Final answer:
The dipole moments of BCl₃, BCl₂H, and BClH₂ increase in the order BCl₃ < BCl₂H < BClH₂ due to differences in molecular geometry and the asymmetry caused by the substitution of chlorine atoms with hydrogen.
Step-by-step explanation:
The question asks to rank the molecules BCl₃, BCl₂H, and BClH₂ in order of increasing dipole moments. Dipole moments arise from differences in electronegativity between bonded atoms and are influenced by the molecular geometry. BCl₃ is a trigonal planar molecule with no net dipole moment because the bond dipoles cancel out due to symmetry. BCl₂H has a trigonal planar geometry as well, but with one hydrogen replacing a chlorine atom. This creates some asymmetry, leading to a small dipole moment. BClH₂ has a bent shape due to the two hydrogens and one chlorine around the boron, resulting in a greater asymmetry and a larger dipole moment compared to BCl₂H. Therefore, the order of increasing dipole moments is BCl₃ < BCl₂H < BClH₂.