Final answer:
The molecules BCl3, BClH2, and BCl2H can be ranked in increasing order of dipole moments based on molecular symmetry and differences in electronegativity. BCl3 has no dipole moment due to its symmetrical shape, whereas BClH2 and BCl2H are not symmetrical and have nonzero dipole moments, with BCl2H having the highest due to having more polar B-Cl bonds.
Step-by-step explanation:
Ranking the molecules BCl3, BCl2H, and BClH2 in order of increasing dipole moments involves understanding both molecular geometry and electronegativity differences. For BCl3, the molecule is trigonal planar and symmetrical, which means any dipole moments from the B-Cl bonds cancel out, resulting in a net dipole moment of zero. In the case of BCl2H and BClH2, we need to compare the difference in electronegativity between B-Cl and B-H bonds as well as the molecule's geometry. The electronegativity difference between boron and hydrogen is smaller (2.04 for B and 2.20 for H) compared to boron and chlorine (3.16 for Cl), which makes B-H less polar than B-Cl.
Furthermore, the molecular geometry for BCl2H and BClH2 is no longer symmetrical, leading to a net nonzero dipole moment for both. The molecule with more B-Cl bonds will have a higher dipole moment due to the greater polarity of the B-Cl bond compared to the B-H bond. Thus, we can rank the molecules in order of increasing dipole moments as: BCl3 < BClH2 < BCl2H.