Which of the following molecules are polar and therefore have a net dipole moment?

Introduction / Context:
Molecular polarity is a key concept in chemistry that helps explain solubility, boiling point, intermolecular forces and many physical properties. A molecule is polar if the distribution of electron density is uneven and the individual bond dipoles do not cancel out, resulting in a net dipole moment. This question asks which among SO2, CH2Cl2 and PCl3 are polar. Correctly identifying the shape and symmetry of each molecule is essential to determining whether it is polar.

Given Data / Assumptions:

• SO2 consists of one sulfur and two oxygen atoms.
• CH2Cl2 consists of one carbon, two hydrogen atoms and two chlorine atoms.
• PCl3 consists of one phosphorus and three chlorine atoms.
• We assume standard valence shell electron pair repulsion theory for molecular shapes.

Concept / Approach:
Polarity depends on both bond polarity and molecular geometry. Individual bonds may be polar if atoms have different electronegativities. If the molecule is symmetric, bond dipoles may cancel and the molecule can still be nonpolar. SO2 has a bent structure, not linear, so its bond dipoles do not cancel and it is polar. CH2Cl2 has a tetrahedral arrangement but different atoms around the carbon (two hydrogens and two chlorines), so the bond dipoles do not fully cancel and the molecule is polar. PCl3 has a trigonal pyramidal shape due to one lone pair on phosphorus, which prevents complete cancellation of bond dipoles, again giving a net dipole moment. Thus all three molecules are polar.

Step-by-Step Solution:
Step 1: For SO2, apply valence shell electron pair repulsion theory and note the presence of a lone pair on sulfur that leads to a bent geometry. Step 2: Recognise that in a bent molecule with polar sulfur oxygen bonds, the bond dipoles cannot cancel completely. Step 3: For CH2Cl2, recall that the molecule has a tetrahedral shape but different surrounding atoms, so the polar carbon chlorine bonds are not symmetrically opposed. Step 4: For PCl3, identify the trigonal pyramidal shape caused by a lone pair on phosphorus and accept that the polar phosphorus chlorine bonds produce a net dipole. Step 5: Conclude that SO2, CH2Cl2 and PCl3 are all polar molecules and choose the option that includes all of them.

Verification / Alternative check:
An additional verification is to consider physical properties and typical textbook classifications. SO2 is often mentioned as a polar molecule responsible for certain atmospheric phenomena. CH2Cl2 is known to be polar and is often used as a polar organic solvent. PCl3 is also recognised as polar due to its pyramidal structure. None of these molecules have a fully symmetric geometry that would allow complete cancellation of bond dipoles. These supporting facts confirm that all the listed molecules are polar.

Why Other Options Are Wrong:
Options that name only one of the molecules as polar ignore the polarity and geometry of the others.
The option stating none of the molecules are polar conflicts with both molecular shape analysis and standard textbook information.
Since each molecule separately has a net dipole, any answer that excludes one or more of them is incomplete or incorrect.

Common Pitfalls:
A common mistake is to assume that any molecule with a tetrahedral or trigonal structure is nonpolar, without checking the actual atoms involved or the presence of lone pairs. Another pitfall is to focus only on electronegativity differences and forget to consider geometry, which decides whether bond dipoles cancel. Drawing simple three dimensional sketches and marking bond dipoles can help you avoid these errors and confidently determine molecular polarity.

Final Answer:
All three molecules listed, SO2, CH2Cl2 and PCl3, are polar, so the correct answer is all of the above.