can you please tell me if I have the correct molecule type

PO4 3- polar

SO3 polar

NO2- polar

BrCl polar

phosphate tetrahedral in shape; therefore is non-polar.

SO3 is trigonal planar which makes it non-polar.(see http://www.tutor-homework.com/Chemistry_Help/Molecular_Geometry/049_Sulfur_Trioxide_SO3.html)
NO2- is trigonal planar electronic geometry but molecular geometry is bent or v-shaped which makes it polar.
BrCl is polar because although linear there is a light difference in electronegativity between Br and Cl.

calculate number of molecules in carbon atom

To determine if a molecule is polar or nonpolar, you need to consider both the molecular geometry and the polarity of the individual bonds.

1. PO4 3- (phosphate ion):
To determine the molecular geometry, we need to know the Lewis structure. The Lewis structure for PO4 3- is:

O
╱ ╲
O ═ P ═ O

O

In this structure, the central phosphorus (P) atom is bonded to four oxygen (O) atoms. Each oxygen atom has a double bond with the phosphorus atom, and the remaining electrons are lone pairs on the oxygen atoms.
The molecule has a tetrahedral geometry with the phosphorus atom at the center and oxygen atoms at the corners. However, the presence of lone pairs on the oxygen atoms makes the molecule polar.

2. SO3 (sulfur trioxide):
The Lewis structure for SO3 is:

O
╱ ╲
O ═ S ═ O

O

In this structure, the central sulfur (S) atom is bonded to three oxygen (O) atoms. Each oxygen atom has a double bond with the sulfur atom. The molecule has a trigonal planar geometry. Although the individual oxygen-sulfur bonds are polar due to differences in electronegativity, the molecule, as a whole, is nonpolar because the dipole moments cancel each other out.

3. NO2- (nitrite ion):
The Lewis structure for NO2- is:

O

N ═ O

In this structure, the central nitrogen (N) atom is bonded to one oxygen atom with a double bond and another oxygen atom with a single bond. The molecule has a bent or V-shaped geometry. The nitrogen-oxygen double bond is more polar than the single bond, and the molecule, as a whole, is polar due to the uneven distribution of electron density.

4. BrCl (bromine chloride):
To determine the molecular geometry, we need to know the Lewis structure. The Lewis structure for BrCl is:

Cl
|
Cl ═ Br

In this structure, the bromine (Br) atom is bonded to one chlorine (Cl) atom. The molecule has a linear geometry. Both the bromine-chlorine bond and bromine-chlorine dipoles are polar, resulting in an overall polar molecule.

In conclusion:
- PO4 3- (phosphate ion) is polar.
- SO3 (sulfur trioxide) is nonpolar.
- NO2- (nitrite ion) is polar.
- BrCl (bromine chloride) is polar.