Problem 40 - Chemistry The Central Science In Si Units

Question

(a) Consider the following two molecules: \(\mathrm{PCl}_{3}\) and \(\mathrm{BCl}_{3}\). Which molecule has a nonzero dipole moment? (b) Consider the following two molecules: \(\mathrm{XeF}_{4}\) and \(\mathrm{SF}_{4}\). Which molecule has a zero dipole moment?

Step-by-Step Solution

Answer

(a) \(\mathrm{PCl}_3\) has a non-zero dipole moment. (b) \(\mathrm{XeF}_4\) has a zero dipole moment.

Step 1: Understanding Dipole Moments in Molecules

A molecule has a non-zero dipole moment if the individual bond dipoles do not cancel each other out. This occurs when the molecule has an asymmetric shape. Conversely, molecules with symmetrical shapes usually have a dipole moment of zero because the bond dipoles cancel out.

Step 2: Analyzing the Shape of \(\mathrm{PCl}_3\)

\(\mathrm{PCl}_3\) has a trigonal pyramidal shape as phosphorus is bonded to three chlorine atoms with one lone pair of electrons on phosphorus. This arrangement is asymmetrical, leading to a non-zero dipole moment.

Step 3: Analyzing the Shape of \(\mathrm{BCl}_3\)

\(\mathrm{BCl}_3\) has a trigonal planar shape with the boron atom at the center and three chlorine atoms symmetrically arranged around it. This symmetrical structure causes the dipoles to cancel out, resulting in a net dipole moment of zero.

Step 4: Determining the Non-Zero Dipole Moment in \(\mathrm{PCl}_3\) and \(\mathrm{BCl}_3\)

Among \(\mathrm{PCl}_3\) and \(\mathrm{BCl}_3\), \(\mathrm{PCl}_3\) has a non-zero dipole moment due to its asymmetrical shape.

Step 5: Analyzing the Shape of \(\mathrm{XeF}_4\)

\(\mathrm{XeF}_4\) has a square planar shape as xenon is bonded to four fluorine atoms with two lone pairs. This symmetrical arrangement ensures that any fluorine dipoles are cancelled out, resulting in a zero dipole moment.

Step 6: Analyzing the Shape of \(\mathrm{SF}_4\)

\(\mathrm{SF}_4\) has a seesaw shape as sulfur is bonded to four fluorine atoms with one lone pair. This asymmetry leads to a non-zero dipole moment.

Step 7: Determining the Zero Dipole Moment in \(\mathrm{XeF}_4\) and \(\mathrm{SF}_4\)

Among \(\mathrm{XeF}_4\) and \(\mathrm{SF}_4\), \(\mathrm{XeF}_4\) has a zero dipole moment due to its symmetrical square planar shape.

Key Concepts

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. This arrangement plays a crucial role in determining the chemical properties and reactivity of the molecule. Different molecular geometries can arise due to variations in the number of bonded atoms and lone pairs around the central atom.
The structures of molecules like \(\mathrm{PCl}_3\) and \(\mathrm{BCl}_3\) illustrate how geometry influences dipole moments.

• \(\mathrm{PCl}_3\) has a trigonal pyramidal shape, characterized by three chlorine atoms bonded to a central phosphorus atom with a lone pair, making it asymmetrical.
• \(\mathrm{BCl}_3\) exhibits trigonal planar geometry with three chlorine atoms symmetrically arranged around a central boron atom.

Understanding these geometries helps in predicting whether a molecule will have a polar character or be nonpolar.

Dipole Moment Calculation

Dipole moments are a measure of the separation of positive and negative charges within a molecule. They occur when there is an unequal distribution of electrons in the bonds, resulting from differences in electronegativity between atoms.
To calculate the dipole moment, consider:

• The vector sum of all bond dipoles within the molecule.
• The bond dipole is determined by the difference in electronegativity between the bonded atoms and the distance between them.

The overall dipole moment is the vector sum of these individual dipoles. For example, in \(\mathrm{PCl}_3\), the bond dipoles do not cancel due to the triangular pyramidal shape, resulting in a net dipole moment. In contrast, \(\mathrm{BCl}_3\)'s symmetric planar arrangement leads to the cancellation of dipoles, yielding a zero dipole moment.

Symmetry in Molecules

Symmetry plays a key role in determining the net dipole moment of a molecule. Molecular symmetry affects how bond dipoles interact with each other:

• If a molecule is symmetrical, such as \(\mathrm{BCl}_3\) with its trigonal planar shape, the bond dipoles can cancel each other out, leading to no overall dipole moment.
• In contrast, asymmetrical shapes like that of \(\mathrm{PCl}_3\) result in a non-zero net dipole moment because the bond dipoles do not cancel.

Molecules like \(\mathrm{XeF}_4\) with a square planar shape are often symmetric, which explains their zero dipole moment even though they contain polar bonds. The importance of symmetry in understanding molecular behavior makes it a fundamental concept in chemistry.

Bond Polarity

Bond polarity is all about the difference in electronegativity between two atoms. When one atom is more electronegative, it attracts electrons more strongly, resulting in a polar bond with a partial positive and negative end.
Here's how bond polarity plays into our molecule examples:

• In \(\mathrm{PCl}_3\), phosphorus and chlorine form polar bonds due to their electronegativity difference. These polar bonds are not symmetrically arranged, leading to an overall non-zero dipole moment.
• For \(\mathrm{BCl}_3\), although the \(\text{B-Cl}\) bonds are also polar, their trigonal planar symmetry leads them to cancel each other, resulting in a zero dipole moment.

This concept is essential in predicting the molecular dipole moment based on the arrangement and polarity of individual bonds. Understanding bond polarity helps to determine the solubility, boiling point, and general behavior of molecules in chemical reactions.