Problem 81 - Chemistry: The Central Science

Question

The \(\mathrm{PF}_{3}\) molecule has a dipole moment of \(1.03 \mathrm{D}\), but \(\mathrm{BF}_{3}\) has a dipole moment of zero. How can you explain the difference?

Step-by-Step Solution

Answer

The difference in dipole moments between PF3 and BF3 molecules can be explained by their molecular structures and electronegativity differences. PF3 has a trigonal pyramidal structure, and its bond dipoles do not cancel out, resulting in a dipole moment of \(1.03 D\). In contrast, BF3 has a trigonal planar structure, where the bond dipoles are symmetrically distributed and cancel each other out, leading to a dipole moment of zero.

Step 1: Understand Dipole Moment

A dipole moment is a measure of the separation of positive and negative charges in a molecule, resulting from the difference in electronegativity between the atoms. If the electronegativity difference between two bonded atoms is significant, the bond will have a dipole moment, and if the molecule has an asymmetric distribution of these dipoles, the molecule as a whole will have a nonzero dipole moment.

Step 2: Consider Molecular Structure

The molecular structures of PF3 and BF3 are both based on a central atom (P and B, respectively) with three F atoms bonded to it. PF3 has a trigonal pyramidal structure, while BF3 has a trigonal planar structure. In the trigonal pyramidal structure of PF3, the three F atoms all lie below the plane of the central P atom. In the trigonal planar structure of BF3, the three F atoms lie in the plane with the central B atom, at 120-degree angles from each other.

Step 3: Analyze Electronegativity Differences

In a molecule, the difference in electronegativity between the central atom and the outer atoms results in an uneven distribution of electron density, creating bond dipoles. In both PF3 and BF3, the electronegativity of the F atoms is significantly greater than that of the central atoms, P and B, respectively. This will result in bond dipoles pointing towards the F atoms.

Step 4: Determine the Molecular Dipole Moment

Now we can analyze the dipole moment for each molecule. In PF3, the molecular shape is trigonal pyramidal, and the bond dipoles do not cancel each other out. Therefore, PF3 has a nonzero dipole moment, which is found to be \(1.03 D\). In BF3, the molecular shape is trigonal planar. The bond dipoles are symmetrically distributed, with each bond dipole oriented at a 120-degree angle from the other two. In this case, the bond dipoles cancel each other out, resulting in a net dipole moment of zero.

Step 5: Explain the Difference in Dipole Moments

The difference in dipole moments between the PF3 and BF3 molecules can be explained by their respective molecular structures and the electronegativity differences between their atoms. The trigonal pyramidal structure of PF3 leads to a nonzero dipole moment, while the trigonal planar structure of BF3 causes the bond dipoles to cancel each other out, resulting in a dipole moment of zero.