Step 1: Understand that molecular polarity depends on both the polarity of individual bonds and the geometry of the molecule. A molecule is polar if it has a net dipole moment, meaning the bond dipoles do not cancel out.
Step 2: Analyze the molecular geometry of each molecule using VSEPR theory: CO_2 is linear, CCl_4 is tetrahedral, BF_3 is trigonal planar, and NH_3 is trigonal pyramidal.
Step 3: Consider the electronegativity differences and bond dipoles. For example, in CO_2, the C=O bonds are polar, but because the molecule is linear and symmetrical, the dipoles cancel out, making it nonpolar.
Step 4: Evaluate the symmetry and dipole cancellation in each molecule. CCl_4 is symmetrical tetrahedral with identical C-Cl bonds, so dipoles cancel. BF_3 is trigonal planar and symmetrical, so dipoles cancel as well.
Step 5: Recognize that NH_3 has a trigonal pyramidal shape with a lone pair on nitrogen, causing an asymmetrical distribution of charge. This results in a net dipole moment, making NH_3 polar.