of fluorine is 3.98. The difference in electronegativity between them is 1.94. This indicates that the bonds between boron and fluorine are significantly polar, with fluorine being the more electronegative atom and acquiring a partial negative charge (δ-) while boron acquires a partial positive charge (δ+).

Vector Sum of Bond Dipoles:
Since BF3 has a trigonal planar geometry, the dipole moments of the three B-F bonds are in the same plane. However, due to the symmetry of the molecule, these dipole moments cancel each other out, resulting in a net dipole moment of zero. Therefore, BF3 is a nonpolar molecule.

Conclusion:
The value of the dipole moment for the BF3 molecule is zero, indicating that it is a nonpolar molecule. This is due to the symmetric arrangement of the three fluorine atoms around the central boron atom, which results in the cancellation of the individual bond dipoles.