Step 1: Understand dipole moment and molecular geometry
Dipole moment depends on the difference in electronegativity between atoms and the geometry of the molecule. Molecules with symmetrical geometry often have zero dipole moment, while asymmetrical molecules have non-zero dipole moments.
Step 2: Analyze each molecule
- \( \mathrm{H_2O} \): Bent shape due to lone pairs on oxygen, polar molecule with a high dipole moment of about 1.85 D.
- \( \mathrm{BF_3} \): Trigonal planar and symmetrical, dipole moments cancel out, so net dipole moment is 0.
- \( \mathrm{NH_3} \): Trigonal pyramidal shape with lone pair on nitrogen, dipole moment approximately 1.47 D.
- \( \mathrm{NF_3} \): Also trigonal pyramidal, but due to electronegativity differences and bond dipoles partially canceling, it has a smaller dipole moment around 0.23 D.
Step 3: Match molecules with dipole moments
- \( \mathrm{H_2O} \) → 1.85 D (IV)
- \( \mathrm{BF_3} \) → 0 (I)
- \( \mathrm{NH_3} \) → 1.47 D (III)
- \( \mathrm{NF_3} \) → 0.23 D (II)
Step 4: Conclusion
The correct matching is:
\( \mathrm{H_2O} \) – IV, \( \mathrm{BF_3} \) – I, \( \mathrm{NH_3} \) – III, \( \mathrm{NF_3} \) – II.