How is #"CO"_2# nonpolar?

By symmetry.

Polarity is a vector concept, i.e. a bond is polar because the electric dipole moment #vecmu# points in a given direction (#x,y,z#) with a given magnitude #|vecmu|#, i.e.

#vecmu = << mu_x, mu_y, mu_z >>#

As vectors of identical magnitudes in exactly opposite directions add to cancel out completely, a "perfectly symmetrical" compound must be nonpolar, so that

#sum_i vecmu_i = 0#

For #"CO"_2#, we would have...

So, what do we mean by "perfectly symmetrical"? We mean the parent geometries of each so-called VSEPR structure, i.e. the ones with no lone pairs of electrons:

• two-atom linear, e.g. #"N"_2#
• three-atom linear, e.g. #"CO"_2#
• trigonal planar, e.g. #"BF"_3#
• tetrahedral, e.g. #"CCl"_4#
• trigonal bipyramidal, e.g. #"PF"_5#
• octahedral, e.g. #"SF"_6#
• etc.

all of which were NONPOLAR as listed above.

The following, more usual examples, are POLAR:

• #"NO"^(+)#, i.e. #:"N"-=stackrel((+))("O": )#, two-atom linear
• #"N"_2"O"#, i.e. #:stackrel((-))ddot"N"=stackrel((+))"N"=ddot"O":#, three-atom linear
• #"AlF"_2"Cl"#, trigonal planar
• #"CH"_3"Cl"#, tetrahedral
• #"PF"_3"Cl"_2#, trigonal bipyramidal
• #"SF"_5"Cl"#, octahedral