To determine which of the given molecules is both polar and has a tetrahedral molecular geometry, let's analyze each option step-by-step:
### Option a.) [tex]\( \text{CH}_2\text{Cl}_2 \)[/tex] (Dichloromethane)
1. Molecular Geometry: Dichloromethane has a central carbon atom bonded to two hydrogen atoms and two chlorine atoms. Carbon forms four single bonds, so the molecular geometry is tetrahedral.
2. Polarity: The C-H and C-Cl bonds have different electronegativities. Chlorine is more electronegative than hydrogen, creating a situation where the dipole moments do not cancel out. This leads to a net dipole moment, making the molecule polar.
### Option b.) [tex]\( \text{BF}_3 \)[/tex] (Boron Trifluoride)
1. Molecular Geometry: Boron trifluoride has a central boron atom bonded to three fluorine atoms. Boron forms three single bonds with no lone pairs, so the molecular geometry is trigonal planar.
2. Polarity: The symmetry of the trigonal planar shape means that the dipoles of the B-F bonds cancel out, making the molecule nonpolar.
### Option c.) [tex]\( \text{CH}_2\text{O} \)[/tex] (Formaldehyde)
1. Molecular Geometry: Formaldehyde has a central carbon atom bonded to two hydrogen atoms and one oxygen atom, with a double bond to oxygen. The carbon forms a total of three regions of electron density, leading to a trigonal planar geometry for the atom arrangement.
2. Polarity: The molecule is polar due to the significant difference in electronegativity between oxygen and hydrogen, resulting in a net dipole moment.
### Option d.) [tex]\( \text{PO}_4^{3-} \)[/tex] (Phosphate Ion)
1. Molecular Geometry: The phosphate ion has a central phosphorus atom bonded to four oxygen atoms. With no lone pairs on phosphorus, the structure is tetrahedral.
2. Polarity: As an ion, it is not considered a neutral molecule and has a charge of -3, so it is different from typical polar molecules that we compare based on symmetry and dipole moments.
### Conclusion
The molecule that is both polar and has a tetrahedral molecular geometry is option a.) [tex]\( \text{CH}_2\text{Cl}_2 \)[/tex] (Dichloromethane). This molecule has the appropriate molecular geometry and a net dipole moment due to the difference in electronegativity between its bonded atoms.
Therefore, the correct answer is:
a.) [tex]\( \text{CH}_2\text{Cl}_2 \)[/tex]
