Which of the following molecules is nonpolar and has a completely symmetrical three dimensional molecular shape?

Introduction / Context:
Polarity of molecules is a key concept in chemistry because it influences solubility, boiling point, and intermolecular forces. This question asks which listed molecule is nonpolar and has a symmetrical three dimensional shape. Understanding both molecular geometry and bond polarity is essential to answer correctly.

Given Data / Assumptions:
- The molecules listed are common small molecules: NH3, HCl, H2O, CH4, and HF.
- Some of these have polar bonds, but the overall molecular polarity depends on both bond polarity and shape.
- Symmetry of the molecule can cause bond dipoles to cancel out, producing a nonpolar molecule.

Concept / Approach:
A molecule is nonpolar if the vector sum of its bond dipoles is zero. This often occurs when the molecule is highly symmetrical and all surrounding atoms around the central atom are identical. Methane CH4 is tetrahedral with four identical C–H bonds arranged symmetrically. Even though each C–H bond is slightly polar, the symmetry causes the individual dipole moments to cancel, resulting in an overall nonpolar molecule.

Step-by-Step Solution:
Step 1: Recall the shapes: NH3 is trigonal pyramidal, H2O is bent, CH4 is tetrahedral, and HCl and HF are linear diatomic molecules. Step 2: Identify which shapes are symmetrical: the tetrahedral geometry of CH4 is highly symmetrical, while bent and trigonal pyramidal geometries are not. Step 3: For diatomic molecules like HCl and HF, there is only one bond and it is polar, so the whole molecule is polar. Step 4: For CH4, consider four identical C–H bonds oriented to the corners of a tetrahedron around carbon. Step 5: Because CH4 is symmetrical and all bonds are equivalent, the individual bond dipole moments cancel and the molecule is nonpolar.

Verification / Alternative check:
Check polarity experimentally or conceptually through solubility behaviour. CH4 is a nonpolar gas, poorly soluble in water, and shows weak intermolecular forces. In contrast, NH3 and H2O form hydrogen bonds and are clearly polar, as seen in their high boiling points. HCl and HF each have a permanent dipole because of the electronegativity difference between hydrogen and the halogen; with no opposing bonds, the dipole cannot cancel. This confirms that CH4 alone matches both conditions: nonpolar and symmetrical.

Why Other Options Are Wrong:
- NH3: Trigonal pyramidal and polar; the lone pair on nitrogen breaks symmetry and produces a net dipole.
- HCl: Linear but consists of one polar bond, so the molecule is polar, not nonpolar.
- H2O: Bent shape with polar bonds, so the dipoles do not cancel and the molecule is strongly polar.
- HF: Also a diatomic polar molecule with a strong hydrogen fluoride bond dipole, so it is polar overall.

Common Pitfalls:
Students often think that any molecule with polar bonds must be polar, ignoring molecular geometry. Another mistake is to assume that all tetrahedral molecules are polar, but symmetry matters. Remember that a molecule can have polar bonds and still be nonpolar if the shape is symmetrical and all outer atoms are identical, as in methane CH4.

Final Answer:
The nonpolar molecule with a symmetrical three dimensional shape is CH4 (methane).