Problem 50 - Chemistry Principles and Practice

Question

Indicate which of the following molecules are polar. Draw the molecular structure of each polar molecule, including the arrows that indicate the bond dipoles and the molecular dipole moment. (a) \(\mathrm{SiH}_{4}\) (b) \(\mathrm{PCl}_{3}\) (c) \(\mathrm{IF}_{5}\)

Step-by-Step Solution

Answer

SiH4 is nonpolar; PCl3 and IF5 are polar.

Step 1: Determine Molecular Geometry for SiH4

The molecule \( \mathrm{SiH}_{4} \) features silicon (Si) at the center bonded to four hydrogen (H) atoms. The geometry of \( \mathrm{SiH}_{4} \) is tetrahedral, with equal bond angles of 109.5°. This symmetrical shape leads to bond dipoles canceling out.

Step 2: Assess Bond Dipoles for SiH4

Each Si-H bond could have a dipole due to differences in electronegativity. However, in \( \mathrm{SiH}_{4} \), the tetrahedral symmetry means all bond dipoles cancel out, resulting in no net molecular dipole moment.

Step 3: Determine Molecular Geometry for PCl3

In \( \mathrm{PCl}_{3} \), phosphorus (P) is central with three attached chlorine (Cl) atoms. It has a trigonal pyramidal geometry due to the lone pair on phosphorus, leading to an asymmetrical shape.

Step 4: Assess Bond Dipoles for PCl3

The P-Cl bonds are polar due to chlorine's higher electronegativity compared to phosphorus. The molecule's trigonal pyramidal shape means the dipoles do not cancel out, resulting in a net molecular dipole moment directed from the base of the pyramid upwards.

Step 5: Determine Molecular Geometry for IF5

In the \( \mathrm{IF}_{5} \) molecule, iodine (I) is central with five fluorine (F) atoms bonded to it. The geometry is square pyramidal, with one lone pair on iodine, contributing to an asymmetric distribution.

Step 6: Assess Bond Dipoles for IF5

Each I-F bond is polar due to fluorine's higher electronegativity. The molecular shape does not allow bond dipoles to fully cancel, resulting in an overall molecular dipole moment.

Key Concepts

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. It plays a critical role in determining the molecule's properties and behavior. Geometry is determined by the number of atoms bonded to a central atom and the number of lone pairs present. For example, in the molecule \( \mathrm{SiH}_4 \), the geometry is tetrahedral because there are four hydrogen atoms symmetrically arranged around the central silicon atom. The symmetric geometry results in equal bond angles of 109.5°, which can cancel out dipoles if the atoms have similar electronegativity.
On the other hand, the geometry of \( \mathrm{PCl}_3 \) is trigonal pyramidal. This is due to three chlorine atoms attached to phosphorus with a lone pair causing the shape to deviate from symmetry, leading to a net dipole moment. Lastly, \( \mathrm{IF}_5 \) has a square pyramidal geometry, again due to the presence of a lone pair on the iodine, distorting the shape from perfect symmetry. This difference in symmetry affects both dipole moments and molecular polarity.

Dipole Moment

A dipole moment is a measure of the separation of positive and negative charges within a molecule. It reflects the polarity of a molecule, indicating how charge is distributed with respect to bond lengths and angles. If a molecule has polar bonds, this does not automatically imply a net dipole moment.
For instance, in \( \mathrm{SiH}_4 \), while the \( \mathrm{Si-H} \) bonds are slightly polar, the symmetrical tetrahedral shape causes these dipoles to cancel out, leaving no overall dipole moment.

• In contrast, \( \mathrm{PCl}_3 \) exhibits a polar nature due to its trigonal pyramidal structure. This shape avoids the cancellation of dipole moments, leading to a resulting dipole directed upwards from the base of the pyramid.
• Similarly, \( \mathrm{IF}_5 \) with its square pyramidal shape manifests an overall dipole moment as the \( \mathrm{I-F} \) dipoles do not cancel out entirely due to the geometric distortion.

Understanding dipole moments helps predict the interaction of molecules with external electric fields and other molecules.

Electronegativity

Electronegativity describes an atom's ability to attract and hold onto electrons within a chemical bond. It is a crucial concept in determining bond polarity and molecular characteristics.
For a molecule like \( \mathrm{SiH}_4 \), silicon and hydrogen have a small difference in electronegativity, resulting in non-polar covalent bonds. This balance means no significant charge separation occurs across bonds.

• In the case of \( \mathrm{PCl}_3 \), chlorine atoms are significantly more electronegative than phosphorus. This difference results in polar \( \mathrm{P-Cl} \) bonds, contributing to the molecule's overall polarity.
• In \( \mathrm{IF}_5 \), fluorine is much more electronegative than iodine. The \( \mathrm{I-F} \) bonds are thus polar, which is critical in the absence of symmetry; it leads to net dipole moments and molecular polarity.

Electronegativity differences in bonds determine their contribution to molecular dipoles, thus influencing the molecule's chemical behavior and interactions.

Symmetry in Molecules

Symmetry in molecules refers to the arrangement of atoms in a way that indicates if a molecule can be divided into symmetrical parts. Symmetry significantly affects whether molecules possess net dipole moments or not.
In \( \mathrm{SiH}_4 \), the molecule is highly symmetrical due to its tetrahedral shape. This symmetry causes the individual bond dipoles to cancel each other, resulting in a non-polar molecule.

• Conversely, in \( \mathrm{PCl}_3 \), the absence of symmetry—owing to the trigonal pyramidal shape created by a lone pair on phosphorus—prevents the cancellation of dipoles, leading to a polar molecule.
• Similarly, the \( \mathrm{IF}_5 \) molecule, with its square pyramidal geometry, is asymmetrical due to the influence of an unshared pair of electrons on iodine. This asymmetry leads to a non-unitary direction of dipoles, making \( \mathrm{IF}_5 \) polar.

Overall, symmetry considerations help in deducing the existence of a net dipole and understanding the physical and chemical characteristics of molecules.